Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2352,2,Mod(961,2352)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2352, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2352.961");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2352.q (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(18.7808145554\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 147) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 961.2 | ||
Root | \(0.707107 + 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2352.961 |
Dual form | 2352.2.q.bd.1537.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2352\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1471\) | \(1765\) | \(2257\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.500000 | + | 0.866025i | 0.288675 | + | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.292893 | + | 0.507306i | −0.130986 | + | 0.226874i | −0.924057 | − | 0.382255i | \(-0.875148\pi\) |
0.793071 | + | 0.609129i | \(0.208481\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | − | 1.73205i | −0.301511 | − | 0.522233i | 0.674967 | − | 0.737848i | \(-0.264158\pi\) |
−0.976478 | + | 0.215615i | \(0.930824\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.41421 | 1.50163 | 0.750816 | − | 0.660511i | \(-0.229660\pi\) | ||||
0.750816 | + | 0.660511i | \(0.229660\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.585786 | −0.151249 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.12132 | − | 5.40629i | −0.757031 | − | 1.31122i | −0.944358 | − | 0.328919i | \(-0.893316\pi\) |
0.187327 | − | 0.982298i | \(-0.440018\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.41421 | − | 2.44949i | 0.324443 | − | 0.561951i | −0.656957 | − | 0.753928i | \(-0.728157\pi\) |
0.981399 | + | 0.191977i | \(0.0614899\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.82843 | − | 3.16693i | 0.381253 | − | 0.660350i | −0.609988 | − | 0.792410i | \(-0.708826\pi\) |
0.991242 | + | 0.132060i | \(0.0421592\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.32843 | + | 4.03295i | 0.465685 | + | 0.806591i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.17157 | −0.217556 | −0.108778 | − | 0.994066i | \(-0.534694\pi\) | ||||
−0.108778 | + | 0.994066i | \(0.534694\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.41421 | − | 5.91359i | −0.613211 | − | 1.06211i | −0.990696 | − | 0.136097i | \(-0.956544\pi\) |
0.377485 | − | 0.926016i | \(-0.376789\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.00000 | − | 1.73205i | 0.174078 | − | 0.301511i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.00000 | − | 3.46410i | 0.328798 | − | 0.569495i | −0.653476 | − | 0.756948i | \(-0.726690\pi\) |
0.982274 | + | 0.187453i | \(0.0600231\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.70711 | + | 4.68885i | 0.433484 | + | 0.750816i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.24264 | −0.350242 | −0.175121 | − | 0.984547i | \(-0.556032\pi\) | ||||
−0.175121 | + | 0.984547i | \(0.556032\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.65685 | 0.862662 | 0.431331 | − | 0.902194i | \(-0.358044\pi\) | ||||
0.431331 | + | 0.902194i | \(0.358044\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.292893 | − | 0.507306i | −0.0436619 | − | 0.0756247i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.41421 | − | 2.44949i | 0.206284 | − | 0.357295i | −0.744257 | − | 0.667893i | \(-0.767196\pi\) |
0.950541 | + | 0.310599i | \(0.100530\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.12132 | − | 5.40629i | 0.437072 | − | 0.757031i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.00000 | + | 1.73205i | 0.137361 | + | 0.237915i | 0.926497 | − | 0.376303i | \(-0.122805\pi\) |
−0.789136 | + | 0.614218i | \(0.789471\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.17157 | 0.157975 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.82843 | 0.374634 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.41421 | − | 5.91359i | −0.444493 | − | 0.769884i | 0.553524 | − | 0.832833i | \(-0.313283\pi\) |
−0.998017 | + | 0.0629492i | \(0.979949\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.87868 | + | 3.25397i | −0.240540 | + | 0.416628i | −0.960868 | − | 0.277006i | \(-0.910658\pi\) |
0.720328 | + | 0.693634i | \(0.243991\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.58579 | + | 2.74666i | −0.196693 | + | 0.340682i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.82843 | + | 4.89898i | 0.345547 | + | 0.598506i | 0.985453 | − | 0.169948i | \(-0.0543599\pi\) |
−0.639906 | + | 0.768453i | \(0.721027\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.65685 | 0.440234 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.3137 | 1.58005 | 0.790023 | − | 0.613077i | \(-0.210068\pi\) | ||||
0.790023 | + | 0.613077i | \(0.210068\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.94975 | + | 5.10911i | 0.345242 | + | 0.597976i | 0.985398 | − | 0.170269i | \(-0.0544636\pi\) |
−0.640156 | + | 0.768245i | \(0.721130\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.32843 | + | 4.03295i | −0.268864 | + | 0.465685i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.17157 | − | 2.02922i | 0.131812 | − | 0.228306i | −0.792563 | − | 0.609790i | \(-0.791254\pi\) |
0.924375 | + | 0.381485i | \(0.124587\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 15.3137 | 1.68090 | 0.840449 | − | 0.541891i | \(-0.182291\pi\) | ||||
0.840449 | + | 0.541891i | \(0.182291\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.65685 | 0.396642 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.585786 | − | 1.01461i | −0.0628029 | − | 0.108778i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.87868 | − | 4.98602i | 0.305139 | − | 0.528517i | −0.672153 | − | 0.740412i | \(-0.734630\pi\) |
0.977292 | + | 0.211895i | \(0.0679636\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.41421 | − | 5.91359i | 0.354037 | − | 0.613211i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.828427 | + | 1.43488i | 0.0849948 | + | 0.147215i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.41421 | 0.549730 | 0.274865 | − | 0.961483i | \(-0.411367\pi\) | ||||
0.274865 | + | 0.961483i | \(0.411367\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.00000 | 0.201008 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.53553 | − | 14.7840i | −0.849317 | − | 1.47106i | −0.881818 | − | 0.471589i | \(-0.843681\pi\) |
0.0325010 | − | 0.999472i | \(-0.489653\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.24264 | + | 10.8126i | −0.615106 | + | 1.06539i | 0.375260 | + | 0.926919i | \(0.377553\pi\) |
−0.990366 | + | 0.138475i | \(0.955780\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.82843 | + | 10.0951i | −0.563455 | + | 0.975933i | 0.433736 | + | 0.901040i | \(0.357195\pi\) |
−0.997192 | + | 0.0748933i | \(0.976138\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.82843 | − | 4.89898i | −0.270914 | − | 0.469237i | 0.698182 | − | 0.715920i | \(-0.253993\pi\) |
−0.969096 | + | 0.246683i | \(0.920659\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.00000 | 0.379663 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 17.3137 | 1.62874 | 0.814368 | − | 0.580348i | \(-0.197084\pi\) | ||||
