Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [432,2,Mod(47,432)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(432, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([9, 0, 7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("432.47");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 432 = 2^{4} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 432.be (of order \(18\), degree \(6\), 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: | \(3.44953736732\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{18})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 383.5 | ||
Character | \(\chi\) | \(=\) | 432.383 |
Dual form | 432.2.be.a.335.5 |
$q$-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 \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).
\(n\) | \(271\) | \(325\) | \(353\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{5}{18}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.873396 | − | 1.49572i | 0.504256 | − | 0.863554i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.268878 | − | 0.738735i | −0.120246 | − | 0.330372i | 0.864937 | − | 0.501880i | \(-0.167358\pi\) |
−0.985183 | + | 0.171508i | \(0.945136\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.49766 | + | 0.616732i | −1.32199 | + | 0.233103i | −0.789718 | − | 0.613470i | \(-0.789773\pi\) |
−0.532273 | + | 0.846573i | \(0.678662\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.47436 | − | 2.61271i | −0.491453 | − | 0.870904i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.77372 | − | 1.73749i | −1.43933 | − | 0.523873i | −0.499740 | − | 0.866176i | \(-0.666571\pi\) |
−0.939590 | + | 0.342302i | \(0.888793\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.34250 | − | 3.64379i | −1.20439 | − | 1.01061i | −0.999494 | − | 0.0318218i | \(-0.989869\pi\) |
−0.204899 | − | 0.978783i | \(-0.565686\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.33978 | − | 0.243043i | −0.345929 | − | 0.0627534i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.45925 | + | 3.72925i | 1.56660 | + | 0.904476i | 0.996562 | + | 0.0828560i | \(0.0264042\pi\) |
0.570036 | + | 0.821620i | \(0.306929\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.31140 | − | 1.33449i | 0.530271 | − | 0.306152i | −0.210856 | − | 0.977517i | \(-0.567625\pi\) |
0.741127 | + | 0.671365i | \(0.234292\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.13239 | + | 5.77017i | −0.465325 | + | 1.25915i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.749727 | − | 4.25191i | 0.156329 | − | 0.886585i | −0.801232 | − | 0.598354i | \(-0.795822\pi\) |
0.957561 | − | 0.288231i | \(-0.0930672\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.35679 | − | 2.81668i | 0.671358 | − | 0.563336i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.19559 | − | 0.0767079i | −0.999891 | − | 0.0147624i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.09583 | + | 3.68947i | 0.574882 | + | 0.685117i | 0.972625 | − | 0.232379i | \(-0.0746511\pi\) |
−0.397744 | + | 0.917497i | \(0.630207\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.76226 | − | 0.487060i | −0.496116 | − | 0.0874786i | −0.0800087 | − | 0.996794i | \(-0.525495\pi\) |
−0.416107 | + | 0.909316i | \(0.636606\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −6.76815 | + | 5.62263i | −1.17818 | + | 0.978774i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.39604 | + | 2.41802i | 0.235974 | + | 0.408720i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.526507 | − | 0.911937i | 0.0865573 | − | 0.149922i | −0.819496 | − | 0.573084i | \(-0.805747\pi\) |
0.906054 | + | 0.423163i | \(0.139080\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −9.24281 | + | 3.31269i | −1.48003 | + | 0.530455i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.18342 | + | 1.41034i | −0.184818 | + | 0.220258i | −0.850496 | − | 0.525981i | \(-0.823698\pi\) |
0.665678 | + | 0.746239i | \(0.268143\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.64664 | − | 10.0191i | 0.556107 | − | 1.52789i | −0.269130 | − | 0.963104i | \(-0.586736\pi\) |
0.825237 | − | 0.564787i | \(-0.191042\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.53368 | + | 1.79166i | −0.228628 | + | 0.267085i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.36451 | + | 7.73852i | 0.199034 | + | 1.12878i | 0.906555 | + | 0.422087i | \(0.138702\pi\) |
−0.707521 | + | 0.706692i | \(0.750187\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.27542 | − | 1.92010i | 0.753632 | − | 0.274300i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 11.2194 | − | 6.40412i | 1.57103 | − | 0.896755i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 3.08817i | − | 0.424192i | −0.977249 | − | 0.212096i | \(-0.931971\pi\) | ||
0.977249 | − | 0.212096i | \(-0.0680290\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.99368i | 0.538508i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.0227487 | − | 4.62274i | 0.00301313 | − | 0.612297i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.15076 | − | 1.87472i | 0.670572 | − | 0.244068i | 0.0157780 | − | 0.999876i | \(-0.494977\pi\) |
0.654794 | + | 0.755807i | \(0.272755\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.62926 | − | 9.24000i | −0.208606 | − | 1.18306i | −0.891664 | − | 0.452698i | \(-0.850462\pi\) |
0.683058 | − | 0.730364i | \(-0.260649\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 6.76815 | + | 8.22910i | 0.852706 | + | 1.03677i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.52419 | + | 4.18769i | −0.189053 | + | 0.519419i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.27089 | + | 7.47336i | −0.766111 | + | 0.913016i | −0.998218 | − | 0.0596746i | \(-0.980994\pi\) |
0.232107 | + | 0.972690i | \(0.425438\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5.70486 | − | 4.83499i | −0.686785 | − | 0.582064i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.72857 | + | 2.99398i | −0.205144 | + | 0.355320i | −0.950179 | − | 0.311706i | \(-0.899100\pi\) |
0.745035 | + | 0.667026i | \(0.232433\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.99284 | − | 8.64785i | −0.584367 | − | 1.01215i | −0.994954 | − | 0.100332i | \(-0.968009\pi\) |
0.410587 | − | 0.911822i | \(-0.365324\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.28116 | − | 7.48089i | −0.147935 | − | 0.863819i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 17.7684 | + | 3.13305i | 2.02490 | + | 0.357044i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.929972 | − | 1.10830i | −0.104630 | − | 0.124693i | 0.711188 | − | 0.703002i | \(-0.248157\pi\) |
−0.815818 | + | 0.578309i | \(0.803713\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.65254 | + | 7.70415i | −0.516949 | + | 0.856016i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.12835 | − | 0.946797i | 0.123852 | − | 0.103925i | −0.578758 | − | 0.815500i | \(-0.696462\pi\) |
0.702610 | + | 0.711575i | \(0.252018\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.01818 | − | 5.77438i | 0.110437 | − | 0.626320i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 8.22230 | − | 1.40813i | 0.881523 | − | 0.150967i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.10319 | + | 1.79163i | −0.328938 | + | 0.189912i | −0.655369 | − | 0.755308i | \(-0.727487\pi\) |
0.326432 | + | 0.945221i | \(0.394154\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 17.4358 | + | 10.0666i | 1.82777 | + | 1.05526i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.14105 | + | 3.70617i | −0.325712 | + | 0.384312i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.60732 | − | 1.34870i | −0.164907 | − | 0.138374i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.87618 | − | 1.04684i | −0.292031 | − | 0.106291i | 0.191850 | − | 0.981424i | \(-0.438551\pi\) |
−0.483882 | + | 0.875133i | \(0.660773\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.49860 | + | 15.0340i | 0.251119 | + | 1.51098i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.66552 | − | 1.70429i | 0.961755 | − | 0.169583i | 0.329339 | − | 0.944212i | \(-0.393174\pi\) |
0.632417 | + | 0.774628i | \(0.282063\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.73206 | + | 7.50626i | 0.269197 | + | 0.739614i | 0.998465 | + | 0.0553854i | \(0.0176387\pi\) |
