Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1512,2,Mod(505,1512)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1512, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1512.505");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1512.r (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(12.0733807856\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.2091141441.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} + x^{6} + 3x^{5} - 15x^{4} + 9x^{3} + 9x^{2} - 27x + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | no (minimal twist has level 504) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 505.3 | ||
Root | \(0.199732 - 1.72050i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1512.505 |
Dual form | 1512.2.r.e.1009.3 |
$q$-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 \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1081\) | \(1135\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.300268 | + | 0.520080i | 0.134284 | + | 0.232587i | 0.925324 | − | 0.379178i | \(-0.123793\pi\) |
−0.791040 | + | 0.611765i | \(0.790460\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.500000 | − | 0.866025i | 0.188982 | − | 0.327327i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.800268 | + | 1.38611i | −0.241290 | + | 0.417926i | −0.961082 | − | 0.276263i | \(-0.910904\pi\) |
0.719792 | + | 0.694190i | \(0.244237\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.165178 | − | 0.286096i | −0.0458120 | − | 0.0793487i | 0.842210 | − | 0.539149i | \(-0.181254\pi\) |
−0.888022 | + | 0.459801i | \(0.847921\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.44990 | 0.351652 | 0.175826 | − | 0.984421i | \(-0.443740\pi\) | ||||
0.175826 | + | 0.984421i | \(0.443740\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.57918 | 0.591705 | 0.295852 | − | 0.955234i | \(-0.404396\pi\) | ||||
0.295852 | + | 0.955234i | \(0.404396\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.924682 | + | 1.60160i | 0.192809 | + | 0.333956i | 0.946180 | − | 0.323640i | \(-0.104907\pi\) |
−0.753371 | + | 0.657596i | \(0.771573\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.31968 | − | 4.01780i | 0.463936 | − | 0.803560i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.75950 | − | 3.04755i | 0.326732 | − | 0.565916i | −0.655130 | − | 0.755517i | \(-0.727386\pi\) |
0.981861 | + | 0.189601i | \(0.0607193\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.81034 | + | 8.33176i | 0.863963 | + | 1.49643i | 0.868073 | + | 0.496436i | \(0.165358\pi\) |
−0.00411031 | + | 0.999992i | \(0.501308\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.600537 | 0.101509 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.600537 | 0.0987276 | 0.0493638 | − | 0.998781i | \(-0.484281\pi\) | ||||
0.0493638 | + | 0.998781i | \(0.484281\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.31034 | + | 5.73368i | 0.516989 | + | 0.895450i | 0.999805 | + | 0.0197291i | \(0.00628037\pi\) |
−0.482817 | + | 0.875721i | \(0.660386\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.81481 | + | 3.14334i | −0.276756 | + | 0.479355i | −0.970577 | − | 0.240793i | \(-0.922593\pi\) |
0.693821 | + | 0.720148i | \(0.255926\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.95477 | − | 3.38576i | 0.285132 | − | 0.493864i | −0.687509 | − | 0.726176i | \(-0.741296\pi\) |
0.972641 | + | 0.232312i | \(0.0746291\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.500000 | − | 0.866025i | −0.0714286 | − | 0.123718i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.27166 | 1.27356 | 0.636780 | − | 0.771046i | \(-0.280266\pi\) | ||||
0.636780 | + | 0.771046i | \(0.280266\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.961181 | −0.129606 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.93476 | − | 12.0113i | −0.902828 | − | 1.56374i | −0.823806 | − | 0.566872i | \(-0.808154\pi\) |
−0.0790221 | − | 0.996873i | \(-0.525180\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.59433 | − | 4.49351i | 0.332169 | − | 0.575334i | −0.650768 | − | 0.759277i | \(-0.725553\pi\) |
0.982937 | + | 0.183943i | \(0.0588861\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.0991952 | − | 0.171811i | 0.0123036 | − | 0.0213105i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.90467 | + | 10.2272i | 0.721370 | + | 1.24945i | 0.960451 | + | 0.278450i | \(0.0898206\pi\) |
−0.239081 | + | 0.971000i | \(0.576846\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.17972 | 0.496041 | 0.248021 | − | 0.968755i | \(-0.420220\pi\) | ||||
0.248021 | + | 0.968755i | \(0.420220\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.13969 | 0.484514 | 0.242257 | − | 0.970212i | \(-0.422112\pi\) | ||||
0.242257 | + | 0.970212i | \(0.422112\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.800268 | + | 1.38611i | 0.0911990 | + | 0.157961i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.06538 | + | 7.04144i | −0.457391 | + | 0.792224i | −0.998822 | − | 0.0485208i | \(-0.984549\pi\) |
0.541431 | + | 0.840745i | \(0.317883\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.78959 | + | 4.83171i | −0.306197 | + | 0.530349i | −0.977527 | − | 0.210809i | \(-0.932390\pi\) |
0.671330 | + | 0.741159i | \(0.265723\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.435359 | + | 0.754064i | 0.0472213 | + | 0.0817897i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.83069 | 0.406053 | 0.203026 | − | 0.979173i | \(-0.434922\pi\) | ||||
0.203026 | + | 0.979173i | \(0.434922\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.330355 | −0.0346306 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.774447 | + | 1.34138i | 0.0794565 | + | 0.137623i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.974782 | − | 1.68837i | 0.0989741 | − | 0.171428i | −0.812286 | − | 0.583259i | \(-0.801777\pi\) |
0.911260 | + | 0.411831i | \(0.135111\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.79520 | − | 15.2337i | 0.875155 | − | 1.51581i | 0.0185572 | − | 0.999828i | \(-0.494093\pi\) |
