Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1440,2,Mod(127,1440)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1440, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1440.127");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1440.x (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: | \(11.4984578911\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 160) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 703.1 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1440.703 |
Dual form | 1440.2.x.a.127.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1440\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(641\) | \(901\) | \(991\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | + | 2.00000i | −0.447214 | + | 0.894427i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.00000 | − | 3.00000i | −1.13389 | − | 1.13389i | −0.989524 | − | 0.144370i | \(-0.953885\pi\) |
−0.144370 | − | 0.989524i | \(-0.546115\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 2.00000i | − | 0.603023i | −0.953463 | − | 0.301511i | \(-0.902509\pi\) | ||
0.953463 | − | 0.301511i | \(-0.0974911\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.00000 | + | 3.00000i | 0.832050 | + | 0.832050i | 0.987797 | − | 0.155747i | \(-0.0497784\pi\) |
−0.155747 | + | 0.987797i | \(0.549778\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.00000 | + | 1.00000i | −0.242536 | + | 0.242536i | −0.817898 | − | 0.575363i | \(-0.804861\pi\) |
0.575363 | + | 0.817898i | \(0.304861\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.00000 | 0.917663 | 0.458831 | − | 0.888523i | \(-0.348268\pi\) | ||||
0.458831 | + | 0.888523i | \(0.348268\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | − | 1.00000i | 0.208514 | − | 0.208514i | −0.595121 | − | 0.803636i | \(-0.702896\pi\) |
0.803636 | + | 0.595121i | \(0.202896\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.00000 | − | 4.00000i | −0.600000 | − | 0.800000i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.0000i | 1.79605i | 0.439941 | + | 0.898027i | \(0.354999\pi\) | ||||
−0.439941 | + | 0.898027i | \(0.645001\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 9.00000 | − | 3.00000i | 1.52128 | − | 0.507093i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.00000 | + | 1.00000i | −0.164399 | + | 0.164399i | −0.784512 | − | 0.620113i | \(-0.787087\pi\) |
0.620113 | + | 0.784512i | \(0.287087\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.0000 | 1.56174 | 0.780869 | − | 0.624695i | \(-0.214777\pi\) | ||||
0.780869 | + | 0.624695i | \(0.214777\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.00000 | − | 5.00000i | 0.762493 | − | 0.762493i | −0.214280 | − | 0.976772i | \(-0.568740\pi\) |
0.976772 | + | 0.214280i | \(0.0687403\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.00000 | + | 3.00000i | 0.437595 | + | 0.437595i | 0.891202 | − | 0.453607i | \(-0.149863\pi\) |
−0.453607 | + | 0.891202i | \(0.649863\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 11.0000i | 1.57143i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.00000 | + | 5.00000i | 0.686803 | + | 0.686803i | 0.961524 | − | 0.274721i | \(-0.0885855\pi\) |
−0.274721 | + | 0.961524i | \(0.588586\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.00000 | + | 2.00000i | 0.539360 | + | 0.269680i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 12.0000 | 1.56227 | 0.781133 | − | 0.624364i | \(-0.214642\pi\) | ||||
0.781133 | + | 0.624364i | \(0.214642\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.00000 | 0.256074 | 0.128037 | − | 0.991769i | \(-0.459132\pi\) | ||||
0.128037 | + | 0.991769i | \(0.459132\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −9.00000 | + | 3.00000i | −1.11631 | + | 0.372104i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.00000 | − | 1.00000i | −0.122169 | − | 0.122169i | 0.643379 | − | 0.765548i | \(-0.277532\pi\) |
−0.765548 | + | 0.643379i | \(0.777532\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 2.00000i | − | 0.237356i | −0.992933 | − | 0.118678i | \(-0.962134\pi\) | ||
0.992933 | − | 0.118678i | \(-0.0378657\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.00000 | + | 1.00000i | 0.117041 | + | 0.117041i | 0.763202 | − | 0.646160i | \(-0.223626\pi\) |
−0.646160 | + | 0.763202i | \(0.723626\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6.00000 | + | 6.00000i | −0.683763 | + | 0.683763i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.00000 | 0.900070 | 0.450035 | − | 0.893011i | \(-0.351411\pi\) | ||||
0.450035 | + | 0.893011i | \(0.351411\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.00000 | + | 5.00000i | −0.548821 | + | 0.548821i | −0.926100 | − | 0.377279i | \(-0.876860\pi\) |
0.377279 | + | 0.926100i | \(0.376860\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.00000 | − | 3.00000i | −0.108465 | − | 0.325396i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 16.0000i | 1.69600i | 0.529999 | + | 0.847998i | \(0.322192\pi\) | ||||
−0.529999 | + | 0.847998i | \(0.677808\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 18.0000i | − | 1.88691i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.00000 | + | 8.00000i | −0.410391 | + | 0.820783i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.00000 | + | 3.00000i | −0.304604 | + | 0.304604i | −0.842812 | − | 0.538208i | \(-0.819101\pi\) |
0.538208 | + | 0.842812i | \(0.319101\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.00000 | −0.597022 | −0.298511 | − | 0.954406i | \(-0.596490\pi\) | ||||
−0.298511 | + | 0.954406i | \(0.596490\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.00000 | + | 9.00000i | −0.886796 | + | 0.886796i | −0.994214 | − | 0.107418i | \(-0.965742\pi\) |
0.107418 | + | 0.994214i | \(0.465742\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.00000 | − | 3.00000i | −0.290021 | − | 0.290021i | 0.547068 | − | 0.837088i | \(-0.315744\pi\) |
