Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2352,2,Mod(2255,2352)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2352, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2352.2255");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2352.h (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: | \(18.7808145554\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.8275904784.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} + 5x^{6} - 6x^{5} + 4x^{4} - 18x^{3} + 45x^{2} - 81x + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 336) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2255.5 | ||
Root | \(1.73142 - 0.0465589i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2352.2255 |
Dual form | 2352.2.h.n.2255.6 |
$q$-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 \(\left(\mathbb{Z}/2352\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1471\) | \(1765\) | \(2257\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 0.825391 | − | 1.52274i | 0.476540 | − | 0.879153i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.94333i | 1.76351i | 0.471708 | + | 0.881755i | \(0.343638\pi\) | ||||
−0.471708 | + | 0.881755i | \(0.656362\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.63746 | − | 2.51371i | −0.545820 | − | 0.837903i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.52848 | −1.06388 | −0.531938 | − | 0.846783i | \(-0.678536\pi\) | ||||
−0.531938 | + | 0.846783i | \(0.678536\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.00000 | 0.554700 | 0.277350 | − | 0.960769i | \(-0.410544\pi\) | ||||
0.277350 | + | 0.960769i | \(0.410544\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 6.00465 | + | 3.25479i | 1.55039 | + | 0.840383i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.02742i | 1.21933i | 0.792660 | + | 0.609664i | \(0.208696\pi\) | ||||
−0.792660 | + | 0.609664i | \(0.791304\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 3.04547i | − | 0.698680i | −0.936996 | − | 0.349340i | \(-0.886406\pi\) | ||
0.936996 | − | 0.349340i | \(-0.113594\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.65078 | −0.344212 | −0.172106 | − | 0.985078i | \(-0.555057\pi\) | ||||
−0.172106 | + | 0.985078i | \(0.555057\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −10.5498 | −2.10997 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.17926 | + | 0.418627i | −0.996749 | + | 0.0805648i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.80257i | 1.26320i | 0.775292 | + | 0.631602i | \(0.217603\pi\) | ||||
−0.775292 | + | 0.631602i | \(0.782397\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 1.73205i | − | 0.311086i | −0.987829 | − | 0.155543i | \(-0.950287\pi\) | ||
0.987829 | − | 0.155543i | \(-0.0497126\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.91238 | + | 5.37295i | −0.506980 | + | 0.935310i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.27492 | 0.209595 | 0.104798 | − | 0.994494i | \(-0.466581\pi\) | ||||
0.104798 | + | 0.994494i | \(0.466581\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.65078 | − | 3.04547i | 0.264337 | − | 0.487666i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.16818i | 0.338612i | 0.985563 | + | 0.169306i | \(0.0541527\pi\) | ||||
−0.985563 | + | 0.169306i | \(0.945847\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 0.837253i | − | 0.127680i | −0.997960 | − | 0.0638400i | \(-0.979665\pi\) | ||
0.997960 | − | 0.0638400i | \(-0.0203347\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 9.91238 | − | 6.45704i | 1.47765 | − | 0.962558i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.95235 | 0.722374 | 0.361187 | − | 0.932493i | \(-0.382372\pi\) | ||||
0.361187 | + | 0.932493i | \(0.382372\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.65544 | + | 4.14959i | 1.07198 | + | 0.581058i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.66181i | 1.32715i | 0.748109 | + | 0.663576i | \(0.230962\pi\) | ||||
−0.748109 | + | 0.663576i | \(0.769038\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 13.9140i | − | 1.87616i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.63746 | − | 2.51371i | −0.614246 | − | 0.332949i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −10.1316 | −1.31902 | −0.659512 | − | 0.751694i | \(-0.729237\pi\) | ||||
−0.659512 | + | 0.751694i | \(0.729237\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.2749 | −1.44361 | −0.721803 | − | 0.692099i | \(-0.756686\pi\) | ||||
−0.721803 | + | 0.692099i | \(0.756686\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 7.88666i | 0.978219i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 16.0646i | 1.96261i | 0.192468 | + | 0.981303i | \(0.438351\pi\) | ||||
−0.192468 | + | 0.981303i | \(0.561649\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.36254 | + | 2.51371i | −0.164031 | + | 0.302615i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.3585 | −1.22933 | −0.614665 | − | 0.788788i | \(-0.710709\pi\) | ||||
−0.614665 | + | 0.788788i | \(0.710709\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.27492 | −0.851465 | −0.425732 | − | 0.904849i | \(-0.639983\pi\) | ||||
−0.425732 | + | 0.904849i | \(0.639983\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −8.70774 | + | 16.0646i | −1.00548 | + | 1.85498i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.19615i | 0.584613i | 0.956325 | + | 0.292306i | \(0.0944227\pi\) | ||||
−0.956325 | + | 0.292306i | \(0.905577\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.63746 | + | 8.23219i | −0.404162 | + | 0.914687i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.17926 | −0.568498 | −0.284249 | − | 0.958751i | \(-0.591744\pi\) | ||||
−0.284249 | + | 0.958751i | \(0.591744\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −19.8248 | −2.15030 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 10.3585 | + | 5.61478i | 1.11055 | + | 0.601968i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 7.19559i | − | 0.762731i | −0.924424 | − | 0.381366i | \(-0.875454\pi\) | ||
0.924424 | − | 0.381366i | \(-0.124546\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.63746 | − | 1.42962i | −0.273492 | − | 0.148245i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 12.0093 | 1.23213 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.27492 | 0.434052 | 0.217026 | − | 0.976166i | \(-0.430364\pi\) | ||||
0.217026 | + | 0.976166i | \(0.430364\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.77774 | + | 8.86957i | 0.580685 | + | 0.891425i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 12.9141i | − | 1.28500i | −0.766286 | − | 0.642499i | \(-0.777898\pi\) | ||
0.766286 | − | 0.642499i | \(-0.222102\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.83507i | 0.476414i | 0.971214 | + | 0.238207i | \(0.0765596\pi\) | ||||