0.856598 | − | 0.515985i | \(-0.172574\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.30547 | + | 9.18935i | 0.522764 | + | 0.905454i | 0.999649 | + | 0.0264880i | \(0.00843237\pi\) |
−0.476885 | + | 0.878966i | \(0.658234\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.43949 | 0.332508 | 0.166254 | − | 0.986083i | \(-0.446833\pi\) | ||||
0.166254 | + | 0.986083i | \(0.446833\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.55010 | −0.531603 | −0.265802 | − | 0.964028i | \(-0.585637\pi\) | ||||
−0.265802 | + | 0.964028i | \(0.585637\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.38079 | + | 7.58775i | 0.412110 | + | 0.713796i | 0.995120 | − | 0.0986691i | \(-0.0314585\pi\) |
−0.583010 | + | 0.812465i | \(0.698125\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.555305 | + | 0.961817i | −0.0517825 | + | 0.0896899i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.724950 | − | 1.25565i | 0.0664561 | − | 0.115105i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.21914 | + | 7.30777i | 0.383558 | + | 0.664342i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.78879 | 0.517765 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.1521 | −0.989590 | −0.494795 | − | 0.869010i | \(-0.664757\pi\) | ||||
−0.494795 | + | 0.869010i | \(0.664757\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.59993 | − | 4.50322i | −0.227157 | − | 0.393448i | 0.729807 | − | 0.683653i | \(-0.239610\pi\) |
−0.956964 | + | 0.290205i | \(0.906276\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.28959 | − | 2.23364i | 0.111822 | − | 0.193681i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.39399 | − | 7.61062i | 0.375404 | − | 0.650219i | −0.614983 | − | 0.788540i | \(-0.710837\pi\) |
0.990387 | + | 0.138321i | \(0.0441706\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.50934 | + | 7.81040i | 0.382477 | + | 0.662469i | 0.991416 | − | 0.130748i | \(-0.0417378\pi\) |
−0.608939 | + | 0.793217i | \(0.708404\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.528746 | 0.0442159 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.11329 | 0.175499 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −0.525620 | − | 0.910400i | −0.0430604 | − | 0.0745829i | 0.843692 | − | 0.536828i | \(-0.180377\pi\) |
−0.886752 | + | 0.462245i | \(0.847044\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.48932 | − | 11.2398i | 0.528094 | − | 0.914685i | −0.471370 | − | 0.881936i | \(-0.656240\pi\) |
0.999464 | − | 0.0327494i | \(-0.0104263\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.88879 | + | 5.00352i | −0.232033 | + | 0.401893i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.86699 | + | 17.0901i | 0.787471 | + | 1.36394i | 0.927511 | + | 0.373795i | \(0.121944\pi\) |
−0.140040 | + | 0.990146i | \(0.544723\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.84936 | 0.145750 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −22.9214 | −1.79534 | −0.897672 | − | 0.440664i | \(-0.854743\pi\) | ||||
−0.897672 | + | 0.440664i | \(0.854743\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.61508 | + | 2.79740i | 0.124978 | + | 0.216469i | 0.921725 | − | 0.387845i | \(-0.126780\pi\) |
−0.796746 | + | 0.604314i | \(0.793447\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.44543 | − | 11.1638i | 0.495803 | − | 0.858755i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.08052 | − | 12.2638i | 0.538322 | − | 0.932401i | −0.460672 | − | 0.887570i | \(-0.652392\pi\) |
0.998995 | − | 0.0448312i | \(-0.0142750\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.31968 | − | 4.01780i | −0.175351 | − | 0.303717i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −7.06790 | −0.528280 | −0.264140 | − | 0.964484i | \(-0.585088\pi\) | ||||
−0.264140 | + | 0.964484i | \(0.585088\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −19.6207 | −1.45839 | −0.729197 | − | 0.684304i | \(-0.760106\pi\) | ||||
−0.729197 | + | 0.684304i | \(0.760106\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.180322 | + | 0.312327i | 0.0132575 | + | 0.0229627i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.16031 | + | 2.00971i | −0.0848502 | + | 0.146965i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.1096 | + | 17.5104i | −0.731505 | + | 1.26700i | 0.224734 | + | 0.974420i | \(0.427849\pi\) |
−0.956240 | + | 0.292584i | \(0.905485\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.89473 | − | 15.4061i | −0.640257 | − | 1.10896i | −0.985375 | − | 0.170398i | \(-0.945495\pi\) |
0.345119 | − | 0.938559i | \(-0.387839\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −8.04150 | −0.572933 | −0.286467 | − | 0.958090i | \(-0.592481\pi\) | ||||
−0.286467 | + | 0.958090i | \(0.592481\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.0332 | 0.994790 | 0.497395 | − | 0.867524i | \(-0.334290\pi\) | ||||
0.497395 | + | 0.867524i | \(0.334290\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.75950 | − | 3.04755i | −0.123493 | − | 0.213896i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.98798 | + | 3.44328i | −0.138847 | + | 0.240489i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.06404 | + | 3.57502i | −0.142772 | + | 0.247289i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.32622 | − | 12.6894i | −0.504358 | − | 0.873574i | −0.999987 | − | 0.00503962i | \(-0.998396\pi\) |
0.495629 | − | 0.868534i | \(-0.334938\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.17972 | −0.148656 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.62068 | 0.653095 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.239491 | − | 0.414811i | −0.0161099 | − | 0.0279032i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.02696 | − | 12.1711i | 0.470560 | − | 0.815034i | −0.528873 | − | 0.848701i | \(-0.677385\pi\) |
0.999433 | + | 0.0336670i | \(0.0107185\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.40601 | − | 4.16733i | 0.159692 | − | 0.276596i | −0.775065 | − | 0.631881i | \(-0.782283\pi\) |