−0.837088 | + | 0.547068i | \(0.815744\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.00000i | 0.383131i | 0.981480 | + | 0.191565i | \(0.0613564\pi\) | ||||
−0.981480 | + | 0.191565i | \(0.938644\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.00000 | + | 3.00000i | 0.282216 | + | 0.282216i | 0.833992 | − | 0.551776i | \(-0.186050\pi\) |
−0.551776 | + | 0.833992i | \(0.686050\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.00000 | + | 3.00000i | 0.0932505 | + | 0.279751i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.00000 | 0.550019 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.00000 | 0.636364 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.0000 | − | 2.00000i | 0.983870 | − | 0.178885i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.00000 | − | 7.00000i | −0.621150 | − | 0.621150i | 0.324676 | − | 0.945825i | \(-0.394745\pi\) |
−0.945825 | + | 0.324676i | \(0.894745\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 10.0000i | − | 0.873704i | −0.899533 | − | 0.436852i | \(-0.856093\pi\) | ||
0.899533 | − | 0.436852i | \(-0.143907\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −12.0000 | − | 12.0000i | −1.04053 | − | 1.04053i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 11.0000 | − | 11.0000i | 0.939793 | − | 0.939793i | −0.0584943 | − | 0.998288i | \(-0.518630\pi\) |
0.998288 | + | 0.0584943i | \(0.0186300\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.0000 | 1.01783 | 0.508913 | − | 0.860818i | \(-0.330047\pi\) | ||||
0.508913 | + | 0.860818i | \(0.330047\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.00000 | − | 6.00000i | 0.501745 | − | 0.501745i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 4.00000i | − | 0.327693i | −0.986486 | − | 0.163846i | \(-0.947610\pi\) | ||
0.986486 | − | 0.163846i | \(-0.0523901\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 6.00000i | − | 0.488273i | −0.969741 | − | 0.244137i | \(-0.921495\pi\) | ||
0.969741 | − | 0.244137i | \(-0.0785045\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −20.0000 | − | 10.0000i | −1.60644 | − | 0.803219i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.00000 | + | 1.00000i | −0.0798087 | + | 0.0798087i | −0.745884 | − | 0.666076i | \(-0.767973\pi\) |
0.666076 | + | 0.745884i | \(0.267973\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.00000 | −0.472866 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.00000 | − | 1.00000i | 0.0783260 | − | 0.0783260i | −0.666858 | − | 0.745184i | \(-0.732361\pi\) |
0.745184 | + | 0.666858i | \(0.232361\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.00000 | − | 1.00000i | −0.0773823 | − | 0.0773823i | 0.667356 | − | 0.744739i | \(-0.267426\pi\) |
−0.744739 | + | 0.667356i | \(0.767426\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.00000i | 0.384615i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.00000 | + | 5.00000i | 0.380143 | + | 0.380143i | 0.871154 | − | 0.491011i | \(-0.163372\pi\) |
−0.491011 | + | 0.871154i | \(0.663372\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.00000 | + | 21.0000i | −0.226779 | + | 1.58745i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.0000 | 0.896922 | 0.448461 | − | 0.893802i | \(-0.351972\pi\) | ||||
0.448461 | + | 0.893802i | \(0.351972\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 22.0000 | 1.63525 | 0.817624 | − | 0.575753i | \(-0.195291\pi\) | ||||
0.817624 | + | 0.575753i | \(0.195291\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.00000 | − | 3.00000i | −0.0735215 | − | 0.220564i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.00000 | + | 2.00000i | 0.146254 | + | 0.146254i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 14.0000i | 1.01300i | 0.862239 | + | 0.506502i | \(0.169062\pi\) | ||||
−0.862239 | + | 0.506502i | \(0.830938\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −15.0000 | − | 15.0000i | −1.07972 | − | 1.07972i | −0.996534 | − | 0.0831899i | \(-0.973489\pi\) |
−0.0831899 | − | 0.996534i | \(-0.526511\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 13.0000 | − | 13.0000i | 0.926212 | − | 0.926212i | −0.0712470 | − | 0.997459i | \(-0.522698\pi\) |
0.997459 | + | 0.0712470i | \(0.0226979\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.0000 | −1.13421 | −0.567105 | − | 0.823646i | \(-0.691937\pi\) | ||||
−0.567105 | + | 0.823646i | \(0.691937\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −10.0000 | + | 20.0000i | −0.698430 | + | 1.39686i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 8.00000i | − | 0.553372i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 14.0000i | − | 0.963800i | −0.876226 | − | 0.481900i | \(-0.839947\pi\) | ||
0.876226 | − | 0.481900i | \(-0.160053\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.00000 | + | 15.0000i | 0.340997 | + | 1.02299i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 30.0000 | − | 30.0000i | 2.03653 | − | 2.03653i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.00000 | −0.403604 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.00000 | + | 1.00000i | −0.0669650 | + | 0.0669650i | −0.739796 | − | 0.672831i | \(-0.765078\pi\) |
0.672831 | + | 0.739796i | \(0.265078\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.00000 | + | 5.00000i | 0.331862 | + | 0.331862i | 0.853293 | − | 0.521431i | \(-0.174602\pi\) |
−0.521431 | + | 0.853293i | \(0.674602\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.00000i | 0.528655i | 0.964433 | + | 0.264327i | \(0.0851500\pi\) | ||||
−0.964433 | + | 0.264327i | \(0.914850\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −21.0000 | − | 21.0000i | −1.37576 | − | 1.37576i | −0.851658 | − | 0.524097i | \(-0.824403\pi\) |
−0.524097 | − | 0.851658i | \(-0.675597\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.00000 | + | 3.00000i | −0.587095 | + | 0.195698i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −16.0000 | −1.03495 | −0.517477 | − | 0.855697i | \(-0.673129\pi\) | ||||