−0.729268 | + | 0.684229i | \(0.760139\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.83598 | + | 0.0237980i | 0.471943 | + | 0.00232245i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 15.2633 | 1.47555 | 0.737777 | − | 0.675044i | \(-0.235875\pi\) | ||||
0.737777 | + | 0.675044i | \(0.235875\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.31092 | 0.125563 | 0.0627817 | − | 0.998027i | \(-0.480003\pi\) | ||||
0.0627817 | + | 0.998027i | \(0.480003\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.904154 | − | 1.58399i | −0.0858185 | − | 0.150346i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.0329085 | − | 0.0904152i | −0.00309577 | − | 0.00850555i | 0.938135 | − | 0.346269i | \(-0.112552\pi\) |
−0.941231 | + | 0.337764i | \(0.890329\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.34262 | + | 0.589395i | −0.311701 | + | 0.0549613i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.11778 | + | 16.7179i | −0.288239 | + | 1.54557i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −24.8922 | − | 9.06002i | −2.28186 | − | 0.830531i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.3430 | + | 9.51791i | 1.03118 | + | 0.865265i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.07588 | + | 3.00184i | 0.0970091 | + | 0.270667i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −6.38745 | − | 3.68780i | −0.571311 | − | 0.329847i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.78038 | − | 5.64670i | 0.867868 | − | 0.501064i | 0.00122880 | − | 0.999999i | \(-0.499609\pi\) |
0.866639 | + | 0.498935i | \(0.166276\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −11.8007 | − | 14.2049i | −1.03900 | − | 1.25068i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.07281 | − | 11.7555i | 0.181102 | − | 1.02708i | −0.749759 | − | 0.661711i | \(-0.769831\pi\) |
0.930862 | − | 0.365372i | \(-0.119058\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.26147 | + | 6.09310i | −0.629649 | + | 0.528339i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.34031 | + | 3.85879i | 0.115355 | + | 0.332111i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.22440 | − | 3.84269i | −0.275479 | − | 0.328303i | 0.610511 | − | 0.792008i | \(-0.290964\pi\) |
−0.885990 | + | 0.463705i | \(0.846520\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.82044 | − | 1.02630i | −0.493684 | − | 0.0870497i | −0.0787369 | − | 0.996895i | \(-0.525089\pi\) |
−0.414947 | + | 0.909846i | \(0.636200\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 12.7664 | + | 4.71787i | 1.07513 | + | 0.397316i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 14.3988 | + | 24.9395i | 1.20409 | + | 2.08554i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.89314 | − | 3.27901i | 0.157217 | − | 0.272307i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.73561 | − | 9.56756i | 0.143150 | − | 0.789119i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −13.2535 | + | 15.7949i | −1.08577 | + | 1.29397i | −0.132723 | + | 0.991153i | \(0.542372\pi\) |
−0.953048 | + | 0.302819i | \(0.902072\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.71324 | − | 4.70708i | 0.139421 | − | 0.383057i | −0.850256 | − | 0.526369i | \(-0.823553\pi\) |
0.989678 | + | 0.143312i | \(0.0457753\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.220216 | − | 22.3744i | 0.0178034 | − | 1.80886i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.382900 | + | 2.17154i | 0.0307553 | + | 0.174422i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.7218 | + | 4.63034i | −1.01531 | + | 0.369542i | −0.795469 | − | 0.605995i | \(-0.792775\pi\) |
−0.219838 | + | 0.975536i | \(0.570553\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.61903 | − | 2.69719i | −0.366313 | − | 0.213901i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 15.3341i | 1.20850i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 7.88546i | − | 0.617637i | −0.951121 | − | 0.308819i | \(-0.900066\pi\) | ||
0.951121 | − | 0.308819i | \(-0.0999336\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 5.97343 | + | 3.48807i | 0.465031 | + | 0.271546i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 17.4302 | − | 6.34409i | 1.34879 | − | 0.490920i | 0.436221 | − | 0.899839i | \(-0.356316\pi\) |
0.912571 | + | 0.408919i | \(0.134094\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.32267 | + | 18.8438i | 0.255590 | + | 1.44952i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.89446 | − | 4.07151i | −0.527233 | − | 0.311356i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.11376 | − | 16.7974i | 0.464820 | − | 1.27708i | −0.457000 | − | 0.889467i | \(-0.651076\pi\) |
0.921821 | − | 0.387617i | \(-0.126702\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −10.0038 | + | 11.9220i | −0.756214 | + | 0.901221i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.69459 | − | 9.34148i | 0.127374 | − | 0.702149i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5.34490 | + | 9.25764i | −0.399497 | + | 0.691949i | −0.993664 | − | 0.112393i | \(-0.964148\pi\) |
0.594167 | + | 0.804342i | \(0.297482\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.113154 | − | 0.195989i | −0.00841069 | − | 0.0145678i | 0.861789 | − | 0.507266i | \(-0.169344\pi\) |
−0.870200 | + | 0.492698i | \(0.836011\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −15.2435 | − | 5.63327i | −1.12683 | − | 0.416423i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.815246 | − | 0.143750i | −0.0599381 | − | 0.0105687i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −24.3551 | − | 29.0253i | −1.78102 | − | 2.12254i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 18.2197 | − | 2.93599i | 1.32529 | − | 0.213562i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −13.7279 | + | 11.5191i | −0.993319 | + | 0.833493i | −0.986045 | − | 0.166480i | \(-0.946760\pi\) |
−0.00727404 | + | 0.999974i | \(0.502315\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.973127 | − | 5.51888i | 0.0700472 | − | 0.397258i | −0.929545 | − | 0.368708i | \(-0.879800\pi\) |
0.999592 | − | 0.0285493i | \(-0.00908874\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.93238 | + | 5.93728i | 0.353215 | + | 0.425177i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 14.2915 | − | 8.25120i | 1.01823 | − | 0.587873i | 0.104637 | − | 0.994510i | \(-0.466632\pi\) |
0.913590 | + | 0.406637i | \(0.133299\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.43752 | − | 4.29405i | −0.527231 | − | 0.304397i | 0.212657 | − | 0.977127i | \(-0.431788\pi\) |
−0.739888 | + | 0.672730i | \(0.765122\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.70108 | + | 15.9067i | 0.402123 | + | 1.12197i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −13.1036 | − | 10.9952i | −0.919691 | − | 0.771713i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.36006 | + | 0.495022i | 0.0949908 | + | 0.0345738i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −12.2144 | + | 4.31002i | −0.848959 | + | 0.299567i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −13.3526 | + | 2.35443i | −0.923620 | + | 0.162859i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.01203 | + | 11.0230i | 0.276200 | + | 0.758852i | 0.997785 | + | 0.0665263i | \(0.0211916\pi\) |
−0.721585 | + | 0.692326i | \(0.756586\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.96842 | + | 5.20039i | 0.203393 | + | 0.356325i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −8.38192 | −0.571642 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.96182 | 0.676253 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −17.2955 | − | 0.0851116i | −1.16872 | − | 0.00575131i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −14.4607 | − | 39.7304i | −0.972730 | − | 2.67255i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 23.3625 | − | 4.11943i | 1.56447 | − | 0.275858i | 0.676737 | − | 0.736225i | \(-0.263393\pi\) |
0.887729 | + | 0.460367i | \(0.152282\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −12.3083 | − | 4.61753i | −0.820552 | − | 0.307835i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 9.14518 | + | 3.32857i | 0.606987 | + | 0.220925i | 0.627184 | − | 0.778871i | \(-0.284207\pi\) |
−0.0201973 | + | 0.999796i | \(0.506429\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.04383 | − | 4.23227i | −0.333306 | − | 0.279677i | 0.460740 | − | 0.887535i | \(-0.347584\pi\) |
