Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5184,2,Mod(2593,5184)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5184, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5184.2593");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5184 = 2^{6} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5184.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(41.3944484078\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 16x^{8} - 24x^{7} + 96x^{5} + 304x^{4} + 384x^{3} + 288x^{2} + 144x + 36 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{12}\cdot 3^{4} \) |
Twist minimal: | no (minimal twist has level 576) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2593.5 | ||
Root | \(0.583700 + 2.17840i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5184.2593 |
Dual form | 5184.2.d.q.2593.11 |
$q$-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 \(\left(\mathbb{Z}/5184\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(1217\) | \(2431\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 1.73205i | − 0.774597i | −0.921954 | − | 0.387298i | \(-0.873408\pi\) | ||||
0.921954 | − | 0.387298i | \(-0.126592\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.61328 | 1.36569 | 0.682846 | − | 0.730562i | \(-0.260742\pi\) | ||||
0.682846 | + | 0.730562i | \(0.260742\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 0.734191i | − 0.221367i | −0.993856 | − | 0.110683i | \(-0.964696\pi\) | ||||
0.993856 | − | 0.110683i | \(-0.0353040\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.609577i | 0.169066i | 0.996421 | + | 0.0845331i | \(0.0269399\pi\) | ||||
−0.996421 | + | 0.0845331i | \(0.973060\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.52420 | −1.33982 | −0.669908 | − | 0.742444i | \(-0.733666\pi\) | ||||
−0.669908 | + | 0.742444i | \(0.733666\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 2.00000i | − 0.458831i | −0.973329 | − | 0.229416i | \(-0.926318\pi\) | ||||
0.973329 | − | 0.229416i | \(-0.0736815\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.73576 | −0.987474 | −0.493737 | − | 0.869611i | \(-0.664369\pi\) | ||||
−0.493737 | + | 0.869611i | \(0.664369\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.00000 | 0.400000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.83614i | 1.45514i | 0.686036 | + | 0.727568i | \(0.259349\pi\) | ||||
−0.686036 | + | 0.727568i | \(0.740651\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.41901 | −1.69170 | −0.845852 | − | 0.533417i | \(-0.820908\pi\) | ||||
−0.845852 | + | 0.533417i | \(0.820908\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 6.25839i | − 1.05786i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 2.34163i | − 0.384961i | −0.981301 | − | 0.192481i | \(-0.938347\pi\) | ||||
0.981301 | − | 0.192481i | \(-0.0616532\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.52420 | −1.33126 | −0.665628 | − | 0.746284i | \(-0.731836\pi\) | ||||
−0.665628 | + | 0.746284i | \(0.731836\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 10.2584i | − 1.56439i | −0.623034 | − | 0.782195i | \(-0.714100\pi\) | ||||
0.623034 | − | 0.782195i | \(-0.285900\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −11.7606 | −1.71547 | −0.857733 | − | 0.514096i | \(-0.828128\pi\) | ||||
−0.857733 | + | 0.514096i | \(0.828128\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.05582 | 0.865117 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 13.0323i | − 1.79012i | −0.445942 | − | 0.895062i | \(-0.647131\pi\) | ||||
0.445942 | − | 0.895062i | \(-0.352869\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.27166 | −0.171470 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.20999i | 0.157527i | 0.996893 | + | 0.0787637i | \(0.0250973\pi\) | ||||
−0.996893 | + | 0.0787637i | \(0.974903\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 11.3002i | − 1.44685i | −0.690404 | − | 0.723424i | \(-0.742567\pi\) | ||||
0.690404 | − | 0.723424i | \(-0.257433\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.05582 | 0.130958 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.31421i | 0.771403i | 0.922624 | + | 0.385702i | \(0.126041\pi\) | ||||
−0.922624 | + | 0.385702i | \(0.873959\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.63999 | 0.313309 | 0.156655 | − | 0.987653i | \(-0.449929\pi\) | ||||
0.156655 | + | 0.987653i | \(0.449929\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.05582 | −0.240615 | −0.120308 | − | 0.992737i | \(-0.538388\pi\) | ||||
−0.120308 | + | 0.992737i | \(0.538388\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 2.65284i | − 0.302319i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.49081 | 0.280238 | 0.140119 | − | 0.990135i | \(-0.455251\pi\) | ||||
0.140119 | + | 0.990135i | \(0.455251\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.2584i | 1.34553i | 0.739855 | + | 0.672767i | \(0.234894\pi\) | ||||
−0.739855 | + | 0.672767i | \(0.765106\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.56819i | 1.03782i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.94418 | −0.206083 | −0.103041 | − | 0.994677i | \(-0.532857\pi\) | ||||
−0.103041 | + | 0.994677i | \(0.532857\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.20257i | 0.230892i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.46410 | −0.355409 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −15.5726 | −1.58116 | −0.790579 | − | 0.612360i | \(-0.790220\pi\) | ||||