0.934758 | + | 0.355286i | \(0.115616\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.68419 | − | 2.91710i | −0.111294 | − | 0.192767i | 0.804998 | − | 0.593277i | \(-0.202166\pi\) |
−0.916292 | + | 0.400510i | \(0.868833\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −20.9137 | −1.37010 | −0.685051 | − | 0.728495i | \(-0.740220\pi\) | ||||
−0.685051 | + | 0.728495i | \(0.740220\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.34782 | 0.153155 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.60614 | + | 16.6383i | 0.621370 | + | 1.07624i | 0.989231 | + | 0.146363i | \(0.0467568\pi\) |
−0.367861 | + | 0.929881i | \(0.619910\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.88912 | − | 15.3964i | 0.572599 | − | 0.991770i | −0.423699 | − | 0.905803i | \(-0.639269\pi\) |
0.996298 | − | 0.0859672i | \(-0.0273980\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.300268 | − | 0.520080i | 0.0191834 | − | 0.0332267i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.426023 | − | 0.737894i | −0.0271072 | − | 0.0469510i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −20.5531 | −1.29730 | −0.648649 | − | 0.761088i | \(-0.724665\pi\) | ||||
−0.648649 | + | 0.761088i | \(0.724665\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.95997 | −0.186092 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −12.6943 | − | 21.9871i | −0.791846 | − | 1.37152i | −0.924823 | − | 0.380399i | \(-0.875787\pi\) |
0.132976 | − | 0.991119i | \(-0.457547\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.300268 | − | 0.520080i | 0.0186578 | − | 0.0323162i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −15.3557 | + | 26.5969i | −0.946874 | + | 1.64003i | −0.194918 | + | 0.980820i | \(0.562444\pi\) |
−0.751956 | + | 0.659213i | \(0.770889\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.78398 | + | 4.82200i | 0.171019 | + | 0.296213i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −13.7402 | −0.837757 | −0.418878 | − | 0.908042i | \(-0.637577\pi\) | ||||
−0.418878 | + | 0.908042i | \(0.637577\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.64977 | 0.464690 | 0.232345 | − | 0.972633i | \(-0.425360\pi\) | ||||
0.232345 | + | 0.972633i | \(0.425360\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.71273 | + | 6.43064i | 0.223886 | + | 0.387782i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.19174 | − | 7.26030i | 0.251857 | − | 0.436229i | −0.712180 | − | 0.701997i | \(-0.752292\pi\) |
0.964037 | + | 0.265768i | \(0.0856254\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −12.7786 | + | 22.1333i | −0.762310 | + | 1.32036i | 0.179347 | + | 0.983786i | \(0.442602\pi\) |
−0.941657 | + | 0.336574i | \(0.890732\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.46132 | − | 9.45928i | −0.324641 | − | 0.562296i | 0.656798 | − | 0.754066i | \(-0.271910\pi\) |
−0.981440 | + | 0.191771i | \(0.938577\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.62068 | 0.390807 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.8978 | −0.876341 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 13.9994 | + | 24.2477i | 0.817853 | + | 1.41656i | 0.907261 | + | 0.420569i | \(0.138169\pi\) |
−0.0894073 | + | 0.995995i | \(0.528497\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.16457 | − | 7.21325i | 0.242471 | − | 0.419972i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.305473 | − | 0.529095i | 0.0176660 | − | 0.0305984i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.81481 | + | 3.14334i | 0.104604 | + | 0.181179i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.11598 | 0.178420 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −33.0259 | −1.88489 | −0.942443 | − | 0.334367i | \(-0.891477\pi\) | ||||
−0.942443 | + | 0.334367i | \(0.891477\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −13.0143 | − | 22.5415i | −0.737975 | − | 1.27821i | −0.953406 | − | 0.301692i | \(-0.902449\pi\) |
0.215430 | − | 0.976519i | \(-0.430885\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.46618 | − | 9.46771i | 0.308967 | − | 0.535146i | −0.669170 | − | 0.743110i | \(-0.733350\pi\) |
0.978137 | + | 0.207963i | \(0.0666834\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −5.98593 | + | 10.3679i | −0.336203 | + | 0.582321i | −0.983715 | − | 0.179734i | \(-0.942476\pi\) |
0.647512 | + | 0.762055i | \(0.275810\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.81615 | + | 4.87772i | 0.157674 | + | 0.273100i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.73956 | 0.208074 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.53264 | −0.0850153 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.95477 | − | 3.38576i | −0.107770 | − | 0.186663i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11.6176 | + | 20.1223i | −0.638561 | + | 1.10602i | 0.347188 | + | 0.937796i | \(0.387137\pi\) |
−0.985749 | + | 0.168224i | \(0.946197\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.54597 | + | 6.14180i | −0.193737 | + | 0.335562i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.89594 | − | 6.74796i | −0.212225 | − | 0.367585i | 0.740185 | − | 0.672403i | \(-0.234738\pi\) |
−0.952411 | + | 0.304818i | \(0.901404\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −15.3983 | −0.833862 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −9.26198 | − | 16.0422i | −0.497209 | − | 0.861192i | 0.502785 | − | 0.864411i | \(-0.332309\pi\) |
−0.999995 | + | 0.00321932i | \(0.998975\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.958498 | − | 1.66017i | 0.0513072 | − | 0.0888667i | −0.839231 | − | 0.543775i | \(-0.816995\pi\) |
0.890538 | + | 0.454908i | \(0.150328\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −0.869778 | + | 1.50650i | −0.0462936 | + | 0.0801829i | −0.888244 | − | 0.459372i | \(-0.848074\pi\) |
