Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [756,2,Mod(377,756)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(756, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("756.377");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 756.f (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.03669039281\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 4x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2\cdot 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 377.3 | ||
Root | \(-1.93185i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 756.377 |
Dual form | 756.2.f.d.377.4 |
$q$-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 \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(325\) | \(379\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.73205 | 0.774597 | 0.387298 | − | 0.921954i | \(-0.373408\pi\) | ||||
0.387298 | + | 0.921954i | \(0.373408\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | − | 2.44949i | −0.377964 | − | 0.925820i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 4.24264i | − | 1.27920i | −0.768706 | − | 0.639602i | \(-0.779099\pi\) | ||
0.768706 | − | 0.639602i | \(-0.220901\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.44949i | 0.679366i | 0.940540 | + | 0.339683i | \(0.110320\pi\) | ||||
−0.940540 | + | 0.339683i | \(0.889680\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.73205 | 0.420084 | 0.210042 | − | 0.977692i | \(-0.432640\pi\) | ||||
0.210042 | + | 0.977692i | \(0.432640\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 2.44949i | − | 0.561951i | −0.959715 | − | 0.280976i | \(-0.909342\pi\) | ||
0.959715 | − | 0.280976i | \(-0.0906580\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 8.48528i | − | 1.76930i | −0.466252 | − | 0.884652i | \(-0.654396\pi\) | ||
0.466252 | − | 0.884652i | \(-0.345604\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.00000 | −0.400000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 4.24264i | − | 0.787839i | −0.919145 | − | 0.393919i | \(-0.871119\pi\) | ||
0.919145 | − | 0.393919i | \(-0.128881\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.34847i | 1.31982i | 0.751343 | + | 0.659912i | \(0.229406\pi\) | ||||
−0.751343 | + | 0.659912i | \(0.770594\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.73205 | − | 4.24264i | −0.292770 | − | 0.717137i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.00000 | 0.164399 | 0.0821995 | − | 0.996616i | \(-0.473806\pi\) | ||||
0.0821995 | + | 0.996616i | \(0.473806\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.73205 | −0.270501 | −0.135250 | − | 0.990811i | \(-0.543184\pi\) | ||||
−0.135250 | + | 0.990811i | \(0.543184\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.00000 | 1.06749 | 0.533745 | − | 0.845645i | \(-0.320784\pi\) | ||||
0.533745 | + | 0.845645i | \(0.320784\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 12.1244 | 1.76852 | 0.884260 | − | 0.466996i | \(-0.154664\pi\) | ||||
0.884260 | + | 0.466996i | \(0.154664\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.00000 | + | 4.89898i | −0.714286 | + | 0.699854i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 7.34847i | − | 0.990867i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.66025 | 1.12747 | 0.563735 | − | 0.825956i | \(-0.309364\pi\) | ||||
0.563735 | + | 0.825956i | \(0.309364\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 2.44949i | − | 0.313625i | −0.987628 | − | 0.156813i | \(-0.949878\pi\) | ||
0.987628 | − | 0.156813i | \(-0.0501218\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.24264i | 0.526235i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.0000 | −1.22169 | −0.610847 | − | 0.791748i | \(-0.709171\pi\) | ||||
−0.610847 | + | 0.791748i | \(0.709171\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 8.48528i | − | 1.00702i | −0.863990 | − | 0.503509i | \(-0.832042\pi\) | ||
0.863990 | − | 0.503509i | \(-0.167958\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 9.79796i | − | 1.14676i | −0.819288 | − | 0.573382i | \(-0.805631\pi\) | ||
0.819288 | − | 0.573382i | \(-0.194369\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −10.3923 | + | 4.24264i | −1.18431 | + | 0.483494i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.00000 | 0.562544 | 0.281272 | − | 0.959628i | \(-0.409244\pi\) | ||||
0.281272 | + | 0.959628i | \(0.409244\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −12.1244 | −1.33082 | −0.665410 | − | 0.746478i | \(-0.731743\pi\) | ||||
−0.665410 | + | 0.746478i | \(0.731743\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.00000 | 0.325396 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.3923 | 1.10158 | 0.550791 | − | 0.834643i | \(-0.314326\pi\) | ||||
0.550791 | + | 0.834643i | \(0.314326\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.00000 | − | 2.44949i | 0.628971 | − | 0.256776i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 4.24264i | − | 0.435286i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.44949i | 0.248708i | 0.992238 | + | 0.124354i | \(0.0396858\pi\) | ||||
−0.992238 | + | 0.124354i | \(0.960314\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.3923 | −1.03407 | −0.517036 | − | 0.855963i | \(-0.672965\pi\) | ||||
−0.517036 | + | 0.855963i | \(0.672965\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 19.5959i | 1.93084i | 0.260694 | + | 0.965422i | \(0.416049\pi\) | ||||