−0.790579 | + | 0.612360i | \(0.790220\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 11.2036i | − 1.11480i | −0.830245 | − | 0.557398i | \(-0.811800\pi\) | ||||
0.830245 | − | 0.557398i | \(-0.188200\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.36834 | −0.134826 | −0.0674130 | − | 0.997725i | \(-0.521475\pi\) | ||||
−0.0674130 | + | 0.997725i | \(0.521475\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.4684i | 1.30204i | 0.759062 | + | 0.651019i | \(0.225658\pi\) | ||||
−0.759062 | + | 0.651019i | \(0.774342\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.42084i | 0.136092i | 0.997682 | + | 0.0680458i | \(0.0216764\pi\) | ||||
−0.997682 | + | 0.0680458i | \(0.978324\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.51678 | 0.895263 | 0.447632 | − | 0.894218i | \(-0.352268\pi\) | ||||
0.447632 | + | 0.894218i | \(0.352268\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.20257i | 0.764894i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −19.9605 | −1.82978 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.4610 | 0.950997 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 12.1244i | − 1.08444i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.24495 | −0.199207 | −0.0996035 | − | 0.995027i | \(-0.531757\pi\) | ||||
−0.0996035 | + | 0.995027i | \(0.531757\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.258391i | 0.0225757i | 0.999936 | + | 0.0112878i | \(0.00359311\pi\) | ||||
−0.999936 | + | 0.0112878i | \(0.996407\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 7.22657i | − 0.626623i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.00742 | −0.171505 | −0.0857527 | − | 0.996316i | \(-0.527329\pi\) | ||||
−0.0857527 | + | 0.996316i | \(0.527329\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 2.25839i | − 0.191554i | −0.995403 | − | 0.0957771i | \(-0.969466\pi\) | ||||
0.995403 | − | 0.0957771i | \(-0.0305336\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.447546 | 0.0374256 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 13.5726 | 1.12714 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 14.7643i | − 1.20954i | −0.796399 | − | 0.604771i | \(-0.793265\pi\) | ||||
0.796399 | − | 0.604771i | \(-0.206735\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.65655 | 0.460323 | 0.230162 | − | 0.973152i | \(-0.426075\pi\) | ||||
0.230162 | + | 0.973152i | \(0.426075\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 16.3142i | 1.31039i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.8868i | 1.26791i | 0.773371 | + | 0.633953i | \(0.218569\pi\) | ||||
−0.773371 | + | 0.633953i | \(0.781431\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −17.1116 | −1.34859 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 8.51678i | − 0.667086i | −0.942735 | − | 0.333543i | \(-0.891756\pi\) | ||||
0.942735 | − | 0.333543i | \(-0.108244\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.91165 | 0.302692 | 0.151346 | − | 0.988481i | \(-0.451639\pi\) | ||||
0.151346 | + | 0.988481i | \(0.451639\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.6284 | 0.971417 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 12.1244i | − 0.921798i | −0.887453 | − | 0.460899i | \(-0.847527\pi\) | ||||
0.887453 | − | 0.460899i | \(-0.152473\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 7.22657 | 0.546277 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 6.00000i | − 0.448461i | −0.974536 | − | 0.224231i | \(-0.928013\pi\) | ||||
0.974536 | − | 0.224231i | \(-0.0719869\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.34163i | 0.174052i | 0.996206 | + | 0.0870259i | \(0.0277363\pi\) | ||||
−0.996206 | + | 0.0870259i | \(0.972264\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.05582 | −0.298190 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.05582i | 0.296591i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.36834 | 0.0990092 | 0.0495046 | − | 0.998774i | \(-0.484236\pi\) | ||||
0.0495046 | + | 0.998774i | \(0.484236\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −15.4610 | −1.11290 | −0.556452 | − | 0.830880i | \(-0.687838\pi\) | ||||
−0.556452 | + | 0.830880i | \(0.687838\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 12.9356i | − 0.921625i | −0.887498 | − | 0.460812i | \(-0.847558\pi\) | ||||
0.887498 | − | 0.460812i | \(-0.152442\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 18.7413 | 1.32854 | 0.664269 | − | 0.747493i | \(-0.268743\pi\) | ||||
0.664269 | + | 0.747493i | \(0.268743\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 28.3142i | 1.98727i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 14.7643i | 1.03119i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.46838 | −0.101570 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 8.31421i | − 0.572374i | −0.958174 | − | 0.286187i | \(-0.907612\pi\) | ||||
0.958174 | − | 0.286187i | \(-0.0923878\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −17.7681 | −1.21177 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −34.0336 | −2.31035 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 3.36742i | − 0.226517i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.99817 | −0.535597 | −0.267799 | − | 0.963475i | \(-0.586296\pi\) | ||||
−0.267799 | + | 0.963475i | \(0.586296\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 5.26581i | − 0.349504i | −0.984612 | − | 0.174752i | \(-0.944088\pi\) | ||||
