Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1216,2,Mod(31,1216)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1216, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1216.31");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1216 = 2^{6} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1216.s (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.70980888579\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 31.2 | ||
Root | \(-0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1216.31 |
Dual form | 1216.2.s.b.863.2 |
$q$-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 \(\left(\mathbb{Z}/1216\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(705\) | \(837\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
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 | ||||||||
\(3\) | −1.50000 | + | 0.866025i | −0.866025 | + | 0.500000i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.36603 | − | 1.36603i | 1.05812 | − | 0.610905i | 0.133207 | − | 0.991088i | \(-0.457472\pi\) |
0.924911 | + | 0.380183i | \(0.124139\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.26795i | − | 0.479240i | −0.970867 | − | 0.239620i | \(-0.922977\pi\) | ||
0.970867 | − | 0.239620i | \(-0.0770228\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.46410 | −1.34598 | −0.672989 | − | 0.739653i | \(-0.734990\pi\) | ||||
−0.672989 | + | 0.739653i | \(0.734990\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.36603 | + | 4.09808i | −0.610905 | + | 1.05812i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.73205 | + | 4.73205i | 0.662620 | + | 1.14769i | 0.979925 | + | 0.199367i | \(0.0638887\pi\) |
−0.317305 | + | 0.948323i | \(0.602778\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.500000 | + | 4.33013i | −0.114708 | + | 0.993399i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.09808 | + | 1.90192i | 0.239620 | + | 0.415034i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.63397 | + | 2.09808i | 0.757736 | + | 0.437479i | 0.828482 | − | 0.560015i | \(-0.189205\pi\) |
−0.0707462 | + | 0.997494i | \(0.522538\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.23205 | − | 2.13397i | 0.246410 | − | 0.426795i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 5.19615i | − | 1.00000i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.09808 | + | 1.90192i | −0.203908 | + | 0.353178i | −0.949784 | − | 0.312906i | \(-0.898698\pi\) |
0.745877 | + | 0.666084i | \(0.232031\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.19615 | 0.394441 | 0.197220 | − | 0.980359i | \(-0.436809\pi\) | ||||
0.197220 | + | 0.980359i | \(0.436809\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 6.69615 | − | 3.86603i | 1.16565 | − | 0.672989i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.73205 | − | 3.00000i | −0.292770 | − | 0.507093i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.73205 | 0.777944 | 0.388972 | − | 0.921250i | \(-0.372830\pi\) | ||||
0.388972 | + | 0.921250i | \(0.372830\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.69615 | − | 3.86603i | 1.04576 | − | 0.603772i | 0.124303 | − | 0.992244i | \(-0.460331\pi\) |
0.921460 | + | 0.388473i | \(0.126997\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.73205 | + | 3.00000i | 0.264135 | + | 0.457496i | 0.967337 | − | 0.253495i | \(-0.0815801\pi\) |
−0.703201 | + | 0.710991i | \(0.748247\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.36603 | + | 4.83013i | 1.22031 | + | 0.704546i | 0.964984 | − | 0.262309i | \(-0.0844838\pi\) |
0.255326 | + | 0.966855i | \(0.417817\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.39230 | 0.770329 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −8.19615 | − | 4.73205i | −1.14769 | − | 0.662620i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.73205 | + | 8.19615i | −0.649997 | + | 1.12583i | 0.333126 | + | 0.942882i | \(0.391897\pi\) |
−0.983123 | + | 0.182946i | \(0.941437\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −10.5622 | + | 6.09808i | −1.42420 | + | 0.822264i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.00000 | − | 6.92820i | −0.397360 | − | 0.917663i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.696152 | − | 0.401924i | 0.0906313 | − | 0.0523260i | −0.453999 | − | 0.891002i | \(-0.650003\pi\) |
0.544631 | + | 0.838676i | \(0.316670\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.5622 | − | 6.09808i | −1.35235 | − | 0.780779i | −0.363770 | − | 0.931489i | \(-0.618511\pi\) |
−0.988578 | + | 0.150710i | \(0.951844\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.69615 | + | 2.13397i | 0.451557 | + | 0.260706i | 0.708487 | − | 0.705723i | \(-0.249378\pi\) |
−0.256931 | + | 0.966430i | \(0.582711\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −7.26795 | −0.874958 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.26795 | + | 2.19615i | 0.150478 | + | 0.260635i | 0.931403 | − | 0.363989i | \(-0.118585\pi\) |
−0.780925 | + | 0.624624i | \(0.785252\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.50000 | + | 4.33013i | 0.292603 | + | 0.506803i | 0.974424 | − | 0.224716i | \(-0.0721453\pi\) |