−0.971214 | + | 0.238207i | \(0.923440\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.226914 | −0.0219366 | −0.0109683 | − | 0.999940i | \(-0.503491\pi\) | ||||
−0.0109683 | + | 0.999940i | \(0.503491\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.82475 | −0.749475 | −0.374738 | − | 0.927131i | \(-0.622267\pi\) | ||||
−0.374738 | + | 0.927131i | \(0.622267\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.05231 | − | 1.94136i | 0.0998804 | − | 0.184266i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 2.16818i | − | 0.203965i | −0.994786 | − | 0.101982i | \(-0.967481\pi\) | ||
0.994786 | − | 0.101982i | \(-0.0325186\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 6.50958i | − | 0.607021i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.27492 | − | 5.02742i | −0.302766 | − | 0.464785i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.45017 | 0.131833 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.30156 | + | 1.78959i | 0.297692 | + | 0.161362i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 21.8848i | − | 1.95744i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 4.77753i | − | 0.423937i | −0.977277 | − | 0.211968i | \(-0.932013\pi\) | ||
0.977277 | − | 0.211968i | \(-0.0679874\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.27492 | − | 0.691062i | −0.112250 | − | 0.0608446i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.52848 | 0.308285 | 0.154142 | − | 0.988049i | \(-0.450739\pi\) | ||||
0.154142 | + | 0.988049i | \(0.450739\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.65078 | − | 20.4235i | −0.142077 | − | 1.75778i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.691062i | 0.0590414i | 0.999564 | + | 0.0295207i | \(0.00939809\pi\) | ||||
−0.999564 | + | 0.0295207i | \(0.990602\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 20.8997i | 1.77269i | 0.463026 | + | 0.886345i | \(0.346764\pi\) | ||||
−0.463026 | + | 0.886345i | \(0.653236\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.08762 | − | 7.54112i | 0.344240 | − | 0.635077i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −7.05696 | −0.590133 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −26.8248 | −2.22767 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 7.19559i | − | 0.589486i | −0.955577 | − | 0.294743i | \(-0.904766\pi\) | ||
0.955577 | − | 0.294743i | \(-0.0952340\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.894797i | 0.0728176i | 0.999337 | + | 0.0364088i | \(0.0115918\pi\) | ||||
−0.999337 | + | 0.0364088i | \(0.988408\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 12.6375 | − | 8.23219i | 1.02168 | − | 0.665533i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.83004 | 0.548602 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.3746 | 1.14722 | 0.573608 | − | 0.819130i | \(-0.305543\pi\) | ||||
0.573608 | + | 0.819130i | \(0.305543\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 14.7124 | + | 7.97477i | 1.16677 | + | 0.632440i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.50958i | 0.509869i | 0.966958 | + | 0.254935i | \(0.0820540\pi\) | ||||
−0.966958 | + | 0.254935i | \(0.917946\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −21.1873 | − | 11.4845i | −1.64943 | − | 0.894063i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 14.1139 | 1.09217 | 0.546084 | − | 0.837731i | \(-0.316118\pi\) | ||||
0.546084 | + | 0.837731i | \(0.316118\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.65544 | + | 4.98684i | −0.585426 | + | 0.381353i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.57772i | 0.652152i | 0.945344 | + | 0.326076i | \(0.105727\pi\) | ||||
−0.945344 | + | 0.326076i | \(0.894273\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −8.36254 | + | 15.4278i | −0.628567 | + | 1.15962i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.25391 | 0.616926 | 0.308463 | − | 0.951236i | \(-0.400185\pi\) | ||||
0.308463 | + | 0.951236i | \(0.400185\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.0997 | 1.12235 | 0.561175 | − | 0.827697i | \(-0.310350\pi\) | ||||
0.561175 | + | 0.827697i | \(0.310350\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.30622 | + | 17.1687i | −0.687935 | + | 1.26915i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.02742i | 0.369623i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 17.7391i | − | 1.29721i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −18.6124 | −1.34675 | −0.673374 | − | 0.739302i | \(-0.735156\pi\) | ||||
−0.673374 | + | 0.739302i | \(0.735156\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.0997 | 0.870953 | 0.435477 | − | 0.900200i | \(-0.356580\pi\) | ||||
0.435477 | + | 0.900200i | \(0.356580\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 12.0093 | + | 6.50958i | 0.860004 | + | 0.466160i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 17.9415i | 1.27828i | 0.769091 | + | 0.639139i | \(0.220709\pi\) | ||||
−0.769091 | + | 0.639139i | \(0.779291\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 21.2032i | − | 1.50306i | −0.659700 | − | 0.751529i | \(-0.729317\pi\) | ||
0.659700 | − | 0.751529i | \(-0.270683\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 24.4622 | + | 13.2596i | 1.72543 | + | 0.935260i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.54983 | −0.597146 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.70309 | + | 4.14959i | 0.187878 | + | 0.288416i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 10.7459i | 0.743309i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.78959i | 0.123201i | 0.998101 | + | 0.0616004i | \(0.0196204\pi\) | ||||
−0.998101 | + | 0.0616004i | \(0.980380\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −8.54983 | + | 15.7733i | −0.585825 | + | 1.08077i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.30156 | 0.225165 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −6.00465 | + | 11.0778i | −0.405757 | + | 0.748568i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 10.0548i | 0.676361i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 10.0312i | − | 0.671740i | −0.941908 | − | 0.335870i | \(-0.890970\pi\) | ||
0.941908 | − | 0.335870i | \(-0.109030\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 17.2749 | + | 26.5192i | 1.15166 | + | 1.76795i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 27.5471 | 1.82836 | 0.914182 | − | 0.405303i | \(-0.132834\pi\) | ||||
0.914182 | + | 0.405303i | \(0.132834\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.72508 | 0.576570 | 0.288285 | − | 0.957545i | \(-0.406915\pi\) | ||||
