Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2880,2,Mod(2591,2880)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2880, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 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("2880.2591");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2880 = 2^{6} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2880.b (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: | \(22.9969157821\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{14} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2591.1 | ||
Root | \(-0.965926 + 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2880.2591 |
Dual form | 2880.2.b.b.2591.8 |
$q$-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 \(\left(\mathbb{Z}/2880\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(641\) | \(901\) | \(2431\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 4.44949i | − 1.68175i | −0.541230 | − | 0.840875i | \(-0.682041\pi\) | ||||
0.541230 | − | 0.840875i | \(-0.317959\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.44949i | 1.34157i | 0.741651 | + | 0.670786i | \(0.234043\pi\) | ||||
−0.741651 | + | 0.670786i | \(0.765957\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 1.41421i | − 0.392232i | −0.980581 | − | 0.196116i | \(-0.937167\pi\) | ||||
0.980581 | − | 0.196116i | \(-0.0628330\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.82843i | 0.685994i | 0.939336 | + | 0.342997i | \(0.111442\pi\) | ||||
−0.939336 | + | 0.342997i | \(0.888558\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.82843 | 0.648886 | 0.324443 | − | 0.945905i | \(-0.394823\pi\) | ||||
0.324443 | + | 0.945905i | \(0.394823\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.46410 | 0.722315 | 0.361158 | − | 0.932505i | \(-0.382382\pi\) | ||||
0.361158 | + | 0.932505i | \(0.382382\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.00000 | 0.371391 | 0.185695 | − | 0.982607i | \(-0.440546\pi\) | ||||
0.185695 | + | 0.982607i | \(0.440546\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 4.89898i | − 0.879883i | −0.898027 | − | 0.439941i | \(-0.854999\pi\) | ||||
0.898027 | − | 0.439941i | \(-0.145001\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.44949i | 0.752101i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.34242i | 1.37148i | 0.727844 | + | 0.685742i | \(0.240522\pi\) | ||||
−0.727844 | + | 0.685742i | \(0.759478\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 8.34242i | − 1.30287i | −0.758706 | − | 0.651433i | \(-0.774168\pi\) | ||||
0.758706 | − | 0.651433i | \(-0.225832\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.75663 | 1.42315 | 0.711575 | − | 0.702610i | \(-0.247982\pi\) | ||||
0.711575 | + | 0.702610i | \(0.247982\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −12.7980 | −1.82828 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.00000 | 0.549442 | 0.274721 | − | 0.961524i | \(-0.411414\pi\) | ||||
0.274721 | + | 0.961524i | \(0.411414\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 4.44949i | − 0.599969i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 9.34847i | − 1.21707i | −0.793528 | − | 0.608534i | \(-0.791758\pi\) | ||||
0.793528 | − | 0.608534i | \(-0.208242\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 15.4135i | − 1.97349i | −0.162265 | − | 0.986747i | \(-0.551880\pi\) | ||||
0.162265 | − | 0.986747i | \(-0.448120\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.41421i | 0.175412i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.3137 | 1.38219 | 0.691095 | − | 0.722764i | \(-0.257129\pi\) | ||||
0.691095 | + | 0.722764i | \(0.257129\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.65685 | −0.671345 | −0.335673 | − | 0.941979i | \(-0.608964\pi\) | ||||
−0.335673 | + | 0.941979i | \(0.608964\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.7980 | −1.38085 | −0.690423 | − | 0.723406i | \(-0.742576\pi\) | ||||
−0.690423 | + | 0.723406i | \(0.742576\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 19.7980 | 2.25619 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.10102i | 0.348892i | 0.984667 | + | 0.174446i | \(0.0558135\pi\) | ||||
−0.984667 | + | 0.174446i | \(0.944187\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 0.898979i | − 0.0986758i | −0.998782 | − | 0.0493379i | \(-0.984289\pi\) | ||||
0.998782 | − | 0.0493379i | \(-0.0157111\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 2.82843i | − 0.306786i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 13.9993i | − 1.48392i | −0.670444 | − | 0.741960i | \(-0.733896\pi\) | ||||
0.670444 | − | 0.741960i | \(-0.266104\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.29253 | −0.659636 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.82843 | −0.290191 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −11.7980 | −1.19790 | −0.598951 | − | 0.800786i | \(-0.704415\pi\) | ||||
−0.598951 | + | 0.800786i | \(0.704415\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −15.7980 | −1.57196 | −0.785978 | − | 0.618255i | \(-0.787840\pi\) | ||||