−0.681822 | + | 0.731519i | \(0.738812\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.26795i | 0.492820i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.66025i | 0.645046i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.19615 | + | 14.1962i | 0.922139 | + | 1.59719i | 0.796099 | + | 0.605167i | \(0.206894\pi\) |
0.126041 | + | 0.992025i | \(0.459773\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.50000 | + | 7.79423i | 0.500000 | + | 0.866025i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.39230 | 0.372354 | 0.186177 | − | 0.982516i | \(-0.440390\pi\) | ||||
0.186177 | + | 0.982516i | \(0.440390\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 12.9282 | + | 7.46410i | 1.40226 | + | 0.809595i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 3.80385i | − | 0.407815i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −11.1962 | − | 6.46410i | −1.18679 | − | 0.685193i | −0.229214 | − | 0.973376i | \(-0.573616\pi\) |
−0.957575 | + | 0.288183i | \(0.906949\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.29423 | + | 1.90192i | −0.341596 | + | 0.197220i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.73205 | + | 10.9282i | 0.485498 | + | 1.12121i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.69615 | + | 3.86603i | −0.679891 | + | 0.392535i | −0.799814 | − | 0.600248i | \(-0.795069\pi\) |
0.119923 | + | 0.992783i | \(0.461735\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 14.0263 | + | 8.09808i | 1.39567 | + | 0.805789i | 0.993935 | − | 0.109969i | \(-0.0350750\pi\) |
0.401732 | + | 0.915757i | \(0.368408\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.46410 | −0.932526 | −0.466263 | − | 0.884646i | \(-0.654400\pi\) | ||||
−0.466263 | + | 0.884646i | \(0.654400\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 5.19615 | + | 3.00000i | 0.507093 | + | 0.292770i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.39230i | 0.424620i | 0.977202 | + | 0.212310i | \(0.0680987\pi\) | ||||
−0.977202 | + | 0.212310i | \(0.931901\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.26795 | + | 2.19615i | 0.121448 | + | 0.210353i | 0.920339 | − | 0.391122i | \(-0.127913\pi\) |
−0.798891 | + | 0.601476i | \(0.794580\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.09808 | + | 4.09808i | −0.673720 | + | 0.388972i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 15.5885i | − | 1.46644i | −0.679992 | − | 0.733219i | \(-0.738017\pi\) | ||
0.679992 | − | 0.733219i | \(-0.261983\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 11.4641 | 1.06903 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.00000 | − | 3.46410i | 0.550019 | − | 0.317554i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.92820 | 0.811655 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −6.69615 | + | 11.5981i | −0.603772 | + | 1.04576i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.92820i | 0.619677i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.26795 | − | 2.19615i | 0.112512 | − | 0.194877i | −0.804270 | − | 0.594264i | \(-0.797444\pi\) |
0.916783 | + | 0.399387i | \(0.130777\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −5.19615 | − | 3.00000i | −0.457496 | − | 0.264135i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.964102 | + | 1.66987i | 0.0842339 | + | 0.145897i | 0.905065 | − | 0.425274i | \(-0.139822\pi\) |
−0.820831 | + | 0.571172i | \(0.806489\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.49038 | + | 0.633975i | 0.476076 | + | 0.0549726i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −7.09808 | − | 12.2942i | −0.610905 | − | 1.05812i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −8.96410 | + | 15.5263i | −0.765855 | + | 1.32650i | 0.173939 | + | 0.984757i | \(0.444351\pi\) |
−0.939793 | + | 0.341743i | \(0.888983\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.69615 | − | 4.66987i | 0.228685 | − | 0.396093i | −0.728734 | − | 0.684797i | \(-0.759891\pi\) |
0.957419 | + | 0.288704i | \(0.0932242\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −16.7321 | −1.40909 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.00000i | 0.498273i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −8.08846 | + | 4.66987i | −0.667125 | + | 0.385165i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.36603 | − | 4.83013i | 0.685372 | − | 0.395699i | −0.116504 | − | 0.993190i | \(-0.537169\pi\) |
0.801876 | + | 0.597491i | \(0.203836\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.7321 | −1.36163 | −0.680817 | − | 0.732453i | \(-0.738375\pi\) | ||||
−0.680817 | + | 0.732453i | \(0.738375\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.19615 | − | 3.00000i | 0.417365 | − | 0.240966i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.339746 | − | 0.196152i | 0.0271147 | − | 0.0156547i | −0.486381 | − | 0.873747i | \(-0.661683\pi\) |
