Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2304,2,Mod(577,2304)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2304, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2304.577");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2304 = 2^{8} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2304.k (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(18.3975326257\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | no (minimal twist has level 768) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1729.4 | ||
Root | \(0.258819 - 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2304.1729 |
Dual form | 2304.2.k.e.577.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2304\mathbb{Z}\right)^\times\).
\(n\) | \(1279\) | \(1793\) | \(2053\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.732051 | + | 0.732051i | 0.327383 | + | 0.327383i | 0.851591 | − | 0.524207i | \(-0.175638\pi\) |
−0.524207 | + | 0.851591i | \(0.675638\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.44949i | 0.925820i | 0.886405 | + | 0.462910i | \(0.153195\pi\) | ||||
−0.886405 | + | 0.462910i | \(0.846805\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.86370 | + | 3.86370i | 1.16495 | + | 1.16495i | 0.983377 | + | 0.181573i | \(0.0581188\pi\) |
0.181573 | + | 0.983377i | \(0.441881\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.00000 | − | 3.00000i | 0.832050 | − | 0.832050i | −0.155747 | − | 0.987797i | \(-0.549778\pi\) |
0.987797 | + | 0.155747i | \(0.0497784\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.46410 | 0.840168 | 0.420084 | − | 0.907485i | \(-0.362001\pi\) | ||||
0.420084 | + | 0.907485i | \(0.362001\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.378937 | − | 0.378937i | 0.0869342 | − | 0.0869342i | −0.662302 | − | 0.749237i | \(-0.730421\pi\) |
0.749237 | + | 0.662302i | \(0.230421\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 2.82843i | − | 0.589768i | −0.955533 | − | 0.294884i | \(-0.904719\pi\) | ||
0.955533 | − | 0.294884i | \(-0.0952810\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 3.92820i | − | 0.785641i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.19615 | + | 4.19615i | −0.779206 | + | 0.779206i | −0.979696 | − | 0.200490i | \(-0.935747\pi\) |
0.200490 | + | 0.979696i | \(0.435747\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.34847 | 1.31982 | 0.659912 | − | 0.751343i | \(-0.270594\pi\) | ||||
0.659912 | + | 0.751343i | \(0.270594\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.79315 | + | 1.79315i | −0.303098 | + | 0.303098i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.46410 | − | 6.46410i | −1.06269 | − | 1.06269i | −0.997899 | − | 0.0647930i | \(-0.979361\pi\) |
−0.0647930 | − | 0.997899i | \(-0.520639\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 11.4641i | 1.79039i | 0.445673 | + | 0.895196i | \(0.352964\pi\) | ||||
−0.445673 | + | 0.895196i | \(0.647036\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.44949 | − | 2.44949i | −0.373544 | − | 0.373544i | 0.495222 | − | 0.868766i | \(-0.335087\pi\) |
−0.868766 | + | 0.495222i | \(0.835087\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.82843 | 0.412568 | 0.206284 | − | 0.978492i | \(-0.433863\pi\) | ||||
0.206284 | + | 0.978492i | \(0.433863\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.73205 | − | 6.73205i | −0.924718 | − | 0.924718i | 0.0726399 | − | 0.997358i | \(-0.476858\pi\) |
−0.997358 | + | 0.0726399i | \(0.976858\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.65685i | 0.762770i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.79796 | + | 9.79796i | 1.27559 | + | 1.27559i | 0.943113 | + | 0.332473i | \(0.107883\pi\) |
0.332473 | + | 0.943113i | \(0.392117\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.46410 | + | 6.46410i | −0.827643 | + | 0.827643i | −0.987190 | − | 0.159547i | \(-0.948997\pi\) |
0.159547 | + | 0.987190i | \(0.448997\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.39230 | 0.544798 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.757875 | + | 0.757875i | −0.0925891 | + | 0.0925891i | −0.751884 | − | 0.659295i | \(-0.770855\pi\) |
0.659295 | + | 0.751884i | \(0.270855\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 16.2127i | 1.92409i | 0.272887 | + | 0.962046i | \(0.412021\pi\) | ||||
−0.272887 | + | 0.962046i | \(0.587979\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 4.00000i | − | 0.468165i | −0.972217 | − | 0.234082i | \(-0.924791\pi\) | ||
0.972217 | − | 0.234082i | \(-0.0752085\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −9.46410 | + | 9.46410i | −1.07853 | + | 1.07853i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.44949 | 0.275589 | 0.137795 | − | 0.990461i | \(-0.455999\pi\) | ||||
0.137795 | + | 0.990461i | \(0.455999\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.03528 | − | 1.03528i | 0.113636 | − | 0.113636i | −0.648002 | − | 0.761638i | \(-0.724395\pi\) |
0.761638 | + | 0.648002i | \(0.224395\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.53590 | + | 2.53590i | 0.275057 | + | 0.275057i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 8.92820i | − | 0.946388i | −0.880958 | − | 0.473194i | \(-0.843101\pi\) | ||
0.880958 | − | 0.473194i | \(-0.156899\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.34847 | + | 7.34847i | 0.770329 | + | 0.770329i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.554803 | 0.0569216 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.9282 | 1.51573 | 0.757865 | − | 0.652412i | \(-0.226243\pi\) | ||||
0.757865 | + | 0.652412i | \(0.226243\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.196152 | − | 0.196152i | −0.0195179 | − | 0.0195179i | 0.697280 | − | 0.716798i | \(-0.254393\pi\) |
−0.716798 | + | 0.697280i | \(0.754393\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.10634i | 0.798742i | 0.916789 | + | 0.399371i | \(0.130771\pi\) | ||||