0.984612 | − | 0.174752i | \(-0.0559124\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 16.1852i | − 1.06955i | −0.844995 | − | 0.534774i | \(-0.820397\pi\) | ||||
0.844995 | − | 0.534774i | \(-0.179603\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 28.0968 | 1.84068 | 0.920341 | − | 0.391116i | \(-0.127911\pi\) | ||||
0.920341 | + | 0.391116i | \(0.127911\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 20.3700i | 1.32879i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −18.5922 | −1.20263 | −0.601314 | − | 0.799013i | \(-0.705356\pi\) | ||||
−0.601314 | + | 0.799013i | \(0.705356\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.11164 | −0.586932 | −0.293466 | − | 0.955970i | \(-0.594809\pi\) | ||||
−0.293466 | + | 0.955970i | \(0.594809\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 10.4890i | − 0.670117i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.21915 | 0.0775729 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 21.5800i | 1.36212i | 0.732228 | + | 0.681059i | \(0.238480\pi\) | ||||
−0.732228 | + | 0.681059i | \(0.761520\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.47695i | 0.218594i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5.41998 | −0.338089 | −0.169045 | − | 0.985608i | \(-0.554068\pi\) | ||||
−0.169045 | + | 0.985608i | \(0.554068\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 8.46096i | − 0.525739i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 10.0157 | 0.617597 | 0.308798 | − | 0.951127i | \(-0.400073\pi\) | ||||
0.308798 | + | 0.951127i | \(0.400073\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −22.5726 | −1.38662 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 12.1115i | 0.738452i | 0.929340 | + | 0.369226i | \(0.120377\pi\) | ||||
−0.929340 | + | 0.369226i | \(0.879623\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −20.0572 | −1.21839 | −0.609193 | − | 0.793022i | \(-0.708507\pi\) | ||||
−0.609193 | + | 0.793022i | \(0.708507\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 1.46838i | − 0.0885468i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.49452i | 0.330133i | 0.986282 | + | 0.165067i | \(0.0527840\pi\) | ||||
−0.986282 | + | 0.165067i | \(0.947216\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.16745 | −0.546884 | −0.273442 | − | 0.961888i | \(-0.588162\pi\) | ||||
−0.273442 | + | 0.961888i | \(0.588162\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 22.7752i | 1.35384i | 0.736055 | + | 0.676922i | \(0.236686\pi\) | ||||
−0.736055 | + | 0.676922i | \(0.763314\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −30.8003 | −1.81809 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.5168 | 0.795105 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 21.5959i | − 1.26164i | −0.775927 | − | 0.630822i | \(-0.782718\pi\) | ||||
0.775927 | − | 0.630822i | \(-0.217282\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.09577 | 0.122020 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 2.88681i | − 0.166948i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 37.0665i | − 2.13648i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −19.5726 | −1.12072 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.51678i | 0.486078i | 0.970016 | + | 0.243039i | \(0.0781444\pi\) | ||||
−0.970016 | + | 0.243039i | \(0.921856\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −24.7929 | −1.40588 | −0.702939 | − | 0.711250i | \(-0.748129\pi\) | ||||
−0.702939 | + | 0.711250i | \(0.748129\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.1116 | 0.854160 | 0.427080 | − | 0.904214i | \(-0.359542\pi\) | ||||
0.427080 | + | 0.904214i | \(0.359542\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 12.2210i | − 0.686402i | −0.939262 | − | 0.343201i | \(-0.888489\pi\) | ||||
0.939262 | − | 0.343201i | \(-0.111511\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.75323 | 0.322119 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 11.0484i | 0.614749i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.21915i | 0.0676264i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −42.4945 | −2.34280 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 24.7194i | 1.35870i | 0.733815 | + | 0.679349i | \(0.237738\pi\) | ||||
−0.733815 | + | 0.679349i | \(0.762262\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 10.9365 | 0.597526 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.5168 | 0.736306 | 0.368153 | − | 0.929765i | \(-0.379990\pi\) | ||||
0.368153 | + | 0.929765i | \(0.379990\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.91535i | 0.374487i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3.41160 | −0.184209 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 15.3626i | − 0.824708i | −0.911024 | − | 0.412354i | \(-0.864707\pi\) | ||||
0.911024 | − | 0.412354i | \(-0.135293\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 31.5591i | 1.68932i | 0.535303 | + | 0.844660i | \(0.320197\pi\) | ||||
−0.535303 | + | 0.844660i | \(0.679803\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −27.9926 | −1.48989 | −0.744947 | − | 0.667123i | \(-0.767525\pi\) | ||||
−0.744947 | + | 0.667123i | \(0.767525\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 4.57260i | − 0.242688i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −13.1290 | −0.692921 | −0.346460 | − | 0.938065i | \(-0.612616\pi\) | ||||
