Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [512,2,Mod(129,512)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(512, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("512.129");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 512 = 2^{9} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 512.e (of order \(4\), degree \(2\), 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: | \(4.08834058349\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{16})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{7} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 129.3 | ||
Root | \(-0.923880 - 0.382683i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 512.129 |
Dual form | 512.2.e.i.385.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/512\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(511\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.765367 | + | 0.765367i | 0.441885 | + | 0.441885i | 0.892645 | − | 0.450760i | \(-0.148847\pi\) |
−0.450760 | + | 0.892645i | \(0.648847\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.414214 | − | 0.414214i | 0.185242 | − | 0.185242i | −0.608394 | − | 0.793635i | \(-0.708186\pi\) |
0.793635 | + | 0.608394i | \(0.208186\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.69552i | 1.39677i | 0.715720 | + | 0.698387i | \(0.246099\pi\) | ||||
−0.715720 | + | 0.698387i | \(0.753901\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 1.82843i | − | 0.609476i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.93015 | − | 2.93015i | 0.883474 | − | 0.883474i | −0.110412 | − | 0.993886i | \(-0.535217\pi\) |
0.993886 | + | 0.110412i | \(0.0352171\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.41421 | + | 2.41421i | 0.669582 | + | 0.669582i | 0.957619 | − | 0.288037i | \(-0.0930026\pi\) |
−0.288037 | + | 0.957619i | \(0.593003\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.634051 | 0.163711 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.82843 | −0.685994 | −0.342997 | − | 0.939336i | \(-0.611442\pi\) | ||||
−0.342997 | + | 0.939336i | \(0.611442\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.46088 | + | 4.46088i | 1.02340 | + | 1.02340i | 0.999720 | + | 0.0236776i | \(0.00753751\pi\) |
0.0236776 | + | 0.999720i | \(0.492462\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.82843 | + | 2.82843i | −0.617213 | + | 0.617213i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.75699i | 1.40893i | 0.709739 | + | 0.704464i | \(0.248813\pi\) | ||||
−0.709739 | + | 0.704464i | \(0.751187\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.65685i | 0.931371i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.69552 | − | 3.69552i | 0.711203 | − | 0.711203i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.24264 | − | 5.24264i | −0.973534 | − | 0.973534i | 0.0261248 | − | 0.999659i | \(-0.491683\pi\) |
−0.999659 | + | 0.0261248i | \(0.991683\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.06147 | −0.549856 | −0.274928 | − | 0.961465i | \(-0.588654\pi\) | ||||
−0.274928 | + | 0.961465i | \(0.588654\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.48528 | 0.780787 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.53073 | + | 1.53073i | 0.258741 | + | 0.258741i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.41421 | − | 6.41421i | 1.05449 | − | 1.05449i | 0.0560630 | − | 0.998427i | \(-0.482145\pi\) |
0.998427 | − | 0.0560630i | \(-0.0178548\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.69552i | 0.591756i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 4.00000i | − | 0.624695i | −0.949968 | − | 0.312348i | \(-0.898885\pi\) | ||
0.949968 | − | 0.312348i | \(-0.101115\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.765367 | + | 0.765367i | −0.116717 | + | 0.116717i | −0.763053 | − | 0.646336i | \(-0.776301\pi\) |
0.646336 | + | 0.763053i | \(0.276301\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.757359 | − | 0.757359i | −0.112900 | − | 0.112900i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.06147 | 0.446561 | 0.223280 | − | 0.974754i | \(-0.428323\pi\) | ||||
0.223280 | + | 0.974754i | \(0.428323\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.65685 | −0.950979 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.16478 | − | 2.16478i | −0.303130 | − | 0.303130i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.24264 | + | 3.24264i | −0.445411 | + | 0.445411i | −0.893826 | − | 0.448415i | \(-0.851989\pi\) |
0.448415 | + | 0.893826i | \(0.351989\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 2.42742i | − | 0.327313i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.82843i | 0.904447i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.765367 | + | 0.765367i | −0.0996423 | + | 0.0996423i | −0.755171 | − | 0.655528i | \(-0.772446\pi\) |
0.655528 | + | 0.755171i | \(0.272446\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.757359 | + | 0.757359i | 0.0969699 | + | 0.0969699i | 0.753928 | − | 0.656958i | \(-0.228157\pi\) |
−0.656958 | + | 0.753928i | \(0.728157\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 6.75699 | 0.851300 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.00000 | 0.248069 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.39942 | + | 1.39942i | 0.170966 | + | 0.170966i | 0.787404 | − | 0.616438i | \(-0.211425\pi\) |
−0.616438 | + | 0.787404i | \(0.711425\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5.17157 | + | 5.17157i | −0.622584 | + | 0.622584i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 8.02509i | − | 0.952403i | −0.879336 | − | 0.476201i | \(-0.842013\pi\) | ||
0.879336 | − | 0.476201i | \(-0.157987\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 6.48528i | − | 0.759045i | −0.925183 | − | 0.379522i | \(-0.876088\pi\) | ||
0.925183 | − | 0.379522i | \(-0.123912\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.56420 | + | 3.56420i | −0.411559 | + | 0.411559i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 10.8284 | + | 10.8284i | 1.23401 | + | 1.23401i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −14.7821 | −1.66311 | −0.831557 | − | 0.555440i | \(-0.812550\pi\) | ||||
−0.831557 | + | 0.555440i | \(0.812550\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.171573 | 0.0190637 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −9.68714 | − | 9.68714i | −1.06330 | − | 1.06330i | −0.997856 | − | 0.0654452i | \(-0.979153\pi\) |
−0.0654452 | − | 0.997856i | \(-0.520847\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.17157 | + | 1.17157i | −0.127075 | + | 0.127075i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 8.02509i | − | 0.860380i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 4.82843i | − | 0.511812i | −0.966702 | − | 0.255906i | \(-0.917626\pi\) | ||
0.966702 | − | 0.255906i | \(-0.0823738\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.92177 | + | 8.92177i | −0.935256 | + | 0.935256i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.34315 | − | 2.34315i | −0.242973 | − | 0.242973i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.69552 | 0.379152 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.17157 | 0.525094 | 0.262547 | − | 0.964919i | \(-0.415438\pi\) | ||||
0.262547 | + | 0.964919i | \(0.415438\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.35757 | − | 5.35757i | −0.538456 | − | 0.538456i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.0711 | − | 12.0711i | 1.20112 | − | 1.20112i | 0.227289 | − | 0.973827i | \(-0.427014\pi\) |
0.973827 | − | 0.227289i | \(-0.0729861\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 14.1480i | − | 1.39405i | −0.717049 | − | 0.697023i | \(-0.754508\pi\) | ||
0.717049 | − | 0.697023i | \(-0.245492\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.34315i | 0.228668i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.39942 | + | 1.39942i | −0.135287 | + | 0.135287i | −0.771507 | − | 0.636220i | \(-0.780497\pi\) |