−0.916789 | + | 0.399371i | \(0.869229\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.82843 | − | 2.82843i | −0.273434 | − | 0.273434i | 0.557047 | − | 0.830481i | \(-0.311934\pi\) |
−0.830481 | + | 0.557047i | \(0.811934\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.00000 | − | 1.00000i | 0.0957826 | − | 0.0957826i | −0.657592 | − | 0.753374i | \(-0.728425\pi\) |
0.753374 | + | 0.657592i | \(0.228425\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 18.0000 | 1.69330 | 0.846649 | − | 0.532152i | \(-0.178617\pi\) | ||||
0.846649 | + | 0.532152i | \(0.178617\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.07055 | − | 2.07055i | 0.193080 | − | 0.193080i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.48528i | 0.777844i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 18.8564i | 1.71422i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.53590 | − | 6.53590i | 0.584589 | − | 0.584589i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −19.4201 | −1.72325 | −0.861625 | − | 0.507545i | \(-0.830553\pi\) | ||||
−0.861625 | + | 0.507545i | \(0.830553\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.757875 | + | 0.757875i | −0.0662158 | + | 0.0662158i | −0.739439 | − | 0.673223i | \(-0.764909\pi\) |
0.673223 | + | 0.739439i | \(0.264909\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.928203 | + | 0.928203i | 0.0804854 | + | 0.0804854i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 6.39230i | − | 0.546131i | −0.961995 | − | 0.273066i | \(-0.911962\pi\) | ||
0.961995 | − | 0.273066i | \(-0.0880377\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.89898 | + | 4.89898i | 0.415526 | + | 0.415526i | 0.883658 | − | 0.468132i | \(-0.155073\pi\) |
−0.468132 | + | 0.883658i | \(0.655073\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 23.1822 | 1.93859 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.14359 | −0.510198 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −14.1962 | − | 14.1962i | −1.16299 | − | 1.16299i | −0.983817 | − | 0.179177i | \(-0.942656\pi\) |
−0.179177 | − | 0.983817i | \(-0.557344\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 17.9043i | − | 1.45703i | −0.685029 | − | 0.728516i | \(-0.740211\pi\) | ||
0.685029 | − | 0.728516i | \(-0.259789\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.37945 | + | 5.37945i | 0.432088 | + | 0.432088i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.46410 | + | 8.46410i | −0.675509 | + | 0.675509i | −0.958981 | − | 0.283472i | \(-0.908514\pi\) |
0.283472 | + | 0.958981i | \(0.408514\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.92820 | 0.546019 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.10634 | + | 8.10634i | −0.634938 | + | 0.634938i | −0.949302 | − | 0.314364i | \(-0.898209\pi\) |
0.314364 | + | 0.949302i | \(0.398209\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.07055i | 0.160224i | 0.996786 | + | 0.0801121i | \(0.0255278\pi\) | ||||
−0.996786 | + | 0.0801121i | \(0.974472\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 5.00000i | − | 0.384615i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.80385 | − | 1.80385i | 0.137144 | − | 0.137144i | −0.635202 | − | 0.772346i | \(-0.719083\pi\) |
0.772346 | + | 0.635202i | \(0.219083\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 9.62209 | 0.727362 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.58630 | − | 3.58630i | 0.268053 | − | 0.268053i | −0.560262 | − | 0.828315i | \(-0.689300\pi\) |
0.828315 | + | 0.560262i | \(0.189300\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.00000 | − | 5.00000i | −0.371647 | − | 0.371647i | 0.496430 | − | 0.868077i | \(-0.334644\pi\) |
−0.868077 | + | 0.496430i | \(0.834644\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 9.46410i | − | 0.695815i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 13.3843 | + | 13.3843i | 0.978754 | + | 0.978754i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.07055 | 0.149820 | 0.0749100 | − | 0.997190i | \(-0.476133\pi\) | ||||
0.0749100 | + | 0.997190i | \(0.476133\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.00000 | 0.431889 | 0.215945 | − | 0.976406i | \(-0.430717\pi\) | ||||
0.215945 | + | 0.976406i | \(0.430717\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.19615 | − | 4.19615i | −0.298963 | − | 0.298963i | 0.541644 | − | 0.840608i | \(-0.317802\pi\) |
−0.840608 | + | 0.541644i | \(0.817802\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 3.96524i | − | 0.281088i | −0.990074 | − | 0.140544i | \(-0.955115\pi\) | ||
0.990074 | − | 0.140544i | \(-0.0448852\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −10.2784 | − | 10.2784i | −0.721405 | − | 0.721405i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.39230 | + | 8.39230i | −0.586144 | + | 0.586144i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.92820 | 0.202548 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.89898 | + | 4.89898i | −0.337260 | + | 0.337260i | −0.855335 | − | 0.518075i | \(-0.826649\pi\) |
0.518075 | + | 0.855335i | \(0.326649\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 3.58630i | − | 0.244584i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 18.0000i | 1.22192i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 10.3923 | − | 10.3923i | 0.699062 | − | 0.699062i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 19.4201 | 1.30046 | 0.650231 | − | 0.759736i | \(-0.274672\pi\) | ||||
0.650231 | + | 0.759736i | \(0.274672\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −16.4901 | + | 16.4901i | −1.09449 | + | 1.09449i | −0.0994423 | + | 0.995043i | \(0.531706\pi\) |
−0.995043 | + | 0.0994423i | \(0.968294\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.92820 | + | 1.92820i | 0.127419 | + | 0.127419i | 0.767940 | − | 0.640521i | \(-0.221282\pi\) |
−0.640521 | + | 0.767940i | \(0.721282\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 0.928203i | − | 0.0608086i | −0.999538 | − | 0.0304043i | \(-0.990321\pi\) | ||