0.841950 | + | 0.539555i | \(0.181408\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.25504 | + | 2.17379i | 0.0666104 | + | 0.115373i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3.07616 | 0.162354 | 0.0811768 | − | 0.996700i | \(-0.474132\pi\) | ||||
0.0811768 | + | 0.996700i | \(0.474132\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.3478 | −0.649885 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.24302 | + | 2.15297i | 0.0650625 | + | 0.112692i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.17871 | − | 10.7018i | 0.322526 | − | 0.558632i | −0.658482 | − | 0.752596i | \(-0.728801\pi\) |
0.981009 | + | 0.193964i | \(0.0621346\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.63583 | − | 8.02949i | 0.240680 | − | 0.416870i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12.3999 | − | 21.4773i | −0.642044 | − | 1.11205i | −0.984976 | − | 0.172693i | \(-0.944753\pi\) |
0.342931 | − | 0.939360i | \(-0.388580\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.16252 | −0.0598730 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11.9650 | −0.614602 | −0.307301 | − | 0.951612i | \(-0.599426\pi\) | ||||
−0.307301 | + | 0.951612i | \(0.599426\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5.85810 | + | 10.1465i | 0.299335 | + | 0.518463i | 0.975984 | − | 0.217843i | \(-0.0699020\pi\) |
−0.676649 | + | 0.736306i | \(0.736569\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.480590 | + | 0.832407i | −0.0244932 | + | 0.0424234i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 19.1360 | − | 33.1445i | 0.970232 | − | 1.68049i | 0.275384 | − | 0.961334i | \(-0.411195\pi\) |
0.694848 | − | 0.719156i | \(-0.255472\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.34070 | + | 2.32215i | 0.0678019 | + | 0.117436i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.88282 | −0.245681 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 12.8396 | 0.644402 | 0.322201 | − | 0.946671i | \(-0.395577\pi\) | ||||
0.322201 | + | 0.946671i | \(0.395577\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.1570 | + | 19.3245i | 0.557155 | + | 0.965021i | 0.997732 | + | 0.0673063i | \(0.0214405\pi\) |
−0.440577 | + | 0.897715i | \(0.645226\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.58912 | − | 2.75244i | 0.0791598 | − | 0.137109i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.480590 | + | 0.832407i | −0.0238220 | + | 0.0412609i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.76605 | + | 6.52299i | 0.186219 | + | 0.322541i | 0.943987 | − | 0.329984i | \(-0.107043\pi\) |
−0.757767 | + | 0.652525i | \(0.773710\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −13.8695 | −0.682474 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.35050 | −0.164470 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −14.1245 | − | 24.4644i | −0.690029 | − | 1.19517i | −0.971828 | − | 0.235692i | \(-0.924264\pi\) |
0.281798 | − | 0.959474i | \(-0.409069\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.53395 | + | 16.5133i | −0.464656 | + | 0.804808i | −0.999186 | − | 0.0403414i | \(-0.987155\pi\) |
0.534530 | + | 0.845150i | \(0.320489\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.36330 | − | 5.82541i | 0.163144 | − | 0.282574i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.59433 | − | 4.49351i | −0.125548 | − | 0.217456i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 22.9786 | 1.10684 | 0.553421 | − | 0.832902i | \(-0.313322\pi\) | ||||
0.553421 | + | 0.832902i | \(0.313322\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −29.0806 | −1.39752 | −0.698762 | − | 0.715354i | \(-0.746265\pi\) | ||||
−0.698762 | + | 0.715354i | \(0.746265\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.38492 | + | 4.13081i | 0.114086 | + | 0.197603i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.36777 | − | 12.7613i | 0.351644 | − | 0.609066i | −0.634893 | − | 0.772600i | \(-0.718956\pi\) |
0.986538 | + | 0.163534i | \(0.0522893\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −17.2548 | + | 29.8861i | −0.819799 | + | 1.41993i | 0.0860314 | + | 0.996292i | \(0.472581\pi\) |
−0.905830 | + | 0.423641i | \(0.860752\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.15024 | + | 1.99227i | 0.0545264 | + | 0.0944425i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −11.5508 | −0.545115 | −0.272557 | − | 0.962140i | \(-0.587869\pi\) | ||||
−0.272557 | + | 0.962140i | \(0.587869\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10.5966 | −0.498977 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.0991952 | − | 0.171811i | −0.00465034 | − | 0.00805463i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −18.6995 | + | 32.3884i | −0.874724 | + | 1.51507i | −0.0176677 | + | 0.999844i | \(0.505624\pi\) |
−0.857056 | + | 0.515223i | \(0.827709\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9.13929 | + | 15.8297i | −0.425659 | + | 0.737263i | −0.996482 | − | 0.0838101i | \(-0.973291\pi\) |
0.570823 | + | 0.821073i | \(0.306624\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.24610 | − | 7.35447i | −0.197333 | − | 0.341791i | 0.750330 | − | 0.661064i | \(-0.229895\pi\) |
−0.947663 | + | 0.319273i | \(0.896561\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 14.6746 | 0.679060 | 0.339530 | − | 0.940595i | \(-0.389732\pi\) | ||||
0.339530 | + | 0.940595i | \(0.389732\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11.8093 | 0.545305 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.90467 | − | 5.03103i | −0.133557 | − | 0.231327i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.98287 | − | 10.3626i | 0.274513 | − | 0.475470i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 18.7151 | − | 32.4156i | 0.855117 | − | 1.48111i | −0.0214198 | − | 0.999771i | \(-0.506819\pi\) |
0.876537 | − | 0.481335i | \(-0.159848\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.0991952 | − | 0.171811i | −0.00452291 | − | 0.00783391i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.17078 | 0.0531626 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 33.3216 | 1.50994 | 0.754972 | − | 0.655757i | \(-0.227650\pi\) | ||||