−0.794045 | + | 0.607859i | \(0.792029\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 20.2050 | − | 23.8402i | 1.32939 | − | 1.56857i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −18.4755 | − | 10.6669i | −1.21037 | − | 0.698809i | −0.247532 | − | 0.968880i | \(-0.579620\pi\) |
−0.962841 | + | 0.270070i | \(0.912953\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.34983 | − | 3.08873i | 0.348984 | − | 0.201486i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.46994 | + | 0.422995i | −0.160440 | + | 0.0274765i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.46984 | − | 19.6784i | 0.224445 | − | 1.27289i | −0.639298 | − | 0.768959i | \(-0.720775\pi\) |
0.863743 | − | 0.503933i | \(-0.168114\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.53930 | − | 3.80892i | 0.292402 | − | 0.245354i | −0.484771 | − | 0.874641i | \(-0.661097\pi\) |
0.777173 | + | 0.629287i | \(0.216653\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 7.45974 | + | 13.6877i | 0.478542 | + | 0.878065i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.83689 | − | 3.38087i | −0.181242 | − | 0.215996i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −14.8998 | − | 2.62724i | −0.948054 | − | 0.167167i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.430648 | − | 2.51462i | −0.0272912 | − | 0.159358i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7.81361 | − | 13.5336i | −0.493191 | − | 0.854232i | 0.506778 | − | 0.862076i | \(-0.330836\pi\) |
−0.999969 | + | 0.00784478i | \(0.997503\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −10.9666 | + | 18.9948i | −0.689467 | + | 1.19419i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −7.74759 | − | 6.56624i | −0.485173 | − | 0.411194i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −10.0813 | + | 12.0145i | −0.628856 | + | 0.749441i | −0.982566 | − | 0.185914i | \(-0.940476\pi\) |
0.353710 | + | 0.935355i | \(0.384920\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.27912 | + | 3.51436i | −0.0794808 | + | 0.218372i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.07516 | − | 13.5281i | 0.314145 | − | 0.837369i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.24105 | − | 29.7235i | −0.323177 | − | 1.83283i | −0.522189 | − | 0.852830i | \(-0.674884\pi\) |
0.199012 | − | 0.979997i | \(-0.436227\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.28134 | + | 0.830339i | −0.140141 | + | 0.0510073i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.0305415 | + | 6.20631i | −0.00186911 | + | 0.379820i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 6.99110i | − | 0.426255i | −0.977024 | − | 0.213127i | \(-0.931635\pi\) | ||
0.977024 | − | 0.213127i | \(-0.0683649\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.8898i | 1.32971i | 0.746973 | + | 0.664855i | \(0.231507\pi\) | ||||
−0.746973 | + | 0.664855i | \(0.768493\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 30.2852 | − | 17.2870i | 1.83294 | − | 1.04626i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −20.9183 | + | 7.61364i | −1.26142 | + | 0.459120i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.365886 | − | 2.07504i | −0.0219840 | − | 0.124677i | 0.971841 | − | 0.235639i | \(-0.0757182\pi\) |
−0.993825 | + | 0.110961i | \(0.964607\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.80001 | + | 7.93509i | 0.167632 | + | 0.475061i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.95821 | + | 24.6125i | −0.534402 | + | 1.46826i | 0.319380 | + | 0.947627i | \(0.396525\pi\) |
−0.853782 | + | 0.520631i | \(0.825697\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.7458 | + | 12.8063i | −0.638769 | + | 0.761255i | −0.984175 | − | 0.177198i | \(-0.943297\pi\) |
0.345406 | + | 0.938453i | \(0.387741\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.42110 | + | 1.22615i | −0.202648 | + | 0.0726307i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.26938 | − | 5.66274i | 0.192986 | − | 0.334261i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 19.3146 | + | 33.4538i | 1.13615 | + | 1.96787i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.07783 | + | 3.38765i | −0.239046 | + | 0.198587i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 13.7176 | + | 2.41877i | 0.801388 | + | 0.141306i | 0.559319 | − | 0.828953i | \(-0.311063\pi\) |
0.242069 | + | 0.970259i | \(0.422174\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.76985 | − | 3.30098i | −0.161267 | − | 0.192190i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 24.6690 | + | 9.39346i | 1.43144 | + | 0.545064i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −18.7488 | + | 15.7321i | −1.08427 | + | 0.909810i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.57563 | + | 37.2922i | −0.379013 | + | 2.14949i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5.89269 | − | 15.9454i | 0.338526 | − | 0.916042i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6.38784 | + | 3.68802i | −0.365767 | + | 0.211176i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 21.4253 | + | 12.3699i | 1.22281 | + | 0.705988i | 0.965516 | − | 0.260346i | \(-0.0838365\pi\) |
0.257292 | + | 0.966334i | \(0.417170\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 13.6134 | + | 2.46955i | 0.774441 | + | 0.140488i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 11.6982 | + | 9.81598i | 0.663346 | + | 0.556613i | 0.911088 | − | 0.412213i | \(-0.135244\pi\) |
−0.247742 | + | 0.968826i | \(0.579688\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.3850 | + | 5.23571i | 0.813088 | + | 0.295940i | 0.714899 | − | 0.699228i | \(-0.246473\pi\) |
0.0981890 | + | 0.995168i | \(0.468695\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4.25932 | − | 7.21249i | 0.239986 | − | 0.406378i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −26.1063 | + | 4.60325i | −1.46628 | + | 0.258544i | −0.849080 | − | 0.528265i | \(-0.822843\pi\) |
−0.617197 | + | 0.786809i | \(0.711732\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.36821 | − | 22.9915i | −0.468530 | − | 1.28727i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 13.3309 | − | 22.8296i | 0.744057 | − | 1.27422i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 19.9065 | 1.10763 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −24.8402 | −1.37789 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.14495 | − | 1.96077i | 0.0633161 | − | 0.108431i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −9.54519 | − | 26.2252i | −0.526243 | − | 1.44584i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.9290 | + | 1.92707i | −0.600710 | + | 0.105921i | −0.465730 | − | 0.884927i | \(-0.654208\pi\) |
−0.134980 | + | 0.990848i | \(0.543097\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3.15889 | − | 0.0310908i | −0.173106 | − | 0.00170376i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 7.20693 | + | 2.62311i | 0.393757 | + | 0.143316i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.52591 | − | 5.47589i | −0.355489 | − | 0.298291i | 0.447501 | − | 0.894284i | \(-0.352314\pi\) |
−0.802990 | + | 0.595993i | \(0.796759\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.163978 | − | 0.0297465i | −0.00890606 | − | 0.00161561i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 12.3400 | + | 7.12448i | 0.668247 | + | 0.385812i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4.26308 | − | 2.46129i | 0.230185 | − | 0.132897i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.03787 | + | 5.51440i | −0.109715 | + | 0.296885i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.54186 | + | 14.4156i | −0.136454 | + | 0.773871i | 0.837382 | + | 0.546619i | \(0.184085\pi\) |
−0.973836 | + | 0.227252i | \(0.927026\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.11745 | − | 1.77675i | 0.113345 | − | 0.0951075i | −0.584354 | − | 0.811499i | \(-0.698652\pi\) |
0.697699 | + | 0.716392i | \(0.254208\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 22.2823 | + | 19.2647i | 1.18934 | + | 1.02827i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.00818 | − | 4.77676i | −0.213334 | − | 0.254242i | 0.648756 | − | 0.760996i | \(-0.275289\pi\) |
−0.862090 | + | 0.506755i | \(0.830845\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.67653 | + | 0.471945i | 0.142056 | + | 0.0250482i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −35.2920 | + | 29.3188i | −1.86785 | + | 1.55171i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 12.3686 | + | 21.4231i | 0.652791 | + | 1.13067i | 0.982443 | + | 0.186564i | \(0.0597353\pi\) |
