Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2880,2,Mod(431,2880)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2880, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2880.431");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2880 = 2^{6} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2880.bl (of order \(4\), 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: | \(22.9969157821\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 720) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1871.1 | ||
Character | \(\chi\) | \(=\) | 2880.1871 |
Dual form | 2880.2.bl.b.431.1 |
$q$-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 \(\left(\mathbb{Z}/2880\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(641\) | \(901\) | \(2431\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) |
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 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.707107 | + | 0.707107i | −0.316228 | + | 0.316228i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.49261 | −1.69805 | −0.849024 | − | 0.528355i | \(-0.822809\pi\) | ||||
−0.849024 | + | 0.528355i | \(0.822809\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.37014 | + | 4.37014i | 1.31765 | + | 1.31765i | 0.915634 | + | 0.402012i | \(0.131689\pi\) |
0.402012 | + | 0.915634i | \(0.368311\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.44518 | − | 1.44518i | 0.400820 | − | 0.400820i | −0.477702 | − | 0.878522i | \(-0.658530\pi\) |
0.878522 | + | 0.477702i | \(0.158530\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 6.69649i | − | 1.62414i | −0.583561 | − | 0.812069i | \(-0.698341\pi\) | ||
0.583561 | − | 0.812069i | \(-0.301659\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.91147 | + | 1.91147i | 0.438521 | + | 0.438521i | 0.891514 | − | 0.452993i | \(-0.149644\pi\) |
−0.452993 | + | 0.891514i | \(0.649644\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 1.18773i | − | 0.247659i | −0.992303 | − | 0.123830i | \(-0.960482\pi\) | ||
0.992303 | − | 0.123830i | \(-0.0395177\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 1.00000i | − | 0.200000i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.16029 | + | 2.16029i | 0.401155 | + | 0.401155i | 0.878640 | − | 0.477485i | \(-0.158451\pi\) |
−0.477485 | + | 0.878640i | \(0.658451\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.28465i | 0.769546i | 0.923011 | + | 0.384773i | \(0.125720\pi\) | ||||
−0.923011 | + | 0.384773i | \(0.874280\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.17676 | − | 3.17676i | 0.536970 | − | 0.536970i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.00767006 | + | 0.00767006i | 0.00126095 | + | 0.00126095i | 0.707737 | − | 0.706476i | \(-0.249716\pi\) |
−0.706476 | + | 0.707737i | \(0.749716\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.93930 | 0.771389 | 0.385694 | − | 0.922627i | \(-0.373962\pi\) | ||||
0.385694 | + | 0.922627i | \(0.373962\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.61608 | + | 2.61608i | −0.398949 | + | 0.398949i | −0.877862 | − | 0.478913i | \(-0.841031\pi\) |
0.478913 | + | 0.877862i | \(0.341031\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −12.9356 | −1.88686 | −0.943429 | − | 0.331574i | \(-0.892420\pi\) | ||||
−0.943429 | + | 0.331574i | \(0.892420\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 13.1836 | 1.88337 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.04040 | + | 6.04040i | −0.829712 | + | 0.829712i | −0.987477 | − | 0.157765i | \(-0.949571\pi\) |
0.157765 | + | 0.987477i | \(0.449571\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.18031 | −0.833353 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.51088 | − | 6.51088i | −0.847644 | − | 0.847644i | 0.142195 | − | 0.989839i | \(-0.454584\pi\) |
−0.989839 | + | 0.142195i | \(0.954584\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.14755 | − | 1.14755i | 0.146928 | − | 0.146928i | −0.629816 | − | 0.776744i | \(-0.716870\pi\) |
0.776744 | + | 0.629816i | \(0.216870\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.04379i | 0.253501i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.87653 | + | 5.87653i | 0.717932 | + | 0.717932i | 0.968181 | − | 0.250249i | \(-0.0805126\pi\) |
−0.250249 | + | 0.968181i | \(0.580513\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.93153i | 1.05998i | 0.848005 | + | 0.529989i | \(0.177804\pi\) | ||||
−0.848005 | + | 0.529989i | \(0.822196\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.7131i | 1.60500i | 0.596654 | + | 0.802498i | \(0.296496\pi\) | ||||
−0.596654 | + | 0.802498i | \(0.703504\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −19.6333 | − | 19.6333i | −2.23743 | − | 2.23743i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.10759i | 0.462140i | 0.972937 | + | 0.231070i | \(0.0742226\pi\) | ||||
−0.972937 | + | 0.231070i | \(0.925777\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.52750 | + | 4.52750i | −0.496958 | + | 0.496958i | −0.910490 | − | 0.413532i | \(-0.864295\pi\) |
0.413532 | + | 0.910490i | \(0.364295\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.73514 | + | 4.73514i | 0.513598 | + | 0.513598i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −12.3387 | −1.30790 | −0.653950 | − | 0.756538i | \(-0.726889\pi\) | ||||
−0.653950 | + | 0.756538i | \(0.726889\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.49261 | + | 6.49261i | −0.680611 | + | 0.680611i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.70322 | −0.277345 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.38827 | −0.851700 | −0.425850 | − | 0.904794i | \(-0.640025\pi\) | ||||
−0.425850 | + | 0.904794i | \(0.640025\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.91015 | + | 2.91015i | −0.289571 | + | 0.289571i | −0.836911 | − | 0.547339i | \(-0.815641\pi\) |