0.999538 | − | 0.0304043i | \(-0.00967948\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.07055 | + | 2.07055i | 0.135068 | + | 0.135068i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.07055 | 0.133933 | 0.0669664 | − | 0.997755i | \(-0.478668\pi\) | ||||
0.0669664 | + | 0.997755i | \(0.478668\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.7846 | −0.952360 | −0.476180 | − | 0.879348i | \(-0.657979\pi\) | ||||
−0.476180 | + | 0.879348i | \(0.657979\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.732051 | + | 0.732051i | 0.0467690 | + | 0.0467690i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 2.27362i | − | 0.144667i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.52056 | + | 9.52056i | 0.600932 | + | 0.600932i | 0.940560 | − | 0.339628i | \(-0.110301\pi\) |
−0.339628 | + | 0.940560i | \(0.610301\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 10.9282 | − | 10.9282i | 0.687050 | − | 0.687050i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −18.7846 | −1.17175 | −0.585876 | − | 0.810401i | \(-0.699249\pi\) | ||||
−0.585876 | + | 0.810401i | \(0.699249\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 15.8338 | − | 15.8338i | 0.983861 | − | 0.983861i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 22.6274i | 1.39527i | 0.716455 | + | 0.697633i | \(0.245763\pi\) | ||||
−0.716455 | + | 0.697633i | \(0.754237\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 9.85641i | − | 0.605474i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −10.7321 | + | 10.7321i | −0.654345 | + | 0.654345i | −0.954036 | − | 0.299691i | \(-0.903116\pi\) |
0.299691 | + | 0.954036i | \(0.403116\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.10634 | −0.492425 | −0.246213 | − | 0.969216i | \(-0.579186\pi\) | ||||
−0.246213 | + | 0.969216i | \(0.579186\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 15.1774 | − | 15.1774i | 0.915232 | − | 0.915232i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 18.8564 | + | 18.8564i | 1.13297 | + | 1.13297i | 0.989681 | + | 0.143291i | \(0.0457685\pi\) |
0.143291 | + | 0.989681i | \(0.454231\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.9282i | 0.771232i | 0.922659 | + | 0.385616i | \(0.126011\pi\) | ||||
−0.922659 | + | 0.385616i | \(0.873989\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.6264 | − | 12.6264i | −0.750561 | − | 0.750561i | 0.224023 | − | 0.974584i | \(-0.428081\pi\) |
−0.974584 | + | 0.224023i | \(0.928081\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −28.0812 | −1.65758 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.00000 | −0.294118 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9.66025 | + | 9.66025i | 0.564358 | + | 0.564358i | 0.930542 | − | 0.366184i | \(-0.119336\pi\) |
−0.366184 | + | 0.930542i | \(0.619336\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 14.3452i | 0.835210i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8.48528 | − | 8.48528i | −0.490716 | − | 0.490716i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.00000 | − | 6.00000i | 0.345834 | − | 0.345834i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −9.46410 | −0.541913 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.41473 | − | 6.41473i | 0.366108 | − | 0.366108i | −0.499948 | − | 0.866056i | \(-0.666647\pi\) |
0.866056 | + | 0.499948i | \(0.166647\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 12.8295i | − | 0.727492i | −0.931498 | − | 0.363746i | \(-0.881498\pi\) | ||
0.931498 | − | 0.363746i | \(-0.118502\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 23.8564i | − | 1.34844i | −0.738529 | − | 0.674222i | \(-0.764479\pi\) | ||
0.738529 | − | 0.674222i | \(-0.235521\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.26795 | − | 1.26795i | 0.0712151 | − | 0.0712151i | −0.670602 | − | 0.741817i | \(-0.733964\pi\) |
0.741817 | + | 0.670602i | \(0.233964\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −32.4254 | −1.81547 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.31268 | − | 1.31268i | 0.0730393 | − | 0.0730393i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −11.7846 | − | 11.7846i | −0.653693 | − | 0.653693i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.92820i | 0.381964i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.5558 | − | 10.5558i | −0.580201 | − | 0.580201i | 0.354757 | − | 0.934958i | \(-0.384563\pi\) |
−0.934958 | + | 0.354757i | \(0.884563\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.10961 | −0.0606242 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 17.8564 | 0.972700 | 0.486350 | − | 0.873764i | \(-0.338328\pi\) | ||||
0.486350 | + | 0.873764i | \(0.338328\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 28.3923 | + | 28.3923i | 1.53753 | + | 1.53753i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.5959i | 1.05808i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −6.69213 | − | 6.69213i | −0.359252 | − | 0.359252i | 0.504285 | − | 0.863537i | \(-0.331756\pi\) |
−0.863537 | + | 0.504285i | \(0.831756\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.39230 | − | 1.39230i | 0.0745284 | − | 0.0745284i | −0.668860 | − | 0.743388i | \(-0.733217\pi\) |
0.743388 | + | 0.668860i | \(0.233217\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −12.9282 | −0.688099 | −0.344049 | − | 0.938952i | \(-0.611799\pi\) | ||||
−0.344049 | + | 0.938952i | \(0.611799\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −11.8685 | + | 11.8685i | −0.629915 | + | 0.629915i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 30.1518i | − | 1.59135i | −0.605725 | − | 0.795674i | \(-0.707117\pi\) | ||
0.605725 | − | 0.795674i | \(-0.292883\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.7128i | 0.984885i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.92820 | − | 2.92820i | 0.153269 | − | 0.153269i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 27.7023 | 1.44605 | 0.723023 | − | 0.690824i | \(-0.242752\pi\) | ||||