−0.517477 | + | 0.855697i | \(0.673129\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.00000 | −0.128831 | −0.0644157 | − | 0.997923i | \(-0.520518\pi\) | ||||
−0.0644157 | + | 0.997923i | \(0.520518\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −22.0000 | − | 11.0000i | −1.40553 | − | 0.702764i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 12.0000 | + | 12.0000i | 0.763542 | + | 0.763542i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.00000i | 0.378717i | 0.981908 | + | 0.189358i | \(0.0606408\pi\) | ||||
−0.981908 | + | 0.189358i | \(0.939359\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.00000 | − | 2.00000i | −0.125739 | − | 0.125739i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5.00000 | + | 5.00000i | −0.311891 | + | 0.311891i | −0.845642 | − | 0.533751i | \(-0.820782\pi\) |
0.533751 | + | 0.845642i | \(0.320782\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.00000 | 0.372822 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −11.0000 | + | 11.0000i | −0.678289 | + | 0.678289i | −0.959613 | − | 0.281324i | \(-0.909226\pi\) |
0.281324 | + | 0.959613i | \(0.409226\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −15.0000 | + | 5.00000i | −0.921443 | + | 0.307148i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 20.0000i | 1.21942i | 0.792624 | + | 0.609711i | \(0.208714\pi\) | ||||
−0.792624 | + | 0.609711i | \(0.791286\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 14.0000i | − | 0.850439i | −0.905090 | − | 0.425220i | \(-0.860197\pi\) | ||
0.905090 | − | 0.425220i | \(-0.139803\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −8.00000 | + | 6.00000i | −0.482418 | + | 0.361814i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.0000 | − | 11.0000i | 0.660926 | − | 0.660926i | −0.294672 | − | 0.955598i | \(-0.595211\pi\) |
0.955598 | + | 0.294672i | \(0.0952105\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.00000 | −0.357930 | −0.178965 | − | 0.983855i | \(-0.557275\pi\) | ||||
−0.178965 | + | 0.983855i | \(0.557275\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.00000 | + | 7.00000i | −0.416107 | + | 0.416107i | −0.883859 | − | 0.467753i | \(-0.845064\pi\) |
0.467753 | + | 0.883859i | \(0.345064\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −30.0000 | − | 30.0000i | −1.77084 | − | 1.77084i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15.0000i | 0.882353i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −11.0000 | − | 11.0000i | −0.642627 | − | 0.642627i | 0.308574 | − | 0.951200i | \(-0.400148\pi\) |
−0.951200 | + | 0.308574i | \(0.900148\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −12.0000 | + | 24.0000i | −0.698667 | + | 1.39733i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.00000 | 0.346989 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −30.0000 | −1.72917 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.00000 | + | 4.00000i | −0.114520 | + | 0.229039i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −17.0000 | − | 17.0000i | −0.970241 | − | 0.970241i | 0.0293286 | − | 0.999570i | \(-0.490663\pi\) |
−0.999570 | + | 0.0293286i | \(0.990663\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 18.0000i | − | 1.02069i | −0.859971 | − | 0.510343i | \(-0.829518\pi\) | ||
0.859971 | − | 0.510343i | \(-0.170482\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.00000 | + | 9.00000i | 0.508710 | + | 0.508710i | 0.914130 | − | 0.405420i | \(-0.132875\pi\) |
−0.405420 | + | 0.914130i | \(0.632875\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 13.0000 | − | 13.0000i | 0.730153 | − | 0.730153i | −0.240497 | − | 0.970650i | \(-0.577310\pi\) |
0.970650 | + | 0.240497i | \(0.0773105\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.00000 | + | 4.00000i | −0.222566 | + | 0.222566i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.00000 | − | 21.0000i | 0.166410 | − | 1.16487i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 18.0000i | − | 0.992372i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 26.0000i | 1.42909i | 0.699590 | + | 0.714545i | \(0.253366\pi\) | ||||
−0.699590 | + | 0.714545i | \(0.746634\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.00000 | − | 1.00000i | 0.163908 | − | 0.0546358i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −15.0000 | + | 15.0000i | −0.817102 | + | 0.817102i | −0.985687 | − | 0.168585i | \(-0.946080\pi\) |
0.168585 | + | 0.985687i | \(0.446080\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 20.0000 | 1.08306 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 12.0000 | − | 12.0000i | 0.647939 | − | 0.647939i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9.00000 | + | 9.00000i | 0.483145 | + | 0.483145i | 0.906135 | − | 0.422989i | \(-0.139019\pi\) |
−0.422989 | + | 0.906135i | \(0.639019\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.00000i | 0.428230i | 0.976808 | + | 0.214115i | \(0.0686868\pi\) | ||||
−0.976808 | + | 0.214115i | \(0.931313\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 15.0000 | + | 15.0000i | 0.798369 | + | 0.798369i | 0.982838 | − | 0.184469i | \(-0.0590565\pi\) |
−0.184469 | + | 0.982838i | \(0.559057\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.00000 | + | 2.00000i | 0.212298 | + | 0.106149i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −32.0000 | −1.68890 | −0.844448 | − | 0.535638i | \(-0.820071\pi\) | ||||
−0.844448 | + | 0.535638i | \(0.820071\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.00000 | −0.157895 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.00000 | + | 1.00000i | −0.157027 | + | 0.0523424i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −15.0000 | − | 15.0000i | −0.782994 | − | 0.782994i | 0.197341 | − | 0.980335i | \(-0.436769\pi\) |
−0.980335 | + | 0.197341i | \(0.936769\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 30.0000i | − | 1.55752i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −9.00000 | − | 9.00000i | −0.466002 | − | 0.466002i | 0.434614 | − | 0.900617i | \(-0.356885\pi\) |