−0.346460 | + | 0.938065i | \(0.612616\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.0000 | 0.789474 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.56078i | 0.186380i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.4798 | −0.703642 | −0.351821 | − | 0.936067i | \(-0.614437\pi\) | ||||
−0.351821 | + | 0.936067i | \(0.614437\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 47.0894i | − 2.44476i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 5.59120i | − 0.289501i | −0.989468 | − | 0.144751i | \(-0.953762\pi\) | ||||
0.989468 | − | 0.144751i | \(-0.0462380\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.77673 | −0.246014 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 33.0894i | − 1.69969i | −0.527035 | − | 0.849844i | \(-0.676696\pi\) | ||||
0.527035 | − | 0.849844i | \(-0.323304\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −15.2247 | −0.777948 | −0.388974 | − | 0.921249i | \(-0.627170\pi\) | ||||
−0.388974 | + | 0.921249i | \(0.627170\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.59485 | −0.234175 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 6.11694i | − 0.310141i | −0.987903 | − | 0.155071i | \(-0.950439\pi\) | ||||
0.987903 | − | 0.155071i | \(-0.0495605\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 26.1613 | 1.32303 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 4.31421i | − 0.217071i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 22.2054i | − 1.11446i | −0.830358 | − | 0.557230i | \(-0.811864\pi\) | ||||
0.830358 | − | 0.557230i | \(-0.188136\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 30.1042 | 1.50333 | 0.751666 | − | 0.659543i | \(-0.229250\pi\) | ||||
0.751666 | + | 0.659543i | \(0.229250\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 5.74161i | − 0.286010i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.71920 | −0.0852177 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9.11164 | −0.450541 | −0.225271 | − | 0.974296i | \(-0.572327\pi\) | ||||
−0.225271 | + | 0.974296i | \(0.572327\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.37204i | 0.215134i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 21.2322 | 1.04225 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 22.8310i | − 1.11537i | −0.830054 | − | 0.557683i | \(-0.811690\pi\) | ||||
0.830054 | − | 0.557683i | \(-0.188310\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 24.5342i | 1.19573i | 0.801599 | + | 0.597863i | \(0.203983\pi\) | ||||
−0.801599 | + | 0.597863i | \(0.796017\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −11.0484 | −0.535926 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 40.8310i | − 1.97595i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0.920789 | 0.0443529 | 0.0221764 | − | 0.999754i | \(-0.492940\pi\) | ||||
0.0221764 | + | 0.999754i | \(0.492940\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.05582 | 0.0987963 | 0.0493981 | − | 0.998779i | \(-0.484270\pi\) | ||||
0.0493981 | + | 0.998779i | \(0.484270\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 9.47152i | 0.453084i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −22.0563 | −1.05269 | −0.526344 | − | 0.850272i | \(-0.676438\pi\) | ||||
−0.526344 | + | 0.850272i | \(0.676438\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 27.1952i | 1.29208i | 0.763303 | + | 0.646040i | \(0.223576\pi\) | ||||
−0.763303 | + | 0.646040i | \(0.776424\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.36742i | 0.159631i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9.10422 | −0.429655 | −0.214827 | − | 0.976652i | \(-0.568919\pi\) | ||||
−0.214827 | + | 0.976652i | \(0.568919\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.25839i | 0.294696i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.81497 | 0.178848 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 29.6842 | 1.38857 | 0.694285 | − | 0.719700i | \(-0.255721\pi\) | ||||
0.694285 | + | 0.719700i | \(0.255721\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 23.5084i | − 1.09490i | −0.836839 | − | 0.547448i | \(-0.815599\pi\) | ||||
0.836839 | − | 0.547448i | \(-0.184401\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.90150 | −0.367214 | −0.183607 | − | 0.983000i | \(-0.558777\pi\) | ||||
−0.183607 | + | 0.983000i | \(0.558777\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 3.06324i | − 0.141750i | −0.997485 | − | 0.0708748i | \(-0.977421\pi\) | ||||
0.997485 | − | 0.0708748i | \(-0.0225791\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 22.8150i | 1.05350i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7.53162 | −0.346304 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 4.00000i | − 0.183533i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −14.2073 | −0.649147 | −0.324573 | − | 0.945860i | \(-0.605221\pi\) | ||||
−0.324573 | + | 0.945860i | \(0.605221\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.42740 | 0.0650839 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 26.9725i | 1.22476i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −22.1088 | −1.00184 | −0.500922 | − | 0.865492i | \(-0.667006\pi\) | ||||
−0.500922 | + | 0.865492i | \(0.667006\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 39.5301i | 1.78397i | 0.452068 | + | 0.891983i | \(0.350686\pi\) | ||||
−0.452068 | + | 0.891983i | \(0.649314\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 43.2884i | − 1.94961i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 9.53904 | 0.427884 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 11.8532i | − 0.530624i | −0.964163 | − | 0.265312i | \(-0.914525\pi\) | ||||