−0.260694 | + | 0.965422i | \(0.583951\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.48528i | 0.820303i | 0.912017 | + | 0.410152i | \(0.134524\pi\) | ||||
−0.912017 | + | 0.410152i | \(0.865476\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.0000 | 1.24517 | 0.622587 | − | 0.782551i | \(-0.286082\pi\) | ||||
0.622587 | + | 0.782551i | \(0.286082\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 12.7279i | 1.19734i | 0.800995 | + | 0.598671i | \(0.204304\pi\) | ||||
−0.800995 | + | 0.598671i | \(0.795696\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 14.6969i | − | 1.37050i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.73205 | − | 4.24264i | −0.158777 | − | 0.388922i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −12.1244 | −1.08444 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −13.0000 | −1.15356 | −0.576782 | − | 0.816898i | \(-0.695692\pi\) | ||||
−0.576782 | + | 0.816898i | \(0.695692\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.3923 | 0.907980 | 0.453990 | − | 0.891007i | \(-0.350000\pi\) | ||||
0.453990 | + | 0.891007i | \(0.350000\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.00000 | + | 2.44949i | −0.520266 | + | 0.212398i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 21.2132i | 1.81237i | 0.422885 | + | 0.906183i | \(0.361017\pi\) | ||||
−0.422885 | + | 0.906183i | \(0.638983\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.2474i | 1.03882i | 0.854527 | + | 0.519408i | \(0.173847\pi\) | ||||
−0.854527 | + | 0.519408i | \(0.826153\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 10.3923 | 0.869048 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 7.34847i | − | 0.610257i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 12.7279i | 1.04271i | 0.853339 | + | 0.521356i | \(0.174574\pi\) | ||||
−0.853339 | + | 0.521356i | \(0.825426\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.00000 | −0.406894 | −0.203447 | − | 0.979086i | \(-0.565214\pi\) | ||||
−0.203447 | + | 0.979086i | \(0.565214\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 12.7279i | 1.02233i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.34847i | 0.586472i | 0.956040 | + | 0.293236i | \(0.0947321\pi\) | ||||
−0.956040 | + | 0.293236i | \(0.905268\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −20.7846 | + | 8.48528i | −1.63806 | + | 0.668734i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.00000 | −0.0783260 | −0.0391630 | − | 0.999233i | \(-0.512469\pi\) | ||||
−0.0391630 | + | 0.999233i | \(0.512469\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −19.0526 | −1.47433 | −0.737166 | − | 0.675712i | \(-0.763836\pi\) | ||||
−0.737166 | + | 0.675712i | \(0.763836\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.00000 | 0.538462 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 20.7846 | 1.58022 | 0.790112 | − | 0.612962i | \(-0.210022\pi\) | ||||
0.790112 | + | 0.612962i | \(0.210022\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.00000 | + | 4.89898i | 0.151186 | + | 0.370328i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.24264i | 0.317110i | 0.987350 | + | 0.158555i | \(0.0506835\pi\) | ||||
−0.987350 | + | 0.158555i | \(0.949317\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 4.89898i | − | 0.364138i | −0.983286 | − | 0.182069i | \(-0.941721\pi\) | ||
0.983286 | − | 0.182069i | \(-0.0582795\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.73205 | 0.127343 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 7.34847i | − | 0.537373i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 8.48528i | − | 0.613973i | −0.951714 | − | 0.306987i | \(-0.900679\pi\) | ||
0.951714 | − | 0.306987i | \(-0.0993207\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.00000 | 0.503871 | 0.251936 | − | 0.967744i | \(-0.418933\pi\) | ||||
0.251936 | + | 0.967744i | \(0.418933\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 21.2132i | 1.51138i | 0.654931 | + | 0.755689i | \(0.272698\pi\) | ||||
−0.654931 | + | 0.755689i | \(0.727302\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.79796i | 0.694559i | 0.937762 | + | 0.347279i | \(0.112894\pi\) | ||||
−0.937762 | + | 0.347279i | \(0.887106\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −10.3923 | + | 4.24264i | −0.729397 | + | 0.297775i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.00000 | −0.209529 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −10.3923 | −0.718851 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.00000 | −0.550743 | −0.275371 | − | 0.961338i | \(-0.588801\pi\) | ||||
−0.275371 | + | 0.961338i | \(0.588801\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 12.1244 | 0.826874 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 18.0000 | − | 7.34847i | 1.22192 | − | 0.498847i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.24264i | 0.285391i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 22.0454i | − | 1.47627i | −0.674653 | − | 0.738135i | \(-0.735707\pi\) | ||
0.674653 | − | 0.738135i | \(-0.264293\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 14.6969i | − | 0.971201i | −0.874181 | − | 0.485601i | \(-0.838601\pi\) | ||
0.874181 | − | 0.485601i | \(-0.161399\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 4.24264i | − | 0.277945i | −0.990296 | − | 0.138972i | \(-0.955620\pi\) | ||