0.636220 | + | 0.771507i | \(0.280497\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.24264 | − | 9.24264i | −0.885284 | − | 0.885284i | 0.108781 | − | 0.994066i | \(-0.465305\pi\) |
−0.994066 | + | 0.108781i | \(0.965305\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.81845 | 0.931926 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.65685 | 0.720296 | 0.360148 | − | 0.932895i | \(-0.382726\pi\) | ||||
0.360148 | + | 0.932895i | \(0.382726\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.79884 | + | 2.79884i | 0.260993 | + | 0.260993i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.41421 | − | 4.41421i | 0.408094 | − | 0.408094i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 10.4525i | − | 0.958179i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 6.17157i | − | 0.561052i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.06147 | − | 3.06147i | 0.276043 | − | 0.276043i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4.00000 | + | 4.00000i | 0.357771 | + | 0.357771i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.7206 | −1.04004 | −0.520018 | − | 0.854155i | \(-0.674075\pi\) | ||||
−0.520018 | + | 0.854155i | \(0.674075\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.17157 | −0.103151 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.3212 | − | 10.3212i | −0.901766 | − | 0.901766i | 0.0938226 | − | 0.995589i | \(-0.470091\pi\) |
−0.995589 | + | 0.0938226i | \(0.970091\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −16.4853 | + | 16.4853i | −1.42946 | + | 1.42946i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 3.06147i | − | 0.263489i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 12.9706i | 1.10815i | 0.832467 | + | 0.554075i | \(0.186928\pi\) | ||||
−0.832467 | + | 0.554075i | \(0.813072\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −14.2793 | + | 14.2793i | −1.21116 | + | 1.21116i | −0.240511 | + | 0.970646i | \(0.577315\pi\) |
−0.970646 | + | 0.240511i | \(0.922685\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.34315 | + | 2.34315i | 0.197328 | + | 0.197328i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 14.1480 | 1.18312 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.34315 | −0.360679 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −5.09494 | − | 5.09494i | −0.420223 | − | 0.420223i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.24264 | + | 1.24264i | −0.101801 | + | 0.101801i | −0.756173 | − | 0.654372i | \(-0.772933\pi\) |
0.654372 | + | 0.756173i | \(0.272933\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.634051i | 0.0515983i | 0.999667 | + | 0.0257992i | \(0.00821304\pi\) | ||||
−0.999667 | + | 0.0257992i | \(0.991787\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.17157i | 0.418097i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.26810 | + | 1.26810i | −0.101856 | + | 0.101856i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.58579 | − | 1.58579i | −0.126560 | − | 0.126560i | 0.640990 | − | 0.767549i | \(-0.278524\pi\) |
−0.767549 | + | 0.640990i | \(0.778524\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.96362 | −0.393641 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −24.9706 | −1.96796 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.82683 | + | 3.82683i | 0.299741 | + | 0.299741i | 0.840912 | − | 0.541171i | \(-0.182019\pi\) |
−0.541171 | + | 0.840912i | \(0.682019\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.85786 | − | 1.85786i | 0.144635 | − | 0.144635i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.69552i | 0.285968i | 0.989725 | + | 0.142984i | \(0.0456697\pi\) | ||||
−0.989725 | + | 0.142984i | \(0.954330\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 1.34315i | − | 0.103319i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 8.15640 | − | 8.15640i | 0.623736 | − | 0.623736i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −13.5858 | − | 13.5858i | −1.03291 | − | 1.03291i | −0.999440 | − | 0.0334684i | \(-0.989345\pi\) |
−0.0334684 | − | 0.999440i | \(-0.510655\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −17.2095 | −1.30092 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.17157 | −0.0880608 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.15640 | + | 8.15640i | 0.609638 | + | 0.609638i | 0.942851 | − | 0.333213i | \(-0.108133\pi\) |
−0.333213 | + | 0.942851i | \(0.608133\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.0711 | − | 10.0711i | 0.748577 | − | 0.748577i | −0.225635 | − | 0.974212i | \(-0.572446\pi\) |
0.974212 | + | 0.225635i | \(0.0724458\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.15932i | 0.0856991i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 5.31371i | − | 0.390672i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8.28772 | + | 8.28772i | −0.606058 | + | 0.606058i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 13.6569 | + | 13.6569i | 0.993390 | + | 0.993390i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.7206 | 0.848073 | 0.424037 | − | 0.905645i | \(-0.360613\pi\) | ||||
0.424037 | + | 0.905645i | \(0.360613\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.485281 | 0.0349313 | 0.0174657 | − | 0.999847i | \(-0.494440\pi\) | ||||
0.0174657 | + | 0.999847i | \(0.494440\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.53073 | + | 1.53073i | 0.109618 | + | 0.109618i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −7.58579 | + | 7.58579i | −0.540465 | + | 0.540465i | −0.923665 | − | 0.383200i | \(-0.874822\pi\) |
0.383200 | + | 0.923665i | \(0.374822\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.3547i | 0.875798i | 0.899024 | + | 0.437899i | \(0.144277\pi\) | ||||
−0.899024 | + | 0.437899i | \(0.855723\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.14214i | 0.151095i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 19.3743 | − | 19.3743i | 1.35981 | − | 1.35981i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.65685 | − | 1.65685i | −0.115720 | − | 0.115720i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 12.3547 | 0.858708 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 26.1421 | 1.80829 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.42450 | + | 9.42450i | 0.648810 | + | 0.648810i | 0.952705 | − | 0.303896i | \(-0.0982874\pi\) |
−0.303896 | + | 0.952705i | \(0.598287\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.14214 | − | 6.14214i | 0.420852 | − | 0.420852i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.634051i | 0.0432419i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 11.3137i | − | 0.768025i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.96362 | − | 4.96362i | 0.335410 | − | 0.335410i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.82843 | − | 6.82843i | −0.459330 | − | 0.459330i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.06147 | −0.205011 | −0.102506 | − | 0.994732i | \(-0.532686\pi\) | ||||
−0.102506 | + | 0.994732i | \(0.532686\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8.51472 | 0.567648 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.765367 | + | 0.765367i | 0.0507992 | + | 0.0507992i | 0.732050 | − | 0.681251i | \(-0.238564\pi\) |
−0.681251 | + | 0.732050i | \(0.738564\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.75736 | − | 2.75736i | 0.182211 | − | 0.182211i | −0.610107 | − | 0.792319i | \(-0.708874\pi\) |
0.792319 | + | 0.610107i | \(0.208874\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 16.5754i | 1.09058i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 20.8284i | 1.36452i | 0.731112 | + | 0.682258i | \(0.239002\pi\) | ||||