0.814368 | + | 0.580348i | \(0.197084\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.07107 | + | 1.85514i | 0.0998776 | + | 0.172993i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.70711 | + | 4.68885i | −0.250272 | + | 0.433484i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.50000 | − | 6.06218i | 0.318182 | − | 0.551107i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.12132 | − | 1.94218i | −0.101106 | − | 0.175121i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −5.65685 | −0.505964 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.65685 | −0.856907 | −0.428454 | − | 0.903564i | \(-0.640941\pi\) | ||||
−0.428454 | + | 0.903564i | \(0.640941\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.82843 | + | 4.89898i | 0.249029 | + | 0.431331i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.65685 | − | 6.33386i | 0.319501 | − | 0.553392i | −0.660883 | − | 0.750489i | \(-0.729818\pi\) |
0.980384 | + | 0.197097i | \(0.0631514\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.292893 | − | 0.507306i | 0.0252082 | − | 0.0436619i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 7.07107 | + | 12.2474i | 0.604122 | + | 1.04637i | 0.992190 | + | 0.124739i | \(0.0398094\pi\) |
−0.388067 | + | 0.921631i | \(0.626857\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.34315 | 0.538019 | 0.269009 | − | 0.963138i | \(-0.413304\pi\) | ||||
0.269009 | + | 0.963138i | \(0.413304\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.82843 | 0.238197 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.41421 | − | 9.37769i | −0.452759 | − | 0.784202i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.343146 | − | 0.594346i | 0.0284967 | − | 0.0493577i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.65685 | − | 4.60181i | 0.217658 | − | 0.376995i | −0.736434 | − | 0.676510i | \(-0.763492\pi\) |
0.954092 | + | 0.299515i | \(0.0968249\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.00000 | + | 10.3923i | 0.488273 | + | 0.845714i | 0.999909 | − | 0.0134886i | \(-0.00429367\pi\) |
−0.511636 | + | 0.859202i | \(0.670960\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.24264 | 0.504688 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.00000 | 0.321288 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.1213 | − | 17.5306i | −0.807769 | − | 1.39910i | −0.914406 | − | 0.404799i | \(-0.867341\pi\) |
0.106636 | − | 0.994298i | \(-0.465992\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.00000 | + | 1.73205i | −0.0793052 | + | 0.137361i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.65685 | − | 9.79796i | 0.443079 | − | 0.767435i | −0.554837 | − | 0.831959i | \(-0.687219\pi\) |
0.997916 | + | 0.0645236i | \(0.0205528\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.585786 | + | 1.01461i | 0.0456034 | + | 0.0789874i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −19.7990 | −1.53209 | −0.766046 | − | 0.642786i | \(-0.777779\pi\) | ||||
−0.766046 | + | 0.642786i | \(0.777779\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 16.3137 | 1.25490 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.41421 | + | 2.44949i | 0.108148 | + | 0.187317i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.46447 | + | 6.00063i | −0.263398 | + | 0.456220i | −0.967143 | − | 0.254234i | \(-0.918177\pi\) |
0.703744 | + | 0.710453i | \(0.251510\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.41421 | − | 5.91359i | 0.256628 | − | 0.444493i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.17157 | − | 7.22538i | −0.311798 | − | 0.540050i | 0.666954 | − | 0.745099i | \(-0.267598\pi\) |
−0.978752 | + | 0.205049i | \(0.934265\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.41421 | −0.402435 | −0.201218 | − | 0.979547i | \(-0.564490\pi\) | ||||
−0.201218 | + | 0.979547i | \(0.564490\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.75736 | −0.277752 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.17157 | + | 2.02922i | 0.0861358 | + | 0.149191i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.24264 | + | 10.8126i | −0.456507 | + | 0.790693i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.00000 | + | 15.5885i | −0.651217 | + | 1.12794i | 0.331611 | + | 0.943416i | \(0.392408\pi\) |
−0.982828 | + | 0.184525i | \(0.940925\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.65685 | + | 14.9941i | 0.623134 | + | 1.07930i | 0.988899 | + | 0.148592i | \(0.0474742\pi\) |
−0.365765 | + | 0.930707i | \(0.619192\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.17157 | −0.227121 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.00000 | 0.142494 | 0.0712470 | − | 0.997459i | \(-0.477302\pi\) | ||||
0.0712470 | + | 0.997459i | \(0.477302\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.17157 | + | 8.95743i | 0.366603 | + | 0.634975i | 0.989032 | − | 0.147701i | \(-0.0471874\pi\) |
−0.622429 | + | 0.782676i | \(0.713854\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.82843 | + | 4.89898i | −0.199502 | + | 0.345547i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.656854 | − | 1.13770i | 0.0458767 | − | 0.0794608i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.82843 | + | 3.16693i | 0.127084 | + | 0.220117i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.65685 | −0.391293 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.9706 | 1.44367 | 0.721837 | − | 0.692064i | \(-0.243298\pi\) | ||||
0.721837 | + | 0.692064i | \(0.243298\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.65685 | + | 11.5300i | 0.456120 | + | 0.790023i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.65685 | + | 2.86976i | −0.112997 | + | 0.195716i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.94975 | + | 5.10911i | −0.199325 | + | 0.345242i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −16.8995 | − | 29.2708i | −1.13678 | − | 1.96897i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.97056 | 0.600713 | 0.300357 | − | 0.953827i | \(-0.402894\pi\) | ||||
0.300357 | + | 0.953827i | \(0.402894\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.65685 | −0.310457 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −7.89949 | − | 13.6823i | −0.524308 | − | 0.908128i | −0.999599 | − | 0.0282996i | \(-0.990991\pi\) |
0.475292 | − | 0.879828i | \(-0.342343\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.12132 | + | 7.13834i | −0.272345 | + | 0.471715i | −0.969462 | − | 0.245243i | \(-0.921132\pi\) |
0.697117 | + | 0.716957i | \(0.254466\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −11.0711 | + | 19.1757i | −0.725290 | + | 1.25624i | 0.233565 | + | 0.972341i | \(0.424961\pi\) |
−0.958855 | + | 0.283898i | \(0.908372\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.828427 | + | 1.43488i | 0.0540406 | + | 0.0936011i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.34315 | 0.152204 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.34315 | 0.280935 | 0.140467 | − | 0.990085i | \(-0.455139\pi\) | ||||
0.140467 | + | 0.990085i | \(0.455139\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.87868 | + | 6.71807i | 0.249848 | + | 0.432749i | 0.963483 | − | 0.267768i | \(-0.0862861\pi\) |