0.288285 | + | 0.957545i | \(0.406915\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 0.691062i | − | 0.0452730i | −0.999744 | − | 0.0226365i | \(-0.992794\pi\) | ||
0.999744 | − | 0.0226365i | \(-0.00720603\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 19.5287i | 1.27391i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 7.91238 | + | 4.28886i | 0.513964 | + | 0.278591i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 16.9617 | 1.09716 | 0.548579 | − | 0.836099i | \(-0.315169\pi\) | ||||
0.548579 | + | 0.836099i | \(0.315169\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.00000 | 0.450910 | 0.225455 | − | 0.974254i | \(-0.427613\pi\) | ||||
0.225455 | + | 0.974254i | \(0.427613\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 9.53313 | + | 12.3337i | 0.611551 | + | 0.791205i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 6.09095i | − | 0.387558i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.27492 | + | 7.88666i | −0.270912 | + | 0.499796i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 11.7824 | 0.743698 | 0.371849 | − | 0.928293i | \(-0.378724\pi\) | ||||
0.371849 | + | 0.928293i | \(0.378724\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.82475 | 0.366199 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −16.3632 | + | 30.1879i | −1.02470 | + | 1.89044i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 17.2504i | 1.07605i | 0.842928 | + | 0.538026i | \(0.180830\pi\) | ||||
−0.842928 | + | 0.538026i | \(0.819170\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 17.0997 | − | 11.1389i | 1.05844 | − | 0.689482i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −21.9140 | −1.35128 | −0.675638 | − | 0.737234i | \(-0.736132\pi\) | ||||
−0.675638 | + | 0.737234i | \(0.736132\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −38.0997 | −2.34044 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −10.9570 | − | 5.93918i | −0.670558 | − | 0.363472i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 3.94333i | − | 0.240429i | −0.992748 | − | 0.120214i | \(-0.961642\pi\) | ||
0.992748 | − | 0.120214i | \(-0.0383582\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 3.40656i | − | 0.206934i | −0.994633 | − | 0.103467i | \(-0.967006\pi\) | ||
0.994633 | − | 0.103467i | \(-0.0329936\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 37.2249 | 2.24474 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 13.2749 | 0.797612 | 0.398806 | − | 0.917035i | \(-0.369425\pi\) | ||||
0.398806 | + | 0.917035i | \(0.369425\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.35387 | + | 2.83616i | −0.260659 | + | 0.169797i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 15.7733i | − | 0.940957i | −0.882411 | − | 0.470478i | \(-0.844081\pi\) | ||
0.882411 | − | 0.470478i | \(-0.155919\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 20.4811i | − | 1.21747i | −0.793372 | − | 0.608737i | \(-0.791677\pi\) | ||
0.793372 | − | 0.608737i | \(-0.208323\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 9.91238 | − | 18.2870i | 0.587158 | − | 1.08323i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.27492 | −0.486760 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.52848 | − | 6.50958i | 0.206843 | − | 0.381598i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 13.3071i | 0.777409i | 0.921362 | + | 0.388705i | \(0.127077\pi\) | ||||
−0.921362 | + | 0.388705i | \(0.872923\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 39.9523i | − | 2.32611i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 18.2749 | − | 1.47712i | 1.06042 | − | 0.0857109i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.30156 | −0.190934 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −19.6647 | − | 10.6592i | −1.12971 | − | 0.612353i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 44.4607i | − | 2.54581i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 17.3205i | − | 0.988534i | −0.869310 | − | 0.494267i | \(-0.835437\pi\) | ||
0.869310 | − | 0.494267i | \(-0.164563\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.36254 | + | 3.99082i | 0.418840 | + | 0.227030i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 22.3678 | 1.26836 | 0.634182 | − | 0.773184i | \(-0.281337\pi\) | ||||
0.634182 | + | 0.773184i | \(0.281337\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.45017 | −0.251538 | −0.125769 | − | 0.992060i | \(-0.540140\pi\) | ||||
−0.125769 | + | 0.992060i | \(0.540140\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.11151i | 0.343256i | 0.985162 | + | 0.171628i | \(0.0549028\pi\) | ||||
−0.985162 | + | 0.171628i | \(0.945097\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 24.0027i | − | 1.34389i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.187293 | + | 0.345531i | −0.0104537 | + | 0.0192857i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 15.3109 | 0.851920 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −21.0997 | −1.17040 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −6.45848 | + | 11.9150i | −0.357155 | + | 0.658903i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 28.2465i | 1.55257i | 0.630382 | + | 0.776285i | \(0.282898\pi\) | ||||
−0.630382 | + | 0.776285i | \(0.717102\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.08762 | − | 3.20477i | −0.114401 | − | 0.175620i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −63.3481 | −3.46108 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −20.8248 | −1.13440 | −0.567198 | − | 0.823581i | \(-0.691973\pi\) | ||||
−0.567198 | + | 0.823581i | \(0.691973\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.30156 | − | 1.78959i | −0.179316 | − | 0.0971974i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.11151i | 0.330957i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −9.91238 | − | 5.37295i | −0.533664 | − | 0.289270i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 22.3678 | 1.20077 | 0.600384 | − | 0.799712i | \(-0.295014\pi\) | ||||
0.600384 | + | 0.799712i | \(0.295014\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.45017 | 0.291741 | 0.145870 | − | 0.989304i | \(-0.453402\pi\) | ||||
0.145870 | + | 0.989304i | \(0.453402\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −10.3585 | + | 0.837253i | −0.552897 | + | 0.0446893i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.02742i | 0.267582i | 0.991010 | + | 0.133791i | \(0.0427151\pi\) | ||||
−0.991010 | + | 0.133791i | \(0.957285\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 40.8471i | − | 2.16794i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 22.8217 | 1.20448 | 0.602241 | − | 0.798315i | \(-0.294275\pi\) | ||||
