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 | 647.31 | ||
Character | \(\chi\) | \(=\) | 684.647 |
Dual form | 684.2.c.b.647.32 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.39577 | − | 0.227661i | 0.986958 | − | 0.160981i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.89634 | − | 0.635524i | 0.948170 | − | 0.317762i | ||||
\(5\) | 2.96037i | 1.32392i | 0.749540 | + | 0.661959i | \(0.230275\pi\) | ||||
−0.749540 | + | 0.661959i | \(0.769725\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.79268i | 1.05553i | 0.849389 | + | 0.527767i | \(0.176971\pi\) | ||||
−0.849389 | + | 0.527767i | \(0.823029\pi\) | |||||||
\(8\) | 2.50217 | − | 1.31877i | 0.884650 | − | 0.466255i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.673961 | + | 4.13199i | 0.213125 | + | 1.30665i | ||||
\(11\) | 1.59280 | 0.480248 | 0.240124 | − | 0.970742i | \(-0.422812\pi\) | ||||
0.240124 | + | 0.970742i | \(0.422812\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.51231 | −1.80619 | −0.903096 | − | 0.429440i | \(-0.858711\pi\) | ||||
−0.903096 | + | 0.429440i | \(0.858711\pi\) | |||||||
\(14\) | 0.635785 | + | 3.89794i | 0.169921 | + | 1.04177i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.19222 | − | 2.41034i | 0.798054 | − | 0.602585i | ||||
\(17\) | 2.52959i | 0.613516i | 0.951788 | + | 0.306758i | \(0.0992442\pi\) | ||||
−0.951788 | + | 0.306758i | \(0.900756\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000i | 0.229416i | ||||||||
\(20\) | 1.88139 | + | 5.61387i | 0.420691 | + | 1.25530i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.22318 | − | 0.362619i | 0.473984 | − | 0.0773106i | ||||
\(23\) | 4.93288 | 1.02858 | 0.514289 | − | 0.857617i | \(-0.328056\pi\) | ||||
0.514289 | + | 0.857617i | \(0.328056\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.76379 | −0.752757 | ||||||||
\(26\) | −9.08968 | + | 1.48260i | −1.78263 | + | 0.290762i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.77482 | + | 5.29588i | 0.335409 | + | 1.00083i | ||||
\(29\) | − | 7.17104i | − | 1.33163i | −0.746117 | − | 0.665815i | \(-0.768084\pi\) | ||
0.746117 | − | 0.665815i | \(-0.231916\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.92056i | 0.344943i | 0.985015 | + | 0.172471i | \(0.0551753\pi\) | ||||
−0.985015 | + | 0.172471i | \(0.944825\pi\) | |||||||
\(32\) | 3.90686 | − | 4.09102i | 0.690641 | − | 0.723198i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.575890 | + | 3.53072i | 0.0987642 | + | 0.605514i | ||||
\(35\) | −8.26737 | −1.39744 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.232255 | 0.0381825 | 0.0190912 | − | 0.999818i | \(-0.493923\pi\) | ||||
0.0190912 | + | 0.999818i | \(0.493923\pi\) | |||||||
\(38\) | 0.227661 | + | 1.39577i | 0.0369315 | + | 0.226424i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.90404 | + | 7.40734i | 0.617283 | + | 1.17120i | ||||
\(41\) | − | 6.49372i | − | 1.01415i | −0.861902 | − | 0.507074i | \(-0.830727\pi\) | ||
0.861902 | − | 0.507074i | \(-0.169273\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 2.68176i | − | 0.408964i | −0.978870 | − | 0.204482i | \(-0.934449\pi\) | ||
0.978870 | − | 0.204482i | \(-0.0655510\pi\) | |||||||
\(44\) | 3.02049 | − | 1.01226i | 0.455357 | − | 0.152605i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.88517 | − | 1.12303i | 1.01516 | − | 0.165581i | ||||
\(47\) | 12.6975 | 1.85212 | 0.926060 | − | 0.377376i | \(-0.123174\pi\) | ||||
0.926060 | + | 0.377376i | \(0.123174\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.799071 | −0.114153 | ||||||||
\(50\) | −5.25338 | + | 0.856868i | −0.742939 | + | 0.121179i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −12.3496 | + | 4.13873i | −1.71258 | + | 0.573939i | ||||
\(53\) | 3.18560i | 0.437576i | 0.975772 | + | 0.218788i | \(0.0702103\pi\) | ||||
−0.975772 | + | 0.218788i | \(0.929790\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.71528i | 0.635808i | ||||||||
\(56\) | 3.68290 | + | 6.98776i | 0.492148 | + | 0.933779i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.63257 | − | 10.0091i | −0.214367 | − | 1.31426i | ||||
\(59\) | 13.0918 | 1.70440 | 0.852202 | − | 0.523212i | \(-0.175266\pi\) | ||||
0.852202 | + | 0.523212i | \(0.175266\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.431148 | 0.0552028 | 0.0276014 | − | 0.999619i | \(-0.491213\pi\) | ||||
0.0276014 | + | 0.999619i | \(0.491213\pi\) | |||||||
\(62\) | 0.437237 | + | 2.68066i | 0.0555292 | + | 0.340444i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4.52170 | − | 6.59956i | 0.565213 | − | 0.824945i | ||||
\(65\) | − | 19.2789i | − | 2.39125i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 16.3299i | − | 1.99502i | −0.0705335 | − | 0.997509i | \(-0.522470\pi\) | ||
0.0705335 | − | 0.997509i | \(-0.477530\pi\) | |||||||
\(68\) | 1.60762 | + | 4.79697i | 0.194952 | + | 0.581718i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −11.5393 | + | 1.88216i | −1.37921 | + | 0.224961i | ||||
\(71\) | −7.97855 | −0.946880 | −0.473440 | − | 0.880826i | \(-0.656988\pi\) | ||||
−0.473440 | + | 0.880826i | \(0.656988\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.9265 | −1.39590 | −0.697948 | − | 0.716149i | \(-0.745903\pi\) | ||||
−0.697948 | + | 0.716149i | \(0.745903\pi\) | |||||||
\(74\) | 0.324174 | − | 0.0528754i | 0.0376845 | − | 0.00614664i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.635524 | + | 1.89634i | 0.0728997 | + | 0.217525i | ||||
\(77\) | 4.44819i | 0.506918i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.31738i | 0.598252i | 0.954214 | + | 0.299126i | \(0.0966951\pi\) | ||||
−0.954214 | + | 0.299126i | \(0.903305\pi\) | |||||||
\(80\) | 7.13550 | + | 9.45014i | 0.797773 | + | 1.05656i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.47837 | − | 9.06373i | −0.163258 | − | 1.00092i | ||||
\(83\) | −5.22797 | −0.573844 | −0.286922 | − | 0.957954i | \(-0.592632\pi\) | ||||
−0.286922 | + | 0.957954i | \(0.592632\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.48853 | −0.812245 | ||||||||
\(86\) | −0.610532 | − | 3.74311i | −0.0658354 | − | 0.403630i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.98546 | − | 2.10054i | 0.424851 | − | 0.223918i | ||||
\(89\) | − | 8.73011i | − | 0.925390i | −0.886518 | − | 0.462695i | \(-0.846882\pi\) | ||
0.886518 | − | 0.462695i | \(-0.153118\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 18.1868i | − | 1.90650i | ||||||
\(92\) | 9.35443 | − | 3.13497i | 0.975267 | − | 0.326843i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 17.7228 | − | 2.89073i | 1.82796 | − | 0.298156i | ||||
\(95\) | −2.96037 | −0.303727 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.65258 | −0.370863 | −0.185432 | − | 0.982657i | \(-0.559368\pi\) | ||||
−0.185432 | + | 0.982657i | \(0.559368\pi\) | |||||||
\(98\) | −1.11532 | + | 0.181917i | −0.112664 | + | 0.0183764i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −7.13742 | + | 2.39198i | −0.713742 | + | 0.239198i | ||||
\(101\) | − | 4.79873i | − | 0.477491i | −0.971082 | − | 0.238746i | \(-0.923264\pi\) | ||
0.971082 | − | 0.238746i | \(-0.0767362\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 17.3050i | 1.70511i | 0.522634 | + | 0.852557i | \(0.324949\pi\) | ||||
−0.522634 | + | 0.852557i | \(0.675051\pi\) | |||||||
\(104\) | −16.2949 | + | 8.58823i | −1.59785 | + | 0.842146i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.725238 | + | 4.44636i | 0.0704413 | + | 0.431869i | ||||
\(107\) | 8.61213 | 0.832566 | 0.416283 | − | 0.909235i | \(-0.363333\pi\) | ||||
0.416283 | + | 0.909235i | \(0.363333\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11.6043 | −1.11149 | −0.555745 | − | 0.831353i | \(-0.687567\pi\) | ||||
−0.555745 | + | 0.831353i | \(0.687567\pi\) | |||||||
\(110\) | 1.07349 | + | 6.58144i | 0.102353 | + | 0.627516i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 6.73132 | + | 8.91485i | 0.636050 | + | 0.842374i | ||||
\(113\) | 6.68847i | 0.629199i | 0.949225 | + | 0.314599i | \(0.101870\pi\) | ||||