0.547339 | + | 0.836911i | \(0.315641\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.5754 | 1.14055 | 0.570277 | − | 0.821452i | \(-0.306836\pi\) | ||||
0.570277 | + | 0.821452i | \(0.306836\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.53540 | − | 3.53540i | −0.341780 | − | 0.341780i | 0.515256 | − | 0.857036i | \(-0.327697\pi\) |
−0.857036 | + | 0.515256i | \(0.827697\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.33976 | + | 6.33976i | −0.607239 | + | 0.607239i | −0.942224 | − | 0.334985i | \(-0.891269\pi\) |
0.334985 | + | 0.942224i | \(0.391269\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.54008i | 0.427095i | 0.976933 | + | 0.213547i | \(0.0685018\pi\) | ||||
−0.976933 | + | 0.213547i | \(0.931498\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.839854 | + | 0.839854i | 0.0783168 | + | 0.0783168i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 30.0847i | 2.75786i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 27.1962i | 2.47239i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0.707107 | + | 0.707107i | 0.0632456 | + | 0.0632456i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.51781i | 0.578362i | 0.957274 | + | 0.289181i | \(0.0933830\pi\) | ||||
−0.957274 | + | 0.289181i | \(0.906617\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.77886 | + | 2.77886i | −0.242790 | + | 0.242790i | −0.818003 | − | 0.575213i | \(-0.804919\pi\) |
0.575213 | + | 0.818003i | \(0.304919\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.58748 | − | 8.58748i | −0.744629 | − | 0.744629i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.63676 | 0.567017 | 0.283508 | − | 0.958970i | \(-0.408502\pi\) | ||||
0.283508 | + | 0.958970i | \(0.408502\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.05388 | + | 7.05388i | −0.598302 | + | 0.598302i | −0.939861 | − | 0.341558i | \(-0.889045\pi\) |
0.341558 | + | 0.939861i | \(0.389045\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 12.6312 | 1.05628 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.05511 | −0.253713 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.52545 | − | 9.52545i | 0.780355 | − | 0.780355i | −0.199535 | − | 0.979891i | \(-0.563943\pi\) |
0.979891 | + | 0.199535i | \(0.0639432\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −23.5203 | −1.91405 | −0.957027 | − | 0.290000i | \(-0.906345\pi\) | ||||
−0.957027 | + | 0.290000i | \(0.906345\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.02971 | − | 3.02971i | −0.243352 | − | 0.243352i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.1912 | − | 10.1912i | 0.813348 | − | 0.813348i | −0.171786 | − | 0.985134i | \(-0.554954\pi\) |
0.985134 | + | 0.171786i | \(0.0549537\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.33602i | 0.420537i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 16.0686 | + | 16.0686i | 1.25859 | + | 1.25859i | 0.951766 | + | 0.306823i | \(0.0992661\pi\) |
0.306823 | + | 0.951766i | \(0.400734\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 0.149541i | − | 0.0115718i | −0.999983 | − | 0.00578592i | \(-0.998158\pi\) | ||
0.999983 | − | 0.00578592i | \(-0.00184173\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.82294i | 0.678687i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.93140 | − | 5.93140i | −0.450956 | − | 0.450956i | 0.444716 | − | 0.895672i | \(-0.353305\pi\) |
−0.895672 | + | 0.444716i | \(0.853305\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.49261i | 0.339609i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 13.5103 | − | 13.5103i | 1.00981 | − | 1.00981i | 0.00985834 | − | 0.999951i | \(-0.496862\pi\) |
0.999951 | − | 0.00985834i | \(-0.00313806\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.5235 | + | 11.5235i | 0.856536 | + | 0.856536i | 0.990928 | − | 0.134393i | \(-0.0429083\pi\) |
−0.134393 | + | 0.990928i | \(0.542908\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.0108471 | −0.000797495 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 29.2646 | − | 29.2646i | 2.14004 | − | 2.14004i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.81786 | 0.565680 | 0.282840 | − | 0.959167i | \(-0.408723\pi\) | ||||
0.282840 | + | 0.959167i | \(0.408723\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −23.4854 | −1.69052 | −0.845258 | − | 0.534358i | \(-0.820553\pi\) | ||||
−0.845258 | + | 0.534358i | \(0.820553\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −12.3998 | + | 12.3998i | −0.883453 | + | 0.883453i | −0.993884 | − | 0.110431i | \(-0.964777\pi\) |
0.110431 | + | 0.993884i | \(0.464777\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.42807 | 0.101233 | 0.0506167 | − | 0.998718i | \(-0.483881\pi\) | ||||
0.0506167 | + | 0.998718i | \(0.483881\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −9.70533 | − | 9.70533i | −0.681180 | − | 0.681180i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.49261 | + | 3.49261i | −0.243935 | + | 0.243935i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 16.7068i | 1.15563i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.18871 | − | 9.18871i | −0.632577 | − | 0.632577i | 0.316137 | − | 0.948714i | \(-0.397614\pi\) |
−0.948714 | + | 0.316137i | \(0.897614\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 3.69970i | − | 0.252318i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 19.2493i | − | 1.30673i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −9.67761 | − | 9.67761i | −0.650986 | − | 0.650986i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 1.56615i | − | 0.104877i | −0.998624 | − | 0.0524385i | \(-0.983301\pi\) | ||
0.998624 | − | 0.0524385i | \(-0.0166994\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −8.36008 | + | 8.36008i | −0.554878 | + | 0.554878i | −0.927845 | − | 0.372967i | \(-0.878341\pi\) |