0.723023 | + | 0.690824i | \(0.242752\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 16.4901 | − | 16.4901i | 0.856123 | − | 0.856123i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11.3923 | − | 11.3923i | −0.589871 | − | 0.589871i | 0.347725 | − | 0.937596i | \(-0.386954\pi\) |
−0.937596 | + | 0.347725i | \(0.886954\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 25.1769i | 1.29668i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −15.0759 | − | 15.0759i | −0.774396 | − | 0.774396i | 0.204476 | − | 0.978872i | \(-0.434451\pi\) |
−0.978872 | + | 0.204476i | \(0.934451\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −0.554803 | −0.0283491 | −0.0141746 | − | 0.999900i | \(-0.504512\pi\) | ||||
−0.0141746 | + | 0.999900i | \(0.504512\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −13.8564 | −0.706188 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.26795 | − | 3.26795i | −0.165692 | − | 0.165692i | 0.619391 | − | 0.785083i | \(-0.287380\pi\) |
−0.785083 | + | 0.619391i | \(0.787380\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 9.79796i | − | 0.495504i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.79315 | + | 1.79315i | 0.0902232 | + | 0.0902232i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.3205 | − | 18.3205i | 0.919480 | − | 0.919480i | −0.0775115 | − | 0.996991i | \(-0.524697\pi\) |
0.996991 | + | 0.0775115i | \(0.0246975\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.39230 | 0.119466 | 0.0597330 | − | 0.998214i | \(-0.480975\pi\) | ||||
0.0597330 | + | 0.998214i | \(0.480975\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 22.0454 | − | 22.0454i | 1.09816 | − | 1.09816i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 49.9507i | − | 2.47597i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 22.9282i | − | 1.13373i | −0.823812 | − | 0.566863i | \(-0.808157\pi\) | ||
0.823812 | − | 0.566863i | \(-0.191843\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −24.0000 | + | 24.0000i | −1.18096 | + | 1.18096i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.51575 | 0.0744052 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −14.4195 | + | 14.4195i | −0.704440 | + | 0.704440i | −0.965360 | − | 0.260920i | \(-0.915974\pi\) |
0.260920 | + | 0.965360i | \(0.415974\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.0717968 | + | 0.0717968i | 0.00349916 | + | 0.00349916i | 0.708854 | − | 0.705355i | \(-0.249212\pi\) |
−0.705355 | + | 0.708854i | \(0.749212\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 13.6077i | − | 0.660070i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −15.8338 | − | 15.8338i | −0.766249 | − | 0.766249i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −23.9401 | −1.15315 | −0.576577 | − | 0.817043i | \(-0.695612\pi\) | ||||
−0.576577 | + | 0.817043i | \(0.695612\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.14359 | 0.103015 | 0.0515073 | − | 0.998673i | \(-0.483597\pi\) | ||||
0.0515073 | + | 0.998673i | \(0.483597\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.07180 | − | 1.07180i | −0.0512710 | − | 0.0512710i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 28.4601i | − | 1.35833i | −0.733986 | − | 0.679164i | \(-0.762342\pi\) | ||
0.733986 | − | 0.679164i | \(-0.237658\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.480473 | + | 0.480473i | 0.0228280 | + | 0.0228280i | 0.718429 | − | 0.695601i | \(-0.244862\pi\) |
−0.695601 | + | 0.718429i | \(0.744862\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.53590 | − | 6.53590i | 0.309831 | − | 0.309831i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −14.3923 | −0.679215 | −0.339607 | − | 0.940567i | \(-0.610294\pi\) | ||||
−0.339607 | + | 0.940567i | \(0.610294\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −44.2939 | + | 44.2939i | −2.08572 | + | 2.08572i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 10.7589i | 0.504385i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 20.7846i | − | 0.972263i | −0.873886 | − | 0.486132i | \(-0.838408\pi\) | ||
0.873886 | − | 0.486132i | \(-0.161592\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 16.0526 | − | 16.0526i | 0.747642 | − | 0.747642i | −0.226394 | − | 0.974036i | \(-0.572694\pi\) |
0.974036 | + | 0.226394i | \(0.0726936\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.72311 | −0.219502 | −0.109751 | − | 0.993959i | \(-0.535005\pi\) | ||||
−0.109751 | + | 0.993959i | \(0.535005\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −12.9038 | + | 12.9038i | −0.597116 | + | 0.597116i | −0.939544 | − | 0.342428i | \(-0.888751\pi\) |
0.342428 | + | 0.939544i | \(0.388751\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.85641 | − | 1.85641i | −0.0857209 | − | 0.0857209i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 18.9282i | − | 0.870320i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.48854 | − | 1.48854i | −0.0682990 | − | 0.0682990i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −38.8401 | −1.77465 | −0.887325 | − | 0.461145i | \(-0.847439\pi\) | ||||
−0.887325 | + | 0.461145i | \(0.847439\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −38.7846 | −1.76843 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 10.9282 | + | 10.9282i | 0.496224 | + | 0.496224i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 22.8033i | 1.03332i | 0.856192 | + | 0.516658i | \(0.172824\pi\) | ||||
−0.856192 | + | 0.516658i | \(0.827176\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15.4548 | − | 15.4548i | −0.697466 | − | 0.697466i | 0.266397 | − | 0.963863i | \(-0.414167\pi\) |
−0.963863 | + | 0.266397i | \(0.914167\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −14.5359 | + | 14.5359i | −0.654664 | + | 0.654664i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −39.7128 | −1.78136 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.82843 | − | 2.82843i | 0.126618 | − | 0.126618i | −0.640958 | − | 0.767576i | \(-0.721463\pi\) |
0.767576 | + | 0.640958i | \(0.221463\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 33.1833i | − | 1.47957i | −0.672844 | − | 0.739784i | \(-0.734928\pi\) | ||