−0.949225 | + | 0.314599i | \(0.898130\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 14.6032i | 1.36175i | ||||||||
\(116\) | −4.55737 | − | 13.5987i | −0.423142 | − | 1.26261i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 18.2731 | − | 2.98049i | 1.68218 | − | 0.274376i | ||||
\(119\) | −7.06434 | −0.647587 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.46299 | −0.769362 | ||||||||
\(122\) | 0.601783 | − | 0.0981556i | 0.0544829 | − | 0.00888659i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.22056 | + | 3.64204i | 0.109610 | + | 0.327065i | ||||
\(125\) | 3.65965i | 0.327329i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.42275i | 0.658662i | 0.944214 | + | 0.329331i | \(0.106823\pi\) | ||||
−0.944214 | + | 0.329331i | \(0.893177\pi\) | |||||||
\(128\) | 4.80879 | − | 10.2409i | 0.425041 | − | 0.905174i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −4.38904 | − | 26.9088i | −0.384945 | − | 2.36006i | ||||
\(131\) | −17.2451 | −1.50671 | −0.753356 | − | 0.657612i | \(-0.771566\pi\) | ||||
−0.753356 | + | 0.657612i | \(0.771566\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.79268 | −0.242156 | ||||||||
\(134\) | −3.71769 | − | 22.7928i | −0.321160 | − | 1.96900i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.33594 | + | 6.32947i | 0.286055 | + | 0.542747i | ||||
\(137\) | 6.76538i | 0.578005i | 0.957328 | + | 0.289003i | \(0.0933236\pi\) | ||||
−0.957328 | + | 0.289003i | \(0.906676\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 13.7252i | − | 1.16416i | −0.813133 | − | 0.582079i | \(-0.802240\pi\) | ||
0.813133 | − | 0.582079i | \(-0.197760\pi\) | |||||||
\(140\) | −15.6778 | + | 5.25412i | −1.32501 | + | 0.444054i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −11.1362 | + | 1.81641i | −0.934530 | + | 0.152429i | ||||
\(143\) | −10.3728 | −0.867419 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 21.2289 | 1.76297 | ||||||||
\(146\) | −16.6467 | + | 2.71521i | −1.37769 | + | 0.224712i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.440435 | − | 0.147604i | 0.0362035 | − | 0.0121330i | ||||
\(149\) | 1.02994i | 0.0843762i | 0.999110 | + | 0.0421881i | \(0.0134329\pi\) | ||||
−0.999110 | + | 0.0421881i | \(0.986567\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 17.3841i | − | 1.41470i | −0.706863 | − | 0.707350i | \(-0.749890\pi\) | ||
0.706863 | − | 0.707350i | \(-0.250110\pi\) | |||||||
\(152\) | 1.31877 | + | 2.50217i | 0.106966 | + | 0.202953i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.01268 | + | 6.20864i | 0.0816040 | + | 0.500306i | ||||
\(155\) | −5.68557 | −0.456676 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 23.9572 | 1.91199 | 0.955995 | − | 0.293384i | \(-0.0947816\pi\) | ||||
0.955995 | + | 0.293384i | \(0.0947816\pi\) | |||||||
\(158\) | 1.21056 | + | 7.42183i | 0.0963070 | + | 0.590449i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 12.1109 | + | 11.5657i | 0.957454 | + | 0.914352i | ||||
\(161\) | 13.7760i | 1.08570i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 6.89717i | − | 0.540228i | −0.962828 | − | 0.270114i | \(-0.912939\pi\) | ||
0.962828 | − | 0.270114i | \(-0.0870614\pi\) | |||||||
\(164\) | −4.12692 | − | 12.3143i | −0.322258 | − | 0.961586i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −7.29703 | + | 1.19020i | −0.566360 | + | 0.0923778i | ||||
\(167\) | −13.8381 | −1.07083 | −0.535413 | − | 0.844591i | \(-0.679844\pi\) | ||||
−0.535413 | + | 0.844591i | \(0.679844\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 29.4102 | 2.26233 | ||||||||
\(170\) | −10.4522 | + | 1.70485i | −0.801651 | + | 0.130756i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.70432 | − | 5.08553i | −0.129953 | − | 0.387768i | ||||
\(173\) | − | 7.85803i | − | 0.597435i | −0.954342 | − | 0.298718i | \(-0.903441\pi\) | ||
0.954342 | − | 0.298718i | \(-0.0965589\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 10.5111i | − | 0.794561i | ||||||
\(176\) | 5.08457 | − | 3.83919i | 0.383264 | − | 0.289390i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1.98751 | − | 12.1852i | −0.148970 | − | 0.913321i | ||||
\(179\) | −11.1237 | −0.831424 | −0.415712 | − | 0.909496i | \(-0.636468\pi\) | ||||
−0.415712 | + | 0.909496i | \(0.636468\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −22.1559 | −1.64683 | −0.823417 | − | 0.567436i | \(-0.807935\pi\) | ||||
−0.823417 | + | 0.567436i | \(0.807935\pi\) | |||||||
\(182\) | −4.14043 | − | 25.3846i | −0.306909 | − | 1.88163i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 12.3429 | − | 6.50533i | 0.909931 | − | 0.479579i | ||||
\(185\) | 0.687561i | 0.0505505i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.02914i | 0.294640i | ||||||||
\(188\) | 24.0788 | − | 8.06957i | 1.75613 | − | 0.588534i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −4.13199 | + | 0.673961i | −0.299766 | + | 0.0488943i | ||||
\(191\) | 17.2539 | 1.24845 | 0.624225 | − | 0.781245i | \(-0.285415\pi\) | ||||
0.624225 | + | 0.781245i | \(0.285415\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.96124 | −0.357118 | −0.178559 | − | 0.983929i | \(-0.557143\pi\) | ||||
−0.178559 | + | 0.983929i | \(0.557143\pi\) | |||||||
\(194\) | −5.09815 | + | 0.831550i | −0.366026 | + | 0.0597018i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.51531 | + | 0.507829i | −0.108237 | + | 0.0362735i | ||||
\(197\) | 18.4474i | 1.31432i | 0.753749 | + | 0.657162i | \(0.228243\pi\) | ||||
−0.753749 | + | 0.657162i | \(0.771757\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.19745i | 0.155773i | 0.996962 | + | 0.0778866i | \(0.0248172\pi\) | ||||
−0.996962 | + | 0.0778866i | \(0.975183\pi\) | |||||||
\(200\) | −9.41763 | + | 4.96356i | −0.665927 | + | 0.350977i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1.09248 | − | 6.69792i | −0.0768669 | − | 0.471264i | ||||
\(203\) | 20.0264 | 1.40558 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 19.2238 | 1.34265 | ||||||||
\(206\) | 3.93968 | + | 24.1538i | 0.274491 | + | 1.68288i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −20.7887 | + | 15.6969i | −1.44144 | + | 1.08838i | ||||
\(209\) | 1.59280i | 0.110176i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 19.8654i | − | 1.36759i | −0.729673 | − | 0.683796i | \(-0.760328\pi\) | ||
0.729673 | − | 0.683796i | \(-0.239672\pi\) | |||||||
\(212\) | 2.02453 | + | 6.04099i | 0.139045 | + | 0.414897i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 12.0205 | − | 1.96065i | 0.821708 | − | 0.134027i | ||||
\(215\) | 7.93899 | 0.541435 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.36352 | −0.364099 | ||||||||
\(218\) | −16.1969 | + | 2.64185i | −1.09699 | + | 0.178929i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 2.99667 | + | 8.94178i | 0.202036 | + | 0.602854i | ||||
\(221\) | − | 16.4735i | − | 1.10813i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.04524i | 0.0699943i | 0.999387 | + | 0.0349972i | \(0.0111422\pi\) | ||||
−0.999387 | + | 0.0349972i | \(0.988858\pi\) | |||||||
\(224\) | 11.4249 | + | 10.9106i | 0.763360 | + | 0.728996i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.52271 | + | 9.33556i | 0.101289 | + | 0.620992i | ||||
\(227\) | −9.79419 | −0.650063 | −0.325032 | − | 0.945703i | \(-0.605375\pi\) | ||||
−0.325032 | + | 0.945703i | \(0.605375\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.30898 | 0.549073 | 0.274536 | − | 0.961577i | \(-0.411476\pi\) | ||||
0.274536 | + | 0.961577i | \(0.411476\pi\) | |||||||
\(230\) | 3.32457 | + | 20.3826i | 0.219216 | + | 1.34399i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −9.45694 | − | 17.9432i | −0.620879 | − | 1.17803i | ||||
\(233\) | 9.13932i | 0.598737i | 0.954138 | + | 0.299368i | \(0.0967759\pi\) | ||||
−0.954138 | + | 0.299368i | \(0.903224\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 37.5893i | 2.45205i | ||||||||
\(236\) | 24.8265 | − | 8.32015i | 1.61607 | − | 0.541596i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −9.86019 | + | 1.60828i | −0.639141 | + | 0.104249i | ||||