−0.900617 | + | 0.434614i | \(0.856885\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 20.0000 | 1.02733 | 0.513665 | − | 0.857991i | \(-0.328287\pi\) | ||||
0.513665 | + | 0.857991i | \(0.328287\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.00000 | − | 1.00000i | 0.0510976 | − | 0.0510976i | −0.681096 | − | 0.732194i | \(-0.738496\pi\) |
0.732194 | + | 0.681096i | \(0.238496\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.00000 | − | 18.0000i | −0.305788 | − | 0.917365i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 4.00000i | − | 0.202808i | −0.994845 | − | 0.101404i | \(-0.967667\pi\) | ||
0.994845 | − | 0.101404i | \(-0.0323335\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.00000i | 0.101144i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −8.00000 | + | 16.0000i | −0.402524 | + | 0.805047i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 15.0000 | − | 15.0000i | 0.752828 | − | 0.752828i | −0.222178 | − | 0.975006i | \(-0.571317\pi\) |
0.975006 | + | 0.222178i | \(0.0713165\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 22.0000 | 1.09863 | 0.549314 | − | 0.835616i | \(-0.314889\pi\) | ||||
0.549314 | + | 0.835616i | \(0.314889\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −30.0000 | + | 30.0000i | −1.49441 | + | 1.49441i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.00000 | + | 2.00000i | 0.0991363 | + | 0.0991363i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 20.0000i | − | 0.988936i | −0.869196 | − | 0.494468i | \(-0.835363\pi\) | ||
0.869196 | − | 0.494468i | \(-0.164637\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −36.0000 | − | 36.0000i | −1.77144 | − | 1.77144i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.00000 | − | 15.0000i | −0.245440 | − | 0.736321i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −28.0000 | −1.36789 | −0.683945 | − | 0.729534i | \(-0.739737\pi\) | ||||
−0.683945 | + | 0.729534i | \(0.739737\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 34.0000 | 1.65706 | 0.828529 | − | 0.559946i | \(-0.189178\pi\) | ||||
0.828529 | + | 0.559946i | \(0.189178\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7.00000 | + | 1.00000i | 0.339550 | + | 0.0485071i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.00000 | − | 6.00000i | −0.290360 | − | 0.290360i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 30.0000i | 1.44505i | 0.691345 | + | 0.722525i | \(0.257018\pi\) | ||||
−0.691345 | + | 0.722525i | \(0.742982\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 21.0000 | + | 21.0000i | 1.00920 | + | 1.00920i | 0.999957 | + | 0.00923827i | \(0.00294067\pi\) |
0.00923827 | + | 0.999957i | \(0.497059\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.00000 | − | 4.00000i | 0.191346 | − | 0.191346i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16.0000 | 0.763638 | 0.381819 | − | 0.924237i | \(-0.375298\pi\) | ||||
0.381819 | + | 0.924237i | \(0.375298\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −25.0000 | + | 25.0000i | −1.18779 | + | 1.18779i | −0.210108 | + | 0.977678i | \(0.567381\pi\) |
−0.977678 | + | 0.210108i | \(0.932619\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −32.0000 | − | 16.0000i | −1.51695 | − | 0.758473i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 12.0000i | − | 0.566315i | −0.959073 | − | 0.283158i | \(-0.908618\pi\) | ||
0.959073 | − | 0.283158i | \(-0.0913819\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 20.0000i | − | 0.941763i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 36.0000 | + | 18.0000i | 1.68771 | + | 0.843853i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.00000 | − | 9.00000i | 0.421002 | − | 0.421002i | −0.464546 | − | 0.885549i | \(-0.653783\pi\) |
0.885549 | + | 0.464546i | \(0.153783\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.00000 | 0.0931493 | 0.0465746 | − | 0.998915i | \(-0.485169\pi\) | ||||
0.0465746 | + | 0.998915i | \(0.485169\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.0000 | − | 11.0000i | 0.511213 | − | 0.511213i | −0.403685 | − | 0.914898i | \(-0.632271\pi\) |
0.914898 | + | 0.403685i | \(0.132271\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 13.0000 | + | 13.0000i | 0.601568 | + | 0.601568i | 0.940729 | − | 0.339160i | \(-0.110143\pi\) |
−0.339160 | + | 0.940729i | \(0.610143\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.00000i | 0.277054i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −10.0000 | − | 10.0000i | −0.459800 | − | 0.459800i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −12.0000 | − | 16.0000i | −0.550598 | − | 0.734130i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 40.0000 | 1.82765 | 0.913823 | − | 0.406112i | \(-0.133116\pi\) | ||||
0.913823 | + | 0.406112i | \(0.133116\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.00000 | −0.273576 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.00000 | − | 9.00000i | −0.136223 | − | 0.408669i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −19.0000 | − | 19.0000i | −0.860972 | − | 0.860972i | 0.130479 | − | 0.991451i | \(-0.458349\pi\) |
−0.991451 | + | 0.130479i | \(0.958349\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 10.0000i | − | 0.451294i | −0.974209 | − | 0.225647i | \(-0.927550\pi\) | ||
0.974209 | − | 0.225647i | \(-0.0724495\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −6.00000 | + | 6.00000i | −0.269137 | + | 0.269137i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 28.0000 | 1.25345 | 0.626726 | − | 0.779240i | \(-0.284395\pi\) | ||||
0.626726 | + | 0.779240i | \(0.284395\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 17.0000 | − | 17.0000i | 0.757993 | − | 0.757993i | −0.217964 | − | 0.975957i | \(-0.569942\pi\) |