−0.731112 | + | 0.682258i | \(0.760998\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.26810 | − | 1.26810i | 0.0827218 | − | 0.0827218i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −11.3137 | − | 11.3137i | −0.734904 | − | 0.734904i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −12.2459 | −0.792119 | −0.396060 | − | 0.918225i | \(-0.629623\pi\) | ||||
−0.396060 | + | 0.918225i | \(0.629623\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.1716 | 0.848456 | 0.424228 | − | 0.905556i | \(-0.360546\pi\) | ||||
0.424228 | + | 0.905556i | \(0.360546\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −10.9552 | − | 10.9552i | −0.702779 | − | 0.702779i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.75736 | + | 2.75736i | −0.176161 | + | 0.176161i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 21.5391i | 1.37050i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 14.8284i | − | 0.939713i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.7486 | − | 12.7486i | 0.804685 | − | 0.804685i | −0.179139 | − | 0.983824i | \(-0.557331\pi\) |
0.983824 | + | 0.179139i | \(0.0573312\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 19.7990 | + | 19.7990i | 1.24475 | + | 1.24475i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.79337 | −0.112305 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −14.9706 | −0.933838 | −0.466919 | − | 0.884300i | \(-0.654636\pi\) | ||||
−0.466919 | + | 0.884300i | \(0.654636\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 23.7038 | + | 23.7038i | 1.47289 | + | 1.47289i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −9.58579 | + | 9.58579i | −0.593345 | + | 0.593345i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 12.8799i | 0.794210i | 0.917773 | + | 0.397105i | \(0.129985\pi\) | ||||
−0.917773 | + | 0.397105i | \(0.870015\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.68629i | 0.165018i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.69552 | − | 3.69552i | 0.226162 | − | 0.226162i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 18.0711 | + | 18.0711i | 1.10181 | + | 1.10181i | 0.994192 | + | 0.107620i | \(0.0343231\pi\) |
0.107620 | + | 0.994192i | \(0.465677\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.59767 | −0.340034 | −0.170017 | − | 0.985441i | \(-0.554382\pi\) | ||||
−0.170017 | + | 0.985441i | \(0.554382\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −13.6569 | −0.826550 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 13.6453 | + | 13.6453i | 0.822842 | + | 0.822842i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.41421 | − | 2.41421i | 0.145056 | − | 0.145056i | −0.630849 | − | 0.775905i | \(-0.717293\pi\) |
0.775905 | + | 0.630849i | \(0.217293\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.59767i | 0.335124i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 17.7990i | − | 1.06180i | −0.847435 | − | 0.530899i | \(-0.821854\pi\) | ||
0.847435 | − | 0.530899i | \(-0.178146\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.3212 | − | 10.3212i | 0.613531 | − | 0.613531i | −0.330333 | − | 0.943864i | \(-0.607161\pi\) |
0.943864 | + | 0.330333i | \(0.107161\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.82843 | + | 2.82843i | 0.167542 | + | 0.167542i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 14.7821 | 0.872558 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.00000 | −0.529412 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.95815 | + | 3.95815i | 0.232031 | + | 0.232031i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0.414214 | − | 0.414214i | 0.0241986 | − | 0.0241986i | −0.694904 | − | 0.719103i | \(-0.744553\pi\) |
0.719103 | + | 0.694904i | \(0.244553\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.634051i | 0.0369159i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 21.6569i | − | 1.25666i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −16.3128 | + | 16.3128i | −0.943394 | + | 0.943394i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.82843 | − | 2.82843i | −0.163028 | − | 0.163028i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 18.4776 | 1.06151 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.627417 | 0.0359258 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.19278 | + | 3.19278i | 0.182222 | + | 0.182222i | 0.792323 | − | 0.610101i | \(-0.208871\pi\) |
−0.610101 | + | 0.792323i | \(0.708871\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 10.8284 | − | 10.8284i | 0.616008 | − | 0.616008i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 24.6005i | 1.39497i | 0.716600 | + | 0.697484i | \(0.245697\pi\) | ||||
−0.716600 | + | 0.697484i | \(0.754303\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 31.3137i | 1.76996i | 0.465633 | + | 0.884978i | \(0.345827\pi\) | ||||
−0.465633 | + | 0.884978i | \(0.654173\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.79884 | − | 2.79884i | 0.157696 | − | 0.157696i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −10.8995 | − | 10.8995i | −0.612177 | − | 0.612177i | 0.331336 | − | 0.943513i | \(-0.392501\pi\) |
−0.943513 | + | 0.331336i | \(0.892501\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −30.7235 | −1.72018 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.14214 | −0.119562 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −12.6173 | − | 12.6173i | −0.702045 | − | 0.702045i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −11.2426 | + | 11.2426i | −0.623629 | + | 0.623629i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 14.1480i | − | 0.782387i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 11.3137i | 0.623745i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.99162 | − | 5.99162i | 0.329329 | − | 0.329329i | −0.523002 | − | 0.852331i | \(-0.675188\pi\) |
0.852331 | + | 0.523002i | \(0.175188\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −11.7279 | − | 11.7279i | −0.642686 | − | 0.642686i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.15932 | 0.0633402 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.00000 | 0.326841 | 0.163420 | − | 0.986557i | \(-0.447747\pi\) | ||||
0.163420 | + | 0.986557i | \(0.447747\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5.86030 | + | 5.86030i | 0.318288 | + | 0.318288i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8.97056 | + | 8.97056i | −0.485783 | + | 0.485783i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.26810i | 0.0684710i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4.28427i | 0.230657i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 10.9552 | − | 10.9552i | 0.588108 | − | 0.588108i | −0.349011 | − | 0.937119i | \(-0.613482\pi\) |
0.937119 | + | 0.349011i | \(0.113482\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.92893 | − | 1.92893i | −0.103253 | − | 0.103253i | 0.653593 | − | 0.756846i | \(-0.273261\pi\) |
−0.756846 | + | 0.653593i | \(0.773261\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 17.8435 | 0.952418 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 22.9706 | 1.22260 | 0.611300 | − | 0.791399i | \(-0.290647\pi\) | ||||
0.611300 | + | 0.791399i | \(0.290647\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.32410 | − | 3.32410i | −0.176425 | − | 0.176425i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 8.00000 | − | 8.00000i | 0.423405 | − | 0.423405i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0.634051i | 0.0334639i | 0.999860 | + | 0.0167320i | \(0.00532620\pi\) | ||||
−0.999860 | + | 0.0167320i | \(0.994674\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 20.7990i | 1.09468i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4.72352 | − | 4.72352i | 0.247920 | − | 0.247920i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.68629 | − | 2.68629i | −0.140607 | − | 0.140607i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.18440 | −0.479422 | −0.239711 | − | 0.970844i | \(-0.577053\pi\) | ||||