\(239\) | −12.1947 | −0.788812 | −0.394406 | − | 0.918936i | \(-0.629050\pi\) | ||||
−0.394406 | + | 0.918936i | \(0.629050\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.6275 | 0.684576 | 0.342288 | − | 0.939595i | \(-0.388798\pi\) | ||||
0.342288 | + | 0.939595i | \(0.388798\pi\) | |||||||
\(242\) | −11.8124 | + | 1.92669i | −0.759328 | + | 0.123852i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0.817604 | − | 0.274005i | 0.0523417 | − | 0.0175414i | ||||
\(245\) | − | 2.36555i | − | 0.151129i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 6.51231i | − | 0.414369i | ||||||
\(248\) | 2.53278 | + | 4.80557i | 0.160831 | + | 0.305154i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0.833160 | + | 5.10802i | 0.0526936 | + | 0.323060i | ||||
\(251\) | 12.9935 | 0.820141 | 0.410070 | − | 0.912054i | \(-0.365504\pi\) | ||||
0.410070 | + | 0.912054i | \(0.365504\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.85710 | 0.493972 | ||||||||
\(254\) | 1.68987 | + | 10.3604i | 0.106032 | + | 0.650072i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4.38050 | − | 15.3887i | 0.273781 | − | 0.961792i | ||||
\(257\) | − | 4.73511i | − | 0.295368i | −0.989035 | − | 0.147684i | \(-0.952818\pi\) | ||
0.989035 | − | 0.147684i | \(-0.0471818\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.648614i | 0.0403029i | ||||||||
\(260\) | −12.2522 | − | 36.5593i | −0.759848 | − | 2.26731i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −24.0702 | + | 3.92604i | −1.48706 | + | 0.242552i | ||||
\(263\) | 9.75716 | 0.601652 | 0.300826 | − | 0.953679i | \(-0.402738\pi\) | ||||
0.300826 | + | 0.953679i | \(0.402738\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.43056 | −0.579315 | ||||||||
\(266\) | −3.89794 | + | 0.635785i | −0.238998 | + | 0.0389825i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −10.3781 | − | 30.9671i | −0.633942 | − | 1.89162i | ||||
\(269\) | 14.9609i | 0.912179i | 0.889934 | + | 0.456090i | \(0.150750\pi\) | ||||
−0.889934 | + | 0.456090i | \(0.849250\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.0101i | 0.972545i | 0.873807 | + | 0.486272i | \(0.161644\pi\) | ||||
−0.873807 | + | 0.486272i | \(0.838356\pi\) | |||||||
\(272\) | 6.09718 | + | 8.07501i | 0.369696 | + | 0.489619i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.54021 | + | 9.44290i | 0.0930477 | + | 0.570467i | ||||
\(275\) | −5.99496 | −0.361510 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 12.7524 | 0.766215 | 0.383107 | − | 0.923704i | \(-0.374854\pi\) | ||||
0.383107 | + | 0.923704i | \(0.374854\pi\) | |||||||
\(278\) | −3.12470 | − | 19.1572i | −0.187407 | − | 1.14897i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −20.6864 | + | 10.9027i | −1.23625 | + | 0.651564i | ||||
\(281\) | 5.93967i | 0.354331i | 0.984181 | + | 0.177166i | \(0.0566928\pi\) | ||||
−0.984181 | + | 0.177166i | \(0.943307\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 13.0937i | − | 0.778341i | −0.921166 | − | 0.389170i | \(-0.872762\pi\) | ||
0.921166 | − | 0.389170i | \(-0.127238\pi\) | |||||||
\(284\) | −15.1301 | + | 5.07056i | −0.897803 | + | 0.300883i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −14.4781 | + | 2.36149i | −0.856106 | + | 0.139638i | ||||
\(287\) | 18.1349 | 1.07047 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 10.6012 | 0.623598 | ||||||||
\(290\) | 29.6307 | − | 4.83300i | 1.73997 | − | 0.283804i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −22.6168 | + | 7.57960i | −1.32355 | + | 0.443563i | ||||
\(293\) | − | 15.4720i | − | 0.903881i | −0.892048 | − | 0.451941i | \(-0.850732\pi\) | ||
0.892048 | − | 0.451941i | \(-0.149268\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 38.7565i | 2.25649i | ||||||||
\(296\) | 0.581141 | − | 0.306291i | 0.0337782 | − | 0.0178028i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0.234478 | + | 1.43756i | 0.0135829 | + | 0.0832758i | ||||
\(299\) | −32.1245 | −1.85781 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.48930 | 0.431676 | ||||||||
\(302\) | −3.95769 | − | 24.2642i | −0.227739 | − | 1.39625i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.41034 | + | 3.19222i | 0.138243 | + | 0.183086i | ||||
\(305\) | 1.27636i | 0.0730840i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 32.8979i | 1.87758i | 0.344487 | + | 0.938791i | \(0.388053\pi\) | ||||
−0.344487 | + | 0.938791i | \(0.611947\pi\) | |||||||
\(308\) | 2.82693 | + | 8.43528i | 0.161079 | + | 0.480645i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −7.93574 | + | 1.29438i | −0.450720 | + | 0.0735160i | ||||
\(311\) | 5.33532 | 0.302538 | 0.151269 | − | 0.988493i | \(-0.451664\pi\) | ||||
0.151269 | + | 0.988493i | \(0.451664\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.1147 | −0.684762 | −0.342381 | − | 0.939561i | \(-0.611233\pi\) | ||||
−0.342381 | + | 0.939561i | \(0.611233\pi\) | |||||||
\(314\) | 33.4386 | − | 5.45411i | 1.88705 | − | 0.307793i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.37932 | + | 10.0836i | 0.190102 | + | 0.567245i | ||||
\(317\) | 0.940229i | 0.0528085i | 0.999651 | + | 0.0264042i | \(0.00840571\pi\) | ||||
−0.999651 | + | 0.0264042i | \(0.991594\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 11.4220i | − | 0.639512i | ||||||
\(320\) | 19.5371 | + | 13.3859i | 1.09216 | + | 0.748295i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 3.13625 | + | 19.2281i | 0.174777 | + | 1.07154i | ||||
\(323\) | −2.52959 | −0.140750 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 24.5110 | 1.35962 | ||||||||
\(326\) | −1.57022 | − | 9.62685i | −0.0869663 | − | 0.533182i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −8.56371 | − | 16.2484i | −0.472852 | − | 0.897167i | ||||
\(329\) | 35.4601i | 1.95498i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 0.610977i | − | 0.0335824i | −0.999859 | − | 0.0167912i | \(-0.994655\pi\) | ||
0.999859 | − | 0.0167912i | \(-0.00534505\pi\) | |||||||
\(332\) | −9.91401 | + | 3.32250i | −0.544102 | + | 0.182346i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −19.3148 | + | 3.15040i | −1.05686 | + | 0.172382i | ||||
\(335\) | 48.3426 | 2.64124 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.73617 | 0.312469 | 0.156235 | − | 0.987720i | \(-0.450064\pi\) | ||||
0.156235 | + | 0.987720i | \(0.450064\pi\) | |||||||
\(338\) | 41.0499 | − | 6.69557i | 2.23282 | − | 0.364191i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −14.2008 | + | 4.75914i | −0.770146 | + | 0.258101i | ||||
\(341\) | 3.05907i | 0.165658i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.3172i | 0.935042i | ||||||||
\(344\) | −3.53662 | − | 6.71021i | −0.190682 | − | 0.361790i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.78897 | − | 10.9680i | −0.0961755 | − | 0.589643i | ||||
\(347\) | −11.8946 | −0.638536 | −0.319268 | − | 0.947665i | \(-0.603437\pi\) | ||||
−0.319268 | + | 0.947665i | \(0.603437\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −25.8304 | −1.38267 | −0.691334 | − | 0.722535i | \(-0.742977\pi\) | ||||
−0.691334 | + | 0.722535i | \(0.742977\pi\) | |||||||
\(350\) | −2.39296 | − | 14.6710i | −0.127909 | − | 0.784198i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 6.22284 | − | 6.51619i | 0.331679 | − | 0.347314i | ||||
\(353\) | − | 37.1794i | − | 1.97886i | −0.145020 | − | 0.989429i | \(-0.546325\pi\) | ||
0.145020 | − | 0.989429i | \(-0.453675\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 23.6195i | − | 1.25359i | ||||||
\(356\) | −5.54820 | − | 16.5553i | −0.294054 | − | 0.877428i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −15.5261 | + | 2.53243i | −0.820580 | + | 0.133843i | ||||
\(359\) | 22.8495 | 1.20595 | 0.602976 | − | 0.797759i | \(-0.293981\pi\) | ||||
0.602976 | + | 0.797759i | \(0.293981\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.00000 | −0.0526316 | ||||||||
\(362\) | −30.9245 | + | 5.04403i | −1.62536 | + | 0.265109i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −11.5582 | − | 34.4884i | −0.605813 | − | 1.80768i | ||||