0.602241 | + | 0.798315i | \(0.294275\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.72508 | 0.511846 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.19695 | − | 2.20822i | 0.0628238 | − | 0.115902i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 28.6874i | − | 1.50157i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 29.5600i | 1.54302i | 0.636219 | + | 0.771508i | \(0.280497\pi\) | ||||
−0.636219 | + | 0.771508i | \(0.719503\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.45017 | − | 3.55030i | 0.283724 | − | 0.184821i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 29.8248 | 1.54427 | 0.772134 | − | 0.635460i | \(-0.219190\pi\) | ||||
0.772134 | + | 0.635460i | \(0.219190\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −33.3248 | − | 18.0635i | −1.72089 | − | 0.932797i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 13.6051i | 0.700700i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 10.3923i | − | 0.533817i | −0.963722 | − | 0.266908i | \(-0.913998\pi\) | ||
0.963722 | − | 0.266908i | \(-0.0860021\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7.27492 | − | 3.94333i | −0.372705 | − | 0.202023i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −28.9710 | −1.48035 | −0.740173 | − | 0.672416i | \(-0.765257\pi\) | ||||
−0.740173 | + | 0.672416i | \(0.765257\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.10461 | + | 1.37097i | −0.106983 | + | 0.0696902i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 22.9689i | 1.16457i | 0.812985 | + | 0.582285i | \(0.197841\pi\) | ||||
−0.812985 | + | 0.582285i | \(0.802159\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 8.29917i | − | 0.419707i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.91238 | − | 5.37295i | 0.146910 | − | 0.271029i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −20.4901 | −1.03097 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.37459 | 0.319931 | 0.159966 | − | 0.987123i | \(-0.448862\pi\) | ||||
0.159966 | + | 0.987123i | \(0.448862\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 36.5740i | − | 1.82642i | −0.407489 | − | 0.913210i | \(-0.633595\pi\) | ||
0.407489 | − | 0.913210i | \(-0.366405\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 3.46410i | − | 0.172559i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −32.4622 | − | 14.3437i | −1.61306 | − | 0.712744i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.49852 | −0.222983 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −16.4502 | −0.813408 | −0.406704 | − | 0.913560i | \(-0.633322\pi\) | ||||
−0.406704 | + | 0.913560i | \(0.633322\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.05231 | + | 0.570396i | 0.0519064 | + | 0.0281356i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 20.4235i | − | 1.00255i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 31.8248 | + | 17.2504i | 1.55846 | + | 0.844757i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 30.1679 | 1.47380 | 0.736899 | − | 0.676002i | \(-0.236289\pi\) | ||||
0.736899 | + | 0.676002i | \(0.236289\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.0997 | 0.540965 | 0.270482 | − | 0.962725i | \(-0.412817\pi\) | ||||
0.270482 | + | 0.962725i | \(0.412817\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −8.10926 | − | 12.4488i | −0.394286 | − | 0.605279i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 53.0384i | − | 2.57274i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5.82475 | + | 10.7459i | −0.281222 | + | 0.518817i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −25.6694 | −1.23645 | −0.618226 | − | 0.786001i | \(-0.712148\pi\) | ||||
−0.618226 | + | 0.786001i | \(0.712148\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.00000 | −0.0961139 | −0.0480569 | − | 0.998845i | \(-0.515303\pi\) | ||||
−0.0480569 | + | 0.998845i | \(0.515303\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −22.1409 | + | 40.8471i | −1.06158 | + | 1.95847i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.02742i | 0.240494i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 9.61260i | − | 0.458784i | −0.973334 | − | 0.229392i | \(-0.926326\pi\) | ||
0.973334 | − | 0.229392i | \(-0.0736738\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −34.1502 | −1.62253 | −0.811263 | − | 0.584681i | \(-0.801220\pi\) | ||||
−0.811263 | + | 0.584681i | \(0.801220\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 28.3746 | 1.34508 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −10.9570 | − | 5.93918i | −0.518248 | − | 0.280914i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 29.3784i | − | 1.38645i | −0.720719 | − | 0.693227i | \(-0.756188\pi\) | ||
0.720719 | − | 0.693227i | \(-0.243812\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 7.65037i | − | 0.360242i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.36254 | + | 0.738558i | 0.0640178 | + | 0.0347005i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 28.6495 | 1.34017 | 0.670084 | − | 0.742286i | \(-0.266258\pi\) | ||||
0.670084 | + | 0.742286i | \(0.266258\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.10461 | − | 26.0383i | −0.0982348 | − | 1.21536i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13.6051i | 0.633654i | 0.948483 | + | 0.316827i | \(0.102618\pi\) | ||||
−0.948483 | + | 0.316827i | \(0.897382\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.9715i | 0.649310i | 0.945832 | + | 0.324655i | \(0.105248\pi\) | ||||
−0.945832 | + | 0.324655i | \(0.894752\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 5.63746 | − | 10.4004i | 0.261431 | − | 0.482305i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −28.9710 | −1.34062 | −0.670308 | − | 0.742083i | \(-0.733838\pi\) | ||||
−0.670308 | + | 0.742083i | \(0.733838\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 11.8647 | − | 21.8887i | 0.546695 | − | 1.00858i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.95423i | 0.135836i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 32.1293i | 1.47419i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 24.2870 | − | 15.8208i | 1.11202 | − | 0.724385i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.49852 | 0.205543 | 0.102771 | − | 0.994705i | \(-0.467229\pi\) | ||||
0.102771 | + | 0.994705i | \(0.467229\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.54983 | 0.116262 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 16.8574i | 0.765455i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.56930i | 0.116426i | 0.998304 | + | 0.0582131i | \(0.0185403\pi\) | ||||
−0.998304 | + | 0.0582131i | \(0.981460\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 9.91238 | + | 5.37295i | 0.448253 | + | 0.242973i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −22.1409 | −0.999206 | −0.499603 | − | 0.866255i | \(-0.666521\pi\) | ||||