0.372967 | + | 0.927845i | \(0.378341\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −12.1157 | − | 12.1157i | −0.800630 | − | 0.800630i | 0.182564 | − | 0.983194i | \(-0.441560\pi\) |
−0.983194 | + | 0.182564i | \(0.941560\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 18.7468 | 1.22815 | 0.614073 | − | 0.789249i | \(-0.289530\pi\) | ||||
0.614073 | + | 0.789249i | \(0.289530\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.14688 | − | 9.14688i | 0.596677 | − | 0.596677i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.624861 | 0.0404189 | 0.0202095 | − | 0.999796i | \(-0.493567\pi\) | ||||
0.0202095 | + | 0.999796i | \(0.493567\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 17.9025 | 1.15320 | 0.576600 | − | 0.817027i | \(-0.304379\pi\) | ||||
0.576600 | + | 0.817027i | \(0.304379\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −9.32218 | + | 9.32218i | −0.595572 | + | 0.595572i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.52481 | 0.351535 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −15.7919 | − | 15.7919i | −0.996779 | − | 0.996779i | 0.00321589 | − | 0.999995i | \(-0.498976\pi\) |
−0.999995 | + | 0.00321589i | \(0.998976\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.19056 | − | 5.19056i | 0.326328 | − | 0.326328i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 16.2199i | − | 1.01177i | −0.862601 | − | 0.505885i | \(-0.831166\pi\) | ||
0.862601 | − | 0.505885i | \(-0.168834\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.0344586 | − | 0.0344586i | −0.00214115 | − | 0.00214115i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.316457i | 0.0195136i | 0.999952 | + | 0.00975679i | \(0.00310573\pi\) | ||||
−0.999952 | + | 0.00975679i | \(0.996894\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 8.54241i | − | 0.524756i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6.71152 | − | 6.71152i | −0.409208 | − | 0.409208i | 0.472254 | − | 0.881462i | \(-0.343441\pi\) |
−0.881462 | + | 0.472254i | \(0.843441\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 11.3985i | − | 0.692411i | −0.938159 | − | 0.346205i | \(-0.887470\pi\) | ||
0.938159 | − | 0.346205i | \(-0.112530\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.37014 | − | 4.37014i | 0.263529 | − | 0.263529i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 17.2648 | + | 17.2648i | 1.03734 | + | 1.03734i | 0.999275 | + | 0.0380679i | \(0.0121203\pi\) |
0.0380679 | + | 0.999275i | \(0.487880\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.69745 | 0.160916 | 0.0804582 | − | 0.996758i | \(-0.474362\pi\) | ||||
0.0804582 | + | 0.996758i | \(0.474362\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.38979 | + | 5.38979i | −0.320389 | + | 0.320389i | −0.848916 | − | 0.528527i | \(-0.822745\pi\) |
0.528527 | + | 0.848916i | \(0.322745\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −22.1903 | −1.30985 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −27.8430 | −1.63782 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3.09213 | + | 3.09213i | −0.180644 | + | 0.180644i | −0.791636 | − | 0.610992i | \(-0.790771\pi\) |
0.610992 | + | 0.791636i | \(0.290771\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.20777 | 0.536097 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.71648 | − | 1.71648i | −0.0992667 | − | 0.0992667i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11.7531 | − | 11.7531i | 0.677435 | − | 0.677435i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.62287i | 0.0929255i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 17.8156 | + | 17.8156i | 1.01679 | + | 1.01679i | 0.999857 | + | 0.0169305i | \(0.00538941\pi\) |
0.0169305 | + | 0.999857i | \(0.494611\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 16.3422i | − | 0.926683i | −0.886180 | − | 0.463342i | \(-0.846650\pi\) | ||
0.886180 | − | 0.463342i | \(-0.153350\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 24.0707i | 1.36056i | 0.732954 | + | 0.680278i | \(0.238141\pi\) | ||||
−0.732954 | + | 0.680278i | \(0.761859\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 13.4498 | + | 13.4498i | 0.755414 | + | 0.755414i | 0.975484 | − | 0.220070i | \(-0.0706287\pi\) |
−0.220070 | + | 0.975484i | \(0.570629\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 18.8815i | 1.05716i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 12.8001 | − | 12.8001i | 0.712218 | − | 0.712218i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.44518 | − | 1.44518i | −0.0801639 | − | 0.0801639i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 58.1148 | 3.20397 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.82091 | + | 3.82091i | −0.210016 | + | 0.210016i | −0.804274 | − | 0.594258i | \(-0.797446\pi\) |
0.594258 | + | 0.804274i | \(0.297446\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8.31066 | −0.454060 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.44837 | −0.0788978 | −0.0394489 | − | 0.999222i | \(-0.512560\pi\) | ||||
−0.0394489 | + | 0.999222i | \(0.512560\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −18.7245 | + | 18.7245i | −1.01399 | + | 1.01399i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −27.7803 | −1.50000 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.90479 | − | 2.90479i | −0.155937 | − | 0.155937i | 0.624826 | − | 0.780764i | \(-0.285170\pi\) |
−0.780764 | + | 0.624826i | \(0.785170\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −22.0266 | + | 22.0266i | −1.17906 | + | 1.17906i | −0.199072 | + | 0.979985i | \(0.563793\pi\) |
−0.979985 | + | 0.199072i | \(0.936207\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.17990i | 0.382147i | 0.981576 | + | 0.191074i | \(0.0611969\pi\) | ||||