0.672844 | − | 0.739784i | \(-0.265072\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 0.287187i | − | 0.0127797i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 19.1244 | − | 19.1244i | 0.847672 | − | 0.847672i | −0.142170 | − | 0.989842i | \(-0.545408\pi\) |
0.989842 | + | 0.142170i | \(0.0454080\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.79796 | 0.433436 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5.93426 | + | 5.93426i | −0.261495 | + | 0.261495i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10.9282 | + | 10.9282i | 0.480622 | + | 0.480622i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13.3205i | 0.583582i | 0.956482 | + | 0.291791i | \(0.0942512\pi\) | ||||
−0.956482 | + | 0.291791i | \(0.905749\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −17.3495 | − | 17.3495i | −0.758641 | − | 0.758641i | 0.217434 | − | 0.976075i | \(-0.430231\pi\) |
−0.976075 | + | 0.217434i | \(0.930231\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 25.4558 | 1.10887 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 15.0000 | 0.652174 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 34.3923 | + | 34.3923i | 1.48970 | + | 1.48970i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 4.14110i | − | 0.179036i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.86370 | + | 3.86370i | 0.166421 | + | 0.166421i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.07180 | − | 6.07180i | 0.261047 | − | 0.261047i | −0.564432 | − | 0.825479i | \(-0.690905\pi\) |
0.825479 | + | 0.564432i | \(0.190905\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.46410 | 0.0627152 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 27.7023 | − | 27.7023i | 1.18446 | − | 1.18446i | 0.205888 | − | 0.978576i | \(-0.433992\pi\) |
0.978576 | − | 0.205888i | \(-0.0660081\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.18016i | 0.135479i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.00000i | 0.255146i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 30.1962 | − | 30.1962i | 1.27945 | − | 1.27945i | 0.338478 | − | 0.940974i | \(-0.390088\pi\) |
0.940974 | − | 0.338478i | \(-0.109912\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −14.6969 | −0.621614 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3.86370 | − | 3.86370i | 0.162836 | − | 0.162836i | −0.620986 | − | 0.783822i | \(-0.713268\pi\) |
0.783822 | + | 0.620986i | \(0.213268\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 13.1769 | + | 13.1769i | 0.554357 | + | 0.554357i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 3.46410i | − | 0.145223i | −0.997360 | − | 0.0726113i | \(-0.976867\pi\) | ||
0.997360 | − | 0.0726113i | \(-0.0231333\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16.7675 | + | 16.7675i | 0.701698 | + | 0.701698i | 0.964775 | − | 0.263077i | \(-0.0847374\pi\) |
−0.263077 | + | 0.964775i | \(0.584737\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −11.1106 | −0.463346 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.85641 | 0.243805 | 0.121903 | − | 0.992542i | \(-0.461100\pi\) | ||||
0.121903 | + | 0.992542i | \(0.461100\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.53590 | + | 2.53590i | 0.105207 | + | 0.105207i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 52.0213i | − | 2.15450i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −20.5569 | − | 20.5569i | −0.848473 | − | 0.848473i | 0.141470 | − | 0.989943i | \(-0.454817\pi\) |
−0.989943 | + | 0.141470i | \(0.954817\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.78461 | − | 2.78461i | 0.114738 | − | 0.114738i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −17.7128 | −0.727378 | −0.363689 | − | 0.931520i | \(-0.618483\pi\) | ||||
−0.363689 | + | 0.931520i | \(0.618483\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.21166 | + | 6.21166i | −0.254653 | + | 0.254653i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 12.6264i | 0.515900i | 0.966158 | + | 0.257950i | \(0.0830470\pi\) | ||||
−0.966158 | + | 0.257950i | \(0.916953\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 35.7128i | − | 1.45676i | −0.685176 | − | 0.728378i | \(-0.740275\pi\) | ||
0.685176 | − | 0.728378i | \(-0.259725\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −13.8038 | + | 13.8038i | −0.561206 | + | 0.561206i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −31.8434 | −1.29248 | −0.646241 | − | 0.763133i | \(-0.723660\pi\) | ||||
−0.646241 | + | 0.763133i | \(0.723660\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.48528 | − | 8.48528i | 0.343278 | − | 0.343278i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 30.3205 | + | 30.3205i | 1.22463 | + | 1.22463i | 0.965966 | + | 0.258667i | \(0.0832833\pi\) |
0.258667 | + | 0.965966i | \(0.416717\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 12.1436i | − | 0.488883i | −0.969664 | − | 0.244441i | \(-0.921395\pi\) | ||
0.969664 | − | 0.244441i | \(-0.0786046\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.48528 | + | 8.48528i | 0.341052 | + | 0.341052i | 0.856763 | − | 0.515711i | \(-0.172472\pi\) |
−0.515711 | + | 0.856763i | \(0.672472\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 21.8695 | 0.876185 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −10.0718 | −0.402872 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −22.3923 | − | 22.3923i | −0.892840 | − | 0.892840i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.933740i | 0.0371716i | 0.999827 | + | 0.0185858i | \(0.00591639\pi\) | ||||
−0.999827 | + | 0.0185858i | \(0.994084\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −14.2165 | − | 14.2165i | −0.564163 | − | 0.564163i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.00000 | − | 3.00000i | 0.118864 | − | 0.118864i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 46.3923 | 1.83239 | 0.916193 | − | 0.400737i | \(-0.131246\pi\) | ||||
0.916193 | + | 0.400737i | \(0.131246\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 25.0769 | − | 25.0769i | 0.988937 | − | 0.988937i | −0.0110028 | − | 0.999939i | \(-0.503502\pi\) |