−0.239711 | + | 0.970844i | \(0.577053\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −7.31371 | −0.380736 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −11.9832 | − | 11.9832i | −0.622139 | − | 0.622139i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.75736 | − | 4.75736i | 0.246327 | − | 0.246327i | −0.573135 | − | 0.819461i | \(-0.694273\pi\) |
0.819461 | + | 0.573135i | \(0.194273\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 6.12293i | 0.316187i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 25.3137i | − | 1.30372i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −18.6089 | + | 18.6089i | −0.955875 | + | 0.955875i | −0.999067 | − | 0.0431915i | \(-0.986247\pi\) |
0.0431915 | + | 0.999067i | \(0.486247\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −8.97056 | − | 8.97056i | −0.459576 | − | 0.459576i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 20.9050 | 1.06820 | 0.534098 | − | 0.845423i | \(-0.320651\pi\) | ||||
0.534098 | + | 0.845423i | \(0.320651\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8.97056 | 0.457182 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.39942 | + | 1.39942i | 0.0711364 | + | 0.0711364i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 14.4142 | − | 14.4142i | 0.730830 | − | 0.730830i | −0.239954 | − | 0.970784i | \(-0.577133\pi\) |
0.970784 | + | 0.239954i | \(0.0771325\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 19.1116i | − | 0.966517i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 15.7990i | − | 0.796954i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6.12293 | + | 6.12293i | −0.308078 | + | 0.308078i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.58579 | − | 3.58579i | −0.179965 | − | 0.179965i | 0.611375 | − | 0.791341i | \(-0.290617\pi\) |
−0.791341 | + | 0.611375i | \(0.790617\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −25.2346 | −1.26331 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7.51472 | −0.375267 | −0.187634 | − | 0.982239i | \(-0.560082\pi\) | ||||
−0.187634 | + | 0.982239i | \(0.560082\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.39104 | − | 7.39104i | −0.368174 | − | 0.368174i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.0710678 | − | 0.0710678i | 0.00353139 | − | 0.00353139i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 37.5892i | − | 1.86323i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 31.3137i | 1.54836i | 0.632964 | + | 0.774182i | \(0.281838\pi\) | ||||
−0.632964 | + | 0.774182i | \(0.718162\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9.92724 | + | 9.92724i | −0.489675 | + | 0.489675i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.82843 | − | 2.82843i | −0.139178 | − | 0.139178i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.02509 | −0.393936 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −21.8579 | −1.07038 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8.79045 | + | 8.79045i | 0.429442 | + | 0.429442i | 0.888438 | − | 0.458996i | \(-0.151791\pi\) |
−0.458996 | + | 0.888438i | \(0.651791\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.07107 | − | 6.07107i | 0.295886 | − | 0.295886i | −0.543514 | − | 0.839400i | \(-0.682907\pi\) |
0.839400 | + | 0.543514i | \(0.182907\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 5.59767i | − | 0.272168i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 13.1716i | − | 0.638915i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.79884 | + | 2.79884i | −0.135445 | + | 0.135445i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 10.8284 | + | 10.8284i | 0.522801 | + | 0.522801i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −25.4558 | −1.22333 | −0.611665 | − | 0.791117i | \(-0.709500\pi\) | ||||
−0.611665 | + | 0.791117i | \(0.709500\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.32410 | − | 3.32410i | −0.159378 | − | 0.159378i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −30.1421 | + | 30.1421i | −1.44189 | + | 1.44189i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 38.1145i | − | 1.81911i | −0.415588 | − | 0.909553i | \(-0.636424\pi\) | ||
0.415588 | − | 0.909553i | \(-0.363576\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 12.1716i | 0.579599i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.39942 | + | 1.39942i | −0.0664883 | + | 0.0664883i | −0.739569 | − | 0.673081i | \(-0.764971\pi\) |
0.673081 | + | 0.739569i | \(0.264971\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.00000 | − | 2.00000i | −0.0948091 | − | 0.0948091i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.90215 | −0.0899687 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.14214 | −0.289865 | −0.144933 | − | 0.989442i | \(-0.546297\pi\) | ||||
−0.144933 | + | 0.989442i | \(0.546297\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −11.7206 | − | 11.7206i | −0.551902 | − | 0.551902i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.485281 | + | 0.485281i | −0.0228005 | + | 0.0228005i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 7.39104i | 0.346497i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 26.6274i | − | 1.24558i | −0.782390 | − | 0.622789i | \(-0.785999\pi\) | ||
0.782390 | − | 0.622789i | \(-0.214001\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −10.4525 | + | 10.4525i | −0.487881 | + | 0.487881i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 27.0416 | + | 27.0416i | 1.25945 | + | 1.25945i | 0.951354 | + | 0.308100i | \(0.0996933\pi\) |
0.308100 | + | 0.951354i | \(0.400307\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 35.6871 | 1.65852 | 0.829260 | − | 0.558864i | \(-0.188762\pi\) | ||||
0.829260 | + | 0.558864i | \(0.188762\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.94113 | −0.0900175 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −26.8966 | − | 26.8966i | −1.24463 | − | 1.24463i | −0.958060 | − | 0.286567i | \(-0.907486\pi\) |
−0.286567 | − | 0.958060i | \(-0.592514\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.17157 | + | 5.17157i | −0.238801 | + | 0.238801i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 2.42742i | − | 0.111849i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.48528i | 0.206233i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −20.7737 | + | 20.7737i | −0.953162 | + | 0.953162i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.92893 | + | 5.92893i | 0.271467 | + | 0.271467i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −35.1618 | −1.60658 | −0.803292 | − | 0.595585i | \(-0.796920\pi\) | ||||
−0.803292 | + | 0.595585i | \(0.796920\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 30.9706 | 1.41214 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −19.1116 | − | 19.1116i | −0.869610 | − | 0.869610i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.14214 | − | 2.14214i | 0.0972694 | − | 0.0972694i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.23172i | 0.282386i | 0.989982 | + | 0.141193i | \(0.0450938\pi\) | ||||
−0.989982 | + | 0.141193i | \(0.954906\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5.85786i | 0.264902i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.56420 | − | 3.56420i | 0.160850 | − | 0.160850i | −0.622093 | − | 0.782943i | \(-0.713717\pi\) |
0.782943 | + | 0.622093i | \(0.213717\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 14.8284 | + | 14.8284i | 0.667839 | + | 0.667839i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.43835 | −0.199489 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 29.6569 | 1.33029 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.4860 | + | 12.4860i | 0.558949 | + | 0.558949i | 0.929008 | − | 0.370059i | \(-0.120663\pi\) |
−0.370059 | + | 0.929008i | \(0.620663\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.82843 | + | 2.82843i | −0.126365 | + | 0.126365i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 22.8072i | − | 1.01692i | −0.861085 | − | 0.508460i | \(-0.830215\pi\) | ||