−0.329652 | + | 0.944103i | \(0.606931\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.93829 | + | 10.2854i | −0.312541 | + | 0.541338i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 24.1431 | − | 8.65305i | 1.26718 | − | 0.454168i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.04600 | + | 6.01359i | −0.264120 | + | 0.314766i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.425247 | − | 1.16836i | 0.0221977 | − | 0.0609877i | −0.928099 | − | 0.372334i | \(-0.878558\pi\) |
0.950297 | + | 0.311346i | \(0.100780\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.42959 | + | 1.01258i | 0.282653 | + | 0.0527128i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.90457 | + | 10.8014i | 0.0988804 | + | 0.560779i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 22.0894 | − | 8.03989i | 1.14375 | − | 0.416290i | 0.300481 | − | 0.953788i | \(-0.402853\pi\) |
0.843265 | + | 0.537498i | \(0.180631\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −11.0947 | + | 6.33293i | −0.572928 | + | 0.327031i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 27.3021i | − | 1.40613i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 4.98764i | − | 0.256198i | −0.991761 | − | 0.128099i | \(-0.959112\pi\) | ||
0.991761 | − | 0.128099i | \(-0.0408875\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.0962579 | − | 19.5605i | 0.00493144 | − | 1.00212i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 28.2451 | − | 10.2804i | 1.44326 | − | 0.525302i | 0.502556 | − | 0.864544i | \(-0.332393\pi\) |
0.940699 | + | 0.339243i | \(0.110171\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.46303 | − | 13.9686i | −0.125528 | − | 0.711903i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −31.5533 | + | 5.24405i | −1.60395 | + | 0.266570i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.00042 | − | 8.24360i | 0.152128 | − | 0.417967i | −0.840096 | − | 0.542438i | \(-0.817501\pi\) |
0.992223 | + | 0.124471i | \(0.0397235\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 20.6991 | − | 24.6682i | 1.04680 | − | 1.24753i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −15.7726 | − | 13.3676i | −0.795620 | − | 0.674304i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.568690 | + | 0.985000i | −0.0286139 | + | 0.0495607i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.80757 | − | 16.9872i | −0.492228 | − | 0.852563i | 0.507732 | − | 0.861515i | \(-0.330484\pi\) |
−0.999960 | + | 0.00895158i | \(0.997151\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.77143 | + | 16.1828i | 0.138745 | + | 0.810154i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 26.5005 | + | 4.67276i | 1.32337 | + | 0.233346i | 0.790299 | − | 0.612722i | \(-0.209925\pi\) |
0.533075 | + | 0.846068i | \(0.321036\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10.2203 | + | 12.1801i | 0.509112 | + | 0.606736i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 6.94229 | + | 1.36552i | 0.344965 | + | 0.0678533i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.09788 | + | 3.43853i | −0.203124 | + | 0.170442i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.36327 | + | 7.73147i | −0.0674092 | + | 0.382297i | 0.932374 | + | 0.361494i | \(0.117733\pi\) |
−0.999784 | + | 0.0208025i | \(0.993378\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −8.56377 | + | 1.46661i | −0.422419 | + | 0.0723424i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −16.8594 | + | 9.73379i | −0.829598 | + | 0.478969i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.00282 | − | 0.578978i | −0.0492265 | − | 0.0284209i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6.61861 | + | 7.80939i | −0.324115 | + | 0.382427i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 11.5624 | + | 9.70203i | 0.564861 | + | 0.473975i | 0.879936 | − | 0.475092i | \(-0.157585\pi\) |
−0.315075 | + | 0.949067i | \(0.602030\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12.2598 | − | 4.46218i | −0.597504 | − | 0.217474i | 0.0255229 | − | 0.999674i | \(-0.491875\pi\) |
−0.623027 | + | 0.782201i | \(0.714097\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 18.2068 | − | 14.9744i | 0.885243 | − | 0.728081i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 32.1864 | − | 5.67533i | 1.56127 | − | 0.275294i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 11.3972 | + | 31.3136i | 0.551550 | + | 1.51537i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 49.8783 | + | 0.245453i | 2.40815 | + | 0.0118506i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.23665 | −0.155904 | −0.0779519 | − | 0.996957i | \(-0.524838\pi\) | ||||
−0.0779519 | + | 0.996957i | \(0.524838\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.26788 | 0.445386 | 0.222693 | − | 0.974889i | \(-0.428515\pi\) | ||||
0.222693 | + | 0.974889i | \(0.428515\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.25103 | − | 5.69549i | −0.155875 | − | 0.273078i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.94121 | − | 10.8284i | −0.188533 | − | 0.517991i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −18.8470 | + | 3.32323i | −0.899516 | + | 0.158609i | −0.604240 | − | 0.796803i | \(-0.706523\pi\) |
−0.295277 | + | 0.955412i | \(0.595412\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −12.7945 | − | 10.9523i | −0.609263 | − | 0.521536i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 16.5782 | + | 6.03398i | 0.787655 | + | 0.286683i | 0.704361 | − | 0.709842i | \(-0.251234\pi\) |
0.0832943 | + | 0.996525i | \(0.473456\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.15792 | + | 1.81071i | 0.102295 | + | 0.0858358i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 12.0492 | + | 33.6188i | 0.569909 | + | 1.59012i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.70349 | + | 0.983512i | 0.0803928 | + | 0.0464148i | 0.539658 | − | 0.841885i | \(-0.318554\pi\) |
−0.459265 | + | 0.888299i | \(0.651887\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.09974 | − | 4.67639i | 0.381402 | − | 0.220203i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5.54414 | − | 6.67367i | −0.260487 | − | 0.313557i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.74843 | − | 15.5871i | 0.128848 | − | 0.730736i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −18.4817 | + | 15.5080i | −0.864539 | + | 0.725434i | −0.962941 | − | 0.269713i | \(-0.913071\pi\) |
0.0984023 | + | 0.995147i | \(0.468627\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −33.2735 | − | 19.8711i | −1.55307 | − | 0.927504i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.876842 | + | 1.04498i | 0.0408386 | + | 0.0486695i | 0.786077 | − | 0.618128i | \(-0.212109\pi\) |
−0.745239 | + | 0.666798i | \(0.767664\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 37.2025 | + | 6.55980i | 1.72895 | + | 0.304860i | 0.947652 | − | 0.319305i | \(-0.103449\pi\) |
0.781293 | + | 0.624164i | \(0.214560\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.58243 | + | 1.32390i | 0.166131 | + | 0.0613944i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −9.08669 | − | 15.7386i | −0.420482 | − | 0.728296i | 0.575505 | − | 0.817798i | \(-0.304806\pi\) |
−0.995987 | + | 0.0895025i | \(0.971472\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 17.3244 | − | 30.0067i | 0.799966 | − | 1.38558i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.18544 | + | 23.0723i | −0.192855 | + | 1.06312i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −34.8160 | + | 41.4921i | −1.60084 | + | 1.90781i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.00006 | − | 10.9901i | 0.183535 | − | 0.504259i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −8.06849 | + | 4.55306i | −0.369431 | + | 0.208470i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.04750 | − | 11.6119i | −0.0935526 | − | 0.530563i | −0.995181 | − | 0.0980521i | \(-0.968739\pi\) |
0.901629 | − | 0.432511i | \(-0.142372\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.60926 | + | 2.04161i | −0.255760 | + | 0.0930892i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 22.9356 | + | 13.3928i | 1.04360 | + | 0.609392i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.40620i | 0.109260i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 27.5642i | − | 1.24905i | −0.781003 | − | 0.624527i | \(-0.785292\pi\) | ||