0.754972 | + | 0.655757i | \(0.227650\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −19.9456 | − | 34.5467i | −0.900131 | − | 1.55907i | −0.827323 | − | 0.561726i | \(-0.810137\pi\) |
−0.0728078 | − | 0.997346i | \(-0.523196\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.55110 | − | 4.41864i | 0.114896 | − | 0.199006i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.08986 | − | 3.61974i | 0.0937430 | − | 0.162368i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −11.0370 | − | 19.1167i | −0.494086 | − | 0.855781i | 0.505891 | − | 0.862597i | \(-0.331164\pi\) |
−0.999977 | + | 0.00681602i | \(0.997830\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9.30820 | 0.415032 | 0.207516 | − | 0.978232i | \(-0.433462\pi\) | ||||
0.207516 | + | 0.978232i | \(0.433462\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.5637 | 0.470077 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.88466 | − | 4.99637i | −0.127860 | − | 0.221460i | 0.794987 | − | 0.606626i | \(-0.207478\pi\) |
−0.922847 | + | 0.385166i | \(0.874144\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.06985 | − | 3.58508i | 0.0915646 | − | 0.158595i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.18613 | + | 5.51854i | −0.140398 | + | 0.243176i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.12868 | + | 5.41903i | 0.137599 | + | 0.238329i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13.2989 | 0.582634 | 0.291317 | − | 0.956627i | \(-0.405907\pi\) | ||||
0.291317 | + | 0.956627i | \(0.405907\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.27523 | 0.186943 | 0.0934713 | − | 0.995622i | \(-0.470204\pi\) | ||||
0.0934713 | + | 0.995622i | \(0.470204\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.97451 | + | 12.0802i | 0.303815 | + | 0.526222i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.78993 | − | 16.9567i | 0.425649 | − | 0.737246i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.09359 | − | 1.89415i | 0.0473686 | − | 0.0820448i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.03277 | + | 1.78881i | 0.0446505 | + | 0.0773370i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.60054 | 0.0689400 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12.2130 | −0.525076 | −0.262538 | − | 0.964922i | \(-0.584560\pi\) | ||||
−0.262538 | + | 0.964922i | \(0.584560\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.66652 | − | 2.88650i | −0.0713858 | − | 0.123644i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −19.0910 | + | 33.0666i | −0.816272 | + | 1.41382i | 0.0921387 | + | 0.995746i | \(0.470630\pi\) |
−0.908411 | + | 0.418079i | \(0.862704\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.53808 | − | 7.86019i | 0.193329 | − | 0.334855i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.06538 | + | 7.04144i | 0.172877 | + | 0.299433i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −36.8404 | −1.56098 | −0.780490 | − | 0.625169i | \(-0.785030\pi\) | ||||
−0.780490 | + | 0.625169i | \(0.785030\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.19906 | 0.0507150 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9.56265 | + | 16.5630i | 0.403018 | + | 0.698047i | 0.994089 | − | 0.108572i | \(-0.0346279\pi\) |
−0.591071 | + | 0.806620i | \(0.701295\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.63083 | + | 4.55672i | −0.110680 | + | 0.191703i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −12.9576 | + | 22.4433i | −0.543212 | + | 0.940871i | 0.455505 | + | 0.890233i | \(0.349459\pi\) |
−0.998717 | + | 0.0506376i | \(0.983875\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 19.5679 | + | 33.8925i | 0.818889 | + | 1.41836i | 0.906501 | + | 0.422203i | \(0.138743\pi\) |
−0.0876117 | + | 0.996155i | \(0.527923\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.57985 | 0.357805 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9.72008 | 0.404652 | 0.202326 | − | 0.979318i | \(-0.435150\pi\) | ||||
0.202326 | + | 0.979318i | \(0.435150\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.78959 | + | 4.83171i | 0.115732 | + | 0.200453i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.41981 | + | 12.8515i | −0.307297 | + | 0.532254i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 6.91088 | − | 11.9700i | 0.285242 | − | 0.494054i | −0.687425 | − | 0.726255i | \(-0.741259\pi\) |
0.972668 | + | 0.232200i | \(0.0745925\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 12.4067 | + | 21.4891i | 0.511211 | + | 0.885444i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 22.1361 | 0.909022 | 0.454511 | − | 0.890741i | \(-0.349814\pi\) | ||||
0.454511 | + | 0.890741i | \(0.349814\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.870718 | 0.0356960 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.28059 | + | 3.95010i | 0.0931824 | + | 0.161397i | 0.908849 | − | 0.417126i | \(-0.136963\pi\) |
−0.815666 | + | 0.578523i | \(0.803629\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10.2116 | + | 17.6870i | −0.416541 | + | 0.721469i | −0.995589 | − | 0.0938238i | \(-0.970091\pi\) |
0.579048 | + | 0.815293i | \(0.303424\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.53375 | + | 4.38858i | −0.103012 | + | 0.178421i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7.11206 | − | 12.3184i | −0.288670 | − | 0.499990i | 0.684823 | − | 0.728710i | \(-0.259880\pi\) |
−0.973492 | + | 0.228719i | \(0.926546\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.29154 | −0.0522499 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −31.3892 | −1.26780 | −0.633899 | − | 0.773416i | \(-0.718546\pi\) | ||||
−0.633899 | + | 0.773416i | \(0.718546\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.51767 | + | 4.36073i | 0.101357 | + | 0.175556i | 0.912244 | − | 0.409647i | \(-0.134348\pi\) |
−0.810887 | + | 0.585203i | \(0.801015\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 19.1803 | − | 33.2212i | 0.770920 | − | 1.33527i | −0.166140 | − | 0.986102i | \(-0.553130\pi\) |