0.861085 | − | 0.508460i | \(-0.169785\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 10.0000i | − | 0.444994i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.02800 | − | 1.02800i | 0.0456550 | − | 0.0456550i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −18.5563 | − | 18.5563i | −0.822496 | − | 0.822496i | 0.163970 | − | 0.986465i | \(-0.447570\pi\) |
−0.986465 | + | 0.163970i | \(0.947570\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 23.9665 | 1.06021 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 32.9706 | 1.45569 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5.86030 | − | 5.86030i | −0.258236 | − | 0.258236i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.97056 | − | 8.97056i | 0.394525 | − | 0.394525i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 20.7962i | − | 0.912853i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.34315i | 0.277898i | 0.990300 | + | 0.138949i | \(0.0443725\pi\) | ||||
−0.990300 | + | 0.138949i | \(0.955628\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −10.0586 | + | 10.0586i | −0.439830 | + | 0.439830i | −0.891955 | − | 0.452125i | \(-0.850666\pi\) |
0.452125 | + | 0.891955i | \(0.350666\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −13.1716 | − | 13.1716i | −0.574855 | − | 0.574855i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8.65914 | 0.377198 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.6569 | −0.985081 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.39942 | + | 1.39942i | 0.0607295 | + | 0.0607295i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 9.65685 | − | 9.65685i | 0.418285 | − | 0.418285i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.15932i | 0.0501216i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 12.4853i | 0.538780i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −19.5056 | + | 19.5056i | −0.840165 | + | 0.840165i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.24264 | − | 7.24264i | −0.311385 | − | 0.311385i | 0.534061 | − | 0.845446i | \(-0.320665\pi\) |
−0.845446 | + | 0.534061i | \(0.820665\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 15.4161 | 0.661569 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −7.65685 | −0.327984 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13.3827 | − | 13.3827i | −0.572201 | − | 0.572201i | 0.360542 | − | 0.932743i | \(-0.382592\pi\) |
−0.932743 | + | 0.360542i | \(0.882592\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.38478 | − | 1.38478i | 0.0591008 | − | 0.0591008i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 46.7736i | − | 1.99262i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 54.6274i | − | 2.32299i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4.06694 | − | 4.06694i | 0.172632 | − | 0.172632i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 8.07107 | + | 8.07107i | 0.341982 | + | 0.341982i | 0.857112 | − | 0.515130i | \(-0.172256\pi\) |
−0.515130 | + | 0.857112i | \(0.672256\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.69552 | −0.156304 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −12.6863 | −0.535616 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 10.5838 | + | 10.5838i | 0.446055 | + | 0.446055i | 0.894041 | − | 0.447986i | \(-0.147859\pi\) |
−0.447986 | + | 0.894041i | \(0.647859\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.17157 | − | 3.17157i | 0.133429 | − | 0.133429i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.634051i | 0.0266276i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 25.6569i | 1.07559i | 0.843075 | + | 0.537796i | \(0.180743\pi\) | ||||
−0.843075 | + | 0.537796i | \(0.819257\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 19.5056 | − | 19.5056i | 0.816284 | − | 0.816284i | −0.169284 | − | 0.985567i | \(-0.554145\pi\) |
0.985567 | + | 0.169284i | \(0.0541455\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8.97056 | + | 8.97056i | 0.374751 | + | 0.374751i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −31.4663 | −1.31224 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17.3137 | 0.720779 | 0.360390 | − | 0.932802i | \(-0.382644\pi\) | ||||
0.360390 | + | 0.932802i | \(0.382644\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.371418 | + | 0.371418i | 0.0154356 | + | 0.0154356i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 35.7990 | − | 35.7990i | 1.48519 | − | 1.48519i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 19.0029i | 0.787018i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 3.65685i | − | 0.151192i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −13.1200 | + | 13.1200i | −0.541521 | + | 0.541521i | −0.923975 | − | 0.382453i | \(-0.875079\pi\) |
0.382453 | + | 0.923975i | \(0.375079\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −13.6569 | − | 13.6569i | −0.562721 | − | 0.562721i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −11.6118 | −0.477646 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −9.31371 | −0.382468 | −0.191234 | − | 0.981544i | \(-0.561249\pi\) | ||||
−0.191234 | + | 0.981544i | \(0.561249\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.32957 | − | 4.32957i | −0.177495 | − | 0.177495i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −9.45584 | + | 9.45584i | −0.387002 | + | 0.387002i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 45.5055i | 1.85931i | 0.368437 | + | 0.929653i | \(0.379893\pi\) | ||||
−0.368437 | + | 0.929653i | \(0.620107\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 20.8284i | − | 0.849609i | −0.905285 | − | 0.424805i | \(-0.860343\pi\) | ||
0.905285 | − | 0.424805i | \(-0.139657\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.55873 | − | 2.55873i | 0.104200 | − | 0.104200i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.55635 | − | 2.55635i | −0.103930 | − | 0.103930i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 29.6569 | 1.20176 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.39104 | + | 7.39104i | 0.299009 | + | 0.299009i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −27.8701 | + | 27.8701i | −1.12566 | + | 1.12566i | −0.134786 | + | 0.990875i | \(0.543035\pi\) |
−0.990875 | + | 0.134786i | \(0.956965\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 2.53620i | − | 0.102270i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 38.4853i | 1.54936i | 0.632354 | + | 0.774680i | \(0.282089\pi\) | ||||
−0.632354 | + | 0.774680i | \(0.717911\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.93015 | − | 2.93015i | 0.117773 | − | 0.117773i | −0.645764 | − | 0.763537i | \(-0.723461\pi\) |
0.763537 | + | 0.645764i | \(0.223461\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 24.9706 | + | 24.9706i | 1.00203 | + | 1.00203i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 17.8435 | 0.714886 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19.9706 | −0.798823 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 20.0083 | + | 20.0083i | 0.799056 | + | 0.799056i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −18.1421 | + | 18.1421i | −0.723374 | + | 0.723374i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 14.1480i | − | 0.563224i | −0.959528 | − | 0.281612i | \(-0.909131\pi\) | ||
0.959528 | − | 0.281612i | \(-0.0908691\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 14.4264i | 0.573398i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4.85483 | + | 4.85483i | −0.192658 | + | 0.192658i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −16.0711 | − | 16.0711i | −0.636759 | − | 0.636759i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −14.6733 | −0.580466 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −38.1421 | −1.50652 | −0.753262 | − | 0.657721i | \(-0.771521\pi\) | ||||