−0.981576 | + | 0.191074i | \(0.938803\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.31555 | − | 6.31555i | −0.335194 | − | 0.335194i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 23.4618i | 1.23826i | 0.785287 | + | 0.619132i | \(0.212516\pi\) | ||||
−0.785287 | + | 0.619132i | \(0.787484\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 11.6926i | − | 0.615399i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −9.69662 | − | 9.69662i | −0.507544 | − | 0.507544i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 2.96970i | − | 0.155017i | −0.996992 | − | 0.0775086i | \(-0.975303\pi\) | ||
0.996992 | − | 0.0775086i | \(-0.0246965\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 27.1372 | − | 27.1372i | 1.40889 | − | 1.40889i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.38231 | − | 5.38231i | −0.278686 | − | 0.278686i | 0.553899 | − | 0.832584i | \(-0.313140\pi\) |
−0.832584 | + | 0.553899i | \(0.813140\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.24398 | 0.321582 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.79894 | + | 8.79894i | −0.451971 | + | 0.451971i | −0.896008 | − | 0.444037i | \(-0.853546\pi\) |
0.444037 | + | 0.896008i | \(0.353546\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −15.1823 | −0.775780 | −0.387890 | − | 0.921706i | \(-0.626796\pi\) | ||||
−0.387890 | + | 0.921706i | \(0.626796\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 27.7657 | 1.41507 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −5.38360 | + | 5.38360i | −0.272959 | + | 0.272959i | −0.830290 | − | 0.557331i | \(-0.811825\pi\) |
0.557331 | + | 0.830290i | \(0.311825\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.95364 | −0.402233 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.90450 | − | 2.90450i | −0.146141 | − | 0.146141i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.98305 | + | 4.98305i | −0.250092 | + | 0.250092i | −0.821008 | − | 0.570916i | \(-0.806588\pi\) |
0.570916 | + | 0.821008i | \(0.306588\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12.2573i | 0.612099i | 0.952016 | + | 0.306050i | \(0.0990074\pi\) | ||||
−0.952016 | + | 0.306050i | \(0.900993\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.19207 | + | 6.19207i | 0.308449 | + | 0.308449i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.0670385i | 0.00332297i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 28.4064i | 1.40461i | 0.711877 | + | 0.702304i | \(0.247845\pi\) | ||||
−0.711877 | + | 0.702304i | \(0.752155\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 29.2508 | + | 29.2508i | 1.43934 | + | 1.43934i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 6.40286i | − | 0.314304i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 11.3131 | − | 11.3131i | 0.552681 | − | 0.552681i | −0.374533 | − | 0.927214i | \(-0.622197\pi\) |
0.927214 | + | 0.374533i | \(0.122197\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.71988 | − | 1.71988i | −0.0838219 | − | 0.0838219i | 0.663953 | − | 0.747775i | \(-0.268878\pi\) |
−0.747775 | + | 0.663953i | \(0.768878\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.69649 | −0.324828 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.15548 | + | 5.15548i | −0.249491 | + | 0.249491i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.03049 | −0.194142 | −0.0970709 | − | 0.995277i | \(-0.530947\pi\) | ||||
−0.0970709 | + | 0.995277i | \(0.530947\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.01068 | 0.288855 | 0.144427 | − | 0.989515i | \(-0.453866\pi\) | ||||
0.144427 | + | 0.989515i | \(0.453866\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.27031 | − | 2.27031i | 0.108604 | − | 0.108604i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 13.1277 | 0.626549 | 0.313275 | − | 0.949663i | \(-0.398574\pi\) | ||||
0.313275 | + | 0.949663i | \(0.398574\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.57959 | + | 1.57959i | 0.0750488 | + | 0.0750488i | 0.743635 | − | 0.668586i | \(-0.233100\pi\) |
−0.668586 | + | 0.743635i | \(0.733100\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8.72478 | − | 8.72478i | 0.413594 | − | 0.413594i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 22.4970i | 1.06170i | 0.847467 | + | 0.530849i | \(0.178127\pi\) | ||||
−0.847467 | + | 0.530849i | \(0.821873\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 21.5854 | + | 21.5854i | 1.01642 | + | 1.01642i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 9.18194i | − | 0.430456i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.39811i | 0.252513i | 0.991998 | + | 0.126256i | \(0.0402962\pi\) | ||||
−0.991998 | + | 0.126256i | \(0.959704\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 21.3939 | + | 21.3939i | 0.996412 | + | 0.996412i | 0.999994 | − | 0.00358156i | \(-0.00114005\pi\) |
−0.00358156 | + | 0.999994i | \(0.501140\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 24.9382i | − | 1.15898i | −0.814980 | − | 0.579489i | \(-0.803252\pi\) | ||
0.814980 | − | 0.579489i | \(-0.196748\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.82512 | + | 3.82512i | −0.177006 | + | 0.177006i | −0.790049 | − | 0.613044i | \(-0.789945\pi\) |
0.613044 | + | 0.790049i | \(0.289945\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −26.4009 | − | 26.4009i | −1.21908 | − | 1.21908i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −22.8653 | −1.05135 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.91147 | − | 1.91147i | 0.0877042 | − | 0.0877042i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −10.0760 | −0.460383 | −0.230192 | − | 0.973145i | \(-0.573935\pi\) | ||||