0.964163 | − | 0.265312i | \(-0.0854750\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −23.4246 | −1.04445 | −0.522226 | − | 0.852807i | \(-0.674898\pi\) | ||||
−0.522226 | + | 0.852807i | \(0.674898\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −19.4051 | −0.863518 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 7.83614i | − 0.347331i | −0.984805 | − | 0.173665i | \(-0.944439\pi\) | ||||
0.984805 | − | 0.173665i | \(-0.0555611\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.42825 | −0.328607 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.37003i | 0.104436i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.63456i | 0.379747i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 27.4535 | 1.20276 | 0.601381 | − | 0.798963i | \(-0.294617\pi\) | ||||
0.601381 | + | 0.798963i | \(0.294617\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 3.83255i | − 0.167586i | −0.996483 | − | 0.0837928i | \(-0.973297\pi\) | ||||
0.996483 | − | 0.0837928i | \(-0.0267034\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 52.0325 | 2.26657 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.572599 | −0.0248956 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 5.19615i | − 0.225070i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 23.3279 | 1.00855 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 4.44613i | − 0.191508i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15.9707i | 0.686632i | 0.939220 | + | 0.343316i | \(0.111550\pi\) | ||||
−0.939220 | + | 0.343316i | \(0.888450\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.46096 | 0.105416 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.4258i | 0.445777i | 0.974844 | + | 0.222888i | \(0.0715486\pi\) | ||||
−0.974844 | + | 0.222888i | \(0.928451\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 15.6723 | 0.667662 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.00000 | 0.382719 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 25.0471i | − 1.06128i | −0.847597 | − | 0.530640i | \(-0.821951\pi\) | ||||
0.847597 | − | 0.530640i | \(-0.178049\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.25327 | 0.264485 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 2.63739i | − 0.111153i | −0.998454 | − | 0.0555764i | \(-0.982300\pi\) | ||||
0.998454 | − | 0.0555764i | \(-0.0176996\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 16.4835i | − 0.693468i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −20.0484 | −0.840473 | −0.420236 | − | 0.907415i | \(-0.638053\pi\) | ||||
−0.420236 | + | 0.907415i | \(0.638053\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.31421i | 0.0968466i | 0.998827 | + | 0.0484233i | \(0.0154196\pi\) | ||||
−0.998827 | + | 0.0484233i | \(0.984580\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −9.47152 | −0.394989 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 24.4610 | 1.01832 | 0.509162 | − | 0.860671i | \(-0.329956\pi\) | ||||
0.509162 | + | 0.860671i | \(0.329956\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 44.2930i | 1.83758i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.56819 | −0.396274 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 19.7268i | 0.814211i | 0.913381 | + | 0.407106i | \(0.133462\pi\) | ||||
−0.913381 | + | 0.407106i | \(0.866538\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 18.8380i | 0.776207i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8.46096 | 0.347450 | 0.173725 | − | 0.984794i | \(-0.444420\pi\) | ||||
0.173725 | + | 0.984794i | \(0.444420\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 34.5726i | 1.41734i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −6.45496 | −0.263742 | −0.131871 | − | 0.991267i | \(-0.542099\pi\) | ||||
−0.131871 | + | 0.991267i | \(0.542099\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.05582 | −0.206231 | −0.103116 | − | 0.994669i | \(-0.532881\pi\) | ||||
−0.103116 | + | 0.994669i | \(0.532881\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 18.1189i | − 0.736639i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.0441760 | −0.00179305 | −0.000896524 | − | 1.00000i | \(-0.500285\pi\) | ||||
−0.000896524 | 1.00000i | \(0.500285\pi\) | ||||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 7.16901i | − 0.290027i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 26.8887i | − 1.08602i | −0.839725 | − | 0.543012i | \(-0.817284\pi\) | ||||
0.839725 | − | 0.543012i | \(-0.182716\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18.4126 | 0.741262 | 0.370631 | − | 0.928780i | \(-0.379141\pi\) | ||||
0.370631 | + | 0.928780i | \(0.379141\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 1.90906i | − 0.0767317i | −0.999264 | − | 0.0383658i | \(-0.987785\pi\) | ||||
0.999264 | − | 0.0383658i | \(-0.0122152\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −7.02488 | −0.281446 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11.0000 | −0.440000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 12.9356i | 0.515777i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.51752 | −0.0604114 | −0.0302057 | − | 0.999544i | \(-0.509616\pi\) | ||||