−0.713636 | + | 0.700517i | \(0.752953\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.500000 | − | 0.866025i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.65685 | − | 13.2621i | 0.487194 | − | 0.843845i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 7.65685 | + | 13.2621i | 0.485233 | + | 0.840449i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4.48528 | −0.283108 | −0.141554 | − | 0.989931i | \(-0.545210\pi\) | ||||
−0.141554 | + | 0.989931i | \(0.545210\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.31371 | −0.459809 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.82843 | + | 3.16693i | 0.114501 | + | 0.198321i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 9.60660 | − | 16.6391i | 0.599243 | − | 1.03792i | −0.393690 | − | 0.919243i | \(-0.628802\pi\) |
0.992933 | − | 0.118677i | \(-0.0378651\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.585786 | − | 1.01461i | 0.0362593 | − | 0.0628029i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −8.65685 | − | 14.9941i | −0.533805 | − | 0.924577i | −0.999220 | − | 0.0394843i | \(-0.987428\pi\) |
0.465416 | − | 0.885092i | \(-0.345905\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.17157 | −0.0719691 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.75736 | 0.352345 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5.36396 | − | 9.29065i | −0.327046 | − | 0.566461i | 0.654878 | − | 0.755735i | \(-0.272720\pi\) |
−0.981924 | + | 0.189274i | \(0.939387\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.07107 | − | 15.7116i | 0.551028 | − | 0.954409i | −0.447173 | − | 0.894448i | \(-0.647569\pi\) |
0.998201 | − | 0.0599610i | \(-0.0190976\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.65685 | − | 8.06591i | 0.280819 | − | 0.486393i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.65685 | − | 11.5300i | −0.399972 | − | 0.692771i | 0.593750 | − | 0.804649i | \(-0.297647\pi\) |
−0.993722 | + | 0.111878i | \(0.964313\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6.82843 | 0.408807 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −16.4853 | −0.983429 | −0.491715 | − | 0.870756i | \(-0.663630\pi\) | ||||
−0.491715 | + | 0.870756i | \(0.663630\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.24264 | + | 7.34847i | 0.252199 | + | 0.436821i | 0.964131 | − | 0.265427i | \(-0.0855130\pi\) |
−0.711932 | + | 0.702248i | \(0.752180\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.828427 | + | 1.43488i | −0.0490718 | + | 0.0849948i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.9853 | + | 19.0271i | −0.646193 | + | 1.11924i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.70711 | + | 4.68885i | 0.158693 | + | 0.274865i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 19.4142 | 1.13419 | 0.567095 | − | 0.823652i | \(-0.308067\pi\) | ||||
0.567095 | + | 0.823652i | \(0.308067\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.00000 | 0.232889 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.00000 | + | 1.73205i | 0.0580259 | + | 0.100504i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 9.89949 | − | 17.1464i | 0.572503 | − | 0.991604i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 8.53553 | − | 14.7840i | 0.490354 | − | 0.849317i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.10051 | − | 1.90613i | −0.0630147 | − | 0.109145i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.85786 | −0.106034 | −0.0530170 | − | 0.998594i | \(-0.516884\pi\) | ||||
−0.0530170 | + | 0.998594i | \(0.516884\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −12.4853 | −0.710263 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −11.0711 | − | 19.1757i | −0.627783 | − | 1.08735i | −0.987996 | − | 0.154481i | \(-0.950629\pi\) |
0.360213 | − | 0.932870i | \(-0.382704\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.94975 | − | 15.5014i | 0.505870 | − | 0.876192i | −0.494107 | − | 0.869401i | \(-0.664505\pi\) |
0.999977 | − | 0.00679098i | \(-0.00216165\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −5.00000 | + | 8.66025i | −0.280828 | + | 0.486408i | −0.971589 | − | 0.236675i | \(-0.923942\pi\) |
0.690761 | + | 0.723083i | \(0.257276\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.17157 | + | 2.02922i | 0.0655955 | + | 0.113615i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −11.6569 | −0.650622 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −17.6569 | −0.982454 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 12.6066 | + | 21.8353i | 0.699288 | + | 1.21120i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.82843 | − | 4.89898i | 0.156412 | − | 0.270914i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.00000 | + | 3.46410i | −0.109930 | + | 0.190404i | −0.915742 | − | 0.401768i | \(-0.868396\pi\) |
0.805812 | + | 0.592172i | \(0.201729\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.00000 | + | 3.46410i | 0.109599 | + | 0.189832i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.31371 | −0.181047 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −18.3431 | −0.999215 | −0.499607 | − | 0.866252i | \(-0.666522\pi\) | ||||
−0.499607 | + | 0.866252i | \(0.666522\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 8.65685 | + | 14.9941i | 0.470176 | + | 0.814368i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.82843 | + | 11.8272i | −0.369780 | + | 0.640478i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.07107 | + | 1.85514i | −0.0576644 | + | 0.0998776i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5.34315 | + | 9.25460i | 0.286835 | + | 0.496813i | 0.973053 | − | 0.230584i | \(-0.0740635\pi\) |
−0.686217 | + | 0.727396i | \(0.740730\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.89949 | 0.529908 | 0.264954 | − | 0.964261i | \(-0.414643\pi\) | ||||
0.264954 | + | 0.964261i | \(0.414643\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.41421 | −0.288989 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5.36396 | − | 9.29065i | −0.285495 | − | 0.494492i | 0.687234 | − | 0.726436i | \(-0.258825\pi\) |
−0.972729 | + | 0.231944i | \(0.925491\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.89949 | + | 6.75412i | −0.206964 | + | 0.358472i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5.82843 | + | 10.0951i | −0.307613 | + | 0.532801i | −0.977840 | − | 0.209355i | \(-0.932863\pi\) |
0.670227 | + | 0.742156i | \(0.266197\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.50000 | + | 9.52628i | 0.289474 | + | 0.501383i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 7.00000 | 0.367405 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.45584 | −0.180887 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.65685 | + | 16.7262i | 0.504084 | + | 0.873099i | 0.999989 | + | 0.00472187i | \(0.00150302\pi\) |
−0.495905 | + | 0.868377i | \(0.665164\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.12132 | − | 1.94218i | 0.0583736 | − | 0.101106i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 16.6569 | − | 28.8505i | 0.862459 | − | 1.49382i | −0.00708885 | − | 0.999975i | \(-0.502256\pi\) |