\(365\) | − | 35.3069i | − | 1.84805i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 27.4061i | − | 1.43059i | −0.698824 | − | 0.715294i | \(-0.746293\pi\) | ||
0.698824 | − | 0.715294i | \(-0.253707\pi\) | |||||||
\(368\) | 15.7468 | − | 11.8899i | 0.820861 | − | 0.619806i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0.156531 | + | 0.959676i | 0.00813765 | + | 0.0498912i | ||||
\(371\) | −8.89637 | −0.461877 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.3325 | 0.534994 | 0.267497 | − | 0.963559i | \(-0.413803\pi\) | ||||
0.267497 | + | 0.963559i | \(0.413803\pi\) | |||||||
\(374\) | 0.917277 | + | 5.62374i | 0.0474313 | + | 0.290797i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 31.7713 | − | 16.7451i | 1.63848 | − | 0.863560i | ||||
\(377\) | 46.7001i | 2.40518i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 22.1448i | − | 1.13750i | −0.822509 | − | 0.568752i | \(-0.807426\pi\) | ||
0.822509 | − | 0.568752i | \(-0.192574\pi\) | |||||||
\(380\) | −5.61387 | + | 1.88139i | −0.287985 | + | 0.0965131i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 24.0825 | − | 3.92805i | 1.23217 | − | 0.200976i | ||||
\(383\) | −0.867347 | −0.0443193 | −0.0221597 | − | 0.999754i | \(-0.507054\pi\) | ||||
−0.0221597 | + | 0.999754i | \(0.507054\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −13.1683 | −0.671117 | ||||||||
\(386\) | −6.92474 | + | 1.12948i | −0.352460 | + | 0.0574891i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −6.92653 | + | 2.32130i | −0.351641 | + | 0.117846i | ||||
\(389\) | 27.5438i | 1.39652i | 0.715842 | + | 0.698262i | \(0.246043\pi\) | ||||
−0.715842 | + | 0.698262i | \(0.753957\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 12.4782i | 0.631049i | ||||||||
\(392\) | −1.99941 | + | 1.05379i | −0.100986 | + | 0.0532244i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 4.19976 | + | 25.7483i | 0.211581 | + | 1.29718i | ||||
\(395\) | −15.7414 | −0.792036 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −24.0324 | −1.20615 | −0.603076 | − | 0.797684i | \(-0.706058\pi\) | ||||
−0.603076 | + | 0.797684i | \(0.706058\pi\) | |||||||
\(398\) | 0.500274 | + | 3.06713i | 0.0250765 | + | 0.153742i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −12.0148 | + | 9.07201i | −0.600741 | + | 0.453601i | ||||
\(401\) | 21.8949i | 1.09338i | 0.837336 | + | 0.546689i | \(0.184112\pi\) | ||||
−0.837336 | + | 0.546689i | \(0.815888\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 12.5073i | − | 0.623033i | ||||||
\(404\) | −3.04971 | − | 9.10003i | −0.151729 | − | 0.452743i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 27.9523 | − | 4.55924i | 1.38725 | − | 0.226271i | ||||
\(407\) | 0.369936 | 0.0183370 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 32.8142 | 1.62256 | 0.811278 | − | 0.584661i | \(-0.198772\pi\) | ||||
0.811278 | + | 0.584661i | \(0.198772\pi\) | |||||||
\(410\) | 26.8320 | − | 4.37651i | 1.32514 | − | 0.216141i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 10.9978 | + | 32.8162i | 0.541821 | + | 1.61674i | ||||
\(413\) | 36.5612i | 1.79906i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 15.4767i | − | 0.759722i | ||||||
\(416\) | −25.4427 | + | 26.6420i | −1.24743 | + | 1.30623i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0.362619 | + | 2.22318i | 0.0177363 | + | 0.108739i | ||||
\(419\) | −15.0937 | −0.737377 | −0.368689 | − | 0.929553i | \(-0.620193\pi\) | ||||
−0.368689 | + | 0.929553i | \(0.620193\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −31.8754 | −1.55351 | −0.776755 | − | 0.629803i | \(-0.783136\pi\) | ||||
−0.776755 | + | 0.629803i | \(0.783136\pi\) | |||||||
\(422\) | −4.52258 | − | 27.7275i | −0.220156 | − | 1.34976i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 4.20107 | + | 7.97091i | 0.204022 | + | 0.387102i | ||||
\(425\) | − | 9.52084i | − | 0.461829i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.20406i | 0.0582685i | ||||||||
\(428\) | 16.3315 | − | 5.47322i | 0.789415 | − | 0.264558i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 11.0810 | − | 1.80740i | 0.534373 | − | 0.0871606i | ||||
\(431\) | 12.8437 | 0.618657 | 0.309329 | − | 0.950955i | \(-0.399896\pi\) | ||||
0.309329 | + | 0.950955i | \(0.399896\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −22.8564 | −1.09841 | −0.549204 | − | 0.835688i | \(-0.685069\pi\) | ||||
−0.549204 | + | 0.835688i | \(0.685069\pi\) | |||||||
\(434\) | −7.48623 | + | 1.22106i | −0.359350 | + | 0.0586129i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −22.0057 | + | 7.37482i | −1.05388 | + | 0.353190i | ||||
\(437\) | 4.93288i | 0.235972i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 20.8570i | 0.995452i | 0.867334 | + | 0.497726i | \(0.165831\pi\) | ||||
−0.867334 | + | 0.497726i | \(0.834169\pi\) | |||||||
\(440\) | 6.21836 | + | 11.7984i | 0.296449 | + | 0.562468i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3.75037 | − | 22.9932i | −0.178387 | − | 1.09367i | ||||
\(443\) | 1.48091 | 0.0703599 | 0.0351800 | − | 0.999381i | \(-0.488800\pi\) | ||||
0.0351800 | + | 0.999381i | \(0.488800\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 25.8444 | 1.22514 | ||||||||
\(446\) | 0.237960 | + | 1.45891i | 0.0112677 | + | 0.0690814i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 18.4305 | + | 12.6277i | 0.870758 | + | 0.596601i | ||||
\(449\) | 23.7798i | 1.12224i | 0.827735 | + | 0.561119i | \(0.189629\pi\) | ||||
−0.827735 | + | 0.561119i | \(0.810371\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 10.3432i | − | 0.487042i | ||||||
\(452\) | 4.25069 | + | 12.6836i | 0.199936 | + | 0.596588i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −13.6704 | + | 2.22976i | −0.641585 | + | 0.104648i | ||||
\(455\) | 53.8397 | 2.52404 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −27.2816 | −1.27618 | −0.638090 | − | 0.769962i | \(-0.720275\pi\) | ||||
−0.638090 | + | 0.769962i | \(0.720275\pi\) | |||||||
\(458\) | 11.5974 | − | 1.89163i | 0.541912 | − | 0.0883901i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 9.28066 | + | 27.6926i | 0.432713 | + | 1.29117i | ||||
\(461\) | − | 28.8557i | − | 1.34394i | −0.740576 | − | 0.671972i | \(-0.765447\pi\) | ||
0.740576 | − | 0.671972i | \(-0.234553\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 34.9248i | 1.62309i | 0.584289 | + | 0.811546i | \(0.301373\pi\) | ||||
−0.584289 | + | 0.811546i | \(0.698627\pi\) | |||||||
\(464\) | −17.2847 | − | 22.8915i | −0.802421 | − | 1.06271i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2.08067 | + | 12.7564i | 0.0963850 | + | 0.590928i | ||||
\(467\) | −3.65656 | −0.169205 | −0.0846027 | − | 0.996415i | \(-0.526962\pi\) | ||||
−0.0846027 | + | 0.996415i | \(0.526962\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 45.6043 | 2.10581 | ||||||||
\(470\) | 8.55762 | + | 52.4659i | 0.394733 | + | 2.42007i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 32.7579 | − | 17.2650i | 1.50780 | − | 0.794687i | ||||
\(473\) | − | 4.27151i | − | 0.196404i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 3.76379i | − | 0.172694i | ||||||
\(476\) | −13.3964 | + | 4.48956i | −0.614023 | + | 0.205779i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −17.0210 | + | 2.77627i | −0.778524 | + | 0.126984i | ||||
\(479\) | 10.7806 | 0.492580 | 0.246290 | − | 0.969196i | \(-0.420788\pi\) | ||||
0.246290 | + | 0.969196i | \(0.420788\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.51252 | −0.0689649 | ||||||||
\(482\) | 14.8335 | − | 2.41946i | 0.675648 | − | 0.110204i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −16.0487 | + | 5.37843i | −0.729487 | + | 0.244474i | ||||
\(485\) | − | 10.8130i | − | 0.490992i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 10.2294i | − | 0.463537i | −0.972771 | − | 0.231768i | \(-0.925549\pi\) | ||
0.972771 | − | 0.231768i | \(-0.0744511\pi\) | |||||||
\(488\) | 1.07881 | − | 0.568584i | 0.0488352 | − | 0.0257386i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −0.538543 | − | 3.30176i | −0.0243289 | − | 0.149158i | ||||