−0.785978 | + | 0.618255i | \(0.787840\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 1.34847i | − 0.132869i | −0.997791 | − | 0.0664343i | \(-0.978838\pi\) | ||||
0.997791 | − | 0.0664343i | \(-0.0211623\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.898979i | 0.0869076i | 0.999055 | + | 0.0434538i | \(0.0138361\pi\) | ||||
−0.999055 | + | 0.0434538i | \(0.986164\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 15.4135i | − 1.47634i | −0.674613 | − | 0.738172i | \(-0.735689\pi\) | ||||
0.674613 | − | 0.738172i | \(-0.264311\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 19.5133i | − 1.83565i | −0.396982 | − | 0.917827i | \(-0.629942\pi\) | ||||
0.396982 | − | 0.917827i | \(-0.370058\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.46410 | −0.323029 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 12.5851 | 1.15367 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.79796 | −0.799814 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 9.34847i | − 0.829543i | −0.909926 | − | 0.414771i | \(-0.863862\pi\) | ||||
0.909926 | − | 0.414771i | \(-0.136138\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 20.4495i | 1.78668i | 0.449381 | + | 0.893340i | \(0.351645\pi\) | ||||
−0.449381 | + | 0.893340i | \(0.648355\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 12.5851i | − 1.09126i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 11.3137i | 0.966595i | 0.875456 | + | 0.483298i | \(0.160561\pi\) | ||||
−0.875456 | + | 0.483298i | \(0.839439\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.3923 | 0.881464 | 0.440732 | − | 0.897639i | \(-0.354719\pi\) | ||||
0.440732 | + | 0.897639i | \(0.354719\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.29253 | 0.526208 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.00000 | −0.166091 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.202041 | 0.0165518 | 0.00827592 | − | 0.999966i | \(-0.497366\pi\) | ||||
0.00827592 | + | 0.999966i | \(0.497366\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 13.7980i | − 1.12286i | −0.827524 | − | 0.561431i | \(-0.810251\pi\) | ||||
0.827524 | − | 0.561431i | \(-0.189749\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.89898i | 0.393496i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.51399i | 0.440064i | 0.975493 | + | 0.220032i | \(0.0706162\pi\) | ||||
−0.975493 | + | 0.220032i | \(0.929384\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − 15.4135i | − 1.21475i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 23.8988 | 1.87190 | 0.935948 | − | 0.352138i | \(-0.114545\pi\) | ||||
0.935948 | + | 0.352138i | \(0.114545\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −0.921404 | −0.0713004 | −0.0356502 | − | 0.999364i | \(-0.511350\pi\) | ||||
−0.0356502 | + | 0.999364i | \(0.511350\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.0000 | 0.846154 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.79796 | −0.744925 | −0.372463 | − | 0.928047i | \(-0.621486\pi\) | ||||
−0.372463 | + | 0.928047i | \(0.621486\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 4.44949i | − 0.336350i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 6.24745i | − 0.466956i | −0.972362 | − | 0.233478i | \(-0.924989\pi\) | ||||
0.972362 | − | 0.233478i | \(-0.0750107\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.09978i | 0.304734i | 0.988324 | + | 0.152367i | \(0.0486896\pi\) | ||||
−0.988324 | + | 0.152367i | \(0.951310\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − 8.34242i | − 0.613347i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −12.5851 | −0.920311 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 18.2419 | 1.31994 | 0.659969 | − | 0.751293i | \(-0.270569\pi\) | ||||
0.659969 | + | 0.751293i | \(0.270569\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.0000 | 0.719816 | 0.359908 | − | 0.932988i | \(-0.382808\pi\) | ||||
0.359908 | + | 0.932988i | \(0.382808\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 17.5959 | 1.25366 | 0.626829 | − | 0.779157i | \(-0.284353\pi\) | ||||
0.626829 | + | 0.779157i | \(0.284353\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 13.7980i | − 0.978111i | −0.872253 | − | 0.489056i | \(-0.837341\pi\) | ||||
0.872253 | − | 0.489056i | \(-0.162659\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 8.89898i | − 0.624586i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.34242i | 0.582660i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 12.5851i | 0.870527i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.84961 | 0.540389 | 0.270195 | − | 0.962806i | \(-0.412912\pi\) | ||||
0.270195 | + | 0.962806i | \(0.412912\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −21.7980 | −1.47974 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.00000 | 0.269069 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 22.2474i | − 1.48980i | −0.667176 | − | 0.744900i | \(-0.732497\pi\) | ||||
0.667176 | − | 0.744900i | \(-0.267503\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 27.5959i | 1.83161i | 0.401628 | + | 0.915803i | \(0.368444\pi\) | ||||