0.990296 | − | 0.138972i | \(-0.0443799\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 21.0000 | 1.36989 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 21.2132i | − | 1.37217i | −0.727522 | − | 0.686084i | \(-0.759328\pi\) | ||
0.727522 | − | 0.686084i | \(-0.240672\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 26.9444i | 1.73564i | 0.496878 | + | 0.867820i | \(0.334480\pi\) | ||||
−0.496878 | + | 0.867820i | \(0.665520\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −8.66025 | + | 8.48528i | −0.553283 | + | 0.542105i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.00000 | 0.381771 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −19.0526 | −1.20259 | −0.601293 | − | 0.799028i | \(-0.705348\pi\) | ||||
−0.601293 | + | 0.799028i | \(0.705348\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −36.0000 | −2.26330 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 10.3923 | 0.648254 | 0.324127 | − | 0.946014i | \(-0.394929\pi\) | ||||
0.324127 | + | 0.946014i | \(0.394929\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.00000 | − | 2.44949i | −0.0621370 | − | 0.152204i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 21.2132i | − | 1.30806i | −0.756468 | − | 0.654031i | \(-0.773077\pi\) | ||
0.756468 | − | 0.654031i | \(-0.226923\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.73205 | −0.105605 | −0.0528025 | − | 0.998605i | \(-0.516815\pi\) | ||||
−0.0528025 | + | 0.998605i | \(0.516815\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 4.89898i | − | 0.297592i | −0.988868 | − | 0.148796i | \(-0.952460\pi\) | ||
0.988868 | − | 0.148796i | \(-0.0475397\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 8.48528i | 0.511682i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.00000 | −0.420589 | −0.210295 | − | 0.977638i | \(-0.567442\pi\) | ||||
−0.210295 | + | 0.977638i | \(0.567442\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 8.48528i | − | 0.506189i | −0.967442 | − | 0.253095i | \(-0.918552\pi\) | ||
0.967442 | − | 0.253095i | \(-0.0814484\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 7.34847i | − | 0.436821i | −0.975857 | − | 0.218411i | \(-0.929913\pi\) | ||
0.975857 | − | 0.218411i | \(-0.0700872\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.73205 | + | 4.24264i | 0.102240 | + | 0.250435i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.0000 | −0.823529 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8.66025 | 0.505937 | 0.252969 | − | 0.967474i | \(-0.418593\pi\) | ||||
0.252969 | + | 0.967474i | \(0.418593\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 15.0000 | 0.873334 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 20.7846 | 1.20201 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.00000 | − | 17.1464i | −0.403473 | − | 0.988304i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 4.24264i | − | 0.242933i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 29.3939i | 1.67760i | 0.544442 | + | 0.838799i | \(0.316741\pi\) | ||||
−0.544442 | + | 0.838799i | \(0.683259\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 22.5167 | 1.27680 | 0.638401 | − | 0.769704i | \(-0.279596\pi\) | ||||
0.638401 | + | 0.769704i | \(0.279596\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 24.4949i | 1.38453i | 0.721642 | + | 0.692267i | \(0.243388\pi\) | ||||
−0.721642 | + | 0.692267i | \(0.756612\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −18.0000 | −1.00781 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 4.24264i | − | 0.236067i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 4.89898i | − | 0.271746i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −12.1244 | − | 29.6985i | −0.668437 | − | 1.63733i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 13.0000 | 0.714545 | 0.357272 | − | 0.934000i | \(-0.383707\pi\) | ||||
0.357272 | + | 0.934000i | \(0.383707\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −17.3205 | −0.946320 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 25.0000 | 1.36184 | 0.680918 | − | 0.732359i | \(-0.261581\pi\) | ||||
0.680918 | + | 0.732359i | \(0.261581\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 31.1769 | 1.68832 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.0000 | + | 7.34847i | 0.917914 | + | 0.396780i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 21.2132i | 1.13878i | 0.822066 | + | 0.569392i | \(0.192821\pi\) | ||||
−0.822066 | + | 0.569392i | \(0.807179\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 19.5959i | 1.04895i | 0.851427 | + | 0.524473i | \(0.175738\pi\) | ||||
−0.851427 | + | 0.524473i | \(0.824262\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.73205 | 0.0921878 | 0.0460939 | − | 0.998937i | \(-0.485323\pi\) | ||||
0.0460939 | + | 0.998937i | \(0.485323\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 14.6969i | − | 0.780033i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 33.9411i | − | 1.79134i | −0.444715 | − | 0.895672i | \(-0.646695\pi\) | ||
0.444715 | − | 0.895672i | \(-0.353305\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.0000 | 0.684211 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 16.9706i | − | 0.888280i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 4.89898i | − | 0.255725i | −0.991792 | − | 0.127862i | \(-0.959188\pi\) | ||