0.869548 | − | 0.493848i | \(-0.164410\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.82843 | − | 4.89898i | −0.146059 | − | 0.252982i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −6.34315 | −0.326689 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −31.3137 | −1.60848 | −0.804239 | − | 0.594307i | \(-0.797427\pi\) | ||||
−0.804239 | + | 0.594307i | \(0.797427\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.82843 | − | 8.36308i | −0.247368 | − | 0.428454i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −14.8284 | + | 25.6836i | −0.757697 | + | 1.31237i | 0.186325 | + | 0.982488i | \(0.440342\pi\) |
−0.944022 | + | 0.329882i | \(0.892991\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.82843 | + | 4.89898i | −0.143777 | + | 0.249029i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −5.07107 | − | 8.78335i | −0.257113 | − | 0.445333i | 0.708354 | − | 0.705857i | \(-0.249438\pi\) |
−0.965467 | + | 0.260524i | \(0.916105\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −22.8284 | −1.15448 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.31371 | 0.368928 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.686292 | + | 1.18869i | 0.0345311 | + | 0.0598096i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −17.1924 | + | 29.7781i | −0.862861 | + | 1.49452i | 0.00629405 | + | 0.999980i | \(0.497997\pi\) |
−0.869155 | + | 0.494539i | \(0.835337\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −11.0711 | + | 19.1757i | −0.552863 | + | 0.957586i | 0.445204 | + | 0.895429i | \(0.353131\pi\) |
−0.998066 | + | 0.0621570i | \(0.980202\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −18.4853 | − | 32.0174i | −0.920817 | − | 1.59490i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.585786 | 0.0291080 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −8.00000 | −0.396545 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.29289 | + | 16.0958i | 0.459504 | + | 0.795884i | 0.998935 | − | 0.0461457i | \(-0.0146939\pi\) |
−0.539431 | + | 0.842030i | \(0.681361\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7.07107 | + | 12.2474i | −0.348790 | + | 0.604122i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.48528 | + | 7.76874i | −0.220174 | + | 0.381352i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.17157 | + | 5.49333i | 0.155313 | + | 0.269009i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −38.8284 | −1.89689 | −0.948446 | − | 0.316938i | \(-0.897345\pi\) | ||||
−0.948446 | + | 0.316938i | \(0.897345\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −28.6274 | −1.39521 | −0.697607 | − | 0.716480i | \(-0.745752\pi\) | ||||
−0.697607 | + | 0.716480i | \(0.745752\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.41421 | + | 2.44949i | 0.0687614 | + | 0.119098i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 14.5355 | − | 25.1763i | 0.705077 | − | 1.22123i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 5.41421 | − | 9.37769i | 0.261401 | − | 0.452759i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.48528 | + | 6.03668i | 0.167880 | + | 0.290777i | 0.937674 | − | 0.347515i | \(-0.112975\pi\) |
−0.769794 | + | 0.638292i | \(0.779641\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11.7574 | −0.565023 | −0.282511 | − | 0.959264i | \(-0.591167\pi\) | ||||
−0.282511 | + | 0.959264i | \(0.591167\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.686292 | 0.0329052 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.17157 | − | 8.95743i | −0.247390 | − | 0.428492i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 17.6569 | − | 30.5826i | 0.842716 | − | 1.45963i | −0.0448746 | − | 0.998993i | \(-0.514289\pi\) |
0.887590 | − | 0.460634i | \(-0.152378\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.514719 | − | 0.891519i | 0.0244550 | − | 0.0423573i | −0.853539 | − | 0.521029i | \(-0.825548\pi\) |
0.877994 | + | 0.478672i | \(0.158882\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.68629 | + | 2.92074i | 0.0799379 | + | 0.138456i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5.31371 | 0.251330 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 17.3137 | 0.817084 | 0.408542 | − | 0.912739i | \(-0.366037\pi\) | ||||
0.408542 | + | 0.912739i | \(0.366037\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.24264 | + | 3.88437i | 0.105602 | + | 0.182908i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −6.00000 | + | 10.3923i | −0.281905 | + | 0.488273i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.00000 | − | 15.5885i | 0.421002 | − | 0.729197i | −0.575036 | − | 0.818128i | \(-0.695012\pi\) |
0.996038 | + | 0.0889312i | \(0.0283451\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.12132 | + | 5.40629i | 0.145691 | + | 0.252344i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −19.4142 | −0.904210 | −0.452105 | − | 0.891965i | \(-0.649327\pi\) | ||||
−0.452105 | + | 0.891965i | \(0.649327\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −18.6274 | −0.865689 | −0.432845 | − | 0.901468i | \(-0.642490\pi\) | ||||
−0.432845 | + | 0.901468i | \(0.642490\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.00000 | + | 3.46410i | 0.0927478 | + | 0.160644i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 19.8995 | − | 34.4669i | 0.920839 | − | 1.59494i | 0.122718 | − | 0.992442i | \(-0.460839\pi\) |
0.798120 | − | 0.602498i | \(-0.205828\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 10.1213 | − | 17.5306i | 0.466366 | − | 0.807769i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5.65685 | − | 9.79796i | −0.260102 | − | 0.450511i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 13.1716 | 0.604353 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.00000 | −0.0915737 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 15.0711 | + | 26.1039i | 0.688615 | + | 1.19272i | 0.972286 | + | 0.233794i | \(0.0751142\pi\) |
−0.283671 | + | 0.958922i | \(0.591553\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10.8284 | − | 18.7554i | 0.493734 | − | 0.855172i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.58579 | + | 2.74666i | −0.0720069 | + | 0.124720i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.31371 | − | 16.1318i | −0.422044 | − | 0.731002i | 0.574095 | − | 0.818789i | \(-0.305354\pi\) |
−0.996139 | + | 0.0877864i | \(0.972021\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 11.3137 | 0.511624 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −38.9706 | −1.75872 | −0.879358 | − | 0.476160i | \(-0.842028\pi\) | ||||
−0.879358 | + | 0.476160i | \(0.842028\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.65685 | + | 6.33386i | 0.164696 | + | 0.285263i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.585786 | + | 1.01461i | −0.0263291 | + | 0.0456034i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9.65685 | + | 16.7262i | −0.432300 | + | 0.748766i | −0.997071 | − | 0.0764820i | \(-0.975631\pi\) |