0.781003 | − | 0.624527i | \(-0.214708\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −11.7944 | − | 6.88713i | −0.533363 | − | 0.311447i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.63911 | + | 1.32453i | −0.164231 | + | 0.0597752i | −0.422827 | − | 0.906210i | \(-0.638962\pi\) |
0.258596 | + | 0.965985i | \(0.416740\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.23780 | + | 35.3763i | 0.280936 | + | 1.59327i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 10.4344 | − | 5.88812i | 0.468989 | − | 0.264651i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.19949 | − | 11.5380i | 0.188373 | − | 0.517550i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12.5019 | + | 14.8992i | −0.559664 | + | 0.666981i | −0.969475 | − | 0.245189i | \(-0.921150\pi\) |
0.409812 | + | 0.912170i | \(0.365594\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.73453 | − | 31.6117i | 0.256200 | − | 1.41230i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −7.58734 | + | 13.1417i | −0.338303 | + | 0.585958i | −0.984114 | − | 0.177540i | \(-0.943186\pi\) |
0.645811 | + | 0.763497i | \(0.276519\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.85786 | − | 6.68201i | −0.171673 | − | 0.297346i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 31.0870 | + | 11.4883i | 1.38062 | + | 0.510214i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 24.1974 | + | 4.26666i | 1.07253 | + | 0.189116i | 0.681911 | − | 0.731436i | \(-0.261149\pi\) |
0.390621 | + | 0.920552i | \(0.372260\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 22.7966 | + | 27.1680i | 1.00846 | + | 1.20184i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −12.1114 | + | 6.75614i | −0.534733 | + | 0.298291i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4.81055 | − | 4.03653i | 0.211978 | − | 0.177871i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.93183 | − | 39.3123i | 0.304861 | − | 1.72895i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −19.7845 | − | 23.8153i | −0.868443 | − | 1.04537i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −15.3333 | + | 8.85266i | −0.671762 | + | 0.387842i | −0.796744 | − | 0.604317i | \(-0.793446\pi\) |
0.124982 | + | 0.992159i | \(0.460113\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −15.4545 | − | 8.92267i | −0.675779 | − | 0.390161i | 0.122484 | − | 0.992471i | \(-0.460914\pi\) |
−0.798263 | + | 0.602309i | \(0.794247\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 9.09476 | + | 25.3755i | 0.396928 | + | 1.10748i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −16.0257 | − | 13.4472i | −0.698092 | − | 0.585769i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.09625 | + | 1.49091i | 0.178098 | + | 0.0648223i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −12.4922 | − | 10.6935i | −0.542115 | − | 0.464056i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 10.2780 | − | 1.81228i | 0.445188 | − | 0.0784986i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.10395 | − | 11.2755i | −0.177429 | − | 0.487482i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 9.17862 | + | 16.0801i | 0.396087 | + | 0.693906i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −28.5195 | −1.22842 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.91858 | 0.383440 | 0.191720 | − | 0.981450i | \(-0.438593\pi\) | ||||
0.191720 | + | 0.981450i | \(0.438593\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −0.391973 | − | 0.00192891i | −0.0168212 | − | 8.27776e-5i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −0.352477 | − | 0.968423i | −0.0150985 | − | 0.0414827i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.30961 | + | 0.230919i | −0.0559947 | + | 0.00987337i | −0.201575 | − | 0.979473i | \(-0.564606\pi\) |
0.145581 | + | 0.989346i | \(0.453495\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −21.7394 | + | 17.8799i | −0.927814 | + | 0.763094i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 12.0793 | + | 4.39649i | 0.514594 | + | 0.187297i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.93625 | + | 3.30291i | 0.167386 | + | 0.140454i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.927043 | + | 1.09383i | −0.0393508 | + | 0.0464305i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 24.3179 | + | 14.0399i | 1.03038 | + | 0.594891i | 0.917094 | − | 0.398671i | \(-0.130528\pi\) |
0.113288 | + | 0.993562i | \(0.463862\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −52.3428 | + | 30.2201i | −2.21386 | + | 1.27818i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −64.6853 | + | 11.0778i | −2.73102 | + | 0.467707i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5.14982 | + | 29.2061i | −0.217039 | + | 1.23089i | 0.660294 | + | 0.751007i | \(0.270432\pi\) |
−0.877333 | + | 0.479882i | \(0.840679\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.0579446 | + | 0.0486213i | −0.00243775 | + | 0.00204551i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 11.5216 | − | 29.8159i | 0.483862 | − | 1.25215i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −7.18324 | − | 8.56066i | −0.301137 | − | 0.358881i | 0.594163 | − | 0.804345i | \(-0.297483\pi\) |
−0.895300 | + | 0.445463i | \(0.853039\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −37.3754 | − | 6.59029i | −1.56411 | − | 0.275795i | −0.676519 | − | 0.736425i | \(-0.736512\pi\) |
−0.887592 | + | 0.460630i | \(0.847624\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 5.23943 | + | 30.5939i | 0.218880 | + | 1.27808i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −9.45960 | − | 16.3845i | −0.394493 | − | 0.683282i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 19.7897 | − | 34.2768i | 0.823856 | − | 1.42696i | −0.0789341 | − | 0.996880i | \(-0.525152\pi\) |
0.902790 | − | 0.430081i | \(-0.141515\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −7.40477 | − | 6.27569i | −0.307732 | − | 0.260809i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.36266 | + | 4.00746i | −0.139507 | + | 0.166258i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.36566 | + | 14.7420i | −0.222223 | + | 0.610553i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 13.1884 | − | 2.19187i | 0.545275 | − | 0.0906226i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −0.480765 | − | 2.72655i | −0.0198433 | − | 0.112537i | 0.973277 | − | 0.229633i | \(-0.0737526\pi\) |
−0.993121 | + | 0.117096i | \(0.962641\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.03466 | + | 2.56041i | −0.289858 | + | 0.105500i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0.140656 | − | 28.5826i | 0.00578582 | − | 1.17573i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 20.8421i | 0.855881i | 0.903807 | + | 0.427941i | \(0.140761\pi\) | ||||
−0.903807 | + | 0.427941i | \(0.859239\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 20.8248i | 0.853733i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −12.9186 | + | 7.37403i | −0.528723 | + | 0.301799i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −26.8393 | + | 9.76870i | −1.09662 | + | 0.399138i | −0.826070 | − | 0.563567i | \(-0.809429\pi\) |
−0.270553 | + | 0.962705i | \(0.587206\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.28624 | − | 29.9798i | −0.215630 | − | 1.22290i | −0.879809 | − | 0.475327i | \(-0.842330\pi\) |
0.664179 | − | 0.747574i | \(-0.268781\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 28.7713 | + | 5.36564i | 1.17166 | + | 0.218506i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.98134 | − | 10.9386i | 0.161864 | − | 0.444719i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 23.6515 | − | 28.1868i | 0.959985 | − | 1.14407i | −0.0295193 | − | 0.999564i | \(-0.509398\pi\) |
0.989505 | − | 0.144502i | \(-0.0461579\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −27.8904 | + | 9.99611i | −1.13018 | + | 0.405063i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 22.2722 | − | 38.5765i | 0.901035 | − | 1.56064i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −0.0873020 | − | 0.151211i | −0.00352609 | − | 0.00610737i | 0.864257 | − | 0.503051i | \(-0.167789\pi\) |