0.991792 | − | 0.127862i | \(-0.0408116\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.0000 | 0.569558 | 0.284779 | − | 0.958593i | \(-0.408080\pi\) | ||||
0.284779 | + | 0.958593i | \(0.408080\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 10.3923 | 0.535231 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −35.0000 | −1.79783 | −0.898915 | − | 0.438124i | \(-0.855643\pi\) | ||||
−0.898915 | + | 0.438124i | \(0.855643\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 19.0526 | 0.973540 | 0.486770 | − | 0.873530i | \(-0.338175\pi\) | ||||
0.486770 | + | 0.873530i | \(0.338175\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −18.0000 | + | 7.34847i | −0.917365 | + | 0.374513i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 29.6985i | − | 1.50577i | −0.658150 | − | 0.752886i | \(-0.728661\pi\) | ||
0.658150 | − | 0.752886i | \(-0.271339\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 14.6969i | − | 0.743256i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8.66025 | 0.435745 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 29.3939i | 1.47524i | 0.675218 | + | 0.737618i | \(0.264050\pi\) | ||||
−0.675218 | + | 0.737618i | \(0.735950\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 8.48528i | − | 0.423735i | −0.977298 | − | 0.211867i | \(-0.932046\pi\) | ||
0.977298 | − | 0.211867i | \(-0.0679545\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −18.0000 | −0.896644 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 4.24264i | − | 0.210300i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 39.1918i | − | 1.93791i | −0.247234 | − | 0.968956i | \(-0.579522\pi\) | ||
0.247234 | − | 0.968956i | \(-0.420478\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −8.66025 | − | 21.2132i | −0.426143 | − | 1.04383i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −21.0000 | −1.03085 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −29.4449 | −1.43848 | −0.719238 | − | 0.694764i | \(-0.755509\pi\) | ||||
−0.719238 | + | 0.694764i | \(0.755509\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.0000 | 0.974740 | 0.487370 | − | 0.873195i | \(-0.337956\pi\) | ||||
0.487370 | + | 0.873195i | \(0.337956\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.46410 | −0.168034 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.00000 | + | 2.44949i | −0.290360 | + | 0.118539i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 16.9706i | − | 0.817443i | −0.912659 | − | 0.408722i | \(-0.865975\pi\) | ||
0.912659 | − | 0.408722i | \(-0.134025\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 22.0454i | − | 1.05943i | −0.848174 | − | 0.529717i | \(-0.822298\pi\) | ||
0.848174 | − | 0.529717i | \(-0.177702\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −20.7846 | −0.994263 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 29.3939i | − | 1.40289i | −0.712722 | − | 0.701447i | \(-0.752538\pi\) | ||
0.712722 | − | 0.701447i | \(-0.247462\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12.7279i | 0.604722i | 0.953194 | + | 0.302361i | \(0.0977748\pi\) | ||||
−0.953194 | + | 0.302361i | \(0.902225\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 18.0000 | 0.853282 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 21.2132i | − | 1.00111i | −0.865704 | − | 0.500556i | \(-0.833129\pi\) | ||
0.865704 | − | 0.500556i | \(-0.166871\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.34847i | 0.346026i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 10.3923 | − | 4.24264i | 0.487199 | − | 0.198898i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.00000 | −0.374224 | −0.187112 | − | 0.982339i | \(-0.559913\pi\) | ||||
−0.187112 | + | 0.982339i | \(0.559913\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 29.4449 | 1.37138 | 0.685692 | − | 0.727892i | \(-0.259500\pi\) | ||||
0.685692 | + | 0.727892i | \(0.259500\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 29.0000 | 1.34774 | 0.673872 | − | 0.738848i | \(-0.264630\pi\) | ||||
0.673872 | + | 0.738848i | \(0.264630\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −20.7846 | −0.961797 | −0.480899 | − | 0.876776i | \(-0.659689\pi\) | ||||
−0.480899 | + | 0.876776i | \(0.659689\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10.0000 | + | 24.4949i | 0.461757 | + | 1.13107i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 29.6985i | − | 1.36554i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.89898i | 0.224781i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 39.8372 | 1.82021 | 0.910103 | − | 0.414381i | \(-0.136002\pi\) | ||||
0.910103 | + | 0.414381i | \(0.136002\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.44949i | 0.111687i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.24264i | 0.192648i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 22.0000 | 0.996915 | 0.498458 | − | 0.866914i | \(-0.333900\pi\) | ||||
0.498458 | + | 0.866914i | \(0.333900\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.7279i | 0.574403i | 0.957870 | + | 0.287202i | \(0.0927249\pi\) | ||||
−0.957870 | + | 0.287202i | \(0.907275\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 7.34847i | − | 0.330958i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −20.7846 | + | 8.48528i | −0.932317 | + | 0.380617i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 19.0000 | 0.850557 | 0.425278 | − | 0.905063i | \(-0.360176\pi\) | ||||