0.937060 | − | 0.349170i | \(-0.113536\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.91535 | − | 3.31748i | 0.0767367 | − | 0.132912i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9.86020 | − | 17.0784i | −0.394408 | − | 0.683135i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.870718 | 0.0347178 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24.0768 | 0.958480 | 0.479240 | − | 0.877684i | \(-0.340912\pi\) | ||||
0.479240 | + | 0.877684i | \(0.340912\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3.34863 | − | 5.79999i | −0.132886 | − | 0.230166i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.165178 | + | 0.286096i | −0.00654457 | + | 0.0113355i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 20.7800 | − | 35.9920i | 0.820760 | − | 1.42160i | −0.0843567 | − | 0.996436i | \(-0.526884\pi\) |
0.905117 | − | 0.425163i | \(-0.139783\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0.924345 | + | 1.60101i | 0.0364526 | + | 0.0631378i | 0.883676 | − | 0.468099i | \(-0.155061\pi\) |
−0.847224 | + | 0.531237i | \(0.821728\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 38.8480 | 1.52727 | 0.763637 | − | 0.645646i | \(-0.223412\pi\) | ||||
0.763637 | + | 0.645646i | \(0.223412\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 22.1987 | 0.871374 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 20.3225 | + | 35.1996i | 0.795281 | + | 1.37747i | 0.922661 | + | 0.385613i | \(0.126010\pi\) |
−0.127380 | + | 0.991854i | \(0.540657\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.56135 | − | 2.70435i | 0.0610072 | − | 0.105668i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 19.2140 | − | 33.2796i | 0.748471 | − | 1.29639i | −0.200084 | − | 0.979779i | \(-0.564121\pi\) |
0.948555 | − | 0.316612i | \(-0.102545\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.72841 | + | 9.92190i | 0.222809 | + | 0.385917i | 0.955660 | − | 0.294472i | \(-0.0951439\pi\) |
−0.732851 | + | 0.680390i | \(0.761811\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.54889 | 0.0600635 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.50793 | 0.251988 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.15231 | + | 7.19202i | 0.160298 | + | 0.277645i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −23.4933 | + | 40.6916i | −0.905601 | + | 1.56855i | −0.0854925 | + | 0.996339i | \(0.527246\pi\) |
−0.820108 | + | 0.572208i | \(0.806087\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −8.03942 | + | 13.9247i | −0.308980 | + | 0.535169i | −0.978140 | − | 0.207950i | \(-0.933321\pi\) |
0.669159 | + | 0.743119i | \(0.266654\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.974782 | − | 1.68837i | −0.0374087 | − | 0.0647938i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.20464 | 0.199150 | 0.0995750 | − | 0.995030i | \(-0.468252\pi\) | ||||
0.0995750 | + | 0.995030i | \(0.468252\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.27750 | 0.201643 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.53147 | − | 2.65258i | −0.0583444 | − | 0.101055i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.783381 | + | 1.35686i | −0.0298012 | + | 0.0516172i | −0.880541 | − | 0.473969i | \(-0.842821\pi\) |
0.850740 | + | 0.525587i | \(0.176154\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2.70802 | + | 4.69043i | −0.102721 | + | 0.177918i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.79966 | + | 8.31326i | 0.181800 | + | 0.314887i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5.94479 | −0.224532 | −0.112266 | − | 0.993678i | \(-0.535811\pi\) | ||||
−0.112266 | + | 0.993678i | \(0.535811\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.54889 | 0.0584176 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −8.79520 | − | 15.2337i | −0.330777 | − | 0.572923i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.53916 | − | 11.3262i | 0.245583 | − | 0.425362i | −0.716712 | − | 0.697369i | \(-0.754354\pi\) |
0.962295 | + | 0.272007i | \(0.0876872\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −8.89607 | + | 15.4084i | −0.333160 | + | 0.577051i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.158766 | + | 0.274990i | 0.00593749 | + | 0.0102840i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 10.5600 | 0.393821 | 0.196910 | − | 0.980422i | \(-0.436909\pi\) | ||||
0.196910 | + | 0.980422i | \(0.436909\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.6109 | 0.395172 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −8.16297 | − | 14.1387i | −0.303165 | − | 0.525097i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5.08052 | − | 8.79972i | 0.188426 | − | 0.326364i | −0.756300 | − | 0.654226i | \(-0.772995\pi\) |
0.944726 | + | 0.327862i | \(0.106328\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.63129 | + | 4.55753i | −0.0973218 | + | 0.168566i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −13.2280 | − | 22.9116i | −0.488589 | − | 0.846260i | 0.511325 | − | 0.859387i | \(-0.329155\pi\) |
−0.999914 | + | 0.0131270i | \(0.995821\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −18.9013 | −0.696237 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 24.3880 | 0.897127 | 0.448563 | − | 0.893751i | \(-0.351936\pi\) | ||||
0.448563 | + | 0.893751i | \(0.351936\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 8.21961 | + | 14.2368i | 0.301548 | + | 0.522297i | 0.976487 | − | 0.215577i | \(-0.0691632\pi\) |
−0.674939 | + | 0.737874i | \(0.735830\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.315654 | − | 0.546728i | 0.0115647 | − | 0.0200306i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.71974 | − | 2.97869i | 0.0628381 | − | 0.108839i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.0653789 | + | 0.113240i | 0.00238571 | + | 0.00413217i | 0.867216 | − | 0.497932i | \(-0.165907\pi\) |