−0.867783 | + | 0.496943i | \(0.834456\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.92829 | − | 1.60192i | 0.0777560 | − | 0.0645957i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 41.1918 | + | 7.26323i | 1.65832 | + | 0.292407i | 0.922853 | − | 0.385152i | \(-0.125851\pi\) |
0.735468 | + | 0.677559i | \(0.236962\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.93870 | + | 3.50220i | 0.118116 | + | 0.140765i | 0.821862 | − | 0.569686i | \(-0.192935\pi\) |
−0.703746 | + | 0.710451i | \(0.748491\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.22143 | + | 22.0337i | −0.169400 | + | 0.884181i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 9.74896 | − | 8.18035i | 0.390584 | − | 0.327739i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.79775 | − | 15.8668i | 0.111910 | − | 0.634673i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −8.14057 | + | 22.0281i | −0.325103 | + | 0.879719i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 6.80168 | − | 3.92695i | 0.271201 | − | 0.156578i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −17.5521 | − | 10.1337i | −0.698740 | − | 0.403418i | 0.108138 | − | 0.994136i | \(-0.465511\pi\) |
−0.806878 | + | 0.590718i | \(0.798844\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 19.9914 | + | 3.62654i | 0.794585 | + | 0.144142i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.80114 | − | 5.70683i | −0.269895 | − | 0.226469i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −29.9049 | − | 10.8845i | −1.18488 | − | 0.431260i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 10.3709 | + | 0.102074i | 0.410268 | + | 0.00403798i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 19.8935 | − | 3.50776i | 0.785747 | − | 0.138548i | 0.233641 | − | 0.972323i | \(-0.424936\pi\) |
0.552105 | + | 0.833775i | \(0.313825\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −14.5397 | − | 39.9476i | −0.573392 | − | 1.57538i | −0.799108 | − | 0.601187i | \(-0.794695\pi\) |
0.225717 | − | 0.974193i | \(-0.427528\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −7.32074 | + | 12.5370i | −0.288254 | + | 0.493644i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −8.10818 | −0.318765 | −0.159383 | − | 0.987217i | \(-0.550950\pi\) | ||||
−0.159383 | + | 0.987217i | \(0.550950\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −27.8456 | −1.09304 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8.70062 | − | 14.9001i | 0.341004 | − | 0.583981i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0.613037 | + | 1.68431i | 0.0239900 | + | 0.0659120i | 0.951110 | − | 0.308854i | \(-0.0999454\pi\) |
−0.927120 | + | 0.374766i | \(0.877723\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9.24154 | + | 1.62953i | −0.361097 | + | 0.0636711i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −15.2331 | + | 25.7949i | −0.594300 | + | 1.00635i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 10.8091 | + | 3.93418i | 0.421062 | + | 0.153254i | 0.543857 | − | 0.839178i | \(-0.316964\pi\) |
−0.122795 | + | 0.992432i | \(0.539186\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.1899 | + | 10.2285i | 0.474131 | + | 0.397843i | 0.848299 | − | 0.529518i | \(-0.177627\pi\) |
−0.374168 | + | 0.927361i | \(0.622072\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −72.0554 | − | 13.0712i | −2.79840 | − | 0.507645i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 6.45363 | + | 3.72601i | 0.250261 | + | 0.144488i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 18.0083 | − | 10.3971i | 0.697285 | − | 0.402578i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 14.2432 | − | 38.5416i | 0.550673 | − | 1.49010i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8.27679 | + | 46.9400i | −0.319522 | + | 1.81210i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 35.1997 | − | 29.5361i | 1.35685 | − | 1.13853i | 0.379909 | − | 0.925024i | \(-0.375955\pi\) |
0.976941 | − | 0.213509i | \(-0.0684893\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −17.6565 | + | 14.3768i | −0.679601 | + | 0.553364i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 33.3997 | + | 39.8042i | 1.28366 | + | 1.52980i | 0.683672 | + | 0.729790i | \(0.260382\pi\) |
0.599984 | + | 0.800012i | \(0.295173\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10.7055 | + | 1.88767i | 0.410840 | + | 0.0724421i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 12.9660 | − | 10.7715i | 0.496858 | − | 0.412764i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −18.8480 | − | 32.6457i | −0.721199 | − | 1.24915i | −0.960520 | − | 0.278212i | \(-0.910258\pi\) |
0.239321 | − | 0.970941i | \(-0.423075\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.97176 | + | 3.41519i | −0.0753371 | + | 0.130488i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −10.7356 | + | 3.84770i | −0.409587 | + | 0.146799i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −11.2526 | + | 13.4104i | −0.428691 | + | 0.510894i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10.5475 | − | 28.9791i | 0.401247 | − | 1.10242i | −0.560423 | − | 0.828207i | \(-0.689361\pi\) |
0.961670 | − | 0.274210i | \(-0.0884164\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −18.0112 | − | 51.0430i | −0.684190 | − | 1.93896i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0.806822 | + | 4.57572i | 0.0306045 | + | 0.173567i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −12.9035 | + | 4.69648i | −0.488754 | + | 0.177892i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −32.0911 | + | 18.3178i | −1.21380 | + | 0.692845i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.12015i | 0.117846i | 0.998263 | + | 0.0589232i | \(0.0187667\pi\) | ||||
−0.998263 | + | 0.0589232i | \(0.981233\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 2.81047i | − | 0.105999i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.0526527 | − | 10.6995i | 0.00198302 | − | 0.402968i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −32.7556 | + | 11.9221i | −1.23190 | + | 0.448376i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.06472 | − | 17.3809i | −0.115098 | − | 0.652753i | −0.986702 | − | 0.162542i | \(-0.948031\pi\) |
0.871604 | − | 0.490211i | \(-0.163080\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.52455 | + | 4.06378i | −0.0571752 | + | 0.152404i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4.14188 | + | 11.3797i | −0.155115 | + | 0.426174i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 14.5521 | − | 17.3426i | 0.544219 | − | 0.648575i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −26.4029 | − | 22.3770i | −0.986034 | − | 0.835684i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0.448200 | − | 0.776305i | 0.0167150 | − | 0.0289513i | −0.857547 | − | 0.514406i | \(-0.828013\pi\) |
0.874262 | + | 0.485454i | \(0.161346\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14.1852 | − | 24.5694i | −0.528283 | − | 0.915013i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.73248 | − | 10.1162i | −0.0644315 | − | 0.376226i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 20.7841 | + | 3.66480i | 0.771902 | + | 0.136107i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 29.2965 | + | 34.9142i | 1.08655 | + | 1.29490i | 0.952706 | + | 0.303895i | \(0.0982871\pi\) |
0.133842 | + | 0.991003i | \(0.457268\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 26.9882 | + | 0.797085i | 0.999564 | + | 0.0295217i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 60.9181 | − | 51.1163i | 2.25314 | − | 1.89061i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.21540 | − | 23.9067i | 0.155699 | − | 0.883014i | −0.802445 | − | 0.596727i | \(-0.796468\pi\) |
0.958144 | − | 0.286287i | \(-0.0924212\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −7.53456 | + | 1.29035i | −0.277916 | + | 0.0475952i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 42.9203 | − | 24.7801i | 1.58099 | − | 0.912786i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −27.2841 | − | 15.7525i | −1.00366 | − | 0.579464i | −0.0943320 | − | 0.995541i | \(-0.530072\pi\) |
−0.909330 | + | 0.416077i | \(0.863405\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −16.9431 | + | 19.9914i | −0.622420 | + | 0.734401i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 22.7123 | + | 19.0578i | 0.833232 | + | 0.699165i | 0.956031 | − | 0.293267i | \(-0.0947425\pi\) |