−0.230192 | + | 0.973145i | \(0.573935\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.0221692 | 0.00101083 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5.93140 | − | 5.93140i | 0.269331 | − | 0.269331i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11.1510 | 0.505302 | 0.252651 | − | 0.967557i | \(-0.418698\pi\) | ||||
0.252651 | + | 0.967557i | \(0.418698\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10.7851 | − | 10.7851i | −0.486725 | − | 0.486725i | 0.420546 | − | 0.907271i | \(-0.361839\pi\) |
−0.907271 | + | 0.420546i | \(0.861839\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 14.4663 | − | 14.4663i | 0.651531 | − | 0.651531i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 40.1259i | − | 1.79989i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10.6160 | − | 10.6160i | −0.475238 | − | 0.475238i | 0.428367 | − | 0.903605i | \(-0.359089\pi\) |
−0.903605 | + | 0.428367i | \(0.859089\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 18.3508i | 0.818224i | 0.912484 | + | 0.409112i | \(0.134161\pi\) | ||||
−0.912484 | + | 0.409112i | \(0.865839\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 4.11558i | − | 0.183141i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −15.9467 | − | 15.9467i | −0.706824 | − | 0.706824i | 0.259042 | − | 0.965866i | \(-0.416593\pi\) |
−0.965866 | + | 0.259042i | \(0.916593\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 61.6076i | − | 2.72536i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −8.18502 | + | 8.18502i | −0.360675 | + | 0.360675i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −56.5306 | − | 56.5306i | −2.48621 | − | 2.48621i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −22.6636 | −0.992908 | −0.496454 | − | 0.868063i | \(-0.665365\pi\) | ||||
−0.496454 | + | 0.868063i | \(0.665365\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.12095 | − | 1.12095i | 0.0490158 | − | 0.0490158i | −0.682174 | − | 0.731190i | \(-0.738965\pi\) |
0.731190 | + | 0.682174i | \(0.238965\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 28.6921 | 1.24985 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 21.5893 | 0.938665 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7.13815 | − | 7.13815i | 0.309188 | − | 0.309188i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.99981 | 0.216161 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 57.6140 | + | 57.6140i | 2.48161 | + | 2.48161i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 32.3559 | − | 32.3559i | 1.39109 | − | 1.39109i | 0.568195 | − | 0.822894i | \(-0.307642\pi\) |
0.822894 | − | 0.568195i | \(-0.192358\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 8.96577i | − | 0.384051i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −19.5398 | − | 19.5398i | −0.835463 | − | 0.835463i | 0.152795 | − | 0.988258i | \(-0.451172\pi\) |
−0.988258 | + | 0.152795i | \(0.951172\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.25864i | 0.351830i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 18.4538i | − | 0.784735i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −25.8255 | − | 25.8255i | −1.09426 | − | 1.09426i | −0.995068 | − | 0.0991915i | \(-0.968374\pi\) |
−0.0991915 | − | 0.995068i | \(-0.531626\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.56140i | 0.319813i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 10.3693 | − | 10.3693i | 0.437013 | − | 0.437013i | −0.453992 | − | 0.891006i | \(-0.650001\pi\) |
0.891006 | + | 0.453992i | \(0.150001\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.21032 | − | 3.21032i | −0.135059 | − | 0.135059i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 44.4509 | 1.86348 | 0.931738 | − | 0.363130i | \(-0.118292\pi\) | ||||
0.931738 | + | 0.363130i | \(0.118292\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 23.7391 | − | 23.7391i | 0.993450 | − | 0.993450i | −0.00652855 | − | 0.999979i | \(-0.502078\pi\) |
0.999979 | + | 0.00652855i | \(0.00207812\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.18773 | −0.0495319 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.99852 | −0.124830 | −0.0624150 | − | 0.998050i | \(-0.519880\pi\) | ||||
−0.0624150 | + | 0.998050i | \(0.519880\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 20.3403 | − | 20.3403i | 0.843858 | − | 0.843858i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −52.7947 | −2.18653 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −20.4168 | − | 20.4168i | −0.842691 | − | 0.842691i | 0.146517 | − | 0.989208i | \(-0.453194\pi\) |
−0.989208 | + | 0.146517i | \(0.953194\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.18998 | + | 8.18998i | −0.337462 | + | 0.337462i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 2.16808i | − | 0.0890322i | −0.999009 | − | 0.0445161i | \(-0.985825\pi\) | ||
0.999009 | − | 0.0445161i | \(-0.0141746\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −21.2731 | − | 21.2731i | −0.872113 | − | 0.872113i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 7.37935i | − | 0.301512i | −0.988571 | − | 0.150756i | \(-0.951829\pi\) | ||
0.988571 | − | 0.150756i | \(-0.0481708\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.20199i | 0.0898209i | 0.998991 | + | 0.0449105i | \(0.0143003\pi\) | ||||
−0.998991 | + | 0.0449105i | \(0.985700\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −19.2306 | − | 19.2306i | −0.781837 | − | 0.781837i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 1.10100i | − | 0.0446880i | −0.999750 | − | 0.0223440i | \(-0.992887\pi\) | ||
0.999750 | − | 0.0223440i | \(-0.00711291\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −18.6943 | + | 18.6943i | −0.756290 | + | 0.756290i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 25.9748 | + | 25.9748i | 1.04911 | + | 1.04911i | 0.998730 | + | 0.0503809i | \(0.0160435\pi\) |
0.0503809 | + | 0.998730i | \(0.483956\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −31.4011 | −1.26416 | −0.632081 | − | 0.774903i | \(-0.717799\pi\) | ||||