\(491\) | −14.1486 | −0.638519 | −0.319260 | − | 0.947667i | \(-0.603434\pi\) | ||||
−0.319260 | + | 0.947667i | \(0.603434\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 18.1398 | 0.816976 | ||||||||
\(494\) | −1.48260 | − | 9.08968i | −0.0667053 | − | 0.408964i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.62921 | + | 6.13085i | 0.207858 | + | 0.275283i | ||||
\(497\) | − | 22.2816i | − | 0.999464i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 28.0736i | 1.25675i | 0.777912 | + | 0.628373i | \(0.216279\pi\) | ||||
−0.777912 | + | 0.628373i | \(0.783721\pi\) | |||||||
\(500\) | 2.32580 | + | 6.93994i | 0.104013 | + | 0.310364i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 18.1359 | − | 2.95811i | 0.809444 | − | 0.132027i | ||||
\(503\) | 9.00219 | 0.401388 | 0.200694 | − | 0.979654i | \(-0.435680\pi\) | ||||
0.200694 | + | 0.979654i | \(0.435680\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 14.2060 | 0.632159 | ||||||||
\(506\) | 10.9667 | − | 1.78876i | 0.487529 | − | 0.0795199i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 4.71734 | + | 14.0761i | 0.209298 | + | 0.624524i | ||||
\(509\) | 16.5791i | 0.734854i | 0.930052 | + | 0.367427i | \(0.119761\pi\) | ||||
−0.930052 | + | 0.367427i | \(0.880239\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 33.3070i | − | 1.47342i | ||||||
\(512\) | 2.61077 | − | 22.4763i | 0.115381 | − | 0.993321i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −1.07800 | − | 6.60911i | −0.0475485 | − | 0.291515i | ||||
\(515\) | −51.2293 | −2.25743 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 20.2246 | 0.889476 | ||||||||
\(518\) | 0.147664 | + | 0.905316i | 0.00648800 | + | 0.0397773i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −25.4243 | − | 48.2390i | −1.11493 | − | 2.11542i | ||||
\(521\) | − | 34.2990i | − | 1.50267i | −0.659922 | − | 0.751334i | \(-0.729411\pi\) | ||
0.659922 | − | 0.751334i | \(-0.270589\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 28.5966i | 1.25044i | 0.780448 | + | 0.625220i | \(0.214991\pi\) | ||||
−0.780448 | + | 0.625220i | \(0.785009\pi\) | |||||||
\(524\) | −32.7026 | + | 10.9597i | −1.42862 | + | 0.478776i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 13.6187 | − | 2.22133i | 0.593805 | − | 0.0968544i | ||||
\(527\) | −4.85824 | −0.211628 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.33335 | 0.0579716 | ||||||||
\(530\) | −13.1629 | + | 2.14697i | −0.571759 | + | 0.0932585i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −5.29588 | + | 1.77482i | −0.229605 | + | 0.0769481i | ||||
\(533\) | 42.2891i | 1.83175i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 25.4951i | 1.10225i | ||||||||
\(536\) | −21.5354 | − | 40.8603i | −0.930187 | − | 1.76489i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 3.40600 | + | 20.8819i | 0.146843 | + | 0.900282i | ||||
\(539\) | −1.27276 | −0.0548217 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −21.4761 | −0.923332 | −0.461666 | − | 0.887054i | \(-0.652748\pi\) | ||||
−0.461666 | + | 0.887054i | \(0.652748\pi\) | |||||||
\(542\) | 3.64488 | + | 22.3464i | 0.156561 | + | 0.959860i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 10.3486 | + | 9.88275i | 0.443693 | + | 0.423719i | ||||
\(545\) | − | 34.3530i | − | 1.47152i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 23.2114i | 0.992450i | 0.868194 | + | 0.496225i | \(0.165281\pi\) | ||||
−0.868194 | + | 0.496225i | \(0.834719\pi\) | |||||||
\(548\) | 4.29956 | + | 12.8295i | 0.183668 | + | 0.548047i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −8.36758 | + | 1.36482i | −0.356795 | + | 0.0581961i | ||||
\(551\) | 7.17104 | 0.305497 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −14.8497 | −0.631476 | ||||||||
\(554\) | 17.7993 | − | 2.90322i | 0.756222 | − | 0.123346i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −8.72271 | − | 26.0277i | −0.369925 | − | 1.10382i | ||||
\(557\) | 0.120205i | 0.00509324i | 0.999997 | + | 0.00254662i | \(0.000810616\pi\) | ||||
−0.999997 | + | 0.00254662i | \(0.999189\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 17.4645i | 0.738668i | ||||||||
\(560\) | −26.3912 | + | 19.9272i | −1.11523 | + | 0.842077i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.35223 | + | 8.29041i | 0.0570405 | + | 0.349710i | ||||
\(563\) | 2.96182 | 0.124826 | 0.0624129 | − | 0.998050i | \(-0.480120\pi\) | ||||
0.0624129 | + | 0.998050i | \(0.480120\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −19.8004 | −0.833007 | ||||||||
\(566\) | −2.98093 | − | 18.2758i | −0.125298 | − | 0.768189i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −19.9637 | + | 10.5219i | −0.837658 | + | 0.441487i | ||||
\(569\) | − | 9.95504i | − | 0.417337i | −0.977986 | − | 0.208669i | \(-0.933087\pi\) | ||
0.977986 | − | 0.208669i | \(-0.0669130\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 44.8390i | − | 1.87646i | −0.346018 | − | 0.938228i | \(-0.612467\pi\) | ||
0.346018 | − | 0.938228i | \(-0.387533\pi\) | |||||||
\(572\) | −19.6704 | + | 6.59218i | −0.822461 | + | 0.275633i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 25.3121 | − | 4.12861i | 1.05651 | − | 0.172325i | ||||
\(575\) | −18.5663 | −0.774269 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 26.3997 | 1.09903 | 0.549516 | − | 0.835483i | \(-0.314812\pi\) | ||||
0.549516 | + | 0.835483i | \(0.314812\pi\) | |||||||
\(578\) | 14.7968 | − | 2.41347i | 0.615465 | − | 0.100387i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 40.2573 | − | 13.4915i | 1.67159 | − | 0.560204i | ||||
\(581\) | − | 14.6001i | − | 0.605712i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.07403i | 0.210145i | ||||||||
\(584\) | −29.8422 | + | 15.7283i | −1.23488 | + | 0.650843i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3.52236 | − | 21.5953i | −0.145507 | − | 0.892092i | ||||
\(587\) | −0.268830 | −0.0110958 | −0.00554791 | − | 0.999985i | \(-0.501766\pi\) | ||||
−0.00554791 | + | 0.999985i | \(0.501766\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.92056 | −0.0791353 | ||||||||
\(590\) | 8.82335 | + | 54.0951i | 0.363252 | + | 2.22706i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0.741409 | − | 0.559814i | 0.0304717 | − | 0.0230082i | ||||
\(593\) | 22.5690i | 0.926796i | 0.886150 | + | 0.463398i | \(0.153370\pi\) | ||||
−0.886150 | + | 0.463398i | \(0.846630\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 20.9131i | − | 0.857352i | ||||||
\(596\) | 0.654554 | + | 1.95312i | 0.0268116 | + | 0.0800031i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −44.8384 | + | 7.31350i | −1.83358 | + | 0.299071i | ||||
\(599\) | −19.9928 | −0.816885 | −0.408443 | − | 0.912784i | \(-0.633928\pi\) | ||||
−0.408443 | + | 0.912784i | \(0.633928\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −20.7269 | −0.845468 | −0.422734 | − | 0.906254i | \(-0.638929\pi\) | ||||
−0.422734 | + | 0.906254i | \(0.638929\pi\) | |||||||
\(602\) | 10.4533 | − | 1.70502i | 0.426046 | − | 0.0694915i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −11.0480 | − | 32.9662i | −0.449538 | − | 1.34138i | ||||
\(605\) | − | 25.0536i | − | 1.01857i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 25.2875i | − | 1.02639i | −0.858273 | − | 0.513194i | \(-0.828462\pi\) | ||
0.858273 | − | 0.513194i | \(-0.171538\pi\) | |||||||
\(608\) | 4.09102 | + | 3.90686i | 0.165913 | + | 0.158444i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.290577 | + | 1.78150i | 0.0117651 | + | 0.0721308i | ||||
\(611\) | −82.6901 | −3.34528 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −32.7837 | −1.32412 | −0.662060 | − | 0.749451i | \(-0.730317\pi\) | ||||
−0.662060 | + | 0.749451i | \(0.730317\pi\) | |||||||
\(614\) | 7.48957 | + | 45.9179i | 0.302255 | + | 1.85309i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 5.86613 | + | 11.1301i | 0.236353 | + | 0.448445i | ||||
\(617\) | − | 17.3406i | − | 0.698107i | −0.937103 | − | 0.349053i | \(-0.886503\pi\) | ||