−0.122799 | + | 0.992432i | \(0.539187\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 15.2319 | + | 5.54394i | 0.558052 | + | 0.203114i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −4.13730 | − | 1.55213i | −0.151376 | − | 0.0567896i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −53.3857 | + | 9.41334i | −1.95067 | + | 0.343956i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.19638 | − | 14.2769i | −0.189618 | − | 0.520972i | 0.808058 | − | 0.589103i | \(-0.200519\pi\) |
−0.997676 | + | 0.0681305i | \(0.978297\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −27.0668 | − | 0.133197i | −0.986370 | − | 0.00485396i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.93794 | −0.143316 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15.3617 | 0.558330 | 0.279165 | − | 0.960243i | \(-0.409942\pi\) | ||||
0.279165 | + | 0.960243i | \(0.409942\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 18.8327 | + | 32.9930i | 0.683582 | + | 1.19757i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −16.5195 | − | 45.3870i | −0.598832 | − | 1.64528i | −0.753606 | − | 0.657326i | \(-0.771687\pi\) |
0.154774 | − | 0.987950i | \(-0.450535\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.58516 | + | 0.808487i | −0.165994 | + | 0.0292692i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −16.5880 | + | 5.85329i | −0.599739 | + | 0.211626i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −29.1983 | − | 10.6273i | −1.05429 | − | 0.383730i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.83911 | − | 1.54319i | −0.0663199 | − | 0.0556490i | 0.609025 | − | 0.793151i | \(-0.291561\pi\) |
−0.675345 | + | 0.737502i | \(0.736005\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9.16527 | + | 25.5722i | 0.330079 | + | 0.920961i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −25.9787 | − | 14.9988i | −0.934389 | − | 0.539470i | −0.0461920 | − | 0.998933i | \(-0.514709\pi\) |
−0.888197 | + | 0.459463i | \(0.848042\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −10.6442 | + | 6.14543i | −0.382351 | + | 0.220750i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.13932 | + | 4.98264i | 0.148497 | + | 0.178751i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.853266 | + | 4.83911i | −0.0305714 | + | 0.173379i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13.4537 | − | 11.2890i | 0.481413 | − | 0.403953i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −15.8017 | − | 19.4064i | −0.564705 | − | 0.693529i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6.84119 | + | 8.15301i | 0.244173 | + | 0.290994i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 38.5152 | + | 6.79128i | 1.37292 | + | 0.242083i | 0.810970 | − | 0.585088i | \(-0.198940\pi\) |
0.561950 | + | 0.827171i | \(0.310051\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −49.0355 | − | 18.1212i | −1.74571 | − | 0.645132i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.170865 | + | 0.295946i | 0.00607524 | + | 0.0105226i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −26.5936 | + | 46.0614i | −0.944365 | + | 1.63569i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.750557 | + | 4.13746i | −0.0266195 | + | 0.146740i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 3.66765 | − | 4.37094i | 0.129915 | − | 0.154827i | −0.697165 | − | 0.716910i | \(-0.745556\pi\) |
0.827080 | + | 0.562084i | \(0.190000\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −20.0452 | + | 55.0736i | −0.709147 | + | 1.94836i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 9.25623 | + | 5.46625i | 0.327053 | + | 0.193140i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 8.80883 | + | 49.9574i | 0.310857 | + | 1.76296i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 11.3279 | − | 4.12300i | 0.399255 | − | 0.145317i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −10.4567 | − | 6.10600i | −0.368094 | − | 0.214941i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.69898i | 0.0948912i | 0.998874 | + | 0.0474456i | \(0.0151081\pi\) | ||||
−0.998874 | + | 0.0474456i | \(0.984892\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 16.7724i | − | 0.588958i | −0.955658 | − | 0.294479i | \(-0.904854\pi\) | ||
0.955658 | − | 0.294479i | \(-0.0951461\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 32.7410 | + | 19.1185i | 1.14828 | + | 0.670514i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5.82527 | + | 2.12022i | −0.204050 | + | 0.0742682i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.94146 | − | 28.0244i | −0.172880 | − | 0.980450i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.594441 | − | 60.3965i | 0.0207714 | − | 2.11043i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −13.8978 | + | 38.1840i | −0.485038 | + | 1.33263i | 0.420087 | + | 0.907484i | \(0.361999\pi\) |
−0.905125 | + | 0.425146i | \(0.860223\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −0.497261 | + | 0.592613i | −0.0173334 | + | 0.0206572i | −0.774642 | − | 0.632401i | \(-0.782070\pi\) |
0.757308 | + | 0.653058i | \(0.226514\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −6.88210 | + | 37.9377i | −0.239604 | + | 1.32082i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −7.01112 | + | 12.1436i | −0.243800 | + | 0.422275i | −0.961794 | − | 0.273775i | \(-0.911728\pi\) |
0.717993 | + | 0.696050i | \(0.245061\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 18.0048 | + | 31.1853i | 0.625334 | + | 1.08311i | 0.988476 | + | 0.151377i | \(0.0483707\pi\) |
−0.363142 | + | 0.931734i | \(0.618296\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.42325 | − | 1.26507i | −0.118751 | − | 0.0438849i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 41.2358 | + | 7.27098i | 1.42874 | + | 0.251925i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −9.37320 | − | 11.1705i | −0.324373 | − | 0.386573i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 14.3142 | + | 2.74245i | 0.494771 | + | 0.0947930i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 23.7095 | − | 19.8946i | 0.818543 | − | 0.686839i | −0.134088 | − | 0.990969i | \(-0.542810\pi\) |
0.952630 | + | 0.304131i | \(0.0983659\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00779 | − | 5.71547i | 0.0347515 | − | 0.197085i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 28.9893 | + | 34.8954i | 0.998445 | + | 1.20186i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 13.0272 | − | 7.52124i | 0.448148 | − | 0.258739i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −45.5440 | − | 26.2948i | −1.56491 | − | 0.903501i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 9.76933 | + | 27.2576i | 0.335282 | + | 0.935479i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.48274 | − | 2.92237i | −0.119387 | − | 0.100177i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 25.5167 | + | 9.28732i | 0.873675 | + | 0.317992i | 0.739655 | − | 0.672987i | \(-0.234989\pi\) |
0.134021 | + | 0.990979i | \(0.457211\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.15400 | + | 6.18792i | −0.0394661 | + | 0.211622i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 30.9412 | − | 5.45576i | 1.05693 | − | 0.186365i | 0.381936 | − | 0.924189i | \(-0.375257\pi\) |
0.674994 | + | 0.737823i | \(0.264146\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14.7909 | + | 40.6376i | 0.504658 | + | 1.38654i | 0.886680 | + | 0.462384i | \(0.153006\pi\) |
−0.382021 | + | 0.924154i | \(0.624772\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5.61441 | − | 9.83590i | −0.191338 | − | 0.335207i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −4.89374 | −0.166585 | −0.0832924 | − | 0.996525i | \(-0.526544\pi\) | ||||
−0.0832924 | + | 0.996525i | \(0.526544\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −14.0527 | −0.477806 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 66.9069 | + | 0.329251i | 2.27228 | + | 0.0111819i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.51377 | + | 6.90652i | 0.0852737 | + | 0.234288i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 54.4627 | − | 9.60324i | 1.84540 | − | 0.325393i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.50541 | + | 9.05804i | 0.0509505 | + | 0.306568i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 24.6155 | + | 8.95932i | 0.832157 | + | 0.302880i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −31.8866 | − | 26.7561i | −1.07674 | − | 0.903488i | −0.0810895 | − | 0.996707i | \(-0.525840\pi\) |