−0.632081 | + | 0.774903i | \(0.717799\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10.6007 | − | 10.6007i | 0.426078 | − | 0.426078i | −0.461212 | − | 0.887290i | \(-0.652585\pi\) |
0.887290 | + | 0.461212i | \(0.152585\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 55.4330 | 2.22088 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.00000 | −0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.0513625 | − | 0.0513625i | 0.00204796 | − | 0.00204796i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13.5474 | −0.539313 | −0.269657 | − | 0.962957i | \(-0.586910\pi\) | ||||
−0.269657 | + | 0.962957i | \(0.586910\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4.60879 | − | 4.60879i | −0.182894 | − | 0.182894i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 19.0526 | − | 19.0526i | 0.754890 | − | 0.754890i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 40.4032i | − | 1.59583i | −0.602770 | − | 0.797915i | \(-0.705937\pi\) | ||
0.602770 | − | 0.797915i | \(-0.294063\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.22995 | + | 2.22995i | 0.0879407 | + | 0.0879407i | 0.749709 | − | 0.661768i | \(-0.230194\pi\) |
−0.661768 | + | 0.749709i | \(0.730194\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.10482i | 0.0827490i | 0.999144 | + | 0.0413745i | \(0.0131737\pi\) | ||||
−0.999144 | + | 0.0413745i | \(0.986826\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 56.9069i | − | 2.23379i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 24.4398 | + | 24.4398i | 0.956402 | + | 0.956402i | 0.999089 | − | 0.0426867i | \(-0.0135917\pi\) |
−0.0426867 | + | 0.999089i | \(0.513592\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 3.92990i | − | 0.153554i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5.67541 | + | 5.67541i | −0.221082 | + | 0.221082i | −0.808954 | − | 0.587872i | \(-0.799966\pi\) |
0.587872 | + | 0.808954i | \(0.299966\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.18787 | − | 9.18787i | −0.357367 | − | 0.357367i | 0.505475 | − | 0.862841i | \(-0.331317\pi\) |
−0.862841 | + | 0.505475i | \(0.831317\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 12.1445 | 0.470945 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.56584 | − | 2.56584i | 0.0993498 | − | 0.0993498i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 10.0299 | 0.387199 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.85854 | −0.225830 | −0.112915 | − | 0.993605i | \(-0.536019\pi\) | ||||
−0.112915 | + | 0.993605i | \(0.536019\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 29.6489 | − | 29.6489i | 1.13950 | − | 1.13950i | 0.150958 | − | 0.988540i | \(-0.451764\pi\) |
0.988540 | − | 0.150958i | \(-0.0482357\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 37.6852 | 1.44623 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 29.4194 | + | 29.4194i | 1.12570 | + | 1.12570i | 0.990868 | + | 0.134834i | \(0.0430501\pi\) |
0.134834 | + | 0.990868i | \(0.456950\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.69290 | + | 4.69290i | −0.179307 | + | 0.179307i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 17.4589i | 0.665130i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −20.6070 | − | 20.6070i | −0.783926 | − | 0.783926i | 0.196565 | − | 0.980491i | \(-0.437021\pi\) |
−0.980491 | + | 0.196565i | \(0.937021\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 9.97570i | − | 0.378400i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 33.0760i | − | 1.25284i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.37293 | − | 3.37293i | −0.127394 | − | 0.127394i | 0.640535 | − | 0.767929i | \(-0.278713\pi\) |
−0.767929 | + | 0.640535i | \(0.778713\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.0293221i | 0.00110591i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 13.0742 | − | 13.0742i | 0.491706 | − | 0.491706i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 34.1260 | + | 34.1260i | 1.28163 | + | 1.28163i | 0.939741 | + | 0.341886i | \(0.111066\pi\) |
0.341886 | + | 0.939741i | \(0.388934\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.08902 | 0.190585 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −8.93163 | + | 8.93163i | −0.334024 | + | 0.334024i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 41.4927 | 1.54742 | 0.773708 | − | 0.633542i | \(-0.218400\pi\) | ||||
0.773708 | + | 0.633542i | \(0.218400\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −52.0036 | −1.93672 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.16029 | − | 2.16029i | 0.0802310 | − | 0.0802310i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15.1442 | 0.561669 | 0.280835 | − | 0.959756i | \(-0.409389\pi\) | ||||
0.280835 | + | 0.959756i | \(0.409389\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 17.5186 | + | 17.5186i | 0.647949 | + | 0.647949i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.53796 | + | 1.53796i | −0.0568060 | + | 0.0568060i | −0.734939 | − | 0.678133i | \(-0.762789\pi\) |
0.678133 | + | 0.734939i | \(0.262789\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 51.3625i | 1.89196i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −35.3121 | − | 35.3121i | −1.29898 | − | 1.29898i | −0.929068 | − | 0.369910i | \(-0.879389\pi\) |
−0.369910 | − | 0.929068i | \(-0.620611\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 38.6663i | 1.41853i | 0.704943 | + | 0.709264i | \(0.250972\pi\) | ||||
−0.704943 | + | 0.709264i | \(0.749028\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 13.4710i | 0.493540i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 15.8832 | + | 15.8832i | 0.580359 | + | 0.580359i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 53.8013i | 1.96324i | 0.190853 | + | 0.981619i | \(0.438875\pi\) | ||||