−0.753262 | + | 0.657721i | \(0.771521\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −13.3827 | − | 13.3827i | −0.527760 | − | 0.527760i | 0.392144 | − | 0.919904i | \(-0.371734\pi\) |
−0.919904 | + | 0.392144i | \(0.871734\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.485281 | + | 0.485281i | −0.0191079 | + | 0.0191079i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 21.5391i | 0.846788i | 0.905946 | + | 0.423394i | \(0.139161\pi\) | ||||
−0.905946 | + | 0.423394i | \(0.860839\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.48528i | 0.176063i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8.65914 | − | 8.65914i | 0.339378 | − | 0.339378i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −4.55635 | − | 4.55635i | −0.178304 | − | 0.178304i | 0.612312 | − | 0.790616i | \(-0.290240\pi\) |
−0.790616 | + | 0.612312i | \(0.790240\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −8.55035 | −0.334090 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −11.8579 | −0.462619 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.02800 | − | 1.02800i | −0.0400452 | − | 0.0400452i | 0.686801 | − | 0.726846i | \(-0.259015\pi\) |
−0.726846 | + | 0.686801i | \(0.759015\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −20.5563 | + | 20.5563i | −0.799549 | + | 0.799549i | −0.983024 | − | 0.183475i | \(-0.941265\pi\) |
0.183475 | + | 0.983024i | \(0.441265\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 10.4525i | − | 0.405942i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 13.6569i | 0.529590i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 35.4244 | − | 35.4244i | 1.37164 | − | 1.37164i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.34315 | − | 2.34315i | −0.0905912 | − | 0.0905912i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.43835 | 0.171341 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −26.8284 | −1.03416 | −0.517080 | − | 0.855937i | \(-0.672981\pi\) | ||||
−0.517080 | + | 0.855937i | \(0.672981\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 17.2095 | + | 17.2095i | 0.662394 | + | 0.662394i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −9.58579 | + | 9.58579i | −0.368412 | + | 0.368412i | −0.866898 | − | 0.498486i | \(-0.833890\pi\) |
0.498486 | + | 0.866898i | \(0.333890\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 19.1116i | 0.733437i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.17157i | 0.0448948i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 23.2011 | − | 23.2011i | 0.887766 | − | 0.887766i | −0.106542 | − | 0.994308i | \(-0.533978\pi\) |
0.994308 | + | 0.106542i | \(0.0339780\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.37258 | + | 5.37258i | 0.205276 | + | 0.205276i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.22078 | 0.161033 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −15.6569 | −0.596479 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −28.7988 | − | 28.7988i | −1.09556 | − | 1.09556i | −0.994924 | − | 0.100634i | \(-0.967913\pi\) |
−0.100634 | − | 0.994924i | \(-0.532087\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 19.7990 | − | 19.7990i | 0.752101 | − | 0.752101i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 11.8294i | 0.448714i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 11.3137i | 0.428537i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −15.9414 | + | 15.9414i | −0.602959 | + | 0.602959i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −17.5858 | − | 17.5858i | −0.664206 | − | 0.664206i | 0.292163 | − | 0.956369i | \(-0.405625\pi\) |
−0.956369 | + | 0.292163i | \(0.905625\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 57.2261 | 2.15832 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.94113 | 0.0731070 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 44.6088 | + | 44.6088i | 1.67769 | + | 1.67769i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 16.7574 | − | 16.7574i | 0.629336 | − | 0.629336i | −0.318565 | − | 0.947901i | \(-0.603201\pi\) |
0.947901 | + | 0.318565i | \(0.103201\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 27.0279i | 1.01363i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 20.6863i | − | 0.774708i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.86030 | − | 5.86030i | 0.219163 | − | 0.219163i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −9.37258 | − | 9.37258i | −0.350026 | − | 0.350026i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −29.5641 | −1.10256 | −0.551278 | − | 0.834321i | \(-0.685860\pi\) | ||||
−0.551278 | + | 0.834321i | \(0.685860\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 52.2843 | 1.94717 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 10.0811 | + | 10.0811i | 0.374920 | + | 0.374920i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 24.4142 | − | 24.4142i | 0.906721 | − | 0.906721i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 22.0643i | 0.818320i | 0.912463 | + | 0.409160i | \(0.134178\pi\) | ||||
−0.912463 | + | 0.409160i | \(0.865822\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 17.2843i | − | 0.640158i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.16478 | − | 2.16478i | 0.0800674 | − | 0.0800674i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 13.1005 | + | 13.1005i | 0.483878 | + | 0.483878i | 0.906368 | − | 0.422490i | \(-0.138844\pi\) |
−0.422490 | + | 0.906368i | \(0.638844\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −4.22078 | −0.155686 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 8.20101 | 0.302088 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 35.1843 | + | 35.1843i | 1.29428 | + | 1.29428i | 0.932115 | + | 0.362162i | \(0.117961\pi\) |
0.362162 | + | 0.932115i | \(0.382039\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −16.4853 | + | 16.4853i | −0.605602 | + | 0.605602i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 27.1367i | 0.995550i | 0.867306 | + | 0.497775i | \(0.165849\pi\) | ||||
−0.867306 | + | 0.497775i | \(0.834151\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.02944i | 0.0377157i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −17.7122 | + | 17.7122i | −0.648056 | + | 0.648056i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −5.17157 | − | 5.17157i | −0.188965 | − | 0.188965i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14.7821 | 0.539405 | 0.269703 | − | 0.962944i | \(-0.413075\pi\) | ||||
0.269703 | + | 0.962944i | \(0.413075\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 19.5147 | 0.711156 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.262632 | + | 0.262632i | 0.00955817 | + | 0.00955817i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 13.3848 | − | 13.3848i | 0.486478 | − | 0.486478i | −0.420715 | − | 0.907193i | \(-0.638221\pi\) |
0.907193 | + | 0.420715i | \(0.138221\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 30.3070i | 1.10007i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 34.6274i | − | 1.25524i | −0.778519 | − | 0.627621i | \(-0.784029\pi\) | ||
0.778519 | − | 0.627621i | \(-0.215971\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 34.1563 | − | 34.1563i | 1.23654 | − | 1.23654i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.14214 | + | 2.14214i | 0.0774491 | + | 0.0774491i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.69552 | −0.133437 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5.17157 | 0.186492 | 0.0932458 | − | 0.995643i | \(-0.470276\pi\) | ||||
0.0932458 | + | 0.995643i | \(0.470276\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −11.4580 | − | 11.4580i | −0.412649 | − | 0.412649i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 28.0711 | − | 28.0711i | 1.00965 | − | 1.00965i | 0.00969311 | − | 0.999953i | \(-0.496915\pi\) |