−0.995646 | + | 0.0932187i | \(0.970284\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 15.5987 | − | 18.4051i | 0.526130 | − | 0.620788i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 17.9282 | + | 10.3508i | 0.604016 | + | 0.348729i | 0.770620 | − | 0.637295i | \(-0.219947\pi\) |
−0.166604 | + | 0.986024i | \(0.553280\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.10427 | + | 1.79225i | −0.104467 | + | 0.0603141i | −0.551323 | − | 0.834292i | \(-0.685877\pi\) |
0.446856 | + | 0.894606i | \(0.352544\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −7.35652 | + | 1.25986i | −0.247287 | + | 0.0423496i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.96954 | − | 11.1698i | 0.0661308 | − | 0.375047i | −0.933724 | − | 0.357994i | \(-0.883461\pi\) |
0.999855 | − | 0.0170523i | \(-0.00542817\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −30.7259 | + | 25.7821i | −1.03051 | + | 0.864704i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 35.5958 | − | 28.6937i | 1.19250 | − | 0.961274i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 13.4809 | + | 16.0659i | 0.451121 | + | 0.537625i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.27607 | + | 1.45929i | 0.276638 | + | 0.0487788i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 7.15569 | + | 41.7832i | 0.238921 | + | 1.39510i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −6.75449 | − | 11.6991i | −0.225275 | − | 0.390187i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 11.5165 | − | 19.9472i | 0.383672 | − | 0.664539i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 50.0356 | + | 42.4062i | 1.66508 | + | 1.41119i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −0.114359 | + | 0.136288i | −0.00380143 | + | 0.00453037i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −19.7858 | + | 54.3610i | −0.656977 | + | 1.80503i | −0.0667822 | + | 0.997768i | \(0.521273\pi\) |
−0.590195 | + | 0.807261i | \(0.700949\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −18.7033 | − | 22.7405i | −0.620348 | − | 0.754255i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.67979 | + | 20.8691i | 0.121917 | + | 0.691426i | 0.983091 | + | 0.183116i | \(0.0586184\pi\) |
−0.861174 | + | 0.508310i | \(0.830270\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7.03147 | + | 2.55925i | −0.232708 | + | 0.0846987i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.0628688 | + | 12.7755i | −0.00207838 | + | 0.422346i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 42.3951i | 1.40001i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 7.68271i | − | 0.253429i | −0.991939 | − | 0.126715i | \(-0.959557\pi\) | ||
0.991939 | − | 0.126715i | \(-0.0404432\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 37.2147 | − | 21.2424i | 1.22627 | − | 0.699962i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 18.4158 | − | 6.70279i | 0.606162 | − | 0.220625i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.801262 | − | 4.54418i | −0.0263453 | − | 0.149412i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 15.5837 | − | 18.2050i | 0.511835 | − | 0.597930i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −6.39595 | + | 17.5727i | −0.209844 | + | 0.576542i | −0.999306 | − | 0.0372578i | \(-0.988138\pi\) |
0.789461 | + | 0.613800i | \(0.210360\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9.63127 | − | 11.4781i | 0.315652 | − | 0.376179i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 24.8992 | − | 8.92404i | 0.815162 | − | 0.292160i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −14.8934 | + | 25.7962i | −0.487068 | + | 0.843626i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.60988 | − | 2.78839i | −0.0525924 | − | 0.0910926i | 0.838531 | − | 0.544854i | \(-0.183415\pi\) |
−0.891123 | + | 0.453762i | \(0.850082\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 20.3950 | − | 16.9431i | 0.665564 | − | 0.552916i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −44.8305 | − | 7.90482i | −1.46143 | − | 0.257690i | −0.614300 | − | 0.789073i | \(-0.710562\pi\) |
−0.847132 | + | 0.531383i | \(0.821673\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.10940 | + | 6.08915i | 0.166385 | + | 0.198290i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −7.06779 | − | 12.6701i | −0.229915 | − | 0.412159i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 7.22304 | − | 6.06085i | 0.234717 | − | 0.196951i | −0.517841 | − | 0.855477i | \(-0.673264\pi\) |
0.752558 | + | 0.658526i | \(0.228820\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9.82954 | + | 55.7461i | −0.319080 | + | 1.80959i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −15.9160 | + | 43.0682i | −0.516111 | + | 1.39658i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 20.9106 | − | 12.0727i | 0.677361 | − | 0.391074i | −0.121499 | − | 0.992592i | \(-0.538770\pi\) |
0.798860 | + | 0.601517i | \(0.205437\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 12.2007 | + | 7.04408i | 0.394806 | + | 0.227941i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −41.6975 | − | 7.56416i | −1.34789 | − | 0.244515i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 13.6478 | + | 11.4518i | 0.440709 | + | 0.369799i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21.7376 | − | 7.91185i | −0.701214 | − | 0.255221i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −22.5035 | − | 39.8785i | −0.725165 | − | 1.28507i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −4.33864 | + | 0.765019i | −0.139666 | + | 0.0246268i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5.43085 | + | 14.9211i | 0.174644 | + | 0.479832i | 0.995872 | − | 0.0907693i | \(-0.0289326\pi\) |
−0.821228 | + | 0.570601i | \(0.806710\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 17.3863 | − | 29.7746i | 0.558528 | − | 0.956498i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −13.9015 | −0.446119 | −0.223059 | − | 0.974805i | \(-0.571604\pi\) | ||||
−0.223059 | + | 0.974805i | \(0.571604\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 20.9909 | 0.672937 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −21.6954 | + | 37.1540i | −0.694808 | + | 1.18988i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −10.0299 | − | 27.5570i | −0.320886 | − | 0.881627i | −0.990326 | − | 0.138761i | \(-0.955688\pi\) |
0.669440 | − | 0.742866i | \(-0.266534\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 17.9267 | − | 3.16096i | 0.572940 | − | 0.101025i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.93277 | − | 3.42506i | −0.0617085 | − | 0.109354i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −17.8368 | − | 6.49207i | −0.568906 | − | 0.207065i | 0.0415207 | − | 0.999138i | \(-0.486780\pi\) |
−0.610427 | + | 0.792073i | \(0.709002\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9.93811 | − | 8.33906i | −0.316655 | − | 0.265705i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −47.5623 | − | 8.62805i | −1.51392 | − | 0.274634i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −39.8662 | − | 23.0167i | −1.26767 | − | 0.731890i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −53.7186 | + | 31.0144i | −1.70643 | + | 0.985206i | −0.767524 | + | 0.641020i | \(0.778512\pi\) |
−0.938902 | + | 0.344186i | \(0.888155\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −6.66295 | + | 18.0297i | −0.211442 | + | 0.572157i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.17239 | + | 6.64893i | −0.0371671 | + | 0.210785i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 21.9558 | − | 18.4231i | 0.695348 | − | 0.583466i | −0.225098 | − | 0.974336i | \(-0.572270\pi\) |
0.920446 | + | 0.390870i | \(0.127826\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.80547 | + | 4.69766i | −0.0887610 | + | 0.148627i |
(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 | 432.2.be.a.383.5 | yes | 36 | |
4.3 | odd | 2 | inner | 432.2.be.a.383.2 | yes | 36 | |
27.11 | odd | 18 | inner | 432.2.be.a.335.2 | ✓ | 36 | |
108.11 | even | 18 | inner | 432.2.be.a.335.5 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
432.2.be.a.335.2 | ✓ | 36 | 27.11 | odd | 18 | inner | |
432.2.be.a.335.5 | yes | 36 | 108.11 | even | 18 | inner | |
432.2.be.a.383.2 | yes | 36 | 4.3 | odd | 2 | inner | |
432.2.be.a.383.5 | yes | 36 | 1.1 | even | 1 | trivial |