0.937103 | − | 0.349053i | \(-0.113497\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.87831i | 0.356849i | 0.983954 | + | 0.178425i | \(0.0571001\pi\) | ||||
−0.983954 | + | 0.178425i | \(0.942900\pi\) | |||||||
\(620\) | −10.7818 | + | 3.61332i | −0.433007 | + | 0.145114i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 7.44687 | − | 1.21464i | 0.298592 | − | 0.0487028i | ||||
\(623\) | 24.3804 | 0.976781 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.6528 | −1.18611 | ||||||||
\(626\) | −16.9093 | + | 2.75804i | −0.675831 | + | 0.110234i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 45.4309 | − | 15.2254i | 1.81289 | − | 0.607558i | ||||
\(629\) | 0.587510i | 0.0234256i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 7.92683i | − | 0.315562i | −0.987474 | − | 0.157781i | \(-0.949566\pi\) | ||
0.987474 | − | 0.157781i | \(-0.0504340\pi\) | |||||||
\(632\) | 7.01239 | + | 13.3050i | 0.278938 | + | 0.529244i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0.214053 | + | 1.31234i | 0.00850115 | + | 0.0521197i | ||||
\(635\) | −21.9741 | −0.872015 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.20380 | 0.206182 | ||||||||
\(638\) | −2.60036 | − | 15.9425i | −0.102949 | − | 0.631171i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 30.3168 | + | 14.2358i | 1.19838 | + | 0.562719i | ||||
\(641\) | − | 16.1509i | − | 0.637923i | −0.947768 | − | 0.318961i | \(-0.896666\pi\) | ||
0.947768 | − | 0.318961i | \(-0.103334\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 19.2221i | 0.758047i | 0.925387 | + | 0.379024i | \(0.123740\pi\) | ||||
−0.925387 | + | 0.379024i | \(0.876260\pi\) | |||||||
\(644\) | 8.75497 | + | 26.1239i | 0.344994 | + | 1.02943i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.53072 | + | 0.575890i | −0.138915 | + | 0.0226581i | ||||
\(647\) | −17.4550 | −0.686229 | −0.343114 | − | 0.939294i | \(-0.611482\pi\) | ||||
−0.343114 | + | 0.939294i | \(0.611482\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 20.8526 | 0.818536 | ||||||||
\(650\) | 34.2116 | − | 5.58019i | 1.34189 | − | 0.218873i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4.38332 | − | 13.0794i | −0.171664 | − | 0.512228i | ||||
\(653\) | − | 47.5883i | − | 1.86227i | −0.364670 | − | 0.931137i | \(-0.618818\pi\) | ||
0.364670 | − | 0.931137i | \(-0.381182\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 51.0519i | − | 1.99476i | ||||||
\(656\) | −15.6521 | − | 20.7294i | −0.611111 | − | 0.809346i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 8.07288 | + | 49.4941i | 0.314713 | + | 1.92948i | ||||
\(659\) | 30.2024 | 1.17652 | 0.588260 | − | 0.808672i | \(-0.299813\pi\) | ||||
0.588260 | + | 0.808672i | \(0.299813\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −11.1151 | −0.432326 | −0.216163 | − | 0.976357i | \(-0.569354\pi\) | ||||
−0.216163 | + | 0.976357i | \(0.569354\pi\) | |||||||
\(662\) | −0.139096 | − | 0.852783i | −0.00540611 | − | 0.0331444i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −13.0813 | + | 6.89448i | −0.507651 | + | 0.267558i | ||||
\(665\) | − | 8.26737i | − | 0.320595i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 35.3739i | − | 1.36968i | ||||||
\(668\) | −26.2418 | + | 8.79446i | −1.01533 | + | 0.340268i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 67.4751 | − | 11.0057i | 2.60679 | − | 0.425189i | ||||
\(671\) | 0.686733 | 0.0265110 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 22.6433 | 0.872835 | 0.436417 | − | 0.899744i | \(-0.356247\pi\) | ||||
0.436417 | + | 0.899744i | \(0.356247\pi\) | |||||||
\(674\) | 8.00637 | − | 1.30590i | 0.308394 | − | 0.0503015i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 55.7718 | − | 18.6909i | 2.14507 | − | 0.718882i | ||||
\(677\) | − | 43.6173i | − | 1.67635i | −0.545401 | − | 0.838175i | \(-0.683623\pi\) | ||
0.545401 | − | 0.838175i | \(-0.316377\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 10.2005i | − | 0.391459i | ||||||
\(680\) | −18.7376 | + | 9.87563i | −0.718553 | + | 0.378713i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0.696432 | + | 4.26976i | 0.0266677 | + | 0.163497i | ||||
\(683\) | 29.7385 | 1.13791 | 0.568956 | − | 0.822368i | \(-0.307347\pi\) | ||||
0.568956 | + | 0.822368i | \(0.307347\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −20.0280 | −0.765231 | ||||||||
\(686\) | 3.94246 | + | 24.1708i | 0.150524 | + | 0.922847i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −6.46395 | − | 8.56076i | −0.246436 | − | 0.326376i | ||||
\(689\) | − | 20.7456i | − | 0.790346i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.79762i | 0.334677i | 0.985899 | + | 0.167339i | \(0.0535173\pi\) | ||||
−0.985899 | + | 0.167339i | \(0.946483\pi\) | |||||||
\(692\) | −4.99397 | − | 14.9015i | −0.189842 | − | 0.566470i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −16.6021 | + | 2.70794i | −0.630208 | + | 0.102792i | ||||
\(695\) | 40.6317 | 1.54125 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 16.4265 | 0.622196 | ||||||||
\(698\) | −36.0532 | + | 5.88057i | −1.36463 | + | 0.222583i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −6.68003 | − | 19.9325i | −0.252482 | − | 0.753379i | ||||
\(701\) | − | 28.2381i | − | 1.06654i | −0.845946 | − | 0.533269i | \(-0.820963\pi\) | ||
0.845946 | − | 0.533269i | \(-0.179037\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.232255i | 0.00875967i | ||||||||
\(704\) | 7.20217 | − | 10.5118i | 0.271442 | − | 0.396178i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −8.46429 | − | 51.8938i | −0.318558 | − | 1.95305i | ||||
\(707\) | 13.4013 | 0.504009 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −30.5503 | −1.14734 | −0.573669 | − | 0.819087i | \(-0.694481\pi\) | ||||
−0.573669 | + | 0.819087i | \(0.694481\pi\) | |||||||
\(710\) | −5.37723 | − | 32.9673i | −0.201804 | − | 1.23724i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −11.5130 | − | 21.8442i | −0.431468 | − | 0.818647i | ||||
\(713\) | 9.47391i | 0.354801i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 30.7074i | − | 1.14839i | ||||||
\(716\) | −21.0943 | + | 7.06938i | −0.788332 | + | 0.264195i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 31.8927 | − | 5.20195i | 1.19022 | − | 0.194135i | ||||
\(719\) | −50.0999 | −1.86841 | −0.934205 | − | 0.356737i | \(-0.883889\pi\) | ||||
−0.934205 | + | 0.356737i | \(0.883889\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −48.3274 | −1.79981 | ||||||||
\(722\) | −1.39577 | + | 0.227661i | −0.0519451 | + | 0.00847267i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −42.0151 | + | 14.0806i | −1.56148 | + | 0.523302i | ||||
\(725\) | 26.9903i | 1.00239i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 10.4157i | − | 0.386296i | −0.981170 | − | 0.193148i | \(-0.938130\pi\) | ||
0.981170 | − | 0.193148i | \(-0.0618697\pi\) | |||||||
\(728\) | −23.9842 | − | 45.5065i | −0.888914 | − | 1.68658i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −8.03802 | − | 49.2803i | −0.297500 | − | 1.82395i | ||||
\(731\) | 6.78375 | 0.250906 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5.74852 | 0.212327 | 0.106163 | − | 0.994349i | \(-0.466143\pi\) | ||||
0.106163 | + | 0.994349i | \(0.466143\pi\) | |||||||
\(734\) | −6.23931 | − | 38.2526i | −0.230297 | − | 1.41193i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 19.2721 | − | 20.1805i | 0.710378 | − | 0.743865i | ||||
\(737\) | − | 26.0103i | − | 0.958103i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0.584322i | 0.0214946i | 0.999942 | + | 0.0107473i | \(0.00342104\pi\) | ||||
−0.999942 | + | 0.0107473i | \(0.996579\pi\) | |||||||
\(740\) | 0.436962 | + | 1.30385i | 0.0160630 | + | 0.0479305i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −12.4173 | + | 2.02536i | −0.455853 | + | 0.0743532i | ||||
\(743\) | 47.9287 | 1.75833 | 0.879167 | − | 0.476514i | \(-0.158100\pi\) | ||||
0.879167 | + | 0.476514i | \(0.158100\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.04901 | −0.111707 | ||||||||