0.975957 | + | 0.217964i | \(0.0699416\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.00000 | − | 12.0000i | 0.266996 | − | 0.533993i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 24.0000i | 1.06378i | 0.846813 | + | 0.531891i | \(0.178518\pi\) | ||||
−0.846813 | + | 0.531891i | \(0.821482\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 6.00000i | − | 0.265424i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −9.00000 | − | 27.0000i | −0.396587 | − | 1.18976i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.00000 | − | 6.00000i | 0.263880 | − | 0.263880i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 14.0000 | 0.613351 | 0.306676 | − | 0.951814i | \(-0.400783\pi\) | ||||
0.306676 | + | 0.951814i | \(0.400783\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −15.0000 | + | 15.0000i | −0.655904 | + | 0.655904i | −0.954408 | − | 0.298504i | \(-0.903512\pi\) |
0.298504 | + | 0.954408i | \(0.403512\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −10.0000 | − | 10.0000i | −0.435607 | − | 0.435607i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 21.0000i | 0.913043i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 30.0000 | + | 30.0000i | 1.29944 | + | 1.29944i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.00000 | − | 3.00000i | 0.389104 | − | 0.129701i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 22.0000 | 0.947607 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 30.0000 | 1.28980 | 0.644900 | − | 0.764267i | \(-0.276899\pi\) | ||||
0.644900 | + | 0.764267i | \(0.276899\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −8.00000 | − | 4.00000i | −0.342682 | − | 0.171341i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11.0000 | + | 11.0000i | 0.470326 | + | 0.470326i | 0.902020 | − | 0.431694i | \(-0.142084\pi\) |
−0.431694 | + | 0.902020i | \(0.642084\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −24.0000 | − | 24.0000i | −1.02058 | − | 1.02058i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −27.0000 | + | 27.0000i | −1.14403 | + | 1.14403i | −0.156320 | + | 0.987706i | \(0.549963\pi\) |
−0.987706 | + | 0.156320i | \(0.950037\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 30.0000 | 1.26886 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −33.0000 | + | 33.0000i | −1.39078 | + | 1.39078i | −0.567213 | + | 0.823571i | \(0.691978\pi\) |
−0.823571 | + | 0.567213i | \(0.808022\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.00000 | + | 3.00000i | −0.378633 | + | 0.126211i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 12.0000i | 0.503066i | 0.967849 | + | 0.251533i | \(0.0809347\pi\) | ||||
−0.967849 | + | 0.251533i | \(0.919065\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 34.0000i | 1.42286i | 0.702759 | + | 0.711428i | \(0.251951\pi\) | ||||
−0.702759 | + | 0.711428i | \(0.748049\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −7.00000 | − | 1.00000i | −0.291920 | − | 0.0417029i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −19.0000 | + | 19.0000i | −0.790980 | + | 0.790980i | −0.981654 | − | 0.190673i | \(-0.938933\pi\) |
0.190673 | + | 0.981654i | \(0.438933\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 30.0000 | 1.24461 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10.0000 | − | 10.0000i | 0.414158 | − | 0.414158i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −23.0000 | − | 23.0000i | −0.949312 | − | 0.949312i | 0.0494643 | − | 0.998776i | \(-0.484249\pi\) |
−0.998776 | + | 0.0494643i | \(0.984249\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 40.0000i | 1.64817i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.00000 | + | 7.00000i | 0.287456 | + | 0.287456i | 0.836073 | − | 0.548618i | \(-0.184846\pi\) |
−0.548618 | + | 0.836073i | \(0.684846\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.00000 | + | 12.0000i | −0.245976 | + | 0.491952i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10.0000 | −0.407909 | −0.203954 | − | 0.978980i | \(-0.565379\pi\) | ||||
−0.203954 | + | 0.978980i | \(0.565379\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −7.00000 | + | 14.0000i | −0.284590 | + | 0.569181i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.00000 | + | 5.00000i | 0.202944 | + | 0.202944i | 0.801260 | − | 0.598316i | \(-0.204163\pi\) |
−0.598316 | + | 0.801260i | \(0.704163\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 18.0000i | 0.728202i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 15.0000 | + | 15.0000i | 0.605844 | + | 0.605844i | 0.941857 | − | 0.336013i | \(-0.109079\pi\) |
−0.336013 | + | 0.941857i | \(0.609079\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −13.0000 | + | 13.0000i | −0.523360 | + | 0.523360i | −0.918585 | − | 0.395224i | \(-0.870667\pi\) |
0.395224 | + | 0.918585i | \(0.370667\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −12.0000 | −0.482321 | −0.241160 | − | 0.970485i | \(-0.577528\pi\) | ||||
−0.241160 | + | 0.970485i | \(0.577528\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 48.0000 | − | 48.0000i | 1.92308 | − | 1.92308i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.00000 | + | 24.0000i | −0.280000 | + | 0.960000i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 2.00000i | − | 0.0797452i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 14.0000i | − | 0.557331i | −0.960388 | − | 0.278666i | \(-0.910108\pi\) | ||
0.960388 | − | 0.278666i | \(-0.0898921\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 21.0000 | − | 7.00000i | 0.833360 | − | 0.277787i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −33.0000 | + | 33.0000i | −1.30751 | + | 1.30751i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −30.0000 | −1.18493 | −0.592464 | − | 0.805597i | \(-0.701845\pi\) | ||||
−0.592464 | + | 0.805597i | \(0.701845\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −27.0000 | + | 27.0000i | −1.06478 | + | 1.06478i | −0.0670247 | + | 0.997751i | \(0.521351\pi\) |
−0.997751 | + | 0.0670247i | \(0.978649\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −29.0000 | − | 29.0000i | −1.14011 | − | 1.14011i | −0.988430 | − | 0.151678i | \(-0.951532\pi\) |