0.999939 | + | 0.0110028i | \(0.00350237\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 21.3147i | 0.837969i | 0.907993 | + | 0.418984i | \(0.137614\pi\) | ||||
−0.907993 | + | 0.418984i | \(0.862386\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 75.7128i | 2.97199i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0.339746 | − | 0.339746i | 0.0132953 | − | 0.0132953i | −0.700428 | − | 0.713723i | \(-0.747007\pi\) |
0.713723 | + | 0.700428i | \(0.247007\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.10961 | −0.0433559 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 16.9706 | − | 16.9706i | 0.661079 | − | 0.661079i | −0.294555 | − | 0.955634i | \(-0.595171\pi\) |
0.955634 | + | 0.294555i | \(0.0951715\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −25.3923 | − | 25.3923i | −0.987646 | − | 0.987646i | 0.0122784 | − | 0.999925i | \(-0.496092\pi\) |
−0.999925 | + | 0.0122784i | \(0.996092\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.35898i | 0.0526991i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 11.8685 | + | 11.8685i | 0.459551 | + | 0.459551i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −49.9507 | −1.92833 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.00000 | 0.308377 | 0.154189 | − | 0.988041i | \(-0.450724\pi\) | ||||
0.154189 | + | 0.988041i | \(0.450724\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −19.6603 | − | 19.6603i | −0.755605 | − | 0.755605i | 0.219914 | − | 0.975519i | \(-0.429422\pi\) |
−0.975519 | + | 0.219914i | \(0.929422\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 36.5665i | 1.40329i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −26.2880 | − | 26.2880i | −1.00588 | − | 1.00588i | −0.999983 | − | 0.00590163i | \(-0.998121\pi\) |
−0.00590163 | − | 0.999983i | \(-0.501879\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.67949 | − | 4.67949i | 0.178794 | − | 0.178794i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −40.3923 | −1.53882 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.96524 | − | 3.96524i | 0.150845 | − | 0.150845i | −0.627650 | − | 0.778495i | \(-0.715983\pi\) |
0.778495 | + | 0.627650i | \(0.215983\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7.17260i | 0.272072i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 39.7128i | 1.50423i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 20.5885 | − | 20.5885i | 0.777615 | − | 0.777615i | −0.201809 | − | 0.979425i | \(-0.564682\pi\) |
0.979425 | + | 0.201809i | \(0.0646822\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.89898 | −0.184769 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.480473 | − | 0.480473i | 0.0180701 | − | 0.0180701i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 20.7128 | + | 20.7128i | 0.777886 | + | 0.777886i | 0.979471 | − | 0.201585i | \(-0.0646092\pi\) |
−0.201585 | + | 0.979471i | \(0.564609\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 20.7846i | − | 0.778390i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 16.9706 | + | 16.9706i | 0.634663 | + | 0.634663i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 31.6675 | 1.18100 | 0.590499 | − | 0.807038i | \(-0.298931\pi\) | ||||
0.590499 | + | 0.807038i | \(0.298931\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −19.8564 | −0.739491 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 16.4833 | + | 16.4833i | 0.612176 | + | 0.612176i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 3.20736i | − | 0.118955i | −0.998230 | − | 0.0594773i | \(-0.981057\pi\) | ||
0.998230 | − | 0.0594773i | \(-0.0189434\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.48528 | − | 8.48528i | −0.313839 | − | 0.313839i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5.00000 | + | 5.00000i | −0.184679 | + | 0.184679i | −0.793391 | − | 0.608712i | \(-0.791686\pi\) |
0.608712 | + | 0.793391i | \(0.291686\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.85641 | −0.215724 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −25.4558 | + | 25.4558i | −0.936408 | + | 0.936408i | −0.998096 | − | 0.0616872i | \(-0.980352\pi\) |
0.0616872 | + | 0.998096i | \(0.480352\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 21.6665i | − | 0.794866i | −0.917631 | − | 0.397433i | \(-0.869901\pi\) | ||
0.917631 | − | 0.397433i | \(-0.130099\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 20.7846i | − | 0.761489i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6.92820 | − | 6.92820i | 0.253151 | − | 0.253151i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21.6937 | 0.791614 | 0.395807 | − | 0.918334i | \(-0.370465\pi\) | ||||
0.395807 | + | 0.918334i | \(0.370465\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 13.1069 | − | 13.1069i | 0.477007 | − | 0.477007i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −17.7846 | − | 17.7846i | −0.646393 | − | 0.646393i | 0.305727 | − | 0.952119i | \(-0.401101\pi\) |
−0.952119 | + | 0.305727i | \(0.901101\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.75129i | 0.135984i | 0.997686 | + | 0.0679921i | \(0.0216593\pi\) | ||||
−0.997686 | + | 0.0679921i | \(0.978341\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.44949 | + | 2.44949i | 0.0886775 | + | 0.0886775i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 58.7878 | 2.12270 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −22.0000 | −0.793340 | −0.396670 | − | 0.917961i | \(-0.629834\pi\) | ||||
−0.396670 | + | 0.917961i | \(0.629834\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −3.41154 | − | 3.41154i | −0.122705 | − | 0.122705i | 0.643088 | − | 0.765792i | \(-0.277653\pi\) |
−0.765792 | + | 0.643088i | \(0.777653\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 28.8663i | − | 1.03691i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.34418 | + | 4.34418i | 0.155646 | + | 0.155646i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −62.6410 | + | 62.6410i | −2.24147 | + | 2.24147i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −12.3923 | −0.442300 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −11.6926 | + | 11.6926i | −0.416798 | + | 0.416798i | −0.884098 | − | 0.467301i | \(-0.845227\pi\) |