0.425278 | + | 0.905063i | \(0.360176\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.73205 | −0.0772283 | −0.0386142 | − | 0.999254i | \(-0.512294\pi\) | ||||
−0.0386142 | + | 0.999254i | \(0.512294\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −18.0000 | −0.800989 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 19.0526 | 0.844490 | 0.422245 | − | 0.906482i | \(-0.361242\pi\) | ||||
0.422245 | + | 0.906482i | \(0.361242\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −24.0000 | + | 9.79796i | −1.06170 | + | 0.433436i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 33.9411i | 1.49562i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 51.4393i | − | 2.26230i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.73205 | −0.0758825 | −0.0379413 | − | 0.999280i | \(-0.512080\pi\) | ||||
−0.0379413 | + | 0.999280i | \(0.512080\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 31.8434i | 1.39241i | 0.717841 | + | 0.696207i | \(0.245130\pi\) | ||||
−0.717841 | + | 0.696207i | \(0.754870\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 12.7279i | 0.554437i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −49.0000 | −2.13043 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 4.24264i | − | 0.183769i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 14.6969i | 0.635404i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 20.7846 | + | 21.2132i | 0.895257 | + | 0.913717i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17.0000 | 0.730887 | 0.365444 | − | 0.930834i | \(-0.380917\pi\) | ||||
0.365444 | + | 0.930834i | \(0.380917\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 22.5167 | 0.964508 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 41.0000 | 1.75303 | 0.876517 | − | 0.481371i | \(-0.159861\pi\) | ||||
0.876517 | + | 0.481371i | \(0.159861\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −10.3923 | −0.442727 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.00000 | − | 12.2474i | −0.212622 | − | 0.520814i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 8.48528i | 0.359533i | 0.983709 | + | 0.179766i | \(0.0575342\pi\) | ||||
−0.983709 | + | 0.179766i | \(0.942466\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 17.1464i | 0.725217i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −20.7846 | −0.875967 | −0.437983 | − | 0.898983i | \(-0.644307\pi\) | ||||
−0.437983 | + | 0.898983i | \(0.644307\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 22.0454i | 0.927457i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 33.9411i | − | 1.42289i | −0.702744 | − | 0.711443i | \(-0.748042\pi\) | ||
0.702744 | − | 0.711443i | \(-0.251958\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −25.0000 | −1.04622 | −0.523109 | − | 0.852266i | \(-0.675228\pi\) | ||||
−0.523109 | + | 0.852266i | \(0.675228\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 16.9706i | 0.707721i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 19.5959i | 0.815789i | 0.913029 | + | 0.407894i | \(0.133737\pi\) | ||||
−0.913029 | + | 0.407894i | \(0.866263\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12.1244 | + | 29.6985i | 0.503003 | + | 1.23210i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −41.5692 | −1.71575 | −0.857873 | − | 0.513862i | \(-0.828214\pi\) | ||||
−0.857873 | + | 0.513862i | \(0.828214\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 18.0000 | 0.741677 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8.66025 | 0.355634 | 0.177817 | − | 0.984064i | \(-0.443096\pi\) | ||||
0.177817 | + | 0.984064i | \(0.443096\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.00000 | − | 7.34847i | −0.122988 | − | 0.301258i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 4.24264i | − | 0.173350i | −0.996237 | − | 0.0866748i | \(-0.972376\pi\) | ||
0.996237 | − | 0.0866748i | \(-0.0276241\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22.0454i | 0.899251i | 0.893217 | + | 0.449625i | \(0.148443\pi\) | ||||
−0.893217 | + | 0.449625i | \(0.851557\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −12.1244 | −0.492925 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 26.9444i | − | 1.09364i | −0.837251 | − | 0.546819i | \(-0.815838\pi\) | ||
0.837251 | − | 0.546819i | \(-0.184162\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 29.6985i | 1.20147i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.00000 | −0.161558 | −0.0807792 | − | 0.996732i | \(-0.525741\pi\) | ||||
−0.0807792 | + | 0.996732i | \(0.525741\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 25.4558i | 1.02481i | 0.858743 | + | 0.512407i | \(0.171246\pi\) | ||||
−0.858743 | + | 0.512407i | \(0.828754\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.44949i | 0.0984533i | 0.998788 | + | 0.0492267i | \(0.0156757\pi\) | ||||
−0.998788 | + | 0.0492267i | \(0.984324\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −10.3923 | − | 25.4558i | −0.416359 | − | 1.01987i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11.0000 | −0.440000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.73205 | 0.0690614 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −37.0000 | −1.47295 | −0.736473 | − | 0.676467i | \(-0.763510\pi\) | ||||