−0.864830 | + | 0.502065i | \(0.832574\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 7.79415 | 0.283658 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 36.1017 | 1.31214 | 0.656069 | − | 0.754701i | \(-0.272218\pi\) | ||||
0.656069 | + | 0.754701i | \(0.272218\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.61027 | − | 7.98523i | −0.167122 | − | 0.289464i | 0.770285 | − | 0.637700i | \(-0.220114\pi\) |
−0.937407 | + | 0.348236i | \(0.886781\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.77505 | + | 4.80653i | −0.100464 | + | 0.174008i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.29093 | + | 3.96801i | −0.0827208 | + | 0.143277i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 22.8660 | + | 39.6050i | 0.824568 | + | 1.42819i | 0.902249 | + | 0.431216i | \(0.141915\pi\) |
−0.0776802 | + | 0.996978i | \(0.524751\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −25.9709 | −0.934109 | −0.467054 | − | 0.884229i | \(-0.654685\pi\) | ||||
−0.467054 | + | 0.884229i | \(0.654685\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 44.6338 | 1.60329 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 8.53797 | + | 14.7882i | 0.305905 | + | 0.529842i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.34490 | + | 5.79353i | −0.119690 | + | 0.207309i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5.92549 | + | 10.2632i | −0.211490 | + | 0.366311i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −25.3821 | − | 43.9630i | −0.904773 | − | 1.56711i | −0.821222 | − | 0.570609i | \(-0.806707\pi\) |
−0.0835512 | − | 0.996503i | \(-0.526626\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8.76158 | 0.311526 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.71410 | −0.0608694 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 13.2977 | + | 23.0322i | 0.471027 | + | 0.815843i | 0.999451 | − | 0.0331379i | \(-0.0105501\pi\) |
−0.528424 | + | 0.848981i | \(0.677217\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.83422 | − | 4.90901i | 0.100267 | − | 0.173668i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.31286 | + | 5.73805i | −0.116908 | + | 0.202491i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.555305 | + | 0.961817i | 0.0195719 | + | 0.0338996i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 21.1540 | 0.743735 | 0.371867 | − | 0.928286i | \(-0.378718\pi\) | ||||
0.371867 | + | 0.928286i | \(0.378718\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −15.4615 | −0.542927 | −0.271464 | − | 0.962449i | \(-0.587508\pi\) | ||||
−0.271464 | + | 0.962449i | \(0.587508\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6.88258 | − | 11.9210i | −0.241086 | − | 0.417573i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.68072 | + | 8.10725i | −0.163758 | + | 0.283637i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13.2843 | − | 23.0091i | 0.463626 | − | 0.803024i | −0.535512 | − | 0.844527i | \(-0.679881\pi\) |
0.999138 | + | 0.0415036i | \(0.0132148\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 12.5469 | + | 21.7318i | 0.437357 | + | 0.757524i | 0.997485 | − | 0.0708819i | \(-0.0225813\pi\) |
−0.560128 | + | 0.828406i | \(0.689248\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −12.8156 | −0.445642 | −0.222821 | − | 0.974859i | \(-0.571526\pi\) | ||||
−0.222821 | + | 0.974859i | \(0.571526\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 37.9832 | 1.31921 | 0.659605 | − | 0.751613i | \(-0.270724\pi\) | ||||
0.659605 | + | 0.751613i | \(0.270724\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.724950 | − | 1.25565i | −0.0251180 | − | 0.0435057i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.969913 | + | 1.67994i | −0.0335652 | + | 0.0581367i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.95638 | + | 5.12060i | −0.102065 | + | 0.176783i | −0.912535 | − | 0.408998i | \(-0.865878\pi\) |
0.810470 | + | 0.585780i | \(0.199212\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8.30829 | + | 14.3904i | 0.286493 | + | 0.496220i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 7.74144 | 0.266313 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.43828 | 0.289943 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.555305 | + | 0.961817i | 0.0190356 | + | 0.0329707i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9.72609 | − | 16.8461i | 0.333015 | − | 0.576799i | −0.650087 | − | 0.759860i | \(-0.725267\pi\) |
0.983101 | + | 0.183061i | \(0.0586007\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −3.42502 | + | 5.93231i | −0.116996 | + | 0.202644i | −0.918576 | − | 0.395244i | \(-0.870660\pi\) |
0.801580 | + | 0.597888i | \(0.203993\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.04742 | − | 5.27828i | −0.103977 | − | 0.180093i | 0.809343 | − | 0.587336i | \(-0.199823\pi\) |
−0.913320 | + | 0.407244i | \(0.866490\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 33.6568 | 1.14569 | 0.572846 | − | 0.819663i | \(-0.305839\pi\) | ||||
0.572846 | + | 0.819663i | \(0.305839\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.50423 | 0.289152 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6.50679 | − | 11.2701i | −0.220728 | − | 0.382312i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.95064 | − | 3.37860i | 0.0660948 | − | 0.114480i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.89439 | − | 5.01324i | 0.0978483 | − | 0.169478i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −8.18905 | − | 14.1839i | −0.276525 | − | 0.478955i | 0.693994 | − | 0.719981i | \(-0.255849\pi\) |
−0.970519 | + | 0.241026i | \(0.922516\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −22.0864 | −0.744108 | −0.372054 | − | 0.928211i | \(-0.621346\pi\) | ||||
−0.372054 | + | 0.928211i | \(0.621346\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 13.1872 | 0.443784 | 0.221892 | − | 0.975071i | \(-0.428777\pi\) | ||||
0.221892 | + | 0.975071i | \(0.428777\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 14.7174 | + | 25.4912i | 0.494160 | + | 0.855911i | 0.999977 | − | 0.00672982i | \(-0.00214218\pi\) |