−0.151678 | − | 0.988430i | \(-0.548468\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 24.0000i | − | 0.942082i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.00000 | + | 1.00000i | 0.0391330 | + | 0.0391330i | 0.726403 | − | 0.687270i | \(-0.241191\pi\) |
−0.687270 | + | 0.726403i | \(0.741191\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 20.0000 | + | 10.0000i | 0.781465 | + | 0.390732i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 36.0000 | 1.40236 | 0.701180 | − | 0.712984i | \(-0.252657\pi\) | ||||
0.701180 | + | 0.712984i | \(0.252657\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −30.0000 | −1.16686 | −0.583432 | − | 0.812162i | \(-0.698291\pi\) | ||||
−0.583432 | + | 0.812162i | \(0.698291\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 36.0000 | − | 12.0000i | 1.39602 | − | 0.465340i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 4.00000i | − | 0.154418i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.00000 | − | 3.00000i | −0.115642 | − | 0.115642i | 0.646918 | − | 0.762560i | \(-0.276058\pi\) |
−0.762560 | + | 0.646918i | \(0.776058\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3.00000 | + | 3.00000i | −0.115299 | + | 0.115299i | −0.762402 | − | 0.647103i | \(-0.775980\pi\) |
0.647103 | + | 0.762402i | \(0.275980\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 18.0000 | 0.690777 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 11.0000 | − | 11.0000i | 0.420903 | − | 0.420903i | −0.464611 | − | 0.885515i | \(-0.653806\pi\) |
0.885515 | + | 0.464611i | \(0.153806\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 11.0000 | + | 33.0000i | 0.420288 | + | 1.26087i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 30.0000i | 1.14291i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 14.0000i | − | 0.532585i | −0.963892 | − | 0.266293i | \(-0.914201\pi\) | ||
0.963892 | − | 0.266293i | \(-0.0857987\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −12.0000 | + | 24.0000i | −0.455186 | + | 0.910372i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −10.0000 | + | 10.0000i | −0.378777 | + | 0.378777i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −34.0000 | −1.28416 | −0.642081 | − | 0.766637i | \(-0.721929\pi\) | ||||
−0.642081 | + | 0.766637i | \(0.721929\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.00000 | + | 4.00000i | −0.150863 | + | 0.150863i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 18.0000 | + | 18.0000i | 0.676960 | + | 0.676960i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 48.0000i | − | 1.80268i | −0.433114 | − | 0.901339i | \(-0.642585\pi\) | ||
0.433114 | − | 0.901339i | \(-0.357415\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 10.0000 | + | 10.0000i | 0.374503 | + | 0.374503i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.00000 | + | 18.0000i | 0.224387 | + | 0.673162i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −16.0000 | −0.596699 | −0.298350 | − | 0.954457i | \(-0.596436\pi\) | ||||
−0.298350 | + | 0.954457i | \(0.596436\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 54.0000 | 2.01107 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3.00000 | − | 3.00000i | −0.111264 | − | 0.111264i | 0.649283 | − | 0.760547i | \(-0.275069\pi\) |
−0.760547 | + | 0.649283i | \(0.775069\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 10.0000i | 0.369863i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 27.0000 | + | 27.0000i | 0.997268 | + | 0.997268i | 0.999996 | − | 0.00272852i | \(-0.000868517\pi\) |
−0.00272852 | + | 0.999996i | \(0.500869\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.00000 | + | 2.00000i | −0.0736709 | + | 0.0736709i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −28.0000 | −1.03000 | −0.514998 | − | 0.857191i | \(-0.672207\pi\) | ||||
−0.514998 | + | 0.857191i | \(0.672207\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 21.0000 | − | 21.0000i | 0.770415 | − | 0.770415i | −0.207764 | − | 0.978179i | \(-0.566619\pi\) |
0.978179 | + | 0.207764i | \(0.0666185\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.00000 | + | 4.00000i | 0.293097 | + | 0.146549i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 18.0000i | 0.657706i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.00000i | 0.0729810i | 0.999334 | + | 0.0364905i | \(0.0116179\pi\) | ||||
−0.999334 | + | 0.0364905i | \(0.988382\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 12.0000 | + | 6.00000i | 0.436725 | + | 0.218362i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 19.0000 | − | 19.0000i | 0.690567 | − | 0.690567i | −0.271790 | − | 0.962357i | \(-0.587616\pi\) |
0.962357 | + | 0.271790i | \(0.0876156\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −18.0000 | −0.652499 | −0.326250 | − | 0.945284i | \(-0.605785\pi\) | ||||
−0.326250 | + | 0.945284i | \(0.605785\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 12.0000 | − | 12.0000i | 0.434429 | − | 0.434429i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 36.0000 | + | 36.0000i | 1.29988 | + | 1.29988i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 8.00000i | 0.288487i | 0.989542 | + | 0.144244i | \(0.0460749\pi\) | ||||
−0.989542 | + | 0.144244i | \(0.953925\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 17.0000 | + | 17.0000i | 0.611448 | + | 0.611448i | 0.943323 | − | 0.331876i | \(-0.107681\pi\) |
−0.331876 | + | 0.943323i | \(0.607681\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 40.0000 | − | 30.0000i | 1.43684 | − | 1.07763i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 40.0000 | 1.43315 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.00000 | −0.143131 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.00000 | − | 3.00000i | −0.0356915 | − | 0.107075i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 31.0000 | + | 31.0000i | 1.10503 | + | 1.10503i | 0.993794 | + | 0.111237i | \(0.0354812\pi\) |