−0.401628 | + | 0.915803i | \(0.631556\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 1.27135i | − 0.0840131i | −0.999117 | − | 0.0420066i | \(-0.986625\pi\) | ||||
0.999117 | − | 0.0420066i | \(-0.0133750\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 22.3417i | 1.46365i | 0.681491 | + | 0.731826i | \(0.261332\pi\) | ||||
−0.681491 | + | 0.731826i | \(0.738668\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.75663 | −0.636452 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 25.1701 | 1.62812 | 0.814060 | − | 0.580781i | \(-0.197253\pi\) | ||||
0.814060 | + | 0.580781i | \(0.197253\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.00000 | 0.257663 | 0.128831 | − | 0.991667i | \(-0.458877\pi\) | ||||
0.128831 | + | 0.991667i | \(0.458877\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 12.7980 | 0.817632 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 4.00000i | − 0.254514i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 25.3485i | − 1.59998i | −0.600013 | − | 0.799991i | \(-0.704838\pi\) | ||||
0.600013 | − | 0.799991i | \(-0.295162\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 15.4135i | 0.969037i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 8.19955i | − 0.511474i | −0.966746 | − | 0.255737i | \(-0.917682\pi\) | ||||
0.966746 | − | 0.255737i | \(-0.0823181\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 37.1195 | 2.30649 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7.84961 | 0.484027 | 0.242014 | − | 0.970273i | \(-0.422192\pi\) | ||||
0.242014 | + | 0.970273i | \(0.422192\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.00000 | −0.245718 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −25.5959 | −1.56061 | −0.780305 | − | 0.625399i | \(-0.784936\pi\) | ||||
−0.780305 | + | 0.625399i | \(0.784936\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.00000i | 0.242983i | 0.992592 | + | 0.121491i | \(0.0387677\pi\) | ||||
−0.992592 | + | 0.121491i | \(0.961232\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.44949i | 0.268314i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 5.79972i | − 0.348471i | −0.984704 | − | 0.174236i | \(-0.944255\pi\) | ||||
0.984704 | − | 0.174236i | \(-0.0557455\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 23.7559i | 1.41716i | 0.705631 | + | 0.708579i | \(0.250663\pi\) | ||||
−0.705631 | + | 0.708579i | \(0.749337\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.0424 | −0.596956 | −0.298478 | − | 0.954416i | \(-0.596479\pi\) | ||||
−0.298478 | + | 0.954416i | \(0.596479\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −37.1195 | −2.19109 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 9.00000 | 0.529412 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.00000 | 0.350524 | 0.175262 | − | 0.984522i | \(-0.443923\pi\) | ||||
0.175262 | + | 0.984522i | \(0.443923\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.34847i | 0.544289i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 4.89898i | − 0.283315i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 15.4135i | 0.882574i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −22.0560 | −1.25880 | −0.629400 | − | 0.777081i | \(-0.716699\pi\) | ||||
−0.629400 | + | 0.777081i | \(0.716699\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.27135 | 0.0720916 | 0.0360458 | − | 0.999350i | \(-0.488524\pi\) | ||||
0.0360458 | + | 0.999350i | \(0.488524\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.00000 | −0.113047 | −0.0565233 | − | 0.998401i | \(-0.518002\pi\) | ||||
−0.0565233 | + | 0.998401i | \(0.518002\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 13.5959 | 0.763623 | 0.381811 | − | 0.924240i | \(-0.375300\pi\) | ||||
0.381811 | + | 0.924240i | \(0.375300\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.89898i | 0.498247i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.00000i | 0.445132i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 1.41421i | − 0.0784465i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − 43.4120i | − 2.39338i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.37113 | 0.295224 | 0.147612 | − | 0.989045i | \(-0.452841\pi\) | ||||
0.147612 | + | 0.989045i | \(0.452841\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −11.3137 | −0.618134 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.20204 | −0.228900 | −0.114450 | − | 0.993429i | \(-0.536511\pi\) | ||||
−0.114450 | + | 0.993429i | \(0.536511\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 21.7980 | 1.18043 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 25.7980i | 1.39296i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 29.3939i | 1.57795i | 0.614428 | + | 0.788973i | \(0.289387\pi\) | ||||
−0.614428 | + | 0.788973i | \(0.710613\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.21393i | 0.386153i | 0.981184 | + | 0.193076i | \(0.0618465\pi\) | ||||
−0.981184 | + | 0.193076i | \(0.938153\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 19.7990i | − 1.05379i | −0.849929 | − | 0.526897i | \(-0.823355\pi\) | ||||