0.467301 | + | 0.884098i | \(0.345227\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 44.0908i | 1.56769i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 38.7846i | 1.37728i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −29.5167 | + | 29.5167i | −1.04553 | + | 1.04553i | −0.0466211 | + | 0.998913i | \(0.514845\pi\) |
−0.998913 | + | 0.0466211i | \(0.985155\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.79796 | 0.346627 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 15.4548 | − | 15.4548i | 0.545389 | − | 0.545389i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.07180 | + | 5.07180i | 0.178757 | + | 0.178757i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 41.3205i | − | 1.45275i | −0.687298 | − | 0.726376i | \(-0.741203\pi\) | ||
0.687298 | − | 0.726376i | \(-0.258797\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −23.7642 | − | 23.7642i | −0.834475 | − | 0.834475i | 0.153650 | − | 0.988125i | \(-0.450897\pi\) |
−0.988125 | + | 0.153650i | \(0.950897\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −11.8685 | −0.415736 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.85641 | −0.0649474 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −28.1962 | − | 28.1962i | −0.984053 | − | 0.984053i | 0.0158223 | − | 0.999875i | \(-0.494963\pi\) |
−0.999875 | + | 0.0158223i | \(0.994963\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 43.9149i | − | 1.53078i | −0.643567 | − | 0.765389i | \(-0.722546\pi\) | ||
0.643567 | − | 0.765389i | \(-0.277454\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.27362 | − | 2.27362i | −0.0790617 | − | 0.0790617i | 0.666470 | − | 0.745532i | \(-0.267804\pi\) |
−0.745532 | + | 0.666470i | \(0.767804\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 28.8564 | − | 28.8564i | 1.00222 | − | 1.00222i | 0.00222690 | − | 0.999998i | \(-0.499291\pi\) |
0.999998 | − | 0.00222690i | \(-0.000708845\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.46410 | 0.120024 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.51575 | + | 1.51575i | −0.0524547 | + | 0.0524547i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 3.38323i | 0.116802i | 0.998293 | + | 0.0584010i | \(0.0186002\pi\) | ||||
−0.998293 | + | 0.0584010i | \(0.981400\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 6.21539i | − | 0.214324i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.66025 | − | 3.66025i | 0.125917 | − | 0.125917i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −46.1886 | −1.58706 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −18.2832 | + | 18.2832i | −0.626741 | + | 0.626741i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 15.2487 | + | 15.2487i | 0.522106 | + | 0.522106i | 0.918207 | − | 0.396101i | \(-0.129637\pi\) |
−0.396101 | + | 0.918207i | \(0.629637\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 19.1769i | 0.655071i | 0.944839 | + | 0.327535i | \(0.106218\pi\) | ||||
−0.944839 | + | 0.327535i | \(0.893782\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11.4896 | + | 11.4896i | 0.392019 | + | 0.392019i | 0.875407 | − | 0.483387i | \(-0.160594\pi\) |
−0.483387 | + | 0.875407i | \(0.660594\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 31.4644 | 1.07106 | 0.535531 | − | 0.844516i | \(-0.320112\pi\) | ||||
0.535531 | + | 0.844516i | \(0.320112\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.64102 | 0.0897972 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.46410 | + | 9.46410i | 0.321048 | + | 0.321048i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.54725i | 0.154078i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 16.0096 | + | 16.0096i | 0.541224 | + | 0.541224i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 23.2487 | − | 23.2487i | 0.785053 | − | 0.785053i | −0.195625 | − | 0.980679i | \(-0.562674\pi\) |
0.980679 | + | 0.195625i | \(0.0626737\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 32.6410 | 1.09970 | 0.549852 | − | 0.835262i | \(-0.314684\pi\) | ||||
0.549852 | + | 0.835262i | \(0.314684\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −18.6622 | + | 18.6622i | −0.628032 | + | 0.628032i | −0.947573 | − | 0.319540i | \(-0.896471\pi\) |
0.319540 | + | 0.947573i | \(0.396471\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 2.62536i | − | 0.0881508i | −0.999028 | − | 0.0440754i | \(-0.985966\pi\) | ||
0.999028 | − | 0.0440754i | \(-0.0140342\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 47.5692i | − | 1.59542i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.07180 | − | 1.07180i | 0.0358663 | − | 0.0358663i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.25071 | 0.175512 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −30.8353 | + | 30.8353i | −1.02841 | + | 1.02841i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −23.3205 | − | 23.3205i | −0.776919 | − | 0.776919i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 7.32051i | − | 0.243342i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 15.2789 | + | 15.2789i | 0.507329 | + | 0.507329i | 0.913706 | − | 0.406377i | \(-0.133208\pi\) |
−0.406377 | + | 0.913706i | \(0.633208\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −51.4665 | −1.70516 | −0.852580 | − | 0.522596i | \(-0.824964\pi\) | ||||
−0.852580 | + | 0.522596i | \(0.824964\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.00000 | 0.264761 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.85641 | − | 1.85641i | −0.0613039 | − | 0.0613039i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 44.6728i | 1.47362i | 0.676100 | + | 0.736810i | \(0.263669\pi\) | ||||