0.111237 | + | 0.993794i | \(0.464519\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 18.0000i | − | 0.640006i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.00000 | + | 6.00000i | 0.213066 | + | 0.213066i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 37.0000 | − | 37.0000i | 1.31061 | − | 1.31061i | 0.389640 | − | 0.920967i | \(-0.372599\pi\) |
0.920967 | − | 0.389640i | \(-0.127401\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.00000 | −0.212265 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.00000 | − | 2.00000i | 0.0705785 | − | 0.0705785i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.00000 | − | 12.0000i | 0.211472 | − | 0.422944i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 16.0000i | 0.562530i | 0.959630 | + | 0.281265i | \(0.0907540\pi\) | ||||
−0.959630 | + | 0.281265i | \(0.909246\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 54.0000i | − | 1.89620i | −0.317978 | − | 0.948098i | \(-0.603004\pi\) | ||
0.317978 | − | 0.948098i | \(-0.396996\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.00000 | + | 3.00000i | 0.0350285 | + | 0.105085i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 20.0000 | − | 20.0000i | 0.699711 | − | 0.699711i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −10.0000 | −0.349002 | −0.174501 | − | 0.984657i | \(-0.555831\pi\) | ||||
−0.174501 | + | 0.984657i | \(0.555831\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7.00000 | − | 7.00000i | 0.244005 | − | 0.244005i | −0.574500 | − | 0.818505i | \(-0.694803\pi\) |
0.818505 | + | 0.574500i | \(0.194803\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 25.0000 | + | 25.0000i | 0.869335 | + | 0.869335i | 0.992399 | − | 0.123064i | \(-0.0392719\pi\) |
−0.123064 | + | 0.992399i | \(0.539272\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 20.0000i | − | 0.694629i | −0.937749 | − | 0.347314i | \(-0.887094\pi\) | ||
0.937749 | − | 0.347314i | \(-0.112906\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −11.0000 | − | 11.0000i | −0.381127 | − | 0.381127i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.00000 | − | 1.00000i | 0.103819 | − | 0.0346064i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 24.0000 | 0.828572 | 0.414286 | − | 0.910147i | \(-0.364031\pi\) | ||||
0.414286 | + | 0.910147i | \(0.364031\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 29.0000 | 1.00000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −10.0000 | − | 5.00000i | −0.344010 | − | 0.172005i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −21.0000 | − | 21.0000i | −0.721569 | − | 0.721569i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.00000i | 0.0685591i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −9.00000 | − | 9.00000i | −0.308154 | − | 0.308154i | 0.536039 | − | 0.844193i | \(-0.319920\pi\) |
−0.844193 | + | 0.536039i | \(0.819920\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 35.0000 | − | 35.0000i | 1.19558 | − | 1.19558i | 0.220100 | − | 0.975477i | \(-0.429362\pi\) |
0.975477 | − | 0.220100i | \(-0.0706383\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −28.0000 | −0.955348 | −0.477674 | − | 0.878537i | \(-0.658520\pi\) | ||||
−0.477674 | + | 0.878537i | \(0.658520\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 13.0000 | − | 13.0000i | 0.442525 | − | 0.442525i | −0.450335 | − | 0.892860i | \(-0.648695\pi\) |
0.892860 | + | 0.450335i | \(0.148695\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −15.0000 | + | 5.00000i | −0.510015 | + | 0.170005i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 16.0000i | − | 0.542763i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 6.00000i | − | 0.203302i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −39.0000 | − | 27.0000i | −1.31844 | − | 0.912767i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7.00000 | − | 7.00000i | 0.236373 | − | 0.236373i | −0.578973 | − | 0.815347i | \(-0.696546\pi\) |
0.815347 | + | 0.578973i | \(0.196546\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 18.0000 | 0.606435 | 0.303218 | − | 0.952921i | \(-0.401939\pi\) | ||||
0.303218 | + | 0.952921i | \(0.401939\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 33.0000 | − | 33.0000i | 1.11054 | − | 1.11054i | 0.117461 | − | 0.993078i | \(-0.462525\pi\) |
0.993078 | − | 0.117461i | \(-0.0374755\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −5.00000 | − | 5.00000i | −0.167884 | − | 0.167884i | 0.618165 | − | 0.786048i | \(-0.287876\pi\) |
−0.786048 | + | 0.618165i | \(0.787876\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 42.0000i | 1.40863i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 12.0000 | + | 12.0000i | 0.401565 | + | 0.401565i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −12.0000 | + | 24.0000i | −0.401116 | + | 0.802232i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10.0000 | −0.333148 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −22.0000 | + | 44.0000i | −0.731305 | + | 1.46261i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 27.0000 | + | 27.0000i | 0.896520 | + | 0.896520i | 0.995127 | − | 0.0986062i | \(-0.0314384\pi\) |
−0.0986062 | + | 0.995127i | \(0.531438\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6.00000i | 0.198789i | 0.995048 | + | 0.0993944i | \(0.0316906\pi\) | ||||
−0.995048 | + | 0.0993944i | \(0.968309\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 10.0000 | + | 10.0000i | 0.330952 | + | 0.330952i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −30.0000 | + | 30.0000i | −0.990687 | + | 0.990687i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −48.0000 | −1.58337 | −0.791687 | − | 0.610927i | \(-0.790797\pi\) | ||||
−0.791687 | + | 0.610927i | \(0.790797\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6.00000 | − | 6.00000i | 0.197492 | − | 0.197492i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.00000 | + | 1.00000i | 0.230159 | + | 0.0328798i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 28.0000i | 0.918650i | 0.888268 | + | 0.459325i | \(0.151909\pi\) | ||||