−0.499603 | + | 0.866255i | \(0.666521\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −34.1993 | −1.54026 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −34.9756 | + | 22.7835i | −1.57204 | + | 1.02404i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 25.6197i | 1.14689i | 0.819243 | + | 0.573447i | \(0.194394\pi\) | ||||
−0.819243 | + | 0.573447i | \(0.805606\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 11.6495 | − | 21.4918i | 0.520461 | − | 0.960182i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 50.9244 | 2.26611 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −7.42852 | + | 13.7046i | −0.329912 | + | 0.608644i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 9.66181i | − | 0.428252i | −0.976806 | − | 0.214126i | \(-0.931310\pi\) | ||
0.976806 | − | 0.214126i | \(-0.0686903\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.27492 | + | 15.7733i | 0.0562890 | + | 0.696409i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −19.0663 | −0.840160 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −17.4743 | −0.768517 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 13.0616 | + | 7.07997i | 0.573341 | + | 0.310776i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 19.4186i | − | 0.850745i | −0.905018 | − | 0.425372i | \(-0.860143\pi\) | ||
0.905018 | − | 0.425372i | \(-0.139857\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 24.7824i | − | 1.08366i | −0.840488 | − | 0.541830i | \(-0.817732\pi\) | ||
0.840488 | − | 0.541830i | \(-0.182268\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8.70774 | 0.379315 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.2749 | −0.881518 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 16.5901 | + | 25.4679i | 0.719949 | + | 1.10521i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.33635i | 0.187828i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 0.894797i | − | 0.0386855i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 6.81271 | − | 12.5685i | 0.293990 | − | 0.542373i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −26.7251 | −1.14900 | −0.574501 | − | 0.818504i | \(-0.694804\pi\) | ||||
−0.574501 | + | 0.818504i | \(0.694804\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 12.4631 | − | 22.9928i | 0.534844 | − | 0.986717i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 30.8556i | − | 1.32171i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 13.0192i | − | 0.556659i | −0.960486 | − | 0.278329i | \(-0.910219\pi\) | ||
0.960486 | − | 0.278329i | \(-0.0897807\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 18.4622 | + | 28.3419i | 0.787948 | + | 1.20960i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 20.7170 | 0.882576 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 7.65544 | + | 4.14959i | 0.324955 | + | 0.176140i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 15.3803i | − | 0.651684i | −0.945424 | − | 0.325842i | \(-0.894352\pi\) | ||
0.945424 | − | 0.325842i | \(-0.105648\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 1.67451i | − | 0.0708241i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −27.0120 | − | 14.6417i | −1.14045 | − | 0.618174i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −28.0009 | −1.18010 | −0.590049 | − | 0.807367i | \(-0.700892\pi\) | ||||
−0.590049 | + | 0.807367i | \(0.700892\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.54983 | 0.359694 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 37.9562i | 1.59121i | 0.605819 | + | 0.795603i | \(0.292846\pi\) | ||||
−0.605819 | + | 0.795603i | \(0.707154\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 17.8542i | − | 0.747176i | −0.927595 | − | 0.373588i | \(-0.878127\pi\) | ||
0.927595 | − | 0.373588i | \(-0.121873\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −15.3625 | + | 28.3419i | −0.641779 | + | 1.18400i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 17.4155 | 0.726276 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −34.0997 | −1.41959 | −0.709794 | − | 0.704409i | \(-0.751212\pi\) | ||||
−0.709794 | + | 0.704409i | \(0.751212\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 9.98696 | − | 18.4246i | 0.415044 | − | 0.765701i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 34.0915i | − | 1.41192i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 19.8248 | − | 12.9141i | 0.819653 | − | 0.533931i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 5.17926 | 0.213771 | 0.106886 | − | 0.994271i | \(-0.465912\pi\) | ||||
0.106886 | + | 0.994271i | \(0.465912\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.27492 | −0.217349 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 27.3202 | + | 14.8087i | 1.12380 | + | 0.609150i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 12.9141i | 0.530317i | 0.964205 | + | 0.265159i | \(0.0854243\pi\) | ||||
−0.964205 | + | 0.265159i | \(0.914576\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −32.2870 | − | 17.5010i | −1.32142 | − | 0.716267i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.19695 | −0.0489062 | −0.0244531 | − | 0.999701i | \(-0.507784\pi\) | ||||
−0.0244531 | + | 0.999701i | \(0.507784\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17.9244 | 0.731152 | 0.365576 | − | 0.930781i | \(-0.380872\pi\) | ||||
0.365576 | + | 0.930781i | \(0.380872\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 40.3818 | − | 26.3052i | 1.64447 | − | 1.07123i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.71848i | 0.232489i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 34.6986i | − | 1.40837i | −0.710016 | − | 0.704186i | \(-0.751312\pi\) | ||
0.710016 | − | 0.704186i | \(-0.248688\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.90469 | 0.400701 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 37.8248 | 1.52773 | 0.763864 | − | 0.645378i | \(-0.223300\pi\) | ||||
0.763864 | + | 0.645378i | \(0.223300\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −7.05696 | + | 13.0192i | −0.284564 | + | 0.524983i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 38.0512i | 1.53188i | 0.642911 | + | 0.765941i | \(0.277727\pi\) | ||||
−0.642911 | + | 0.765941i | \(0.722273\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 10.9260i | − | 0.439154i | −0.975595 | − | 0.219577i | \(-0.929532\pi\) | ||
0.975595 | − | 0.219577i | \(-0.0704677\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8.54983 | − | 0.691062i | 0.343093 | − | 0.0277314i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 33.5498 | 1.34199 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 16.3632 | + | 8.86957i | 0.653482 | + | 0.354216i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 6.40954i | 0.255565i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 37.0219i | − | 1.47382i | −0.675992 | − | 0.736909i | \(-0.736285\pi\) | ||