0.999953 | − | 0.00969311i | \(-0.00308546\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 14.2568i | − | 0.512120i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 36.2843i | 1.30169i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 17.8435 | − | 17.8435i | 0.639311 | − | 0.639311i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −23.5147 | − | 23.5147i | −0.841423 | − | 0.841423i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −38.7485 | −1.38476 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.31371 | −0.0468883 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.62020 | + | 5.62020i | 0.200339 | + | 0.200339i | 0.800145 | − | 0.599807i | \(-0.204756\pi\) |
−0.599807 | + | 0.800145i | \(0.704756\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −9.85786 | + | 9.85786i | −0.350949 | + | 0.350949i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 28.2960i | 1.00609i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.65685i | 0.129859i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.05600 | + | 2.05600i | −0.0729188 | + | 0.0729188i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 28.0711 | + | 28.0711i | 0.994328 | + | 0.994328i | 0.999984 | − | 0.00565577i | \(-0.00180030\pi\) |
−0.00565577 | + | 0.999984i | \(0.501800\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.65914 | −0.306338 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8.82843 | −0.311937 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −19.0029 | − | 19.0029i | −0.670596 | − | 0.670596i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −10.3431 | + | 10.3431i | −0.364548 | + | 0.364548i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 27.6620i | 0.973748i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 24.6863i | − | 0.867924i | −0.900931 | − | 0.433962i | \(-0.857115\pi\) | ||
0.900931 | − | 0.433962i | \(-0.142885\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.66205 | − | 1.66205i | 0.0583625 | − | 0.0583625i | −0.677323 | − | 0.735686i | \(-0.736860\pi\) |
0.735686 | + | 0.677323i | \(0.236860\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.28427 | − | 4.28427i | −0.150256 | − | 0.150256i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3.17025 | 0.111049 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.82843 | −0.238896 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 16.3128 | + | 16.3128i | 0.570016 | + | 0.570016i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −27.2426 | + | 27.2426i | −0.950775 | + | 0.950775i | −0.998844 | − | 0.0480693i | \(-0.984693\pi\) |
0.0480693 | + | 0.998844i | \(0.484693\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 22.0643i | 0.769114i | 0.923101 | + | 0.384557i | \(0.125646\pi\) | ||||
−0.923101 | + | 0.384557i | \(0.874354\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 20.8873i | 0.727203i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −13.1200 | + | 13.1200i | −0.456228 | + | 0.456228i | −0.897415 | − | 0.441187i | \(-0.854557\pi\) |
0.441187 | + | 0.897415i | \(0.354557\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8.75736 | + | 8.75736i | 0.304156 | + | 0.304156i | 0.842637 | − | 0.538482i | \(-0.181002\pi\) |
−0.538482 | + | 0.842637i | \(0.681002\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.69552 | 0.128196 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 18.8284 | 0.652366 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.53073 | + | 1.53073i | 0.0529732 | + | 0.0529732i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −11.3137 | + | 11.3137i | −0.391059 | + | 0.391059i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 29.4554i | − | 1.01691i | −0.861088 | − | 0.508456i | \(-0.830216\pi\) | ||
0.861088 | − | 0.508456i | \(-0.169784\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 25.9706i | 0.895537i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 13.6228 | − | 13.6228i | 0.469193 | − | 0.469193i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.556349 | − | 0.556349i | −0.0191390 | − | 0.0191390i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 22.8072 | 0.783663 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 15.7990 | 0.542220 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 43.3407 | + | 43.3407i | 1.48570 | + | 1.48570i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22.6985 | − | 22.6985i | 0.777181 | − | 0.777181i | −0.202169 | − | 0.979351i | \(-0.564799\pi\) |
0.979351 | + | 0.202169i | \(0.0647991\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 6.75699i | − | 0.231084i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 24.2843i | − | 0.829535i | −0.909927 | − | 0.414767i | \(-0.863863\pi\) | ||
0.909927 | − | 0.414767i | \(-0.136137\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.41904 | − | 8.41904i | 0.287254 | − | 0.287254i | −0.548740 | − | 0.835993i | \(-0.684892\pi\) |
0.835993 | + | 0.548740i | \(0.184892\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 11.3137 | + | 11.3137i | 0.385570 | + | 0.385570i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −0.525265 | −0.0178802 | −0.00894011 | − | 0.999960i | \(-0.502846\pi\) | ||||
−0.00894011 | + | 0.999960i | \(0.502846\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −11.2548 | −0.382676 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −6.88830 | − | 6.88830i | −0.233939 | − | 0.233939i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −43.3137 | + | 43.3137i | −1.46932 | + | 1.46932i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.75699i | 0.228952i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 9.45584i | − | 0.320032i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −14.7821 | + | 14.7821i | −0.499725 | + | 0.499725i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 35.0416 | + | 35.0416i | 1.18327 | + | 1.18327i | 0.978892 | + | 0.204380i | \(0.0655179\pi\) |
0.204380 | + | 0.978892i | \(0.434482\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0.634051 | 0.0213860 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 39.9411 | 1.34565 | 0.672825 | − | 0.739801i | \(-0.265081\pi\) | ||||
0.672825 | + | 0.739801i | \(0.265081\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −20.7737 | − | 20.7737i | −0.699090 | − | 0.699090i | 0.265124 | − | 0.964214i | \(-0.414587\pi\) |
−0.964214 | + | 0.265124i | \(0.914587\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.485281 | + | 0.485281i | −0.0163126 | + | 0.0163126i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 17.2095i | − | 0.577838i | −0.957354 | − | 0.288919i | \(-0.906704\pi\) | ||
0.957354 | − | 0.288919i | \(-0.0932958\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 43.3137i | − | 1.45270i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.502734 | − | 0.502734i | 0.0168422 | − | 0.0168422i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 13.6569 | + | 13.6569i | 0.457009 | + | 0.457009i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.75699 | 0.225861 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −24.9706 | −0.833743 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 16.0502 | + | 16.0502i | 0.535303 | + | 0.535303i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.17157 | − | 9.17157i | 0.305549 | − | 0.305549i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 4.32957i | − | 0.144079i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 8.34315i | − | 0.277336i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 31.8602 | − | 31.8602i | 1.05790 | − | 1.05790i | 0.0596848 | − | 0.998217i | \(-0.480990\pi\) |
0.998217 | − | 0.0596848i | \(-0.0190096\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −22.0711 | − | 22.0711i | −0.732051 | − | 0.732051i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 23.9665 | 0.794045 | 0.397022 | − | 0.917809i | \(-0.370044\pi\) | ||||