0.564771 | + | 0.825248i | \(0.308965\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −9.89949 | − | 17.1464i | −0.442277 | − | 0.766046i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.0000 | 0.444994 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 8.15685 | + | 14.1281i | 0.362259 | + | 0.627450i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 12.7782 | − | 22.1324i | 0.566383 | − | 0.981003i | −0.430537 | − | 0.902573i | \(-0.641676\pi\) |
0.996920 | − | 0.0784305i | \(-0.0249909\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.41421 | + | 2.44949i | −0.0624391 | + | 0.108148i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.65685 | − | 6.33386i | −0.161140 | − | 0.279103i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.65685 | −0.248788 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −6.92893 | −0.304146 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 16.2929 | + | 28.2201i | 0.713805 | + | 1.23635i | 0.963419 | + | 0.268000i | \(0.0863629\pi\) |
−0.249614 | + | 0.968345i | \(0.580304\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.17157 | + | 12.4215i | −0.313591 | + | 0.543156i | −0.979137 | − | 0.203201i | \(-0.934865\pi\) |
0.665546 | + | 0.746357i | \(0.268199\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −21.3137 | + | 36.9164i | −0.928440 | + | 1.60810i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.81371 | + | 8.33759i | 0.209292 | + | 0.362504i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.82843 | 0.296328 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −12.1421 | −0.525934 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.41421 | − | 5.91359i | −0.147609 | − | 0.255667i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4.17157 | − | 7.22538i | 0.180017 | − | 0.311798i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.65685 | − | 4.60181i | 0.114227 | − | 0.197847i | −0.803243 | − | 0.595651i | \(-0.796894\pi\) |
0.917471 | + | 0.397804i | \(0.130228\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.70711 | − | 4.68885i | −0.116173 | − | 0.201218i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.31371 | 0.141944 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.02944 | 0.129529 | 0.0647647 | − | 0.997901i | \(-0.479370\pi\) | ||||
0.0647647 | + | 0.997901i | \(0.479370\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.87868 | − | 3.25397i | −0.0801801 | − | 0.138876i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.65685 | + | 2.86976i | −0.0705844 | + | 0.122256i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.17157 | + | 2.02922i | −0.0497305 | + | 0.0861358i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −13.0000 | − | 22.5167i | −0.550828 | − | 0.954062i | −0.998215 | − | 0.0597213i | \(-0.980979\pi\) |
0.447387 | − | 0.894340i | \(-0.352355\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 30.6274 | 1.29540 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −12.4853 | −0.527129 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −3.41421 | − | 5.91359i | −0.143892 | − | 0.249228i | 0.785067 | − | 0.619411i | \(-0.212628\pi\) |
−0.928959 | + | 0.370183i | \(0.879295\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.07107 | + | 8.78335i | −0.213341 | + | 0.369518i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −0.242641 | + | 0.420266i | −0.0101720 | + | 0.0176185i | −0.871067 | − | 0.491165i | \(-0.836571\pi\) |
0.860895 | + | 0.508783i | \(0.169905\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16.8284 | + | 29.1477i | 0.704248 | + | 1.21979i | 0.966962 | + | 0.254919i | \(0.0820489\pi\) |
−0.262715 | + | 0.964874i | \(0.584618\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −18.0000 | −0.751961 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 17.0294 | 0.710177 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.05025 | + | 12.2114i | 0.293506 | + | 0.508367i | 0.974636 | − | 0.223795i | \(-0.0718446\pi\) |
−0.681130 | + | 0.732162i | \(0.738511\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −8.65685 | + | 14.9941i | −0.359767 | + | 0.623134i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.00000 | − | 3.46410i | 0.0828315 | − | 0.143468i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.58579 | − | 2.74666i | −0.0655642 | − | 0.113561i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 17.1716 | 0.708747 | 0.354373 | − | 0.935104i | \(-0.384694\pi\) | ||||
0.354373 | + | 0.935104i | \(0.384694\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −19.3137 | −0.795807 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.00000 | + | 1.73205i | 0.0411345 | + | 0.0712470i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 10.5355 | − | 18.2481i | 0.432643 | − | 0.749359i | −0.564457 | − | 0.825462i | \(-0.690915\pi\) |
0.997100 | + | 0.0761034i | \(0.0242479\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5.17157 | + | 8.95743i | −0.211658 | + | 0.366603i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.00000 | − | 1.73205i | −0.0408589 | − | 0.0707697i | 0.844873 | − | 0.534967i | \(-0.179676\pi\) |
−0.885732 | + | 0.464198i | \(0.846343\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −0.928932 | −0.0378919 | −0.0189460 | − | 0.999821i | \(-0.506031\pi\) | ||||
−0.0189460 | + | 0.999821i | \(0.506031\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.65685 | −0.230365 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.05025 | + | 3.55114i | 0.0833546 | + | 0.144374i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −14.8284 | + | 25.6836i | −0.601867 | + | 1.04246i | 0.390671 | + | 0.920530i | \(0.372243\pi\) |
−0.992538 | + | 0.121934i | \(0.961090\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.65685 | − | 13.2621i | 0.309763 | − | 0.536526i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −13.6569 | − | 23.6544i | −0.551595 | − | 0.955391i | −0.998160 | − | 0.0606394i | \(-0.980686\pi\) |
0.446565 | − | 0.894751i | \(-0.352647\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.31371 | 0.0529738 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7.51472 | −0.302531 | −0.151266 | − | 0.988493i | \(-0.548335\pi\) | ||||
−0.151266 | + | 0.988493i | \(0.548335\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.48528 | − | 4.30463i | −0.0998919 | − | 0.173018i | 0.811748 | − | 0.584008i | \(-0.198516\pi\) |
−0.911640 | + | 0.410990i | \(0.865183\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.82843 | + | 3.16693i | −0.0733723 | + | 0.127084i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9.98528 | + | 17.2950i | −0.399411 | + | 0.691801i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.82843 | − | 4.89898i | −0.112956 | − | 0.195646i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −24.9706 | −0.995642 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.686292 | −0.0273208 | −0.0136604 | − | 0.999907i | \(-0.504348\pi\) | ||||
−0.0136604 | + | 0.999907i | \(0.504348\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 10.4853 | + | 18.1610i | 0.416753 | + | 0.721837i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.82843 | − | 4.89898i | 0.112243 | − | 0.194410i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6.65685 | + | 11.5300i | −0.263341 | + | 0.456120i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.58579 | + | 4.47871i | 0.102132 | + | 0.176899i | 0.912563 | − | 0.408936i | \(-0.134100\pi\) |