0.675992 | − | 0.736909i | \(-0.263715\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.72508 | + | 1.47712i | 0.108312 | + | 0.0587101i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 18.8394 | 0.747617 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 16.9617 | + | 26.0383i | 0.670993 | + | 1.03006i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.19559i | 0.284209i | 0.989852 | + | 0.142104i | \(0.0453869\pi\) | ||||
−0.989852 | + | 0.142104i | \(0.954613\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 6.09095i | − | 0.240204i | −0.992762 | − | 0.120102i | \(-0.961678\pi\) | ||
0.992762 | − | 0.120102i | \(-0.0383221\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.72508 | − | 5.02742i | 0.107300 | − | 0.197954i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 9.16157 | 0.360178 | 0.180089 | − | 0.983650i | \(-0.442361\pi\) | ||||
0.180089 | + | 0.983650i | \(0.442361\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 35.7492 | 1.40328 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 21.0988i | − | 0.825658i | −0.910808 | − | 0.412829i | \(-0.864541\pi\) | ||
0.910808 | − | 0.412829i | \(-0.135459\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 13.9140i | 0.543663i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 11.9124 | + | 18.2870i | 0.464746 | + | 0.713445i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −45.1895 | −1.76033 | −0.880166 | − | 0.474666i | \(-0.842569\pi\) | ||||
−0.880166 | + | 0.474666i | \(0.842569\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 29.2749 | 1.13866 | 0.569331 | − | 0.822108i | \(-0.307202\pi\) | ||||
0.569331 | + | 0.822108i | \(0.307202\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 15.3109 | + | 8.29917i | 0.594625 | + | 0.322313i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 11.2296i | − | 0.434810i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −15.2749 | − | 8.27968i | −0.590562 | − | 0.320111i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 39.7833 | 1.53582 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12.2749 | 0.473163 | 0.236582 | − | 0.971612i | \(-0.423973\pi\) | ||||
0.236582 | + | 0.971612i | \(0.423973\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 54.6404 | − | 4.41644i | 2.10311 | − | 0.169989i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 12.6160i | 0.484874i | 0.970167 | + | 0.242437i | \(0.0779467\pi\) | ||||
−0.970167 | + | 0.242437i | \(0.922053\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 22.7371 | − | 41.9470i | 0.871289 | − | 1.60741i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 24.6994 | 0.945095 | 0.472547 | − | 0.881305i | \(-0.343335\pi\) | ||||
0.472547 | + | 0.881305i | \(0.343335\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.72508 | −0.104120 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7.20161 | − | 13.2860i | 0.274758 | − | 0.506893i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 19.3236i | 0.736171i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 30.8734i | 1.17448i | 0.809413 | + | 0.587239i | \(0.199785\pi\) | ||||
−0.809413 | + | 0.587239i | \(0.800215\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −82.4144 | −3.12615 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −10.9003 | −0.412879 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.05231 | − | 0.570396i | −0.0398018 | − | 0.0215744i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 22.5759i | 0.852679i | 0.904563 | + | 0.426340i | \(0.140197\pi\) | ||||
−0.904563 | + | 0.426340i | \(0.859803\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 3.88273i | − | 0.146440i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 29.7371 | + | 16.1188i | 1.11997 | + | 0.607071i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −20.3746 | −0.765184 | −0.382592 | − | 0.923917i | \(-0.624968\pi\) | ||||
−0.382592 | + | 0.923917i | \(0.624968\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 13.0616 | − | 8.50848i | 0.489849 | − | 0.319093i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.85924i | 0.107079i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 27.8279i | − | 1.04070i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 14.0000 | − | 25.8281i | 0.522840 | − | 0.964570i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 19.0663 | 0.711052 | 0.355526 | − | 0.934666i | \(-0.384302\pi\) | ||||
0.355526 | + | 0.934666i | \(0.384302\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 5.77774 | − | 10.6592i | 0.214876 | − | 0.396419i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 71.7660i | − | 2.66532i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 10.7534i | − | 0.398821i | −0.979916 | − | 0.199411i | \(-0.936097\pi\) | ||
0.979916 | − | 0.199411i | \(-0.0639027\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 26.6495 | − | 4.33635i | 0.987019 | − | 0.160606i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.20922 | 0.155684 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 33.2749 | 1.22904 | 0.614519 | − | 0.788902i | \(-0.289350\pi\) | ||||
0.614519 | + | 0.788902i | \(0.289350\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 56.6837i | − | 2.08797i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 41.3808i | 1.52222i | 0.648625 | + | 0.761108i | \(0.275344\pi\) | ||||
−0.648625 | + | 0.761108i | \(0.724656\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −9.27492 | − | 5.02742i | −0.340723 | − | 0.184687i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −33.9233 | −1.24453 | −0.622263 | − | 0.782808i | \(-0.713786\pi\) | ||||
−0.622263 | + | 0.782808i | \(0.713786\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 28.3746 | 1.03956 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 8.48083 | + | 13.0192i | 0.310297 | + | 0.476346i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.77534i | 0.320217i | 0.987099 | + | 0.160108i | \(0.0511844\pi\) | ||||
−0.987099 | + | 0.160108i | \(0.948816\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 9.72508 | − | 17.9415i | 0.354402 | − | 0.653824i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.52848 | −0.128415 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15.0997 | −0.548807 | −0.274403 | − | 0.961615i | \(-0.588480\pi\) | ||||
−0.274403 | + | 0.961615i | \(0.588480\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.80770 | − | 8.86957i | 0.174508 | − | 0.321945i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.24136i | 0.153749i | 0.997041 | + | 0.0768746i | \(0.0244941\pi\) | ||||