0.849929 | − | 0.526897i | \(-0.176645\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.65685 | 0.300235 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.54270 | −0.134198 | −0.0670992 | − | 0.997746i | \(-0.521374\pi\) | ||||
−0.0670992 | + | 0.997746i | \(0.521374\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.0000 | −0.578947 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 11.7980 | 0.617533 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.2474i | 0.534912i | 0.963570 | + | 0.267456i | \(0.0861831\pi\) | ||||
−0.963570 | + | 0.267456i | \(0.913817\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 17.7980i | − 0.924024i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 36.3410i | − 1.88166i | −0.338874 | − | 0.940832i | \(-0.610046\pi\) | ||||
0.338874 | − | 0.940832i | \(-0.389954\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 2.82843i | − 0.145671i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −37.4052 | −1.92138 | −0.960689 | − | 0.277628i | \(-0.910452\pi\) | ||||
−0.960689 | + | 0.277628i | \(0.910452\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7.21393 | −0.368615 | −0.184307 | − | 0.982869i | \(-0.559004\pi\) | ||||
−0.184307 | + | 0.982869i | \(0.559004\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −19.7980 | −1.00900 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −37.5959 | −1.90619 | −0.953094 | − | 0.302673i | \(-0.902121\pi\) | ||||
−0.953094 | + | 0.302673i | \(0.902121\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.79796i | 0.495504i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 3.10102i | − 0.156029i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.61377i | 0.482501i | 0.970463 | + | 0.241251i | \(0.0775576\pi\) | ||||
−0.970463 | + | 0.241251i | \(0.922442\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0.142865i | 0.00713432i | 0.999994 | + | 0.00356716i | \(0.00113546\pi\) | ||||
−0.999994 | + | 0.00356716i | \(0.998865\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.92820 | −0.345118 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −37.1195 | −1.83995 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 33.5959 | 1.66121 | 0.830606 | − | 0.556861i | \(-0.187994\pi\) | ||||
0.830606 | + | 0.556861i | \(0.187994\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −41.5959 | −2.04680 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.898979i | 0.0441292i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 4.04541i | − 0.197631i | −0.995106 | − | 0.0988155i | \(-0.968495\pi\) | ||||
0.995106 | − | 0.0988155i | \(-0.0315054\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.6992i | 0.765133i | 0.923928 | + | 0.382566i | \(0.124960\pi\) | ||||
−0.923928 | + | 0.382566i | \(0.875040\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.82843i | 0.137199i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −68.5821 | −3.31892 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −15.1278 | −0.728678 | −0.364339 | − | 0.931266i | \(-0.618705\pi\) | ||||
−0.364339 | + | 0.931266i | \(0.618705\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 15.7980 | 0.759201 | 0.379601 | − | 0.925150i | \(-0.376061\pi\) | ||||
0.379601 | + | 0.925150i | \(0.376061\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 9.79796 | 0.468700 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 21.7980i | 1.04036i | 0.854057 | + | 0.520180i | \(0.174135\pi\) | ||||
−0.854057 | + | 0.520180i | \(0.825865\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 35.5959i | − 1.69121i | −0.533807 | − | 0.845607i | \(-0.679239\pi\) | ||||
0.533807 | − | 0.845607i | \(-0.320761\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 13.9993i | 0.663629i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 20.6417i | 0.974144i | 0.873362 | + | 0.487072i | \(0.161935\pi\) | ||||
−0.873362 | + | 0.487072i | \(0.838065\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 37.1195 | 1.74789 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6.29253 | 0.294998 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.79796 | 0.177661 | 0.0888305 | − | 0.996047i | \(-0.471687\pi\) | ||||
0.0888305 | + | 0.996047i | \(0.471687\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 19.7980 | 0.922083 | 0.461041 | − | 0.887379i | \(-0.347476\pi\) | ||||
0.461041 | + | 0.887379i | \(0.347476\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.1464i | 0.518018i | 0.965875 | + | 0.259009i | \(0.0833960\pi\) | ||||
−0.965875 | + | 0.259009i | \(0.916604\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 28.4949i | 1.31859i | 0.751886 | + | 0.659293i | \(0.229144\pi\) | ||||
−0.751886 | + | 0.659293i | \(0.770856\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 50.3402i | − 2.32450i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.82843 | 0.129777 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −22.0560 | −1.00776 | −0.503881 | − | 0.863773i | \(-0.668095\pi\) | ||||