−0.810431 | + | 0.585835i | \(0.800767\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −50.4264 | −1.98862 | −0.994312 | − | 0.106510i | \(-0.966033\pi\) | ||||
−0.994312 | + | 0.106510i | \(0.966033\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.31371 | −0.130477 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 10.5858 | + | 18.3351i | 0.416170 | + | 0.720828i | 0.995551 | − | 0.0942294i | \(-0.0300387\pi\) |
−0.579380 | + | 0.815057i | \(0.696705\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.82843 | + | 11.8272i | −0.268039 | + | 0.464258i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −9.75736 | + | 16.9002i | −0.381835 | + | 0.661358i | −0.991325 | − | 0.131436i | \(-0.958041\pi\) |
0.609490 | + | 0.792794i | \(0.291374\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.14214 | + | 3.71029i | 0.0837002 | + | 0.144973i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5.89949 | −0.230161 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 13.3137 | 0.518628 | 0.259314 | − | 0.965793i | \(-0.416503\pi\) | ||||
0.259314 | + | 0.965793i | \(0.416503\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.77817 | − | 6.54399i | −0.146954 | − | 0.254532i | 0.783146 | − | 0.621838i | \(-0.213614\pi\) |
−0.930100 | + | 0.367306i | \(0.880280\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 16.8995 | − | 29.2708i | 0.656322 | − | 1.13678i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.14214 | + | 3.71029i | −0.0829438 | + | 0.143663i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4.48528 | + | 7.76874i | 0.173411 | + | 0.300357i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.51472 | 0.290102 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.686292 | 0.0264546 | 0.0132273 | − | 0.999913i | \(-0.495789\pi\) | ||||
0.0132273 | + | 0.999913i | \(0.495789\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.32843 | − | 4.03295i | −0.0896212 | − | 0.155228i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −14.2929 | + | 24.7560i | −0.549321 | + | 0.951451i | 0.449001 | + | 0.893531i | \(0.351780\pi\) |
−0.998321 | + | 0.0579196i | \(0.981553\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.89949 | − | 13.6823i | 0.302709 | − | 0.524308i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −4.17157 | − | 7.22538i | −0.159621 | − | 0.276471i | 0.775111 | − | 0.631825i | \(-0.217694\pi\) |
−0.934732 | + | 0.355354i | \(0.884360\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.28427 | −0.316526 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −8.24264 | −0.314476 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5.41421 | + | 9.37769i | 0.206265 | + | 0.357262i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.6569 | + | 20.1903i | −0.443448 | + | 0.768074i | −0.997943 | − | 0.0641132i | \(-0.979578\pi\) |
0.554495 | + | 0.832187i | \(0.312911\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.85786 | + | 3.21792i | −0.0704728 | + | 0.122062i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.00000 | + | 12.1244i | 0.265144 | + | 0.459243i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −22.1421 | −0.837492 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −22.8284 | −0.862218 | −0.431109 | − | 0.902300i | \(-0.641878\pi\) | ||||
−0.431109 | + | 0.902300i | \(0.641878\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.65685 | − | 9.79796i | −0.213352 | − | 0.369537i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.828427 | + | 1.43488i | −0.0312004 | + | 0.0540406i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10.1421 | + | 17.5667i | −0.380896 | + | 0.659731i | −0.991191 | − | 0.132443i | \(-0.957718\pi\) |
0.610295 | + | 0.792174i | \(0.291051\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.17157 | + | 2.02922i | 0.0439374 | + | 0.0761018i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −24.9706 | −0.935155 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.34315 | 0.237220 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.17157 | + | 3.76127i | 0.0810989 | + | 0.140467i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −12.9706 | + | 22.4657i | −0.483720 | + | 0.837828i | −0.999825 | − | 0.0186972i | \(-0.994048\pi\) |
0.516105 | + | 0.856525i | \(0.327381\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −3.87868 | + | 6.71807i | −0.144250 | + | 0.249848i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.72792 | − | 4.72490i | −0.101312 | − | 0.175478i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.48528 | 0.166350 | 0.0831749 | − | 0.996535i | \(-0.473494\pi\) | ||||
0.0831749 | + | 0.996535i | \(0.473494\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −17.6569 | − | 30.5826i | −0.653062 | − | 1.13114i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.84924 | − | 8.39913i | 0.179111 | − | 0.310229i | −0.762465 | − | 0.647029i | \(-0.776011\pi\) |
0.941576 | + | 0.336800i | \(0.109345\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.65685 | − | 9.79796i | 0.208373 | − | 0.360912i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 13.6569 | + | 23.6544i | 0.502376 | + | 0.870140i | 0.999996 | + | 0.00274517i | \(0.000873816\pi\) |
−0.497621 | + | 0.867395i | \(0.665793\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 15.3137 | 0.562563 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 17.0294 | 0.624749 | 0.312375 | − | 0.949959i | \(-0.398876\pi\) | ||||
0.312375 | + | 0.949959i | \(0.398876\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.55635 | + | 2.69568i | 0.0570202 | + | 0.0987619i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −7.65685 | + | 13.2621i | −0.280150 | + | 0.485233i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.17157 | − | 2.02922i | 0.0427513 | − | 0.0740474i | −0.843858 | − | 0.536567i | \(-0.819721\pi\) |
0.886609 | + | 0.462519i | \(0.153054\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.24264 | − | 3.88437i | −0.0817264 | − | 0.141554i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −7.02944 | −0.255827 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 37.6569 | 1.36866 | 0.684331 | − | 0.729172i | \(-0.260094\pi\) | ||||
0.684331 | + | 0.729172i | \(0.260094\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.65685 | − | 6.33386i | −0.132735 | − | 0.229904i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −23.2635 | + | 40.2935i | −0.843300 | + | 1.46064i | 0.0437901 | + | 0.999041i | \(0.486057\pi\) |
−0.887090 | + | 0.461597i | \(0.847277\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.82843 | + | 3.16693i | −0.0661069 | + | 0.114501i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −18.4853 | − | 32.0174i | −0.667465 | − | 1.15608i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −29.6985 | −1.07095 | −0.535477 | − | 0.844550i | \(-0.679868\pi\) | ||||
−0.535477 | + | 0.844550i | \(0.679868\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 19.2132 | 0.691947 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −10.7782 | − | 18.6683i | −0.387664 | − | 0.671454i | 0.604471 | − | 0.796627i | \(-0.293385\pi\) |