−0.736473 | + | 0.676467i | \(0.763510\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −22.5167 | −0.893546 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −12.0000 | − | 12.2474i | −0.475457 | − | 0.485262i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 21.2132i | 0.837871i | 0.908016 | + | 0.418936i | \(0.137597\pi\) | ||||
−0.908016 | + | 0.418936i | \(0.862403\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14.6969i | 0.579591i | 0.957089 | + | 0.289795i | \(0.0935872\pi\) | ||||
−0.957089 | + | 0.289795i | \(0.906413\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −20.7846 | −0.817127 | −0.408564 | − | 0.912730i | \(-0.633970\pi\) | ||||
−0.408564 | + | 0.912730i | \(0.633970\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 36.7423i | − | 1.44226i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 29.6985i | − | 1.16219i | −0.813835 | − | 0.581096i | \(-0.802624\pi\) | ||
0.813835 | − | 0.581096i | \(-0.197376\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 18.0000 | 0.703318 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 16.9706i | 0.661079i | 0.943792 | + | 0.330540i | \(0.107231\pi\) | ||||
−0.943792 | + | 0.330540i | \(0.892769\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 12.2474i | − | 0.476371i | −0.971220 | − | 0.238185i | \(-0.923447\pi\) | ||
0.971220 | − | 0.238185i | \(-0.0765525\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −10.3923 | + | 4.24264i | −0.402996 | + | 0.164523i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −36.0000 | −1.39393 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −10.3923 | −0.401190 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16.0000 | 0.616755 | 0.308377 | − | 0.951264i | \(-0.400214\pi\) | ||||
0.308377 | + | 0.951264i | \(0.400214\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −31.1769 | −1.19823 | −0.599113 | − | 0.800664i | \(-0.704480\pi\) | ||||
−0.599113 | + | 0.800664i | \(0.704480\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.00000 | − | 2.44949i | 0.230259 | − | 0.0940028i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 38.1838i | 1.46106i | 0.682880 | + | 0.730531i | \(0.260727\pi\) | ||||
−0.682880 | + | 0.730531i | \(0.739273\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 36.7423i | 1.40385i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 22.0454i | 0.838647i | 0.907837 | + | 0.419323i | \(0.137733\pi\) | ||||
−0.907837 | + | 0.419323i | \(0.862267\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 21.2132i | 0.804663i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.00000 | −0.113633 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 12.7279i | − | 0.480727i | −0.970683 | − | 0.240363i | \(-0.922733\pi\) | ||
0.970683 | − | 0.240363i | \(-0.0772666\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 2.44949i | − | 0.0923843i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 10.3923 | + | 25.4558i | 0.390843 | + | 0.957366i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 49.0000 | 1.84023 | 0.920117 | − | 0.391644i | \(-0.128094\pi\) | ||||
0.920117 | + | 0.391644i | \(0.128094\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 62.3538 | 2.33517 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 18.0000 | 0.673162 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −32.9090 | −1.22730 | −0.613649 | − | 0.789579i | \(-0.710299\pi\) | ||||
−0.613649 | + | 0.789579i | \(0.710299\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 48.0000 | − | 19.5959i | 1.78761 | − | 0.729790i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 8.48528i | 0.315135i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7.34847i | 0.272540i | 0.990672 | + | 0.136270i | \(0.0435114\pi\) | ||||
−0.990672 | + | 0.136270i | \(0.956489\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 12.1244 | 0.448435 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 29.3939i | − | 1.08569i | −0.839834 | − | 0.542844i | \(-0.817348\pi\) | ||
0.839834 | − | 0.542844i | \(-0.182652\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 42.4264i | 1.56280i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 38.0000 | 1.39785 | 0.698926 | − | 0.715194i | \(-0.253662\pi\) | ||||
0.698926 | + | 0.715194i | \(0.253662\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 21.2132i | 0.778237i | 0.921188 | + | 0.389118i | \(0.127220\pi\) | ||||
−0.921188 | + | 0.389118i | \(0.872780\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 22.0454i | 0.807681i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 20.7846 | − | 8.48528i | 0.759453 | − | 0.310045i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10.0000 | 0.364905 | 0.182453 | − | 0.983215i | \(-0.441596\pi\) | ||||
0.182453 | + | 0.983215i | \(0.441596\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −8.66025 | −0.315179 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −53.0000 | −1.92632 | −0.963159 | − | 0.268933i | \(-0.913329\pi\) | ||||
−0.963159 | + | 0.268933i | \(0.913329\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −22.5167 | −0.816228 | −0.408114 | − | 0.912931i | \(-0.633813\pi\) | ||||
−0.408114 | + | 0.912931i | \(0.633813\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −13.0000 | − | 31.8434i | −0.470632 | − | 1.15281i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 21.2132i | 0.765964i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.89898i | 0.176662i | 0.996091 | + | 0.0883309i | \(0.0281533\pi\) | ||||