\(746\) | 14.4217 | − | 2.35230i | 0.528016 | − | 0.0861237i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 2.56061 | + | 7.64061i | 0.0936253 | + | 0.279369i | ||||
\(749\) | 24.0509i | 0.878802i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 21.0910i | − | 0.769620i | −0.922996 | − | 0.384810i | \(-0.874267\pi\) | ||
0.922996 | − | 0.384810i | \(-0.125733\pi\) | |||||||
\(752\) | 40.5332 | − | 30.6053i | 1.47809 | − | 1.11606i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 10.6318 | + | 65.1825i | 0.387187 | + | 2.37381i | ||||
\(755\) | 51.4634 | 1.87295 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.92802 | −0.106421 | −0.0532104 | − | 0.998583i | \(-0.516945\pi\) | ||||
−0.0532104 | + | 0.998583i | \(0.516945\pi\) | |||||||
\(758\) | −5.04152 | − | 30.9091i | −0.183116 | − | 1.12267i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −7.40734 | + | 3.90404i | −0.268693 | + | 0.141614i | ||||
\(761\) | − | 35.6476i | − | 1.29223i | −0.763242 | − | 0.646113i | \(-0.776394\pi\) | ||
0.763242 | − | 0.646113i | \(-0.223606\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 32.4071i | − | 1.17322i | ||||||
\(764\) | 32.7193 | − | 10.9653i | 1.18374 | − | 0.396710i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.21062 | + | 0.197461i | −0.0437413 | + | 0.00713456i | ||||
\(767\) | −85.2578 | −3.07848 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −12.7963 | −0.461446 | −0.230723 | − | 0.973019i | \(-0.574109\pi\) | ||||
−0.230723 | + | 0.973019i | \(0.574109\pi\) | |||||||
\(770\) | −18.3799 | + | 2.99790i | −0.662364 | + | 0.108037i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −9.40820 | + | 3.15299i | −0.338608 | + | 0.113479i | ||||
\(773\) | − | 9.65634i | − | 0.347314i | −0.984806 | − | 0.173657i | \(-0.944442\pi\) | ||
0.984806 | − | 0.173657i | \(-0.0555585\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 7.22858i | − | 0.259658i | ||||||
\(776\) | −9.13937 | + | 4.81690i | −0.328084 | + | 0.172917i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 6.27065 | + | 38.4447i | 0.224814 | + | 1.37831i | ||||
\(779\) | 6.49372 | 0.232662 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12.7082 | −0.454737 | ||||||||
\(782\) | 2.84080 | + | 17.4167i | 0.101587 | + | 0.622818i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2.55081 | + | 1.92603i | −0.0911003 | + | 0.0687870i | ||||
\(785\) | 70.9220i | 2.53132i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 21.8326i | 0.778248i | 0.921185 | + | 0.389124i | \(0.127222\pi\) | ||||
−0.921185 | + | 0.389124i | \(0.872778\pi\) | |||||||
\(788\) | 11.7238 | + | 34.9826i | 0.417643 | + | 1.24620i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −21.9714 | + | 3.58371i | −0.781706 | + | 0.127503i | ||||
\(791\) | −18.6788 | −0.664141 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.80777 | −0.0997069 | ||||||||
\(794\) | −33.5437 | + | 5.47124i | −1.19042 | + | 0.194167i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.39653 | + | 4.16712i | 0.0494988 | + | 0.147700i | ||||
\(797\) | 39.7428i | 1.40776i | 0.710317 | + | 0.703882i | \(0.248552\pi\) | ||||
−0.710317 | + | 0.703882i | \(0.751448\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 32.1195i | 1.13631i | ||||||||
\(800\) | −14.7046 | + | 15.3977i | −0.519885 | + | 0.544392i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 4.98461 | + | 30.5602i | 0.176013 | + | 1.07912i | ||||
\(803\) | −18.9966 | −0.670375 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −40.7820 | −1.43738 | ||||||||
\(806\) | −2.84743 | − | 17.4573i | −0.100296 | − | 0.614907i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −6.32841 | − | 12.0072i | −0.222633 | − | 0.422413i | ||||
\(809\) | − | 14.1754i | − | 0.498382i | −0.968454 | − | 0.249191i | \(-0.919835\pi\) | ||
0.968454 | − | 0.249191i | \(-0.0801647\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.34499i | 0.152573i | 0.997086 | + | 0.0762867i | \(0.0243064\pi\) | ||||
−0.997086 | + | 0.0762867i | \(0.975694\pi\) | |||||||
\(812\) | 37.9770 | − | 12.7273i | 1.33273 | − | 0.446640i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0.516345 | − | 0.0842200i | 0.0180979 | − | 0.00295191i | ||||
\(815\) | 20.4182 | 0.715217 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.68176 | 0.0938228 | ||||||||
\(818\) | 45.8010 | − | 7.47051i | 1.60139 | − | 0.261200i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 36.4549 | − | 12.2172i | 1.27306 | − | 0.426643i | ||||
\(821\) | − | 34.0312i | − | 1.18770i | −0.804577 | − | 0.593848i | \(-0.797608\pi\) | ||
0.804577 | − | 0.593848i | \(-0.202392\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 54.0922i | 1.88553i | 0.333452 | + | 0.942767i | \(0.391786\pi\) | ||||
−0.333452 | + | 0.942767i | \(0.608214\pi\) | |||||||
\(824\) | 22.8213 | + | 43.3001i | 0.795018 | + | 1.50843i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 8.32356 | + | 51.0310i | 0.289614 | + | 1.77559i | ||||
\(827\) | 7.38185 | 0.256692 | 0.128346 | − | 0.991729i | \(-0.459033\pi\) | ||||
0.128346 | + | 0.991729i | \(0.459033\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6.55168 | −0.227549 | −0.113775 | − | 0.993507i | \(-0.536294\pi\) | ||||
−0.113775 | + | 0.993507i | \(0.536294\pi\) | |||||||
\(830\) | −3.52345 | − | 21.6019i | −0.122301 | − | 0.749813i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −29.4467 | + | 42.9784i | −1.02088 | + | 1.49001i | ||||
\(833\) | − | 2.02132i | − | 0.0700347i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 40.9659i | − | 1.41768i | ||||||
\(836\) | 1.01226 | + | 3.02049i | 0.0350099 | + | 0.104466i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −21.0674 | + | 3.43626i | −0.727760 | + | 0.118704i | ||||
\(839\) | 23.5892 | 0.814391 | 0.407196 | − | 0.913341i | \(-0.366507\pi\) | ||||
0.407196 | + | 0.913341i | \(0.366507\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.4239 | −0.773237 | ||||||||
\(842\) | −44.4906 | + | 7.25678i | −1.53325 | + | 0.250085i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −12.6250 | − | 37.6716i | −0.434569 | − | 1.29671i | ||||
\(845\) | 87.0652i | 2.99513i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 23.6344i | − | 0.812088i | ||||||
\(848\) | 7.67839 | + | 10.1691i | 0.263677 | + | 0.349209i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −2.16753 | − | 13.2889i | −0.0743455 | − | 0.455805i | ||||
\(851\) | 1.14569 | 0.0392737 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −30.8150 | −1.05509 | −0.527543 | − | 0.849528i | \(-0.676887\pi\) | ||||
−0.527543 | + | 0.849528i | \(0.676887\pi\) | |||||||
\(854\) | 0.274117 | + | 1.68059i | 0.00938010 | + | 0.0575085i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 21.5490 | − | 11.3574i | 0.736530 | − | 0.388188i | ||||
\(857\) | 23.4576i | 0.801295i | 0.916232 | + | 0.400647i | \(0.131215\pi\) | ||||
−0.916232 | + | 0.400647i | \(0.868785\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 22.9148i | 0.781843i | 0.920424 | + | 0.390921i | \(0.127844\pi\) | ||||
−0.920424 | + | 0.390921i | \(0.872156\pi\) | |||||||
\(860\) | 15.0550 | − | 5.04543i | 0.513373 | − | 0.172048i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 17.9268 | − | 2.92400i | 0.610589 | − | 0.0995919i | ||||
\(863\) | 22.2718 | 0.758141 | 0.379071 | − | 0.925368i | \(-0.376244\pi\) | ||||
0.379071 | + | 0.925368i | \(0.376244\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 23.2627 | 0.790955 | ||||||||
\(866\) | −31.9022 | + | 5.20351i | −1.08408 | + | 0.176822i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −10.1711 | + | 3.40865i | −0.345228 | + | 0.115697i | ||||
\(869\) | 8.46953i | 0.287309i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 106.346i | 3.60339i | ||||||||
\(872\) | −29.0359 | + | 15.3034i | −0.983281 | + | 0.518238i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1.12303 | + | 6.88517i | 0.0379869 | + | 0.232894i | ||||
\(875\) | −10.2202 | −0.345507 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −42.2668 | −1.42725 | −0.713624 | − | 0.700529i | \(-0.752947\pi\) | ||||