−0.190853 | + | 0.981619i | \(0.561125\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 16.6314 | − | 16.6314i | 0.605277 | − | 0.605277i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10.7306 | + | 10.7306i | 0.390010 | + | 0.390010i | 0.874691 | − | 0.484681i | \(-0.161064\pi\) |
−0.484681 | + | 0.874691i | \(0.661064\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 19.3367 | 0.700954 | 0.350477 | − | 0.936571i | \(-0.386019\pi\) | ||||
0.350477 | + | 0.936571i | \(0.386019\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 28.4821 | − | 28.4821i | 1.03112 | − | 1.03112i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −18.8187 | −0.679504 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 16.6094 | 0.598949 | 0.299474 | − | 0.954104i | \(-0.403189\pi\) | ||||
0.299474 | + | 0.954104i | \(0.403189\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 27.9353 | − | 27.9353i | 1.00476 | − | 1.00476i | 0.00477424 | − | 0.999989i | \(-0.498480\pi\) |
0.999989 | − | 0.00477424i | \(-0.00151969\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.28465 | 0.153909 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 9.44131 | + | 9.44131i | 0.338270 | + | 0.338270i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −39.0320 | + | 39.0320i | −1.39668 | + | 1.39668i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 14.4126i | 0.514407i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9.37684 | + | 9.37684i | 0.334248 | + | 0.334248i | 0.854197 | − | 0.519949i | \(-0.174049\pi\) |
−0.519949 | + | 0.854197i | \(0.674049\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 20.3968i | − | 0.725227i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 3.31681i | − | 0.117783i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −12.3229 | − | 12.3229i | −0.436498 | − | 0.436498i | 0.454334 | − | 0.890832i | \(-0.349877\pi\) |
−0.890832 | + | 0.454334i | \(0.849877\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 86.6235i | 3.06452i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −59.9281 | + | 59.9281i | −2.11482 | + | 2.11482i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.77314 | − | 3.77314i | −0.132986 | − | 0.132986i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 19.4755 | 0.684721 | 0.342360 | − | 0.939569i | \(-0.388774\pi\) | ||||
0.342360 | + | 0.939569i | \(0.388774\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5.32021 | + | 5.32021i | −0.186818 | + | 0.186818i | −0.794319 | − | 0.607501i | \(-0.792172\pi\) |
0.607501 | + | 0.794319i | \(0.292172\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −22.7244 | −0.796002 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −10.0011 | −0.349895 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −21.3478 | + | 21.3478i | −0.745042 | + | 0.745042i | −0.973544 | − | 0.228502i | \(-0.926617\pi\) |
0.228502 | + | 0.973544i | \(0.426617\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −17.9419 | −0.625414 | −0.312707 | − | 0.949850i | \(-0.601236\pi\) | ||||
−0.312707 | + | 0.949850i | \(0.601236\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −25.7459 | − | 25.7459i | −0.895272 | − | 0.895272i | 0.0997415 | − | 0.995013i | \(-0.468198\pi\) |
−0.995013 | + | 0.0997415i | \(0.968198\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −17.3731 | + | 17.3731i | −0.603394 | + | 0.603394i | −0.941211 | − | 0.337818i | \(-0.890311\pi\) |
0.337818 | + | 0.941211i | \(0.390311\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 88.2836i | − | 3.05885i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.105742 | + | 0.105742i | 0.00365934 | + | 0.00365934i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 19.5757i | − | 0.675827i | −0.941177 | − | 0.337913i | \(-0.890279\pi\) | ||
0.941177 | − | 0.337913i | \(-0.109721\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 19.6663i | − | 0.678149i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6.23876 | − | 6.23876i | −0.214620 | − | 0.214620i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 122.182i | − | 4.19823i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.00910998 | − | 0.00910998i | 0.000312286 | − | 0.000312286i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6.26218 | + | 6.26218i | 0.214413 | + | 0.214413i | 0.806139 | − | 0.591726i | \(-0.201553\pi\) |
−0.591726 | + | 0.806139i | \(0.701553\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −40.9392 | −1.39846 | −0.699229 | − | 0.714898i | \(-0.746473\pi\) | ||||
−0.699229 | + | 0.714898i | \(0.746473\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 24.9076 | − | 24.9076i | 0.849837 | − | 0.849837i | −0.140275 | − | 0.990113i | \(-0.544799\pi\) |
0.990113 | + | 0.140275i | \(0.0447987\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 9.89680 | 0.336891 | 0.168445 | − | 0.985711i | \(-0.446125\pi\) | ||||
0.168445 | + | 0.985711i | \(0.446125\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.38827 | 0.285210 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −17.9507 | + | 17.9507i | −0.608937 | + | 0.608937i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 16.9852 | 0.575522 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.17676 | − | 3.17676i | −0.107394 | − | 0.107394i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 22.2824 | − | 22.2824i | 0.752424 | − | 0.752424i | −0.222507 | − | 0.974931i | \(-0.571424\pi\) |
0.974931 | + | 0.222507i | \(0.0714240\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 47.9458i | 1.61533i | 0.589639 | + | 0.807667i | \(0.299270\pi\) | ||||
−0.589639 | + | 0.807667i | \(0.700730\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 23.2635 | + | 23.2635i | 0.782880 | + | 0.782880i | 0.980316 | − | 0.197436i | \(-0.0632615\pi\) |