−0.0302057 | + | 0.999544i | \(0.509616\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.88836i | 0.154305i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.69148i | 0.146262i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 16.9852 | 0.670874 | 0.335437 | − | 0.942063i | \(-0.391116\pi\) | ||||
0.335437 | + | 0.942063i | \(0.391116\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10.4258i | 0.411155i | 0.978641 | + | 0.205578i | \(0.0659073\pi\) | ||||
−0.978641 | + | 0.205578i | \(0.934093\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 44.2802 | 1.74083 | 0.870417 | − | 0.492315i | \(-0.163849\pi\) | ||||
0.870417 | + | 0.492315i | \(0.163849\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.888365 | 0.0348714 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 33.0766i | − 1.29439i | −0.762325 | − | 0.647194i | \(-0.775942\pi\) | ||||
0.762325 | − | 0.647194i | \(-0.224058\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.447546 | 0.0174871 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 32.2026i | − 1.25443i | −0.778844 | − | 0.627217i | \(-0.784194\pi\) | ||||
0.778844 | − | 0.627217i | \(-0.215806\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 13.0194i | − 0.506398i | −0.967414 | − | 0.253199i | \(-0.918517\pi\) | ||||
0.967414 | − | 0.253199i | \(-0.0814827\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −12.5168 | −0.485380 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 37.1101i | − 1.43691i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8.29654 | −0.320284 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.46096 | −0.287599 | −0.143800 | − | 0.989607i | \(-0.545932\pi\) | ||||
−0.143800 | + | 0.989607i | \(0.545932\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 35.6456i | 1.36997i | 0.728556 | + | 0.684987i | \(0.240192\pi\) | ||||
−0.728556 | + | 0.684987i | \(0.759808\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −56.2682 | −2.15938 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 27.4535i | 1.05048i | 0.850954 | + | 0.525240i | \(0.176025\pi\) | ||||
−0.850954 | + | 0.525240i | \(0.823975\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.47695i | 0.132847i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 7.94418 | 0.302649 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 22.3700i | − 0.850996i | −0.904959 | − | 0.425498i | \(-0.860099\pi\) | ||||
0.904959 | − | 0.425498i | \(-0.139901\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.91165 | −0.148377 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 47.0894 | 1.78364 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 10.4633i | − 0.395193i | −0.980283 | − | 0.197596i | \(-0.936686\pi\) | ||||
0.980283 | − | 0.197596i | \(-0.0633136\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.68325 | −0.176632 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 40.4817i | − 1.52247i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 23.5425i | − 0.884155i | −0.896977 | − | 0.442078i | \(-0.854242\pi\) | ||||
0.896977 | − | 0.442078i | \(-0.145758\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 44.6062 | 1.67051 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 0.775172i | − 0.0289898i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 45.0076 | 1.67850 | 0.839251 | − | 0.543745i | \(-0.182994\pi\) | ||||
0.839251 | + | 0.543745i | \(0.182994\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.94418 | −0.184131 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 15.6723i | 0.582054i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16.7506 | 0.621245 | 0.310622 | − | 0.950533i | \(-0.399463\pi\) | ||||
0.310622 | + | 0.950533i | \(0.399463\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 56.6694i | 2.09599i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 24.3409i | − 0.899050i | −0.893268 | − | 0.449525i | \(-0.851593\pi\) | ||||
0.893268 | − | 0.449525i | \(-0.148407\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.63583 | 0.170763 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 32.0558i | − 1.17919i | −0.807698 | − | 0.589596i | \(-0.799287\pi\) | ||||
0.807698 | − | 0.589596i | \(-0.200713\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 17.9614 | 0.658940 | 0.329470 | − | 0.944166i | \(-0.393130\pi\) | ||||
0.329470 | + | 0.944166i | \(0.393130\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −25.5726 | −0.936908 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 48.6651i | 1.77818i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21.8546 | 0.797485 | 0.398742 | − | 0.917063i | \(-0.369447\pi\) | ||||
0.398742 | + | 0.917063i | \(0.369447\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 9.79743i | − 0.356565i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 52.1292i | − 1.89467i | −0.320248 | − | 0.947334i | \(-0.603766\pi\) | ||||
0.320248 | − | 0.947334i | \(-0.396234\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 32.0894 | 1.16324 | 0.581620 | − | 0.813461i | \(-0.302419\pi\) | ||||
0.581620 | + | 0.813461i | \(0.302419\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.13389i | 0.185859i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −0.737582 | −0.0266326 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.22327 | 0.116234 | 0.0581171 | − | 0.998310i | \(-0.481490\pi\) | ||||
0.0581171 | + | 0.998310i | \(0.481490\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 19.2331i | − 0.691765i | −0.938278 | − | 0.345883i | \(-0.887580\pi\) | ||||