−0.997041 | + | 0.0768746i | \(0.975506\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 32.4622 | + | 49.8336i | 1.17367 | + | 1.80174i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −20.2632 | −0.731662 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −28.8248 | −1.03945 | −0.519724 | − | 0.854334i | \(-0.673965\pi\) | ||||
−0.519724 | + | 0.854334i | \(0.673965\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 26.2679 | + | 14.2384i | 0.946014 | + | 0.512782i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 54.5155i | 1.96079i | 0.197049 | + | 0.980394i | \(0.436864\pi\) | ||||
−0.197049 | + | 0.980394i | \(0.563136\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 18.2728i | 0.656380i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.60313 | 0.236582 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 36.5498 | 1.30786 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.84774 | − | 35.2323i | −0.101770 | − | 1.25910i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 56.6837i | 2.02313i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 37.8016i | 1.34748i | 0.738968 | + | 0.673740i | \(0.235313\pi\) | ||||
−0.738968 | + | 0.673740i | \(0.764687\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −18.0876 | + | 33.3693i | −0.643936 | + | 1.18798i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −22.5498 | −0.800768 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −31.4471 | + | 58.0158i | −1.11531 | + | 2.05761i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 24.7441i | − | 0.876479i | −0.898858 | − | 0.438240i | \(-0.855602\pi\) | ||
0.898858 | − | 0.438240i | \(-0.144398\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 24.8975i | 0.880811i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −18.0876 | + | 11.7825i | −0.639095 | + | 0.416314i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 25.6694 | 0.905853 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −6.00465 | − | 3.25479i | −0.211374 | − | 0.114574i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 48.0110i | 1.68798i | 0.536361 | + | 0.843988i | \(0.319798\pi\) | ||||
−0.536361 | + | 0.843988i | \(0.680202\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.41644i | 0.155082i | 0.996989 | + | 0.0775411i | \(0.0247069\pi\) | ||||
−0.996989 | + | 0.0775411i | \(0.975293\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −5.18729 | − | 2.81174i | −0.181926 | − | 0.0986121i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −25.6694 | −0.899160 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.54983 | −0.0892074 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 39.8263i | 1.38995i | 0.719035 | + | 0.694974i | \(0.244584\pi\) | ||||
−0.719035 | + | 0.694974i | \(0.755416\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 19.5287i | − | 0.680729i | −0.940294 | − | 0.340364i | \(-0.889450\pi\) | ||
0.940294 | − | 0.340364i | \(-0.110550\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 30.7251 | − | 56.6837i | 1.06971 | − | 1.97347i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −8.02700 | −0.279126 | −0.139563 | − | 0.990213i | \(-0.544570\pi\) | ||||
−0.139563 | + | 0.990213i | \(0.544570\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 10.3746 | 0.360324 | 0.180162 | − | 0.983637i | \(-0.442338\pi\) | ||||
0.180162 | + | 0.983637i | \(0.442338\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 10.9570 | − | 20.2142i | 0.380094 | − | 0.701223i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 55.6558i | 1.92605i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.725083 | + | 8.97074i | 0.0250625 | + | 0.310074i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 20.7170 | 0.715232 | 0.357616 | − | 0.933869i | \(-0.383590\pi\) | ||||
0.357616 | + | 0.933869i | \(0.383590\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17.2749 | −0.595687 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −24.0186 | − | 13.0192i | −0.827245 | − | 0.448403i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 35.4900i | − | 1.22089i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −31.1873 | − | 16.9049i | −1.07035 | − | 0.580175i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.10461 | −0.0721451 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 38.5498 | 1.31992 | 0.659961 | − | 0.751300i | \(-0.270573\pi\) | ||||
0.659961 | + | 0.751300i | \(0.270573\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −19.6647 | − | 30.1879i | −0.672520 | − | 1.03240i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 24.3510i | − | 0.831815i | −0.909407 | − | 0.415908i | \(-0.863464\pi\) | ||
0.909407 | − | 0.415908i | \(-0.136536\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 40.4284i | 1.37940i | 0.724095 | + | 0.689700i | \(0.242258\pi\) | ||||
−0.724095 | + | 0.689700i | \(0.757742\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.65078 | −0.0561933 | −0.0280966 | − | 0.999605i | \(-0.508945\pi\) | ||||
−0.0280966 | + | 0.999605i | \(0.508945\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −33.8248 | −1.15008 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −6.83004 | + | 12.6005i | −0.231960 | + | 0.427936i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 18.3345i | − | 0.621956i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 32.1293i | 1.08866i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −7.00000 | − | 10.7459i | −0.236914 | − | 0.363693i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −11.8248 | −0.399293 | −0.199647 | − | 0.979868i | \(-0.563979\pi\) | ||||
−0.199647 | + | 0.979868i | \(0.563979\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 20.2632 | + | 10.9836i | 0.683461 | + | 0.370466i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 22.8739i | − | 0.770642i | −0.922783 | − | 0.385321i | \(-0.874091\pi\) | ||
0.922783 | − | 0.385321i | \(-0.125909\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 38.1051i | 1.28234i | 0.767399 | + | 0.641170i | \(0.221551\pi\) | ||||
−0.767399 | + | 0.641170i | \(0.778449\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −60.8368 | − | 32.9762i | −2.04501 | − | 1.10848i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 25.6694 | 0.861894 | 0.430947 | − | 0.902377i | \(-0.358180\pi\) | ||||