−0.503881 | + | 0.863773i | \(0.668095\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11.7980 | 0.537941 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 11.7980 | 0.535718 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 23.5505i | − 1.06718i | −0.845745 | − | 0.533588i | \(-0.820843\pi\) | ||||
0.845745 | − | 0.533588i | \(-0.179157\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 25.3485i | − 1.14396i | −0.820267 | − | 0.571980i | \(-0.806175\pi\) | ||||
0.820267 | − | 0.571980i | \(-0.193825\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.65685i | 0.254772i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 25.1701i | 1.12903i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 22.3417 | 1.00015 | 0.500076 | − | 0.865982i | \(-0.333306\pi\) | ||||
0.500076 | + | 0.865982i | \(0.333306\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 29.8413 | 1.33056 | 0.665280 | − | 0.746594i | \(-0.268312\pi\) | ||||
0.665280 | + | 0.746594i | \(0.268312\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 15.7980 | 0.703000 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −27.3939 | −1.21421 | −0.607106 | − | 0.794621i | \(-0.707670\pi\) | ||||
−0.607106 | + | 0.794621i | \(0.707670\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 52.4949i | 2.32224i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.34847i | 0.0594207i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 43.4120i | 1.90926i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 23.4702i | 1.02825i | 0.857716 | + | 0.514123i | \(0.171883\pi\) | ||||
−0.857716 | + | 0.514123i | \(0.828117\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.47090 | 0.414134 | 0.207067 | − | 0.978327i | \(-0.433608\pi\) | ||||
0.207067 | + | 0.978327i | \(0.433608\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 13.8564 | 0.603595 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.0000 | −0.478261 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −11.7980 | −0.511026 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 0.898979i | − 0.0388663i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 56.9444i | − 2.45277i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 32.3840i | 1.39230i | 0.717897 | + | 0.696149i | \(0.245105\pi\) | ||||
−0.717897 | + | 0.696149i | \(0.754895\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 15.4135i | 0.660241i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.27135 | −0.0543590 | −0.0271795 | − | 0.999631i | \(-0.508653\pi\) | ||||
−0.0271795 | + | 0.999631i | \(0.508653\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.65685 | 0.240990 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 13.7980 | 0.586749 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −18.2020 | −0.771245 | −0.385623 | − | 0.922657i | \(-0.626013\pi\) | ||||
−0.385623 | + | 0.922657i | \(0.626013\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 14.2020i | 0.598545i | 0.954168 | + | 0.299272i | \(0.0967439\pi\) | ||||
−0.954168 | + | 0.299272i | \(0.903256\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 19.5133i | 0.820929i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − 14.2850i | − 0.598858i | −0.954119 | − | 0.299429i | \(-0.903204\pi\) | ||||
0.954119 | − | 0.299429i | \(-0.0967962\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19.7990 | −0.828562 | −0.414281 | − | 0.910149i | \(-0.635967\pi\) | ||||
−0.414281 | + | 0.910149i | \(0.635967\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.46410 | 0.144463 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 31.3939 | 1.30694 | 0.653472 | − | 0.756951i | \(-0.273312\pi\) | ||||
0.653472 | + | 0.756951i | \(0.273312\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.00000 | −0.165948 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 17.7980i | 0.737116i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 12.4949i | 0.515720i | 0.966182 | + | 0.257860i | \(0.0830173\pi\) | ||||
−0.966182 | + | 0.257860i | \(0.916983\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 13.8564i | − 0.570943i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 13.8564i | 0.569014i | 0.958674 | + | 0.284507i | \(0.0918300\pi\) | ||||
−0.958674 | + | 0.284507i | \(0.908170\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −12.5851 | −0.515937 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 12.5851 | 0.514212 | 0.257106 | − | 0.966383i | \(-0.417231\pi\) | ||||
0.257106 | + | 0.966383i | \(0.417231\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 35.5959 | 1.45199 | 0.725994 | − | 0.687701i | \(-0.241380\pi\) | ||||
0.725994 | + | 0.687701i | \(0.241380\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 8.79796 | 0.357688 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 28.4495i | − 1.15473i | −0.816486 | − | 0.577365i | \(-0.804081\pi\) | ||||
0.816486 | − | 0.577365i | \(-0.195919\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 13.7980i | − 0.558206i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 38.1838i | 1.54223i | 0.636697 | + | 0.771114i | \(0.280300\pi\) | ||||
−0.636697 | + | 0.771114i | \(0.719700\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 36.7696i | 1.48029i | 0.672449 | + | 0.740143i | \(0.265242\pi\) | ||||