−0.888268 | + | 0.459325i | \(0.848091\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 44.0000i | 1.44204i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −6.00000 | + | 2.00000i | −0.196221 | + | 0.0654070i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 21.0000 | − | 21.0000i | 0.686040 | − | 0.686040i | −0.275314 | − | 0.961354i | \(-0.588782\pi\) |
0.961354 | + | 0.275314i | \(0.0887819\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 34.0000 | 1.10837 | 0.554184 | − | 0.832394i | \(-0.313030\pi\) | ||||
0.554184 | + | 0.832394i | \(0.313030\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 10.0000 | − | 10.0000i | 0.325645 | − | 0.325645i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −31.0000 | − | 31.0000i | −1.00736 | − | 1.00736i | −0.999973 | − | 0.00739197i | \(-0.997647\pi\) |
−0.00739197 | − | 0.999973i | \(-0.502353\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.00000i | 0.194768i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 31.0000 | + | 31.0000i | 1.00419 | + | 1.00419i | 0.999991 | + | 0.00419731i | \(0.00133605\pi\) |
0.00419731 | + | 0.999991i | \(0.498664\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −28.0000 | − | 14.0000i | −0.906059 | − | 0.453029i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −66.0000 | −2.13125 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −69.0000 | −2.22581 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 45.0000 | − | 15.0000i | 1.44860 | − | 0.482867i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.00000 | + | 1.00000i | 0.0321578 | + | 0.0321578i | 0.723003 | − | 0.690845i | \(-0.242761\pi\) |
−0.690845 | + | 0.723003i | \(0.742761\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 2.00000i | − | 0.0641831i | −0.999485 | − | 0.0320915i | \(-0.989783\pi\) | ||
0.999485 | − | 0.0320915i | \(-0.0102168\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −36.0000 | − | 36.0000i | −1.15411 | − | 1.15411i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −21.0000 | + | 21.0000i | −0.671850 | + | 0.671850i | −0.958142 | − | 0.286293i | \(-0.907577\pi\) |
0.286293 | + | 0.958142i | \(0.407577\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 32.0000 | 1.02272 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 5.00000 | − | 5.00000i | 0.159475 | − | 0.159475i | −0.622859 | − | 0.782334i | \(-0.714029\pi\) |
0.782334 | + | 0.622859i | \(0.214029\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 13.0000 | + | 39.0000i | 0.414214 | + | 1.24264i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 10.0000i | − | 0.317982i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10.0000i | 0.317660i | 0.987306 | + | 0.158830i | \(0.0507723\pi\) | ||||
−0.987306 | + | 0.158830i | \(0.949228\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 16.0000 | − | 32.0000i | 0.507234 | − | 1.01447i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −17.0000 | + | 17.0000i | −0.538395 | + | 0.538395i | −0.923057 | − | 0.384662i | \(-0.874318\pi\) |
0.384662 | + | 0.923057i | \(0.374318\pi\) | |||||||
\(998\) | 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 | 1440.2.x.a.703.1 | 2 | ||
3.2 | odd | 2 | 160.2.n.d.63.1 | yes | 2 | ||
4.3 | odd | 2 | 1440.2.x.f.703.1 | 2 | |||
5.2 | odd | 4 | 1440.2.x.f.127.1 | 2 | |||
12.11 | even | 2 | 160.2.n.c.63.1 | ✓ | 2 | ||
15.2 | even | 4 | 160.2.n.c.127.1 | yes | 2 | ||
15.8 | even | 4 | 800.2.n.f.607.1 | 2 | |||
15.14 | odd | 2 | 800.2.n.e.543.1 | 2 | |||
20.7 | even | 4 | inner | 1440.2.x.a.127.1 | 2 | ||
24.5 | odd | 2 | 320.2.n.b.63.1 | 2 | |||
24.11 | even | 2 | 320.2.n.g.63.1 | 2 | |||
48.5 | odd | 4 | 1280.2.o.f.383.1 | 2 | |||
48.11 | even | 4 | 1280.2.o.m.383.1 | 2 | |||
48.29 | odd | 4 | 1280.2.o.l.383.1 | 2 | |||
48.35 | even | 4 | 1280.2.o.c.383.1 | 2 | |||
60.23 | odd | 4 | 800.2.n.e.607.1 | 2 | |||
60.47 | odd | 4 | 160.2.n.d.127.1 | yes | 2 | ||
60.59 | even | 2 | 800.2.n.f.543.1 | 2 | |||
120.29 | odd | 2 | 1600.2.n.m.1343.1 | 2 | |||
120.53 | even | 4 | 1600.2.n.c.1407.1 | 2 | |||
120.59 | even | 2 | 1600.2.n.c.1343.1 | 2 | |||
120.77 | even | 4 | 320.2.n.g.127.1 | 2 | |||
120.83 | odd | 4 | 1600.2.n.m.1407.1 | 2 | |||
120.107 | odd | 4 | 320.2.n.b.127.1 | 2 | |||
240.77 | even | 4 | 1280.2.o.m.127.1 | 2 | |||
240.107 | odd | 4 | 1280.2.o.l.127.1 | 2 | |||
240.197 | even | 4 | 1280.2.o.c.127.1 | 2 | |||
240.227 | odd | 4 | 1280.2.o.f.127.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
160.2.n.c.63.1 | ✓ | 2 | 12.11 | even | 2 | ||
160.2.n.c.127.1 | yes | 2 | 15.2 | even | 4 | ||
160.2.n.d.63.1 | yes | 2 | 3.2 | odd | 2 | ||
160.2.n.d.127.1 | yes | 2 | 60.47 | odd | 4 | ||
320.2.n.b.63.1 | 2 | 24.5 | odd | 2 | |||
320.2.n.b.127.1 | 2 | 120.107 | odd | 4 | |||
320.2.n.g.63.1 | 2 | 24.11 | even | 2 | |||
320.2.n.g.127.1 | 2 | 120.77 | even | 4 | |||
800.2.n.e.543.1 | 2 | 15.14 | odd | 2 | |||
800.2.n.e.607.1 | 2 | 60.23 | odd | 4 | |||
800.2.n.f.543.1 | 2 | 60.59 | even | 2 | |||
800.2.n.f.607.1 | 2 | 15.8 | even | 4 | |||
1280.2.o.c.127.1 | 2 | 240.197 | even | 4 | |||
1280.2.o.c.383.1 | 2 | 48.35 | even | 4 | |||
1280.2.o.f.127.1 | 2 | 240.227 | odd | 4 | |||
1280.2.o.f.383.1 | 2 | 48.5 | odd | 4 | |||
1280.2.o.l.127.1 | 2 | 240.107 | odd | 4 | |||
1280.2.o.l.383.1 | 2 | 48.29 | odd | 4 | |||
1280.2.o.m.127.1 | 2 | 240.77 | even | 4 | |||
1280.2.o.m.383.1 | 2 | 48.11 | even | 4 | |||
1440.2.x.a.127.1 | 2 | 20.7 | even | 4 | inner | ||
1440.2.x.a.703.1 | 2 | 1.1 | even | 1 | trivial | ||
1440.2.x.f.127.1 | 2 | 5.2 | odd | 4 | |||
1440.2.x.f.703.1 | 2 | 4.3 | odd | 2 | |||
1600.2.n.c.1343.1 | 2 | 120.59 | even | 2 | |||
1600.2.n.c.1407.1 | 2 | 120.53 | even | 4 | |||
1600.2.n.m.1343.1 | 2 | 120.29 | odd | 2 | |||
1600.2.n.m.1407.1 | 2 | 120.83 | odd | 4 |