−0.992135 | + | 0.125174i | \(0.960051\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 15.8995 | − | 27.5387i | 0.571127 | − | 0.989220i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.17157 | + | 5.49333i | −0.113633 | + | 0.196819i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −13.3137 | − | 23.0600i | −0.476402 | − | 0.825152i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.17157 | 0.0418686 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 11.8579 | 0.423225 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 23.6569 | + | 40.9749i | 0.843276 | + | 1.46060i | 0.887110 | + | 0.461558i | \(0.152709\pi\) |
−0.0438344 | + | 0.999039i | \(0.513957\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 8.65685 | − | 14.9941i | 0.308192 | − | 0.533805i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10.1716 | + | 17.6177i | −0.361203 | + | 0.625622i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.585786 | − | 1.01461i | −0.0207757 | − | 0.0359846i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 28.3848 | 1.00544 | 0.502720 | − | 0.864449i | \(-0.332333\pi\) | ||||
0.502720 | + | 0.864449i | \(0.332333\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −17.6569 | −0.624655 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.87868 | + | 4.98602i | 0.101713 | + | 0.176172i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5.89949 | − | 10.2182i | 0.208189 | − | 0.360593i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5.36396 | − | 9.29065i | 0.188820 | − | 0.327046i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 23.9706 | + | 41.5182i | 0.842760 | + | 1.45970i | 0.887552 | + | 0.460707i | \(0.152404\pi\) |
−0.0447922 | + | 0.998996i | \(0.514263\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.34315 | 0.222738 | 0.111369 | − | 0.993779i | \(-0.464476\pi\) | ||||
0.111369 | + | 0.993779i | \(0.464476\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 18.1421 | 0.636272 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3.31371 | + | 5.73951i | 0.116074 | + | 0.201046i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.00000 | − | 13.8564i | 0.279885 | − | 0.484774i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 16.6569 | − | 28.8505i | 0.581328 | − | 1.00689i | −0.413994 | − | 0.910280i | \(-0.635867\pi\) |
0.995322 | − | 0.0966104i | \(-0.0308001\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12.4853 | − | 21.6251i | −0.435210 | − | 0.753805i | 0.562103 | − | 0.827067i | \(-0.309992\pi\) |
−0.997313 | + | 0.0732621i | \(0.976659\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 9.31371 | 0.324262 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −36.3431 | −1.26378 | −0.631888 | − | 0.775060i | \(-0.717720\pi\) | ||||
−0.631888 | + | 0.775060i | \(0.717720\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −12.3640 | − | 21.4150i | −0.429418 | − | 0.743774i | 0.567404 | − | 0.823440i | \(-0.307948\pi\) |
−0.996822 | + | 0.0796659i | \(0.974615\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6.65685 | − | 11.5300i | 0.230924 | − | 0.399972i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.79899 | − | 10.0441i | 0.200682 | − | 0.347592i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.41421 | + | 5.91359i | 0.118012 | + | 0.204404i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −45.1716 | −1.55950 | −0.779748 | − | 0.626094i | \(-0.784653\pi\) | ||||
−0.779748 | + | 0.626094i | \(0.784653\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.6274 | −0.952670 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −8.24264 | − | 14.2767i | −0.283892 | − | 0.491715i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −4.77817 | + | 8.27604i | −0.164374 | + | 0.284704i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −4.24264 | + | 7.34847i | −0.145607 | + | 0.252199i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7.31371 | − | 12.6677i | −0.250711 | − | 0.434244i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 49.4975 | 1.69476 | 0.847381 | − | 0.530986i | \(-0.178178\pi\) | ||||
0.847381 | + | 0.530986i | \(0.178178\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.65685 | −0.0566632 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −6.29289 | − | 10.8996i | −0.214961 | − | 0.372324i | 0.738299 | − | 0.674473i | \(-0.235629\pi\) |
−0.953261 | + | 0.302149i | \(0.902296\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.27208 | − | 5.66741i | 0.111642 | − | 0.193369i | −0.804791 | − | 0.593559i | \(-0.797722\pi\) |
0.916432 | + | 0.400190i | \(0.131056\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −2.65685 | + | 4.60181i | −0.0904404 | + | 0.156647i | −0.907697 | − | 0.419627i | \(-0.862161\pi\) |
0.817256 | + | 0.576275i | \(0.195494\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.02944 | − | 3.51509i | −0.0690029 | − | 0.119517i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −21.9706 | −0.746159 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.68629 | −0.158972 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 15.3137 | + | 26.5241i | 0.518885 | + | 0.898736i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.70711 | + | 4.68885i | −0.0916217 | + | 0.158693i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5.65685 | + | 9.79796i | −0.191018 | + | 0.330854i | −0.945588 | − | 0.325366i | \(-0.894512\pi\) |
0.754570 | + | 0.656220i | \(0.227846\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 9.70711 | + | 16.8132i | 0.327413 | + | 0.567095i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 30.2426 | 1.01890 | 0.509450 | − | 0.860500i | \(-0.329849\pi\) | ||||
0.509450 | + | 0.860500i | \(0.329849\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 27.3137 | 0.919179 | 0.459590 | − | 0.888131i | \(-0.347996\pi\) | ||||
0.459590 | + | 0.888131i | \(0.347996\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.00000 | + | 3.46410i | 0.0672293 | + | 0.116445i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.41421 | − | 2.44949i | 0.0474846 | − | 0.0822458i | −0.841306 | − | 0.540559i | \(-0.818213\pi\) |
0.888791 | + | 0.458313i | \(0.151546\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.00000 | + | 1.73205i | −0.0335013 | + | 0.0580259i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4.00000 | − | 6.92820i | −0.133855 | − | 0.231843i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.88730 | 0.163364 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 19.7990 | 0.661069 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.00000 | + | 6.92820i | 0.133407 | + | 0.231069i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.24264 | − | 10.8126i | 0.207973 | − | 0.360219i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.58579 | − | 2.74666i | 0.0527133 | − | 0.0913022i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −8.00000 | − | 13.8564i | −0.265636 | − | 0.460094i | 0.702094 | − | 0.712084i | \(-0.252248\pi\) |
−0.967730 | + | 0.251990i | \(0.918915\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 17.0711 | 0.566212 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 34.9706 | 1.15863 | 0.579313 | − | 0.815105i | \(-0.303321\pi\) | ||||