−0.713624 | + | 0.700529i | \(0.752947\pi\) | |||||||
\(878\) | 4.74833 | + | 29.1116i | 0.160249 | + | 0.982469i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 11.3654 | + | 15.0522i | 0.383129 | + | 0.507409i | ||||
\(881\) | − | 0.198847i | − | 0.00669931i | −0.999994 | − | 0.00334966i | \(-0.998934\pi\) | ||
0.999994 | − | 0.00334966i | \(-0.00106623\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 46.1728i | − | 1.55384i | −0.629600 | − | 0.776919i | \(-0.716781\pi\) | ||
0.629600 | − | 0.776919i | \(-0.283219\pi\) | |||||||
\(884\) | −10.4693 | − | 31.2394i | −0.352121 | − | 1.05069i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2.06700 | − | 0.337145i | 0.0694423 | − | 0.0113266i | ||||
\(887\) | 0.538116 | 0.0180682 | 0.00903408 | − | 0.999959i | \(-0.497124\pi\) | ||||
0.00903408 | + | 0.999959i | \(0.497124\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −20.7294 | −0.695241 | ||||||||
\(890\) | 36.0727 | − | 5.88375i | 1.20916 | − | 0.197224i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0.664274 | + | 1.98213i | 0.0222415 | + | 0.0663665i | ||||
\(893\) | 12.6975i | 0.424905i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 32.9303i | − | 1.10074i | ||||||
\(896\) | 28.5995 | + | 13.4294i | 0.955443 | + | 0.448645i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 5.41373 | + | 33.1911i | 0.180659 | + | 1.10760i | ||||
\(899\) | 13.7724 | 0.459336 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8.05827 | −0.268460 | ||||||||
\(902\) | −2.35474 | − | 14.4367i | −0.0784044 | − | 0.480690i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 8.82055 | + | 16.7357i | 0.293367 | + | 0.556621i | ||||
\(905\) | − | 65.5896i | − | 2.18027i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 34.1782i | 1.13487i | 0.823419 | + | 0.567434i | \(0.192064\pi\) | ||||
−0.823419 | + | 0.567434i | \(0.807936\pi\) | |||||||
\(908\) | −18.5731 | + | 6.22445i | −0.616371 | + | 0.206566i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 75.1478 | − | 12.2572i | 2.49112 | − | 0.406322i | ||||
\(911\) | −33.6676 | −1.11546 | −0.557728 | − | 0.830024i | \(-0.688327\pi\) | ||||
−0.557728 | + | 0.830024i | \(0.688327\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.32711 | −0.275587 | ||||||||
\(914\) | −38.0788 | + | 6.21096i | −1.25954 | + | 0.205440i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 15.7567 | − | 5.28056i | 0.520615 | − | 0.174475i | ||||
\(917\) | − | 48.1601i | − | 1.59039i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 10.5231i | − | 0.347124i | −0.984823 | − | 0.173562i | \(-0.944472\pi\) | ||
0.984823 | − | 0.173562i | \(-0.0555277\pi\) | |||||||
\(920\) | 19.2582 | + | 36.5396i | 0.634923 | + | 1.20467i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −6.56932 | − | 40.2759i | −0.216349 | − | 1.32642i | ||||
\(923\) | 51.9588 | 1.71025 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.874158 | −0.0287422 | ||||||||
\(926\) | 7.95101 | + | 48.7469i | 0.261286 | + | 1.60192i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −29.3369 | − | 28.0162i | −0.963031 | − | 0.919678i | ||||
\(929\) | − | 9.92696i | − | 0.325693i | −0.986651 | − | 0.162846i | \(-0.947932\pi\) | ||
0.986651 | − | 0.162846i | \(-0.0520675\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 0.799071i | − | 0.0261885i | ||||||
\(932\) | 5.80826 | + | 17.3313i | 0.190256 | + | 0.567704i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −5.10371 | + | 0.832457i | −0.166999 | + | 0.0272388i | ||||
\(935\) | −11.9277 | −0.390078 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 32.9042 | 1.07493 | 0.537467 | − | 0.843285i | \(-0.319381\pi\) | ||||
0.537467 | + | 0.843285i | \(0.319381\pi\) | |||||||
\(938\) | 63.6531 | − | 10.3823i | 2.07835 | − | 0.338995i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 23.8889 | + | 71.2821i | 0.779170 | + | 2.32497i | ||||
\(941\) | 34.8706i | 1.13675i | 0.822770 | + | 0.568375i | \(0.192428\pi\) | ||||
−0.822770 | + | 0.568375i | \(0.807572\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 32.0328i | − | 1.04313i | ||||||
\(944\) | 41.7918 | − | 31.5557i | 1.36021 | − | 1.02705i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.972456 | − | 5.96204i | −0.0316173 | − | 0.193843i | ||||
\(947\) | −42.4401 | −1.37912 | −0.689558 | − | 0.724230i | \(-0.742195\pi\) | ||||
−0.689558 | + | 0.724230i | \(0.742195\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 77.6693 | 2.52125 | ||||||||
\(950\) | −0.856868 | − | 5.25338i | −0.0278005 | − | 0.170442i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −17.6762 | + | 9.31623i | −0.572888 | + | 0.301941i | ||||
\(953\) | 55.2982i | 1.79128i | 0.444775 | + | 0.895642i | \(0.353284\pi\) | ||||
−0.444775 | + | 0.895642i | \(0.646716\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 51.0780i | 1.65284i | ||||||||
\(956\) | −23.1254 | + | 7.75005i | −0.747928 | + | 0.250655i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 15.0473 | − | 2.45433i | 0.486156 | − | 0.0792959i | ||||
\(959\) | −18.8935 | −0.610104 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 27.3114 | 0.881014 | ||||||||
\(962\) | −2.11113 | + | 0.344341i | −0.0680654 | + | 0.0111020i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 20.1533 | − | 6.75402i | 0.649095 | − | 0.217532i | ||||
\(965\) | − | 14.6871i | − | 0.472794i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 41.3253i | 1.32893i | 0.747318 | + | 0.664466i | \(0.231341\pi\) | ||||
−0.747318 | + | 0.664466i | \(0.768659\pi\) | |||||||
\(968\) | −21.1758 | + | 11.1607i | −0.680617 | + | 0.358719i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2.46169 | − | 15.0924i | −0.0790402 | − | 0.484588i | ||||
\(971\) | 11.0359 | 0.354158 | 0.177079 | − | 0.984197i | \(-0.443335\pi\) | ||||
0.177079 | + | 0.984197i | \(0.443335\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 38.3301 | 1.22881 | ||||||||
\(974\) | −2.32883 | − | 14.2778i | −0.0746204 | − | 0.457491i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.37632 | − | 1.03921i | 0.0440549 | − | 0.0332644i | ||||
\(977\) | 1.86563i | 0.0596867i | 0.999555 | + | 0.0298433i | \(0.00950084\pi\) | ||||
−0.999555 | + | 0.0298433i | \(0.990499\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 13.9053i | − | 0.444416i | ||||||
\(980\) | −1.50336 | − | 4.48588i | −0.0480231 | − | 0.143296i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −19.7482 | + | 3.22110i | −0.630192 | + | 0.102789i | ||||
\(983\) | 36.5993 | 1.16734 | 0.583668 | − | 0.811993i | \(-0.301617\pi\) | ||||
0.583668 | + | 0.811993i | \(0.301617\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −54.6112 | −1.74006 | ||||||||
\(986\) | 25.3190 | − | 4.12973i | 0.806321 | − | 0.131517i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −4.13873 | − | 12.3496i | −0.131671 | − | 0.392892i | ||||
\(989\) | − | 13.2288i | − | 0.420651i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 29.0900i | 0.924075i | 0.886860 | + | 0.462038i | \(0.152882\pi\) | ||||
−0.886860 | + | 0.462038i | \(0.847118\pi\) | |||||||
\(992\) | 7.85706 | + | 7.50336i | 0.249462 | + | 0.238232i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −5.07264 | − | 31.0999i | −0.160894 | − | 0.986429i | ||||
\(995\) | −6.50527 | −0.206231 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 30.1753 | 0.955663 | 0.477831 | − | 0.878452i | \(-0.341423\pi\) | ||||
0.477831 | + | 0.878452i | \(0.341423\pi\) | |||||||
\(998\) | 6.39126 | + | 39.1842i | 0.202312 | + | 1.24036i | ||||
\(999\) | 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.647.31 | yes | 32 | |
3.2 | odd | 2 | inner | 684.2.c.b.647.2 | yes | 32 | |
4.3 | odd | 2 | inner | 684.2.c.b.647.1 | ✓ | 32 | |
12.11 | even | 2 | inner | 684.2.c.b.647.32 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
684.2.c.b.647.1 | ✓ | 32 | 4.3 | odd | 2 | inner | |
684.2.c.b.647.2 | yes | 32 | 3.2 | odd | 2 | inner | |
684.2.c.b.647.31 | yes | 32 | 1.1 | even | 1 | trivial | |
684.2.c.b.647.32 | yes | 32 | 12.11 | even | 2 | inner |