−0.996091 | + | 0.0883309i | \(0.971847\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −39.8372 | −1.43284 | −0.716422 | − | 0.697668i | \(-0.754221\pi\) | ||||
−0.716422 | + | 0.697668i | \(0.754221\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 14.6969i | − | 0.527930i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.24264i | 0.152008i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −36.0000 | −1.28818 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 12.7279i | 0.454279i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 4.89898i | − | 0.174630i | −0.996181 | − | 0.0873149i | \(-0.972171\pi\) | ||
0.996181 | − | 0.0873149i | \(-0.0278286\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 31.1769 | − | 12.7279i | 1.10852 | − | 0.452553i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.00000 | 0.213066 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 10.3923 | 0.368114 | 0.184057 | − | 0.982916i | \(-0.441077\pi\) | ||||
0.184057 | + | 0.982916i | \(0.441077\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 21.0000 | 0.742927 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −41.5692 | −1.46695 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −36.0000 | + | 14.6969i | −1.26883 | + | 0.517999i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 25.4558i | − | 0.894980i | −0.894289 | − | 0.447490i | \(-0.852318\pi\) | ||
0.894289 | − | 0.447490i | \(-0.147682\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 51.4393i | − | 1.80628i | −0.429349 | − | 0.903139i | \(-0.641257\pi\) | ||
0.429349 | − | 0.903139i | \(-0.358743\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.73205 | −0.0606711 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 17.1464i | − | 0.599878i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 25.4558i | 0.888415i | 0.895924 | + | 0.444208i | \(0.146515\pi\) | ||||
−0.895924 | + | 0.444208i | \(0.853485\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −25.0000 | −0.871445 | −0.435723 | − | 0.900081i | \(-0.643507\pi\) | ||||
−0.435723 | + | 0.900081i | \(0.643507\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 38.1838i | 1.32778i | 0.747830 | + | 0.663890i | \(0.231096\pi\) | ||||
−0.747830 | + | 0.663890i | \(0.768904\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 31.8434i | 1.10597i | 0.833193 | + | 0.552983i | \(0.186511\pi\) | ||||
−0.833193 | + | 0.552983i | \(0.813489\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −8.66025 | + | 8.48528i | −0.300060 | + | 0.293998i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −33.0000 | −1.14201 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.73205 | 0.0597970 | 0.0298985 | − | 0.999553i | \(-0.490482\pi\) | ||||
0.0298985 | + | 0.999553i | \(0.490482\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11.0000 | 0.379310 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12.1244 | 0.417091 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.00000 | + | 17.1464i | 0.240523 | + | 0.589158i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 8.48528i | − | 0.290872i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 19.5959i | − | 0.670951i | −0.942049 | − | 0.335476i | \(-0.891103\pi\) | ||
0.942049 | − | 0.335476i | \(-0.108897\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 12.1244 | 0.414160 | 0.207080 | − | 0.978324i | \(-0.433604\pi\) | ||||
0.207080 | + | 0.978324i | \(0.433604\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 39.1918i | 1.33721i | 0.743619 | + | 0.668604i | \(0.233108\pi\) | ||||
−0.743619 | + | 0.668604i | \(0.766892\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 16.9706i | 0.577685i | 0.957377 | + | 0.288842i | \(0.0932703\pi\) | ||||
−0.957377 | + | 0.288842i | \(0.906730\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 36.0000 | 1.22404 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 21.2132i | − | 0.719609i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 24.4949i | − | 0.829978i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 12.1244 | + | 29.6985i | 0.409878 | + | 1.00399i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7.00000 | −0.236373 | −0.118187 | − | 0.992991i | \(-0.537708\pi\) | ||||
−0.118187 | + | 0.992991i | \(0.537708\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 31.1769 | 1.05038 | 0.525188 | − | 0.850986i | \(-0.323995\pi\) | ||||
0.525188 | + | 0.850986i | \(0.323995\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −17.0000 | −0.572096 | −0.286048 | − | 0.958215i | \(-0.592342\pi\) | ||||
−0.286048 | + | 0.958215i | \(0.592342\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −19.0526 | −0.639722 | −0.319861 | − | 0.947464i | \(-0.603636\pi\) | ||||
−0.319861 | + | 0.947464i | \(0.603636\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 13.0000 | + | 31.8434i | 0.436006 | + | 1.06799i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 29.6985i | − | 0.993822i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.34847i | 0.245632i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 31.1769 | 1.03981 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 8.48528i | − | 0.282060i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 13.0000 | 0.431658 | 0.215829 | − | 0.976431i | \(-0.430755\pi\) | ||||