0.579313 | + | 0.815105i | \(0.303321\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −15.3137 | − | 26.5241i | −0.506810 | − | 0.877820i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.10051 | − | 1.90613i | 0.0363816 | − | 0.0630147i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 24.1421 | − | 41.8154i | 0.796376 | − | 1.37936i | −0.125586 | − | 0.992083i | \(-0.540081\pi\) |
0.921962 | − | 0.387280i | \(-0.126585\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.928932 | − | 1.60896i | −0.0306094 | − | 0.0530170i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 72.0833 | 2.37265 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 18.6274 | 0.612466 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −6.24264 | − | 10.8126i | −0.205035 | − | 0.355131i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.60660 | + | 2.78272i | −0.0527109 | + | 0.0912979i | −0.891177 | − | 0.453656i | \(-0.850120\pi\) |
0.838466 | + | 0.544954i | \(0.183453\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 11.0711 | − | 19.1757i | 0.362450 | − | 0.627783i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.65685 | − | 6.33386i | −0.119592 | − | 0.207139i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 33.4142 | 1.09159 | 0.545797 | − | 0.837917i | \(-0.316227\pi\) | ||||
0.545797 | + | 0.837917i | \(0.316227\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 17.8995 | 0.584128 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.60660 | + | 6.24682i | 0.117572 | + | 0.203640i | 0.918805 | − | 0.394712i | \(-0.129156\pi\) |
−0.801233 | + | 0.598352i | \(0.795822\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.10051 | + | 7.10228i | −0.133531 | + | 0.231282i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 26.6569 | − | 46.1710i | 0.866231 | − | 1.50036i | 0.000412082 | − | 1.00000i | \(-0.499869\pi\) |
0.865819 | − | 0.500357i | \(-0.166798\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 15.9706 | + | 27.6618i | 0.518426 | + | 0.897941i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −10.0000 | −0.324272 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.00000 | 0.0647864 | 0.0323932 | − | 0.999475i | \(-0.489687\pi\) | ||||
0.0323932 | + | 0.999475i | \(0.489687\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.27208 | − | 9.13151i | −0.170600 | − | 0.295489i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.17157 | + | 2.02922i | −0.0378716 | + | 0.0655955i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.81371 | + | 13.5337i | −0.252055 | + | 0.436572i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −5.82843 | − | 10.0951i | −0.187818 | − | 0.325311i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −10.1421 | −0.326487 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −22.3431 | −0.718507 | −0.359254 | − | 0.933240i | \(-0.616969\pi\) | ||||
−0.359254 | + | 0.933240i | \(0.616969\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −8.82843 | − | 15.2913i | −0.283610 | − | 0.491227i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.68629 | + | 4.65279i | −0.0862072 | + | 0.149315i | −0.905905 | − | 0.423481i | \(-0.860808\pi\) |
0.819698 | + | 0.572796i | \(0.194141\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −12.6066 | + | 21.8353i | −0.403734 | + | 0.699288i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 13.4142 | + | 23.2341i | 0.429159 | + | 0.743325i | 0.996799 | − | 0.0799522i | \(-0.0254768\pi\) |
−0.567640 | + | 0.823277i | \(0.692143\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −11.5147 | −0.368012 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.65685 | 0.180609 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 18.6274 | + | 32.2636i | 0.594122 | + | 1.02905i | 0.993670 | + | 0.112338i | \(0.0358338\pi\) |
−0.399548 | + | 0.916712i | \(0.630833\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.585786 | + | 1.01461i | −0.0186647 | + | 0.0323282i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 10.3431 | − | 17.9149i | 0.328893 | − | 0.569659i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10.4853 | + | 18.1610i | 0.333076 | + | 0.576904i | 0.983113 | − | 0.182998i | \(-0.0585801\pi\) |
−0.650037 | + | 0.759902i | \(0.725247\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4.00000 | −0.126936 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −6.05887 | −0.192079 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.19239 | + | 8.99348i | 0.164445 | + | 0.284826i | 0.936458 | − | 0.350780i | \(-0.114083\pi\) |
−0.772013 | + | 0.635606i | \(0.780750\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.00000 | + | 3.46410i | −0.0632772 | + | 0.109599i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2352.2.q.bd.961.2 | 4 | ||
4.3 | odd | 2 | 147.2.e.d.79.2 | 4 | |||
7.2 | even | 3 | 2352.2.a.bc.1.1 | 2 | |||
7.3 | odd | 6 | 2352.2.q.bb.1537.1 | 4 | |||
7.4 | even | 3 | inner | 2352.2.q.bd.1537.2 | 4 | ||
7.5 | odd | 6 | 2352.2.a.be.1.2 | 2 | |||
7.6 | odd | 2 | 2352.2.q.bb.961.1 | 4 | |||
12.11 | even | 2 | 441.2.e.g.226.1 | 4 | |||
21.2 | odd | 6 | 7056.2.a.cf.1.2 | 2 | |||
21.5 | even | 6 | 7056.2.a.cv.1.1 | 2 | |||
28.3 | even | 6 | 147.2.e.e.67.2 | 4 | |||
28.11 | odd | 6 | 147.2.e.d.67.2 | 4 | |||
28.19 | even | 6 | 147.2.a.d.1.1 | ✓ | 2 | ||
28.23 | odd | 6 | 147.2.a.e.1.1 | yes | 2 | ||
28.27 | even | 2 | 147.2.e.e.79.2 | 4 | |||
56.5 | odd | 6 | 9408.2.a.dq.1.1 | 2 | |||
56.19 | even | 6 | 9408.2.a.ef.1.1 | 2 | |||
56.37 | even | 6 | 9408.2.a.dt.1.2 | 2 | |||
56.51 | odd | 6 | 9408.2.a.di.1.2 | 2 | |||
84.11 | even | 6 | 441.2.e.g.361.1 | 4 | |||
84.23 | even | 6 | 441.2.a.i.1.2 | 2 | |||
84.47 | odd | 6 | 441.2.a.j.1.2 | 2 | |||
84.59 | odd | 6 | 441.2.e.f.361.1 | 4 | |||
84.83 | odd | 2 | 441.2.e.f.226.1 | 4 | |||
140.19 | even | 6 | 3675.2.a.bf.1.2 | 2 | |||
140.79 | odd | 6 | 3675.2.a.bd.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
147.2.a.d.1.1 | ✓ | 2 | 28.19 | even | 6 | ||
147.2.a.e.1.1 | yes | 2 | 28.23 | odd | 6 | ||
147.2.e.d.67.2 | 4 | 28.11 | odd | 6 | |||
147.2.e.d.79.2 | 4 | 4.3 | odd | 2 | |||
147.2.e.e.67.2 | 4 | 28.3 | even | 6 | |||
147.2.e.e.79.2 | 4 | 28.27 | even | 2 | |||
441.2.a.i.1.2 | 2 | 84.23 | even | 6 | |||
441.2.a.j.1.2 | 2 | 84.47 | odd | 6 | |||
441.2.e.f.226.1 | 4 | 84.83 | odd | 2 | |||
441.2.e.f.361.1 | 4 | 84.59 | odd | 6 | |||
441.2.e.g.226.1 | 4 | 12.11 | even | 2 | |||
441.2.e.g.361.1 | 4 | 84.11 | even | 6 | |||
2352.2.a.bc.1.1 | 2 | 7.2 | even | 3 | |||
2352.2.a.be.1.2 | 2 | 7.5 | odd | 6 | |||
2352.2.q.bb.961.1 | 4 | 7.6 | odd | 2 | |||
2352.2.q.bb.1537.1 | 4 | 7.3 | odd | 6 | |||
2352.2.q.bd.961.2 | 4 | 1.1 | even | 1 | trivial | ||
2352.2.q.bd.1537.2 | 4 | 7.4 | even | 3 | inner | ||
3675.2.a.bd.1.2 | 2 | 140.79 | odd | 6 | |||
3675.2.a.bf.1.2 | 2 | 140.19 | even | 6 | |||
7056.2.a.cf.1.2 | 2 | 21.2 | odd | 6 | |||
7056.2.a.cv.1.1 | 2 | 21.5 | even | 6 | |||
9408.2.a.di.1.2 | 2 | 56.51 | odd | 6 | |||
9408.2.a.dq.1.1 | 2 | 56.5 | odd | 6 | |||
9408.2.a.dt.1.2 | 2 | 56.37 | even | 6 | |||
9408.2.a.ef.1.1 | 2 | 56.19 | even | 6 |