−0.672449 | + | 0.740143i | \(0.734758\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 19.8632 | 0.798370 | 0.399185 | − | 0.916870i | \(-0.369293\pi\) | ||||
0.399185 | + | 0.916870i | \(0.369293\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −62.2896 | −2.49558 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −23.5959 | −0.940831 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.49490i | 0.338177i | 0.985601 | + | 0.169088i | \(0.0540823\pi\) | ||||
−0.985601 | + | 0.169088i | \(0.945918\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 9.34847i | 0.370983i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 18.0990i | 0.717110i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.78534i | 0.268005i | 0.990981 | + | 0.134002i | \(0.0427830\pi\) | ||||
−0.990981 | + | 0.134002i | \(0.957217\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 25.1701 | 0.992612 | 0.496306 | − | 0.868148i | \(-0.334689\pi\) | ||||
0.496306 | + | 0.868148i | \(0.334689\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −40.5836 | −1.59551 | −0.797753 | − | 0.602984i | \(-0.793978\pi\) | ||||
−0.797753 | + | 0.602984i | \(0.793978\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 41.5959 | 1.63278 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 26.0000 | 1.01746 | 0.508729 | − | 0.860927i | \(-0.330115\pi\) | ||||
0.508729 | + | 0.860927i | \(0.330115\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 20.4495i | − 0.799028i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 18.2474i | − 0.710820i | −0.934711 | − | 0.355410i | \(-0.884341\pi\) | ||||
0.934711 | − | 0.355410i | \(-0.115659\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 7.21393i | − 0.280589i | −0.990110 | − | 0.140295i | \(-0.955195\pi\) | ||||
0.990110 | − | 0.140295i | \(-0.0448050\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 12.5851i | 0.488028i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.92820 | 0.268261 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 68.5821 | 2.64758 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 35.3939 | 1.36433 | 0.682167 | − | 0.731197i | \(-0.261038\pi\) | ||||
0.682167 | + | 0.731197i | \(0.261038\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.59592 | 0.0613361 | 0.0306681 | − | 0.999530i | \(-0.490237\pi\) | ||||
0.0306681 | + | 0.999530i | \(0.490237\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 52.4949i | 2.01457i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 15.1010i | − 0.577824i | −0.957356 | − | 0.288912i | \(-0.906706\pi\) | ||||
0.957356 | − | 0.288912i | \(-0.0932936\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 11.3137i | − 0.432275i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 5.65685i | − 0.215509i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.82843 | 0.107598 | 0.0537992 | − | 0.998552i | \(-0.482867\pi\) | ||||
0.0537992 | + | 0.998552i | \(0.482867\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −10.3923 | −0.394203 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 23.5959 | 0.893759 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −27.7980 | −1.04991 | −0.524957 | − | 0.851129i | \(-0.675919\pi\) | ||||
−0.524957 | + | 0.851129i | \(0.675919\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 23.5959i | 0.889937i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 70.2929i | 2.64363i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 21.3561i | 0.802044i | 0.916068 | + | 0.401022i | \(0.131345\pi\) | ||||
−0.916068 | + | 0.401022i | \(0.868655\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 16.9706i | − 0.635553i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.29253 | −0.235327 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 3.11416 | 0.116138 | 0.0580692 | − | 0.998313i | \(-0.481506\pi\) | ||||
0.0580692 | + | 0.998313i | \(0.481506\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.00000 | −0.223452 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.00000 | 0.0742781 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 6.65153i | − 0.246692i | −0.992364 | − | 0.123346i | \(-0.960638\pi\) | ||||
0.992364 | − | 0.123346i | \(-0.0393624\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 30.3984i | − 1.12279i | −0.827548 | − | 0.561395i | \(-0.810265\pi\) | ||||
0.827548 | − | 0.561395i | \(-0.189735\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 50.3402i | 1.85431i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −33.6554 | −1.23803 | −0.619017 | − | 0.785378i | \(-0.712469\pi\) | ||||
−0.619017 | + | 0.785378i | \(0.712469\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 38.0409 | 1.39559 | 0.697793 | − | 0.716300i | \(-0.254166\pi\) | ||||
0.697793 | + | 0.716300i | \(0.254166\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.202041 | −0.00740221 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.00000 | 0.146157 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 22.6969i | − 0.828223i | −0.910226 | − | 0.414112i | \(-0.864092\pi\) | ||||