0.215829 | + | 0.976431i | \(0.430755\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 29.6985i | − | 0.983955i | −0.870608 | − | 0.491977i | \(-0.836274\pi\) | ||
0.870608 | − | 0.491977i | \(-0.163726\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 51.4393i | 1.70239i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −10.3923 | − | 25.4558i | −0.343184 | − | 0.840626i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −5.00000 | −0.164935 | −0.0824674 | − | 0.996594i | \(-0.526280\pi\) | ||||
−0.0824674 | + | 0.996594i | \(0.526280\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 20.7846 | 0.684134 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.00000 | −0.0657596 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −39.8372 | −1.30702 | −0.653508 | − | 0.756920i | \(-0.726703\pi\) | ||||
−0.653508 | + | 0.756920i | \(0.726703\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 12.0000 | + | 12.2474i | 0.393284 | + | 0.401394i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 12.7279i | − | 0.416248i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 2.44949i | − | 0.0800213i | −0.999199 | − | 0.0400107i | \(-0.987261\pi\) | ||
0.999199 | − | 0.0400107i | \(-0.0127392\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −53.6936 | −1.75036 | −0.875180 | − | 0.483797i | \(-0.839257\pi\) | ||||
−0.875180 | + | 0.483797i | \(0.839257\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 14.6969i | 0.478598i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 16.9706i | 0.551469i | 0.961234 | + | 0.275735i | \(0.0889211\pi\) | ||||
−0.961234 | + | 0.275735i | \(0.911079\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 24.0000 | 0.779073 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 50.9117i | − | 1.64919i | −0.565723 | − | 0.824596i | \(-0.691403\pi\) | ||
0.565723 | − | 0.824596i | \(-0.308597\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 14.6969i | − | 0.475582i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 51.9615 | − | 21.2132i | 1.67793 | − | 0.685010i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23.0000 | −0.741935 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 12.1244 | 0.390297 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −46.0000 | −1.47926 | −0.739630 | − | 0.673014i | \(-0.765000\pi\) | ||||
−0.739630 | + | 0.673014i | \(0.765000\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −32.9090 | −1.05610 | −0.528049 | − | 0.849214i | \(-0.677076\pi\) | ||||
−0.528049 | + | 0.849214i | \(0.677076\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 30.0000 | − | 12.2474i | 0.961756 | − | 0.392635i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 42.4264i | 1.35734i | 0.734443 | + | 0.678671i | \(0.237444\pi\) | ||||
−0.734443 | + | 0.678671i | \(0.762556\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 44.0908i | − | 1.40915i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.73205 | −0.0552438 | −0.0276219 | − | 0.999618i | \(-0.508793\pi\) | ||||
−0.0276219 | + | 0.999618i | \(0.508793\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 36.7423i | 1.17071i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 59.3970i | − | 1.88871i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 55.0000 | 1.74713 | 0.873566 | − | 0.486705i | \(-0.161801\pi\) | ||||
0.873566 | + | 0.486705i | \(0.161801\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 16.9706i | 0.538003i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 36.7423i | − | 1.16364i | −0.813317 | − | 0.581821i | \(-0.802340\pi\) | ||
0.813317 | − | 0.581821i | \(-0.197660\pi\) | |||||||
\(998\) | 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 | 756.2.f.d.377.3 | yes | 4 | |
3.2 | odd | 2 | inner | 756.2.f.d.377.1 | ✓ | 4 | |
4.3 | odd | 2 | 3024.2.k.h.1889.4 | 4 | |||
7.6 | odd | 2 | inner | 756.2.f.d.377.2 | yes | 4 | |
9.2 | odd | 6 | 2268.2.x.j.377.3 | 8 | |||
9.4 | even | 3 | 2268.2.x.j.1889.2 | 8 | |||
9.5 | odd | 6 | 2268.2.x.j.1889.4 | 8 | |||
9.7 | even | 3 | 2268.2.x.j.377.1 | 8 | |||
12.11 | even | 2 | 3024.2.k.h.1889.2 | 4 | |||
21.20 | even | 2 | inner | 756.2.f.d.377.4 | yes | 4 | |
28.27 | even | 2 | 3024.2.k.h.1889.1 | 4 | |||
63.13 | odd | 6 | 2268.2.x.j.1889.3 | 8 | |||
63.20 | even | 6 | 2268.2.x.j.377.2 | 8 | |||
63.34 | odd | 6 | 2268.2.x.j.377.4 | 8 | |||
63.41 | even | 6 | 2268.2.x.j.1889.1 | 8 | |||
84.83 | odd | 2 | 3024.2.k.h.1889.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
756.2.f.d.377.1 | ✓ | 4 | 3.2 | odd | 2 | inner | |
756.2.f.d.377.2 | yes | 4 | 7.6 | odd | 2 | inner | |
756.2.f.d.377.3 | yes | 4 | 1.1 | even | 1 | trivial | |
756.2.f.d.377.4 | yes | 4 | 21.20 | even | 2 | inner | |
2268.2.x.j.377.1 | 8 | 9.7 | even | 3 | |||
2268.2.x.j.377.2 | 8 | 63.20 | even | 6 | |||
2268.2.x.j.377.3 | 8 | 9.2 | odd | 6 | |||
2268.2.x.j.377.4 | 8 | 63.34 | odd | 6 | |||
2268.2.x.j.1889.1 | 8 | 63.41 | even | 6 | |||
2268.2.x.j.1889.2 | 8 | 9.4 | even | 3 | |||
2268.2.x.j.1889.3 | 8 | 63.13 | odd | 6 | |||
2268.2.x.j.1889.4 | 8 | 9.5 | odd | 6 | |||
3024.2.k.h.1889.1 | 4 | 28.27 | even | 2 | |||
3024.2.k.h.1889.2 | 4 | 12.11 | even | 2 | |||
3024.2.k.h.1889.3 | 4 | 84.83 | odd | 2 | |||
3024.2.k.h.1889.4 | 4 | 4.3 | odd | 2 |