−0.197436 | + | 0.980316i | \(0.563261\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 32.4020i | − | 1.08795i | −0.839100 | − | 0.543977i | \(-0.816918\pi\) | ||
0.839100 | − | 0.543977i | \(-0.183082\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 29.2820i | − | 0.982087i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −24.7261 | − | 24.7261i | −0.827427 | − | 0.827427i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 19.1065i | 0.638660i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −9.25608 | + | 9.25608i | −0.308707 | + | 0.308707i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 40.4495 | + | 40.4495i | 1.34757 | + | 1.34757i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −16.2967 | −0.541721 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −15.2567 | + | 15.2567i | −0.506589 | + | 0.506589i | −0.913478 | − | 0.406888i | \(-0.866614\pi\) |
0.406888 | + | 0.913478i | \(0.366614\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 45.6786 | 1.51340 | 0.756700 | − | 0.653762i | \(-0.226810\pi\) | ||||
0.756700 | + | 0.653762i | \(0.226810\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −39.5716 | −1.30963 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 12.4843 | − | 12.4843i | 0.412269 | − | 0.412269i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −48.1001 | −1.58668 | −0.793338 | − | 0.608782i | \(-0.791658\pi\) | ||||
−0.793338 | + | 0.608782i | \(0.791658\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 12.9076 | + | 12.9076i | 0.424860 | + | 0.424860i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.00767006 | − | 0.00767006i | 0.000252190 | − | 0.000252190i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 10.8562i | 0.356180i | 0.984014 | + | 0.178090i | \(0.0569918\pi\) | ||||
−0.984014 | + | 0.178090i | \(0.943008\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 25.1999 | + | 25.1999i | 0.825895 | + | 0.825895i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 41.3864i | 1.35348i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 52.5798i | 1.71771i | 0.512220 | + | 0.858854i | \(0.328823\pi\) | ||||
−0.512220 | + | 0.858854i | \(0.671177\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 34.9046 | + | 34.9046i | 1.13786 | + | 1.13786i | 0.988834 | + | 0.149023i | \(0.0476128\pi\) |
0.149023 | + | 0.988834i | \(0.452387\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 5.86657i | − | 0.191042i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 15.6778 | − | 15.6778i | 0.509459 | − | 0.509459i | −0.404902 | − | 0.914360i | \(-0.632694\pi\) |
0.914360 | + | 0.404902i | \(0.132694\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 19.8178 | + | 19.8178i | 0.643314 | + | 0.643314i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −4.85833 | −0.157377 | −0.0786884 | − | 0.996899i | \(-0.525073\pi\) | ||||
−0.0786884 | + | 0.996899i | \(0.525073\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.52806 | + | 5.52806i | −0.178884 | + | 0.178884i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −29.8164 | −0.962822 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12.6418 | 0.407799 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 16.6067 | − | 16.6067i | 0.534588 | − | 0.534588i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 24.0916 | 0.774733 | 0.387367 | − | 0.921926i | \(-0.373385\pi\) | ||||
0.387367 | + | 0.921926i | \(0.373385\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 13.3267 | + | 13.3267i | 0.427673 | + | 0.427673i | 0.887835 | − | 0.460162i | \(-0.152209\pi\) |
−0.460162 | + | 0.887835i | \(0.652209\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 31.6904 | − | 31.6904i | 1.01595 | − | 1.01595i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 34.7266i | − | 1.11100i | −0.831516 | − | 0.555501i | \(-0.812526\pi\) | ||
0.831516 | − | 0.555501i | \(-0.187474\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −53.9219 | − | 53.9219i | −1.72335 | − | 1.72335i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 52.7711i | − | 1.68314i | −0.540152 | − | 0.841568i | \(-0.681633\pi\) | ||
0.540152 | − | 0.841568i | \(-0.318367\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 17.5360i | − | 0.558744i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.10721 | + | 3.10721i | 0.0988035 | + | 0.0988035i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 29.3280i | 0.931634i | 0.884881 | + | 0.465817i | \(0.154239\pi\) | ||||
−0.884881 | + | 0.465817i | \(0.845761\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.00980 | + | 1.00980i | −0.0320128 | + | 0.0320128i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −17.1758 | − | 17.1758i | −0.543964 | − | 0.543964i | 0.380725 | − | 0.924688i | \(-0.375675\pi\) |
−0.924688 | + | 0.380725i | \(0.875675\pi\) | |||||||
\(998\) | 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 | 2880.2.bl.b.1871.1 | 24 | ||
3.2 | odd | 2 | inner | 2880.2.bl.b.1871.7 | 24 | ||
4.3 | odd | 2 | 720.2.bl.b.251.5 | ✓ | 24 | ||
12.11 | even | 2 | 720.2.bl.b.251.8 | yes | 24 | ||
16.3 | odd | 4 | inner | 2880.2.bl.b.431.7 | 24 | ||
16.13 | even | 4 | 720.2.bl.b.611.8 | yes | 24 | ||
48.29 | odd | 4 | 720.2.bl.b.611.5 | yes | 24 | ||
48.35 | even | 4 | inner | 2880.2.bl.b.431.1 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
720.2.bl.b.251.5 | ✓ | 24 | 4.3 | odd | 2 | ||
720.2.bl.b.251.8 | yes | 24 | 12.11 | even | 2 | ||
720.2.bl.b.611.5 | yes | 24 | 48.29 | odd | 4 | ||
720.2.bl.b.611.8 | yes | 24 | 16.13 | even | 4 | ||
2880.2.bl.b.431.1 | 24 | 48.35 | even | 4 | inner | ||
2880.2.bl.b.431.7 | 24 | 16.3 | odd | 4 | inner | ||
2880.2.bl.b.1871.1 | 24 | 1.1 | even | 1 | trivial | ||
2880.2.bl.b.1871.7 | 24 | 3.2 | odd | 2 | inner |