0.430947 | + | 0.902377i | \(0.358180\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 12.8347 | − | 29.0471i | 0.429979 | − | 0.973114i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 15.0822i | − | 0.504708i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 32.5479i | 1.08796i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.72508 | + | 5.02742i | −0.0909879 | + | 0.167861i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 11.7824 | 0.392965 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −48.5739 | −1.61823 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 59.5429i | 1.97927i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 43.8925i | − | 1.45743i | −0.684818 | − | 0.728714i | \(-0.740118\pi\) | ||
0.684818 | − | 0.728714i | \(-0.259882\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −32.4622 | + | 21.1463i | −1.07670 | + | 0.701377i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −17.8693 | −0.592037 | −0.296018 | − | 0.955182i | \(-0.595659\pi\) | ||||
−0.296018 | + | 0.955182i | \(0.595659\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 18.2749 | 0.604811 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −67.7020 | − | 36.6975i | −2.23816 | − | 1.21318i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 35.0596i | − | 1.15651i | −0.815856 | − | 0.578255i | \(-0.803734\pi\) | ||
0.815856 | − | 0.578255i | \(-0.196266\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −26.3746 | − | 14.2962i | −0.869072 | − | 0.471076i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −20.7170 | −0.681910 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −13.4502 | −0.442239 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 12.1540 | − | 7.91723i | 0.399188 | − | 0.260036i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 6.40954i | 0.210290i | 0.994457 | + | 0.105145i | \(0.0335307\pi\) | ||||
−0.994457 | + | 0.105145i | \(0.966469\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 18.4622 | − | 34.0603i | 0.604426 | − | 1.11509i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 69.9512 | 2.28765 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −27.1752 | −0.887777 | −0.443888 | − | 0.896082i | \(-0.646401\pi\) | ||||
−0.443888 | + | 0.896082i | \(0.646401\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.67313 | + | 6.77643i | −0.119868 | + | 0.221141i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0.393027i | 0.0128123i | 0.999979 | + | 0.00640616i | \(0.00203916\pi\) | ||||
−0.999979 | + | 0.00640616i | \(0.997961\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 3.57919i | − | 0.116554i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 12.4631 | 0.404997 | 0.202499 | − | 0.979283i | \(-0.435094\pi\) | ||||
0.202499 | + | 0.979283i | \(0.435094\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −14.5498 | −0.472308 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 9.30622 | + | 5.04438i | 0.301775 | + | 0.163575i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 60.3290i | − | 1.95425i | −0.212670 | − | 0.977124i | \(-0.568216\pi\) | ||
0.212670 | − | 0.977124i | \(-0.431784\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 73.3949i | − | 2.37500i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −36.5498 | − | 19.8116i | −1.18149 | − | 0.640419i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 28.0000 | 0.903226 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.371563 | + | 0.570396i | 0.0119734 | + | 0.0183808i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 47.7130i | 1.53593i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 30.8158i | 0.990970i | 0.868616 | + | 0.495485i | \(0.165010\pi\) | ||||
−0.868616 | + | 0.495485i | \(0.834990\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 12.6375 | − | 23.3144i | 0.405974 | − | 0.748968i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −27.5471 | −0.884028 | −0.442014 | − | 0.897008i | \(-0.645736\pi\) | ||||
−0.442014 | + | 0.897008i | \(0.645736\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −17.4155 | + | 32.1293i | −0.557742 | + | 1.02896i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 27.9013i | 0.892643i | 0.894873 | + | 0.446321i | \(0.147266\pi\) | ||||
−0.894873 | + | 0.446321i | \(0.852734\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 25.3895i | 0.811452i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 12.8127 | + | 19.6691i | 0.409078 | + | 0.627987i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −33.1802 | −1.05828 | −0.529142 | − | 0.848533i | \(-0.677486\pi\) | ||||
−0.529142 | + | 0.848533i | \(0.677486\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −70.7492 | −2.25426 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.38212i | 0.0439490i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 19.1676i | − | 0.608880i | −0.952531 | − | 0.304440i | \(-0.901531\pi\) | ||
0.952531 | − | 0.304440i | \(-0.0984694\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 43.0120 | + | 23.3144i | 1.36495 | + | 0.739861i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 83.6113 | 2.65066 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 21.2749 | 0.673783 | 0.336892 | − | 0.941543i | \(-0.390624\pi\) | ||||
0.336892 | + | 0.941543i | \(0.390624\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −6.60313 | + | 0.533714i | −0.208914 | + | 0.0168860i |
(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 | 2352.2.h.n.2255.5 | 8 | ||
3.2 | odd | 2 | inner | 2352.2.h.n.2255.3 | 8 | ||
4.3 | odd | 2 | inner | 2352.2.h.n.2255.4 | 8 | ||
7.2 | even | 3 | 336.2.bj.g.95.3 | yes | 8 | ||
7.4 | even | 3 | 336.2.bj.e.191.1 | yes | 8 | ||
7.6 | odd | 2 | 2352.2.h.m.2255.4 | 8 | |||
12.11 | even | 2 | inner | 2352.2.h.n.2255.6 | 8 | ||
21.2 | odd | 6 | 336.2.bj.g.95.4 | yes | 8 | ||
21.11 | odd | 6 | 336.2.bj.e.191.2 | yes | 8 | ||
21.20 | even | 2 | 2352.2.h.m.2255.6 | 8 | |||
28.11 | odd | 6 | 336.2.bj.g.191.4 | yes | 8 | ||
28.23 | odd | 6 | 336.2.bj.e.95.2 | yes | 8 | ||
28.27 | even | 2 | 2352.2.h.m.2255.5 | 8 | |||
84.11 | even | 6 | 336.2.bj.g.191.3 | yes | 8 | ||
84.23 | even | 6 | 336.2.bj.e.95.1 | ✓ | 8 | ||
84.83 | odd | 2 | 2352.2.h.m.2255.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
336.2.bj.e.95.1 | ✓ | 8 | 84.23 | even | 6 | ||
336.2.bj.e.95.2 | yes | 8 | 28.23 | odd | 6 | ||
336.2.bj.e.191.1 | yes | 8 | 7.4 | even | 3 | ||
336.2.bj.e.191.2 | yes | 8 | 21.11 | odd | 6 | ||
336.2.bj.g.95.3 | yes | 8 | 7.2 | even | 3 | ||
336.2.bj.g.95.4 | yes | 8 | 21.2 | odd | 6 | ||
336.2.bj.g.191.3 | yes | 8 | 84.11 | even | 6 | ||
336.2.bj.g.191.4 | yes | 8 | 28.11 | odd | 6 | ||
2352.2.h.m.2255.3 | 8 | 84.83 | odd | 2 | |||
2352.2.h.m.2255.4 | 8 | 7.6 | odd | 2 | |||
2352.2.h.m.2255.5 | 8 | 28.27 | even | 2 | |||
2352.2.h.m.2255.6 | 8 | 21.20 | even | 2 | |||
2352.2.h.n.2255.3 | 8 | 3.2 | odd | 2 | inner | ||
2352.2.h.n.2255.4 | 8 | 4.3 | odd | 2 | inner | ||
2352.2.h.n.2255.5 | 8 | 1.1 | even | 1 | trivial | ||
2352.2.h.n.2255.6 | 8 | 12.11 | even | 2 | inner |