0.397022 | + | 0.917809i | \(0.370044\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −56.7696 | −1.87880 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0.480204 | + | 0.480204i | 0.0158751 | + | 0.0158751i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 38.1421 | − | 38.1421i | 1.25956 | − | 1.25956i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 19.0029i | 0.626846i | 0.949614 | + | 0.313423i | \(0.101476\pi\) | ||||
−0.949614 | + | 0.313423i | \(0.898524\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.88730i | 0.161042i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 19.3743 | − | 19.3743i | 0.637712 | − | 0.637712i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 29.8701 | + | 29.8701i | 0.982121 | + | 0.982121i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −25.8686 | −0.849637 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −42.8284 | −1.40516 | −0.702578 | − | 0.711607i | \(-0.747968\pi\) | ||||
−0.702578 | + | 0.711607i | \(0.747968\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −29.6955 | − | 29.6955i | −0.973229 | − | 0.973229i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −18.8284 | + | 18.8284i | −0.616415 | + | 0.616415i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 6.86577i | 0.224535i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 43.4558i | 1.41964i | 0.704383 | + | 0.709820i | \(0.251224\pi\) | ||||
−0.704383 | + | 0.709820i | \(0.748776\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −23.9665 | + | 23.9665i | −0.782116 | + | 0.782116i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.07107 | + | 2.07107i | 0.0675149 | + | 0.0675149i | 0.740058 | − | 0.672543i | \(-0.234798\pi\) |
−0.672543 | + | 0.740058i | \(0.734798\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 27.0279 | 0.880151 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 11.3137 | 0.368035 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −15.1760 | − | 15.1760i | −0.493154 | − | 0.493154i | 0.416144 | − | 0.909299i | \(-0.363381\pi\) |
−0.909299 | + | 0.416144i | \(0.863381\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 15.6569 | − | 15.6569i | 0.508243 | − | 0.508243i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 16.6842i | − | 0.541023i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 11.0294i | − | 0.357279i | −0.983915 | − | 0.178639i | \(-0.942830\pi\) | ||
0.983915 | − | 0.178639i | \(-0.0571695\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.85483 | − | 4.85483i | 0.157099 | − | 0.157099i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −23.5147 | − | 23.5147i | −0.760123 | − | 0.760123i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −47.9329 | −1.54784 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21.6274 | −0.697659 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.55873 | + | 2.55873i | 0.0824540 | + | 0.0824540i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0.201010 | − | 0.201010i | 0.00647074 | − | 0.00647074i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 11.0866i | − | 0.356520i | −0.983983 | − | 0.178260i | \(-0.942953\pi\) | ||
0.983983 | − | 0.178260i | \(-0.0570467\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 19.3137i | − | 0.620446i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −40.7820 | + | 40.7820i | −1.30876 | + | 1.30876i | −0.386445 | + | 0.922313i | \(0.626297\pi\) |
−0.922313 | + | 0.386445i | \(0.873703\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −52.7696 | − | 52.7696i | −1.69171 | − | 1.69171i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −17.2095 | −0.551145 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 47.1127 | 1.50727 | 0.753634 | − | 0.657294i | \(-0.228299\pi\) | ||||
0.753634 | + | 0.657294i | \(0.228299\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −14.1480 | − | 14.1480i | −0.452173 | − | 0.452173i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −16.8995 | + | 16.8995i | −0.539559 | + | 0.539559i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 46.7736i | − | 1.49185i | −0.666031 | − | 0.745924i | \(-0.732008\pi\) | ||
0.666031 | − | 0.745924i | \(-0.267992\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.28427i | 0.200234i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −8.65914 | + | 8.65914i | −0.275623 | + | 0.275623i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −5.17157 | − | 5.17157i | −0.164446 | − | 0.164446i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 27.0279 | 0.858571 | 0.429285 | − | 0.903169i | \(-0.358765\pi\) | ||||
0.429285 | + | 0.903169i | \(0.358765\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 9.17157 | 0.291051 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.11747 | + | 5.11747i | 0.162235 | + | 0.162235i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 20.0711 | − | 20.0711i | 0.635657 | − | 0.635657i | −0.313824 | − | 0.949481i | \(-0.601610\pi\) |
0.949481 | + | 0.313824i | \(0.101610\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 47.4077i | − | 1.49991i |
(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 | 512.2.e.i.129.3 | yes | 8 | |
3.2 | odd | 2 | 4608.2.k.bi.1153.2 | 8 | |||
4.3 | odd | 2 | inner | 512.2.e.i.129.2 | ✓ | 8 | |
8.3 | odd | 2 | 512.2.e.j.129.3 | yes | 8 | ||
8.5 | even | 2 | 512.2.e.j.129.2 | yes | 8 | ||
12.11 | even | 2 | 4608.2.k.bi.1153.1 | 8 | |||
16.3 | odd | 4 | 512.2.e.j.385.3 | yes | 8 | ||
16.5 | even | 4 | inner | 512.2.e.i.385.3 | yes | 8 | |
16.11 | odd | 4 | inner | 512.2.e.i.385.2 | yes | 8 | |
16.13 | even | 4 | 512.2.e.j.385.2 | yes | 8 | ||
24.5 | odd | 2 | 4608.2.k.bd.1153.4 | 8 | |||
24.11 | even | 2 | 4608.2.k.bd.1153.3 | 8 | |||
32.3 | odd | 8 | 1024.2.b.g.513.4 | 8 | |||
32.5 | even | 8 | 1024.2.a.i.1.2 | 4 | |||
32.11 | odd | 8 | 1024.2.a.h.1.2 | 4 | |||
32.13 | even | 8 | 1024.2.b.g.513.3 | 8 | |||
32.19 | odd | 8 | 1024.2.b.g.513.5 | 8 | |||
32.21 | even | 8 | 1024.2.a.h.1.3 | 4 | |||
32.27 | odd | 8 | 1024.2.a.i.1.3 | 4 | |||
32.29 | even | 8 | 1024.2.b.g.513.6 | 8 | |||
48.5 | odd | 4 | 4608.2.k.bi.3457.1 | 8 | |||
48.11 | even | 4 | 4608.2.k.bi.3457.2 | 8 | |||
48.29 | odd | 4 | 4608.2.k.bd.3457.3 | 8 | |||
48.35 | even | 4 | 4608.2.k.bd.3457.4 | 8 | |||
96.5 | odd | 8 | 9216.2.a.w.1.3 | 4 | |||
96.11 | even | 8 | 9216.2.a.bp.1.2 | 4 | |||
96.53 | odd | 8 | 9216.2.a.bp.1.1 | 4 | |||
96.59 | even | 8 | 9216.2.a.w.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
512.2.e.i.129.2 | ✓ | 8 | 4.3 | odd | 2 | inner | |
512.2.e.i.129.3 | yes | 8 | 1.1 | even | 1 | trivial | |
512.2.e.i.385.2 | yes | 8 | 16.11 | odd | 4 | inner | |
512.2.e.i.385.3 | yes | 8 | 16.5 | even | 4 | inner | |
512.2.e.j.129.2 | yes | 8 | 8.5 | even | 2 | ||
512.2.e.j.129.3 | yes | 8 | 8.3 | odd | 2 | ||
512.2.e.j.385.2 | yes | 8 | 16.13 | even | 4 | ||
512.2.e.j.385.3 | yes | 8 | 16.3 | odd | 4 | ||
1024.2.a.h.1.2 | 4 | 32.11 | odd | 8 | |||
1024.2.a.h.1.3 | 4 | 32.21 | even | 8 | |||
1024.2.a.i.1.2 | 4 | 32.5 | even | 8 | |||
1024.2.a.i.1.3 | 4 | 32.27 | odd | 8 | |||
1024.2.b.g.513.3 | 8 | 32.13 | even | 8 | |||
1024.2.b.g.513.4 | 8 | 32.3 | odd | 8 | |||
1024.2.b.g.513.5 | 8 | 32.19 | odd | 8 | |||
1024.2.b.g.513.6 | 8 | 32.29 | even | 8 | |||
4608.2.k.bd.1153.3 | 8 | 24.11 | even | 2 | |||
4608.2.k.bd.1153.4 | 8 | 24.5 | odd | 2 | |||
4608.2.k.bd.3457.3 | 8 | 48.29 | odd | 4 | |||
4608.2.k.bd.3457.4 | 8 | 48.35 | even | 4 | |||
4608.2.k.bi.1153.1 | 8 | 12.11 | even | 2 | |||
4608.2.k.bi.1153.2 | 8 | 3.2 | odd | 2 | |||
4608.2.k.bi.3457.1 | 8 | 48.5 | odd | 4 | |||
4608.2.k.bi.3457.2 | 8 | 48.11 | even | 4 | |||
9216.2.a.w.1.3 | 4 | 96.5 | odd | 8 | |||
9216.2.a.w.1.4 | 4 | 96.59 | even | 8 | |||
9216.2.a.bp.1.1 | 4 | 96.53 | odd | 8 | |||
9216.2.a.bp.1.2 | 4 | 96.11 | even | 8 |