−0.505817 | + | 0.862641i | \(0.668809\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.57606 | + | 9.65801i | −0.187015 | + | 0.323919i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.04170 | − | 8.73249i | 0.168714 | − | 0.292222i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.12227 | − | 3.67587i | −0.0709395 | − | 0.122871i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 33.8553 | 1.12914 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 13.4430 | 0.447850 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −5.89147 | − | 10.2043i | −0.195839 | − | 0.339203i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −9.03916 | + | 15.6563i | −0.300140 | + | 0.519858i | −0.976167 | − | 0.217018i | \(-0.930367\pi\) |
0.676027 | + | 0.736877i | \(0.263700\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.24050 | − | 7.34475i | 0.140494 | − | 0.243343i | −0.787189 | − | 0.616712i | \(-0.788464\pi\) |
0.927683 | + | 0.373369i | \(0.121798\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.46484 | − | 7.73333i | −0.147765 | − | 0.255936i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −5.19987 | −0.171715 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 22.0092 | 0.726017 | 0.363008 | − | 0.931786i | \(-0.381750\pi\) | ||||
0.363008 | + | 0.931786i | \(0.381750\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −0.690396 | − | 1.19580i | −0.0227247 | − | 0.0393603i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.39305 | − | 2.41284i | 0.0458032 | − | 0.0793336i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 21.4107 | − | 37.0845i | 0.702464 | − | 1.21670i | −0.265135 | − | 0.964211i | \(-0.585417\pi\) |
0.967599 | − | 0.252492i | \(-0.0812501\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.28959 | − | 2.23364i | −0.0422646 | − | 0.0732045i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.39362 | −0.0455761 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 8.65749 | 0.282828 | 0.141414 | − | 0.989951i | \(-0.454835\pi\) | ||||
0.141414 | + | 0.989951i | \(0.454835\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 25.9474 | + | 44.9421i | 0.845859 | + | 1.46507i | 0.884873 | + | 0.465833i | \(0.154245\pi\) |
−0.0390132 | + | 0.999239i | \(0.512421\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.12203 | + | 10.6037i | −0.199361 | + | 0.345303i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −11.5394 | + | 19.9869i | −0.374981 | + | 0.649486i | −0.990324 | − | 0.138773i | \(-0.955684\pi\) |
0.615343 | + | 0.788259i | \(0.289017\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.683784 | − | 1.18435i | −0.0221966 | − | 0.0384456i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 22.9656 | 0.743927 | 0.371964 | − | 0.928247i | \(-0.378685\pi\) | ||||
0.371964 | + | 0.928247i | \(0.378685\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −12.1424 | −0.392918 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.39399 | − | 7.61062i | −0.141889 | − | 0.245760i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.7788 | + | 53.3104i | −0.992864 | + | 1.71969i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5.34161 | − | 9.25194i | 0.171953 | − | 0.297830i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −29.4696 | − | 51.0429i | −0.947680 | − | 1.64143i | −0.750294 | − | 0.661104i | \(-0.770088\pi\) |
−0.197386 | − | 0.980326i | \(-0.563245\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −25.8074 | −0.828198 | −0.414099 | − | 0.910232i | \(-0.635903\pi\) | ||||
−0.414099 | + | 0.910232i | \(0.635903\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9.01867 | 0.289125 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −22.4774 | − | 38.9321i | −0.719117 | − | 1.24555i | −0.961350 | − | 0.275329i | \(-0.911213\pi\) |
0.242233 | − | 0.970218i | \(-0.422120\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.06558 | + | 5.30974i | −0.0979764 | + | 0.169700i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4.33576 | + | 7.50976i | −0.138289 | + | 0.239524i | −0.926849 | − | 0.375434i | \(-0.877494\pi\) |
0.788560 | + | 0.614958i | \(0.210827\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.41461 | − | 4.18222i | −0.0769358 | − | 0.133257i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −6.71248 | −0.213445 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.39241 | −0.107763 | −0.0538817 | − | 0.998547i | \(-0.517159\pi\) | ||||
−0.0538817 | + | 0.998547i | \(0.517159\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.21374 | + | 7.29841i | 0.133584 | + | 0.231375i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −14.0201 | + | 24.2836i | −0.444023 | + | 0.769070i | −0.997984 | − | 0.0634730i | \(-0.979782\pi\) |
0.553961 | + | 0.832543i | \(0.313116\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1512.2.r.e.505.3 | 8 | ||
3.2 | odd | 2 | 504.2.r.e.169.4 | ✓ | 8 | ||
4.3 | odd | 2 | 3024.2.r.m.2017.3 | 8 | |||
9.2 | odd | 6 | 4536.2.a.z.1.3 | 4 | |||
9.4 | even | 3 | inner | 1512.2.r.e.1009.3 | 8 | ||
9.5 | odd | 6 | 504.2.r.e.337.4 | yes | 8 | ||
9.7 | even | 3 | 4536.2.a.y.1.2 | 4 | |||
12.11 | even | 2 | 1008.2.r.l.673.1 | 8 | |||
36.7 | odd | 6 | 9072.2.a.cg.1.2 | 4 | |||
36.11 | even | 6 | 9072.2.a.cj.1.3 | 4 | |||
36.23 | even | 6 | 1008.2.r.l.337.1 | 8 | |||
36.31 | odd | 6 | 3024.2.r.m.1009.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.r.e.169.4 | ✓ | 8 | 3.2 | odd | 2 | ||
504.2.r.e.337.4 | yes | 8 | 9.5 | odd | 6 | ||
1008.2.r.l.337.1 | 8 | 36.23 | even | 6 | |||
1008.2.r.l.673.1 | 8 | 12.11 | even | 2 | |||
1512.2.r.e.505.3 | 8 | 1.1 | even | 1 | trivial | ||
1512.2.r.e.1009.3 | 8 | 9.4 | even | 3 | inner | ||
3024.2.r.m.1009.3 | 8 | 36.31 | odd | 6 | |||
3024.2.r.m.2017.3 | 8 | 4.3 | odd | 2 | |||
4536.2.a.y.1.2 | 4 | 9.7 | even | 3 | |||
4536.2.a.z.1.3 | 4 | 9.2 | odd | 6 | |||
9072.2.a.cg.1.2 | 4 | 36.7 | odd | 6 | |||
9072.2.a.cj.1.3 | 4 | 36.11 | even | 6 |