0.938278 | − | 0.345883i | \(-0.112420\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −18.8380 | −0.676682 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 17.0484i | 0.610822i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 1.93826i | − 0.0693563i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 27.5168 | 0.982116 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 36.3700i | 1.29645i | 0.761448 | + | 0.648226i | \(0.224489\pi\) | ||||
−0.761448 | + | 0.648226i | \(0.775511\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 34.3868 | 1.22265 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.88836 | 0.244613 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 14.9577i | − 0.529829i | −0.964272 | − | 0.264915i | \(-0.914656\pi\) | ||||
0.964272 | − | 0.264915i | \(-0.0853437\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 64.9681 | 2.29841 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.50936i | 0.0532643i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 29.6382i | 1.04461i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −0.0409808 | −0.00144081 | −0.000720404 | − | 1.00000i | \(-0.500229\pi\) | ||||
−0.000720404 | 1.00000i | \(0.500229\pi\) | ||||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 43.2568i | 1.51895i | 0.650535 | + | 0.759476i | \(0.274545\pi\) | ||||
−0.650535 | + | 0.759476i | \(0.725455\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −14.7515 | −0.516722 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −20.5168 | −0.717791 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 28.6208i | 0.998871i | 0.866351 | + | 0.499436i | \(0.166459\pi\) | ||||
−0.866351 | + | 0.499436i | \(0.833541\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −42.4118 | −1.47838 | −0.739191 | − | 0.673495i | \(-0.764792\pi\) | ||||
−0.739191 | + | 0.673495i | \(0.764792\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 14.1116i | 0.490710i | 0.969433 | + | 0.245355i | \(0.0789045\pi\) | ||||
−0.969433 | + | 0.245355i | \(0.921096\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 22.6088i | 0.785237i | 0.919701 | + | 0.392618i | \(0.128431\pi\) | ||||
−0.919701 | + | 0.392618i | \(0.871569\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −33.4535 | −1.15910 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 6.77517i | − 0.234464i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 14.1106 | 0.487152 | 0.243576 | − | 0.969882i | \(-0.421680\pi\) | ||||
0.243576 | + | 0.969882i | \(0.421680\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −32.4051 | −1.11742 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 21.8731i | − 0.752456i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 37.7984 | 1.29877 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 11.0894i | 0.380139i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 42.4772i | 1.45439i | 0.686431 | + | 0.727195i | \(0.259176\pi\) | ||||
−0.686431 | + | 0.727195i | \(0.740824\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 33.6842 | 1.15063 | 0.575316 | − | 0.817931i | \(-0.304879\pi\) | ||||
0.575316 | + | 0.817931i | \(0.304879\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 45.9762i | 1.56869i | 0.620327 | + | 0.784344i | \(0.287000\pi\) | ||||
−0.620327 | + | 0.784344i | \(0.713000\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 31.8786 | 1.08516 | 0.542581 | − | 0.840004i | \(-0.317447\pi\) | ||||
0.542581 | + | 0.840004i | \(0.317447\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −21.0000 | −0.714021 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 1.82873i | − 0.0620354i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.84899 | −0.130418 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 43.8087i | − 1.48101i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 52.4147i | 1.76992i | 0.465668 | + | 0.884959i | \(0.345814\pi\) | ||||
−0.465668 | + | 0.884959i | \(0.654186\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 34.0558 | 1.14737 | 0.573685 | − | 0.819076i | \(-0.305513\pi\) | ||||
0.573685 | + | 0.819076i | \(0.305513\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 10.0000i | 0.336527i | 0.985742 | + | 0.168263i | \(0.0538159\pi\) | ||||
−0.985742 | + | 0.168263i | \(0.946184\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 36.1060 | 1.21232 | 0.606161 | − | 0.795342i | \(-0.292709\pi\) | ||||
0.606161 | + | 0.795342i | \(0.292709\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.11164 | −0.272056 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 23.5213i | 0.787110i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −10.3923 | −0.347376 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 73.8087i | − 2.46166i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 71.9930i | 2.39843i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4.05582 | 0.134820 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 42.3700i | − 1.40687i | −0.710758 | − | 0.703437i | \(-0.751648\pi\) | ||||
0.710758 | − | 0.703437i | \(-0.248352\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 50.6642 | 1.67858 | 0.839289 | − | 0.543685i | \(-0.182971\pi\) | ||||
0.839289 | + | 0.543685i | \(0.182971\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.00000 | 0.297857 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.933638i | 0.0308315i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 25.3372 | 0.835796 | 0.417898 | − | 0.908494i | \(-0.362767\pi\) | ||||