0.910226 | − | 0.414112i | \(-0.135908\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 13.7980i | 0.502159i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 19.3704i | 0.704029i | 0.935995 | + | 0.352015i | \(0.114503\pi\) | ||||
−0.935995 | + | 0.352015i | \(0.885497\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 9.61377i | − 0.348499i | −0.984702 | − | 0.174249i | \(-0.944250\pi\) | ||||
0.984702 | − | 0.174249i | \(-0.0557499\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −68.5821 | −2.48284 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −13.2207 | −0.477373 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −9.79796 | −0.353323 | −0.176662 | − | 0.984272i | \(-0.556530\pi\) | ||||
−0.176662 | + | 0.984272i | \(0.556530\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −53.5959 | −1.92771 | −0.963856 | − | 0.266425i | \(-0.914157\pi\) | ||||
−0.963856 | + | 0.266425i | \(0.914157\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 4.89898i | − 0.175977i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 23.5959i | − 0.845411i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 25.1701i | − 0.900658i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 5.51399i | − 0.196803i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8.19955 | −0.292282 | −0.146141 | − | 0.989264i | \(-0.546685\pi\) | ||||
−0.146141 | + | 0.989264i | \(0.546685\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −86.8241 | −3.08711 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −21.7980 | −0.774068 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 47.1918 | 1.67162 | 0.835810 | − | 0.549018i | \(-0.184998\pi\) | ||||
0.835810 | + | 0.549018i | \(0.184998\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 27.5959i | 0.976273i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 52.4949i | − 1.85250i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 15.4135i | 0.543254i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − 1.69994i | − 0.0597668i | −0.999553 | − | 0.0298834i | \(-0.990486\pi\) | ||||
0.999553 | − | 0.0298834i | \(-0.00951360\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −39.9479 | −1.40276 | −0.701381 | − | 0.712787i | \(-0.747433\pi\) | ||||
−0.701381 | + | 0.712787i | \(0.747433\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −23.8988 | −0.837137 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −29.5959 | −1.03290 | −0.516452 | − | 0.856316i | \(-0.672748\pi\) | ||||
−0.516452 | + | 0.856316i | \(0.672748\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 19.5505i | 0.681488i | 0.940156 | + | 0.340744i | \(0.110679\pi\) | ||||
−0.940156 | + | 0.340744i | \(0.889321\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 5.39388i | 0.187563i | 0.995593 | + | 0.0937817i | \(0.0298956\pi\) | ||||
−0.995593 | + | 0.0937817i | \(0.970104\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 37.4694i | − 1.30137i | −0.759349 | − | 0.650684i | \(-0.774482\pi\) | ||||
0.759349 | − | 0.650684i | \(-0.225518\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 36.1981i | − 1.25419i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.921404 | 0.0318865 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −25.1701 | −0.868969 | −0.434484 | − | 0.900679i | \(-0.643069\pi\) | ||||
−0.434484 | + | 0.900679i | \(0.643069\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.0000 | −0.862069 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −11.0000 | −0.378412 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 39.1464i | 1.34509i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 28.8990i | 0.990644i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.67118i | 0.125699i | 0.998023 | + | 0.0628494i | \(0.0200188\pi\) | ||||
−0.998023 | + | 0.0628494i | \(0.979981\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 11.0280i | 0.376709i | 0.982101 | + | 0.188354i | \(0.0603153\pi\) | ||||
−0.982101 | + | 0.188354i | \(0.939685\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10.3923 | 0.354581 | 0.177290 | − | 0.984159i | \(-0.443267\pi\) | ||||
0.177290 | + | 0.984159i | \(0.443267\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −33.0197 | −1.12400 | −0.562002 | − | 0.827136i | \(-0.689969\pi\) | ||||
−0.562002 | + | 0.827136i | \(0.689969\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.79796 | 0.333141 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −13.7980 | −0.468064 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 16.0000i | − 0.542139i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.44949i | 0.150420i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 16.5420i | 0.558583i | 0.960206 | + | 0.279291i | \(0.0900995\pi\) | ||||
−0.960206 | + | 0.279291i | \(0.909900\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 2.97129i | − 0.100105i | −0.998747 | − | 0.0500527i | \(-0.984061\pi\) | ||||
0.998747 | − | 0.0500527i | \(-0.0159389\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 51.6116 | 1.73687 | 0.868434 | − | 0.495805i | \(-0.165127\pi\) | ||||