−0.676100 | + | 0.736810i | \(0.736331\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 48.6381 | + | 48.6381i | 1.60094 | + | 1.60094i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −25.3923 | + | 25.3923i | −0.834894 | + | 0.834894i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 10.6795 | 0.350383 | 0.175191 | − | 0.984534i | \(-0.443946\pi\) | ||||
0.175191 | + | 0.984534i | \(0.443946\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.378937 | − | 0.378937i | 0.0124192 | − | 0.0124192i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 19.5959i | 0.640855i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 2.00000i | − | 0.0653372i | −0.999466 | − | 0.0326686i | \(-0.989599\pi\) | ||
0.999466 | − | 0.0326686i | \(-0.0104006\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 8.33975 | − | 8.33975i | 0.271868 | − | 0.271868i | −0.557984 | − | 0.829852i | \(-0.688425\pi\) |
0.829852 | + | 0.557984i | \(0.188425\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 32.4254 | 1.05592 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −30.3548 | + | 30.3548i | −0.986399 | + | 0.986399i | −0.999909 | − | 0.0135095i | \(-0.995700\pi\) |
0.0135095 | + | 0.999909i | \(0.495700\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −12.0000 | − | 12.0000i | −0.389536 | − | 0.389536i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 25.6077i | − | 0.829515i | −0.909932 | − | 0.414757i | \(-0.863866\pi\) | ||
0.909932 | − | 0.414757i | \(-0.136134\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.51575 | + | 1.51575i | 0.0490485 | + | 0.0490485i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 15.6579 | 0.505619 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 23.0000 | 0.741935 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4.39230 | + | 4.39230i | 0.141393 | + | 0.141393i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 34.8749i | 1.12150i | 0.827985 | + | 0.560750i | \(0.189487\pi\) | ||||
−0.827985 | + | 0.560750i | \(0.810513\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −18.5606 | − | 18.5606i | −0.595639 | − | 0.595639i | 0.343510 | − | 0.939149i | \(-0.388384\pi\) |
−0.939149 | + | 0.343510i | \(0.888384\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −12.0000 | + | 12.0000i | −0.384702 | + | 0.384702i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 27.1769 | 0.869467 | 0.434733 | − | 0.900559i | \(-0.356843\pi\) | ||||
0.434733 | + | 0.900559i | \(0.356843\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 34.4959 | − | 34.4959i | 1.10249 | − | 1.10249i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 35.0507i | − | 1.11794i | −0.829186 | − | 0.558972i | \(-0.811196\pi\) | ||
0.829186 | − | 0.558972i | \(-0.188804\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 6.14359i | − | 0.195751i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −6.92820 | + | 6.92820i | −0.220304 | + | 0.220304i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 12.2474 | 0.389053 | 0.194527 | − | 0.980897i | \(-0.437683\pi\) | ||||
0.194527 | + | 0.980897i | \(0.437683\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.90276 | − | 2.90276i | 0.0920236 | − | 0.0920236i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.53590 | + | 5.53590i | 0.175324 | + | 0.175324i | 0.789314 | − | 0.613990i | \(-0.210437\pi\) |
−0.613990 | + | 0.789314i | \(0.710437\pi\) | |||||||
\(998\) | 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 | 2304.2.k.e.1729.4 | 8 | ||
3.2 | odd | 2 | 768.2.j.f.193.1 | yes | 8 | ||
4.3 | odd | 2 | inner | 2304.2.k.e.1729.3 | 8 | ||
8.3 | odd | 2 | 2304.2.k.l.1729.1 | 8 | |||
8.5 | even | 2 | 2304.2.k.l.1729.2 | 8 | |||
12.11 | even | 2 | 768.2.j.f.193.3 | yes | 8 | ||
16.3 | odd | 4 | inner | 2304.2.k.e.577.4 | 8 | ||
16.5 | even | 4 | 2304.2.k.l.577.1 | 8 | |||
16.11 | odd | 4 | 2304.2.k.l.577.2 | 8 | |||
16.13 | even | 4 | inner | 2304.2.k.e.577.3 | 8 | ||
24.5 | odd | 2 | 768.2.j.e.193.4 | yes | 8 | ||
24.11 | even | 2 | 768.2.j.e.193.2 | ✓ | 8 | ||
32.3 | odd | 8 | 9216.2.a.bc.1.2 | 4 | |||
32.13 | even | 8 | 9216.2.a.bc.1.3 | 4 | |||
32.19 | odd | 8 | 9216.2.a.bi.1.3 | 4 | |||
32.29 | even | 8 | 9216.2.a.bi.1.2 | 4 | |||
48.5 | odd | 4 | 768.2.j.e.577.4 | yes | 8 | ||
48.11 | even | 4 | 768.2.j.e.577.2 | yes | 8 | ||
48.29 | odd | 4 | 768.2.j.f.577.1 | yes | 8 | ||
48.35 | even | 4 | 768.2.j.f.577.3 | yes | 8 | ||
96.5 | odd | 8 | 3072.2.d.h.1537.2 | 8 | |||
96.11 | even | 8 | 3072.2.d.h.1537.3 | 8 | |||
96.29 | odd | 8 | 3072.2.a.l.1.3 | 4 | |||
96.35 | even | 8 | 3072.2.a.r.1.3 | 4 | |||
96.53 | odd | 8 | 3072.2.d.h.1537.7 | 8 | |||
96.59 | even | 8 | 3072.2.d.h.1537.6 | 8 | |||
96.77 | odd | 8 | 3072.2.a.r.1.2 | 4 | |||
96.83 | even | 8 | 3072.2.a.l.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
768.2.j.e.193.2 | ✓ | 8 | 24.11 | even | 2 | ||
768.2.j.e.193.4 | yes | 8 | 24.5 | odd | 2 | ||
768.2.j.e.577.2 | yes | 8 | 48.11 | even | 4 | ||
768.2.j.e.577.4 | yes | 8 | 48.5 | odd | 4 | ||
768.2.j.f.193.1 | yes | 8 | 3.2 | odd | 2 | ||
768.2.j.f.193.3 | yes | 8 | 12.11 | even | 2 | ||
768.2.j.f.577.1 | yes | 8 | 48.29 | odd | 4 | ||
768.2.j.f.577.3 | yes | 8 | 48.35 | even | 4 | ||
2304.2.k.e.577.3 | 8 | 16.13 | even | 4 | inner | ||
2304.2.k.e.577.4 | 8 | 16.3 | odd | 4 | inner | ||
2304.2.k.e.1729.3 | 8 | 4.3 | odd | 2 | inner | ||
2304.2.k.e.1729.4 | 8 | 1.1 | even | 1 | trivial | ||
2304.2.k.l.577.1 | 8 | 16.5 | even | 4 | |||
2304.2.k.l.577.2 | 8 | 16.11 | odd | 4 | |||
2304.2.k.l.1729.1 | 8 | 8.3 | odd | 2 | |||
2304.2.k.l.1729.2 | 8 | 8.5 | even | 2 | |||
3072.2.a.l.1.2 | 4 | 96.83 | even | 8 | |||
3072.2.a.l.1.3 | 4 | 96.29 | odd | 8 | |||
3072.2.a.r.1.2 | 4 | 96.77 | odd | 8 | |||
3072.2.a.r.1.3 | 4 | 96.35 | even | 8 | |||
3072.2.d.h.1537.2 | 8 | 96.5 | odd | 8 | |||
3072.2.d.h.1537.3 | 8 | 96.11 | even | 8 | |||
3072.2.d.h.1537.6 | 8 | 96.59 | even | 8 | |||
3072.2.d.h.1537.7 | 8 | 96.53 | odd | 8 | |||
9216.2.a.bc.1.2 | 4 | 32.3 | odd | 8 | |||
9216.2.a.bc.1.3 | 4 | 32.13 | even | 8 | |||
9216.2.a.bi.1.2 | 4 | 32.29 | even | 8 | |||
9216.2.a.bi.1.3 | 4 | 32.19 | odd | 8 |