0.417898 | + | 0.908494i | \(0.362767\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.60928i | 0.0529700i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 4.68325i | − 0.153984i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −15.3493 | −0.503595 | −0.251798 | − | 0.967780i | \(-0.581022\pi\) | ||||
−0.251798 | + | 0.967780i | \(0.581022\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 12.1116i | − 0.396943i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 7.02488 | 0.229738 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −11.5390 | −0.376964 | −0.188482 | − | 0.982077i | \(-0.560357\pi\) | ||||
−0.188482 | + | 0.982077i | \(0.560357\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 33.1023i | 1.07910i | 0.841952 | + | 0.539552i | \(0.181407\pi\) | ||||
−0.841952 | + | 0.539552i | \(0.818593\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 40.3685 | 1.31458 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 17.2658i | − 0.561063i | −0.959845 | − | 0.280532i | \(-0.909489\pi\) | ||||
0.959845 | − | 0.280532i | \(-0.0905108\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 1.25318i | − 0.0406799i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −29.2159 | −0.946394 | −0.473197 | − | 0.880957i | \(-0.656900\pi\) | ||||
−0.473197 | + | 0.880957i | \(0.656900\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 2.37003i | − 0.0766922i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −7.25337 | −0.234224 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 57.7178 | 1.86186 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 26.7792i | 0.862052i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.00833 | −0.128899 | −0.0644495 | − | 0.997921i | \(-0.520529\pi\) | ||||
−0.0644495 | + | 0.997921i | \(0.520529\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 20.2791i | − 0.650787i | −0.945579 | − | 0.325393i | \(-0.894503\pi\) | ||||
0.945579 | − | 0.325393i | \(-0.105497\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 8.16021i | − 0.261604i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3.30835 | 0.105843 | 0.0529217 | − | 0.998599i | \(-0.483147\pi\) | ||||
0.0529217 | + | 0.998599i | \(0.483147\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.42740i | 0.0456199i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −41.1927 | −1.31384 | −0.656921 | − | 0.753960i | \(-0.728141\pi\) | ||||
−0.656921 | + | 0.753960i | \(0.728141\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −22.4051 | −0.713887 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 48.5813i | 1.54479i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −44.2802 | −1.40661 | −0.703303 | − | 0.710890i | \(-0.748292\pi\) | ||||
−0.703303 | + | 0.710890i | \(0.748292\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 32.4610i | − 1.02908i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 35.6199i | − 1.12809i | −0.825742 | − | 0.564047i | \(-0.809244\pi\) | ||||
0.825742 | − | 0.564047i | \(-0.190756\pi\) | |||||||
\(998\) | 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 | 5184.2.d.q.2593.5 | 12 | ||
3.2 | odd | 2 | 5184.2.d.r.2593.11 | 12 | |||
4.3 | odd | 2 | inner | 5184.2.d.q.2593.2 | 12 | ||
8.3 | odd | 2 | inner | 5184.2.d.q.2593.8 | 12 | ||
8.5 | even | 2 | inner | 5184.2.d.q.2593.11 | 12 | ||
9.2 | odd | 6 | 1728.2.r.e.1441.2 | 12 | |||
9.4 | even | 3 | 576.2.r.e.97.6 | yes | 12 | ||
9.5 | odd | 6 | 1728.2.r.f.289.2 | 12 | |||
9.7 | even | 3 | 576.2.r.f.481.1 | yes | 12 | ||
12.11 | even | 2 | 5184.2.d.r.2593.8 | 12 | |||
24.5 | odd | 2 | 5184.2.d.r.2593.5 | 12 | |||
24.11 | even | 2 | 5184.2.d.r.2593.2 | 12 | |||
36.7 | odd | 6 | 576.2.r.f.481.6 | yes | 12 | ||
36.11 | even | 6 | 1728.2.r.e.1441.5 | 12 | |||
36.23 | even | 6 | 1728.2.r.f.289.5 | 12 | |||
36.31 | odd | 6 | 576.2.r.e.97.1 | ✓ | 12 | ||
72.5 | odd | 6 | 1728.2.r.e.289.2 | 12 | |||
72.11 | even | 6 | 1728.2.r.f.1441.5 | 12 | |||
72.13 | even | 6 | 576.2.r.f.97.1 | yes | 12 | ||
72.29 | odd | 6 | 1728.2.r.f.1441.2 | 12 | |||
72.43 | odd | 6 | 576.2.r.e.481.1 | yes | 12 | ||
72.59 | even | 6 | 1728.2.r.e.289.5 | 12 | |||
72.61 | even | 6 | 576.2.r.e.481.6 | yes | 12 | ||
72.67 | odd | 6 | 576.2.r.f.97.6 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
576.2.r.e.97.1 | ✓ | 12 | 36.31 | odd | 6 | ||
576.2.r.e.97.6 | yes | 12 | 9.4 | even | 3 | ||
576.2.r.e.481.1 | yes | 12 | 72.43 | odd | 6 | ||
576.2.r.e.481.6 | yes | 12 | 72.61 | even | 6 | ||
576.2.r.f.97.1 | yes | 12 | 72.13 | even | 6 | ||
576.2.r.f.97.6 | yes | 12 | 72.67 | odd | 6 | ||
576.2.r.f.481.1 | yes | 12 | 9.7 | even | 3 | ||
576.2.r.f.481.6 | yes | 12 | 36.7 | odd | 6 | ||
1728.2.r.e.289.2 | 12 | 72.5 | odd | 6 | |||
1728.2.r.e.289.5 | 12 | 72.59 | even | 6 | |||
1728.2.r.e.1441.2 | 12 | 9.2 | odd | 6 | |||
1728.2.r.e.1441.5 | 12 | 36.11 | even | 6 | |||
1728.2.r.f.289.2 | 12 | 9.5 | odd | 6 | |||
1728.2.r.f.289.5 | 12 | 36.23 | even | 6 | |||
1728.2.r.f.1441.2 | 12 | 72.29 | odd | 6 | |||
1728.2.r.f.1441.5 | 12 | 72.11 | even | 6 | |||
5184.2.d.q.2593.2 | 12 | 4.3 | odd | 2 | inner | ||
5184.2.d.q.2593.5 | 12 | 1.1 | even | 1 | trivial | ||
5184.2.d.q.2593.8 | 12 | 8.3 | odd | 2 | inner | ||
5184.2.d.q.2593.11 | 12 | 8.5 | even | 2 | inner | ||
5184.2.d.r.2593.2 | 12 | 24.11 | even | 2 | |||
5184.2.d.r.2593.5 | 12 | 24.5 | odd | 2 | |||
5184.2.d.r.2593.8 | 12 | 12.11 | even | 2 | |||
5184.2.d.r.2593.11 | 12 | 3.2 | odd | 2 |