0.868434 | + | 0.495805i | \(0.165127\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 26.7914 | 0.899567 | 0.449784 | − | 0.893137i | \(-0.351501\pi\) | ||||
0.449784 | + | 0.893137i | \(0.351501\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −41.5959 | −1.39508 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 27.5959 | 0.923462 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.24745i | 0.208829i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 9.79796i | − 0.326780i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 11.3137i | 0.376914i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − 4.09978i | − 0.136281i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −32.0983 | −1.06581 | −0.532904 | − | 0.846176i | \(-0.678899\pi\) | ||||
−0.532904 | + | 0.846176i | \(0.678899\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −47.2261 | −1.56467 | −0.782335 | − | 0.622858i | \(-0.785971\pi\) | ||||
−0.782335 | + | 0.622858i | \(0.785971\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.00000 | 0.132381 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 90.9898 | 3.00475 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.10102i | 0.102293i | 0.998691 | + | 0.0511466i | \(0.0162876\pi\) | ||||
−0.998691 | + | 0.0511466i | \(0.983712\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 8.00000i | 0.263323i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.34242i | 0.274297i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 32.2412i | − 1.05780i | −0.848684 | − | 0.528899i | \(-0.822605\pi\) | ||||
0.848684 | − | 0.528899i | \(-0.177395\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −36.1981 | −1.18634 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 12.5851 | 0.411575 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −45.5959 | −1.48955 | −0.744777 | − | 0.667314i | \(-0.767444\pi\) | ||||
−0.744777 | + | 0.667314i | \(0.767444\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −13.5959 | −0.443214 | −0.221607 | − | 0.975136i | \(-0.571130\pi\) | ||||
−0.221607 | + | 0.975136i | \(0.571130\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 28.8990i | − 0.941080i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 32.0000i | − 1.03986i | −0.854209 | − | 0.519930i | \(-0.825958\pi\) | ||||
0.854209 | − | 0.519930i | \(-0.174042\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 16.6848i | 0.541613i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 52.8829i | 1.71305i | 0.516109 | + | 0.856523i | \(0.327380\pi\) | ||||
−0.516109 | + | 0.856523i | \(0.672620\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −18.2419 | −0.590294 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 50.3402 | 1.62557 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.00000 | 0.225806 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −10.0000 | −0.321911 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.24745i | 0.200904i | 0.994942 | + | 0.100452i | \(0.0320289\pi\) | ||||
−0.994942 | + | 0.100452i | \(0.967971\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 17.3485i | 0.556739i | 0.960474 | + | 0.278369i | \(0.0897940\pi\) | ||||
−0.960474 | + | 0.278369i | \(0.910206\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 46.2405i | − 1.48240i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 24.8844i | − 0.796122i | −0.917359 | − | 0.398061i | \(-0.869683\pi\) | ||||
0.917359 | − | 0.398061i | \(-0.130317\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 62.2896 | 1.99078 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 18.5276 | 0.590940 | 0.295470 | − | 0.955352i | \(-0.404524\pi\) | ||||
0.295470 | + | 0.955352i | \(0.404524\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −17.5959 | −0.560653 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 45.7980i | 1.45482i | 0.686203 | + | 0.727410i | \(0.259276\pi\) | ||||
−0.686203 | + | 0.727410i | \(0.740724\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 13.7980i | 0.437425i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 29.6985i | 0.940560i | 0.882517 | + | 0.470280i | \(0.155847\pi\) | ||||
−0.882517 | + | 0.470280i | \(0.844153\pi\) | |||||||
\(998\) | 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 | 2880.2.b.b.2591.1 | ✓ | 8 | |
3.2 | odd | 2 | 2880.2.b.c.2591.1 | yes | 8 | ||
4.3 | odd | 2 | inner | 2880.2.b.b.2591.7 | yes | 8 | |
8.3 | odd | 2 | 2880.2.b.c.2591.8 | yes | 8 | ||
8.5 | even | 2 | 2880.2.b.c.2591.2 | yes | 8 | ||
12.11 | even | 2 | 2880.2.b.c.2591.7 | yes | 8 | ||
24.5 | odd | 2 | inner | 2880.2.b.b.2591.2 | yes | 8 | |
24.11 | even | 2 | inner | 2880.2.b.b.2591.8 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2880.2.b.b.2591.1 | ✓ | 8 | 1.1 | even | 1 | trivial | |
2880.2.b.b.2591.2 | yes | 8 | 24.5 | odd | 2 | inner | |
2880.2.b.b.2591.7 | yes | 8 | 4.3 | odd | 2 | inner | |
2880.2.b.b.2591.8 | yes | 8 | 24.11 | even | 2 | inner | |
2880.2.b.c.2591.1 | yes | 8 | 3.2 | odd | 2 | ||
2880.2.b.c.2591.2 | yes | 8 | 8.5 | even | 2 | ||
2880.2.b.c.2591.7 | yes | 8 | 12.11 | even | 2 | ||
2880.2.b.c.2591.8 | yes | 8 | 8.3 | odd | 2 |