0.513496 | + | 0.858092i | \(0.328350\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 16.3923i | − | 1.29999i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.66025 | − | 4.60770i | 0.209657 | − | 0.363137i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.39230 | −0.735662 | −0.367831 | − | 0.929893i | \(-0.619900\pi\) | ||||
−0.367831 | + | 0.929893i | \(0.619900\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 10.5622 | − | 18.2942i | 0.822264 | − | 1.42420i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.53590 | − | 4.39230i | 0.196234 | − | 0.339887i | −0.751071 | − | 0.660222i | \(-0.770462\pi\) |
0.947304 | + | 0.320335i | \(0.103796\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.50000 | + | 11.2583i | 0.500000 | + | 0.866025i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −12.9282 | − | 22.3923i | −0.982913 | − | 1.70246i | −0.650866 | − | 0.759193i | \(-0.725594\pi\) |
−0.332047 | − | 0.943263i | \(-0.607739\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.70577 | − | 1.56218i | −0.204537 | − | 0.118090i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.696152 | + | 1.20577i | −0.0523260 | + | 0.0906313i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.19615i | 0.388379i | 0.980964 | + | 0.194189i | \(0.0622076\pi\) | ||||
−0.980964 | + | 0.194189i | \(0.937792\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.36603 | − | 4.09808i | 0.175865 | − | 0.304608i | −0.764595 | − | 0.644511i | \(-0.777061\pi\) |
0.940460 | + | 0.339903i | \(0.110394\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 21.1244 | 1.56156 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 11.1962 | − | 6.46410i | 0.823157 | − | 0.475250i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −12.1962 | − | 21.1244i | −0.891871 | − | 1.54477i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −6.58846 | −0.479240 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 17.8564i | − | 1.29204i | −0.763319 | − | 0.646022i | \(-0.776431\pi\) | ||
0.763319 | − | 0.646022i | \(-0.223569\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −21.5885 | + | 12.4641i | −1.55397 | + | 0.897186i | −0.556159 | + | 0.831076i | \(0.687725\pi\) |
−0.997812 | + | 0.0661096i | \(0.978941\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.80385i | 0.556001i | 0.960581 | + | 0.278001i | \(0.0896717\pi\) | ||||
−0.960581 | + | 0.278001i | \(0.910328\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.7321 | + | 6.19615i | 0.760775 | + | 0.439234i | 0.829574 | − | 0.558397i | \(-0.188583\pi\) |
−0.0687990 | + | 0.997631i | \(0.521917\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.39230 | −0.521413 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.41154 | + | 1.39230i | 0.169257 | + | 0.0977206i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 10.5622 | − | 18.2942i | 0.737694 | − | 1.27772i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.23205 | − | 19.3301i | 0.154394 | − | 1.33709i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.0000 | − | 8.66025i | 1.03264 | − | 0.596196i | 0.114902 | − | 0.993377i | \(-0.463345\pi\) |
0.917741 | + | 0.397180i | \(0.130011\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3.80385 | − | 2.19615i | −0.260635 | − | 0.150478i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.19615 | + | 4.73205i | 0.558973 | + | 0.322723i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 2.78461i | − | 0.189032i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −7.50000 | − | 4.33013i | −0.506803 | − | 0.292603i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −12.7583 | − | 22.0981i | −0.854361 | − | 1.47980i | −0.877237 | − | 0.480058i | \(-0.840615\pi\) |
0.0228756 | − | 0.999738i | \(-0.492718\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 18.1244i | − | 1.20296i | −0.798889 | − | 0.601478i | \(-0.794579\pi\) | ||
0.798889 | − | 0.601478i | \(-0.205421\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.7846i | 0.844831i | 0.906402 | + | 0.422415i | \(0.138818\pi\) | ||||
−0.906402 | + | 0.422415i | \(0.861182\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.90192 | − | 8.49038i | −0.322523 | − | 0.558626i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.42820 | − | 5.93782i | −0.224589 | − | 0.389000i | 0.731607 | − | 0.681727i | \(-0.238771\pi\) |
−0.956196 | + | 0.292727i | \(0.905437\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 26.3923 | 1.72164 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −24.5885 | − | 14.1962i | −1.59719 | − | 0.922139i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.85641i | 0.378819i | 0.981898 | + | 0.189410i | \(0.0606574\pi\) | ||||
−0.981898 | + | 0.189410i | \(0.939343\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −22.2846 | − | 12.8660i | −1.43548 | − | 0.828774i | −0.437947 | − | 0.899001i | \(-0.644294\pi\) |
−0.997531 | + | 0.0702273i | \(0.977628\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 12.7583 | − | 7.36603i | 0.815100 | − | 0.470598i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5.08846 | + | 2.93782i | −0.322468 | + | 0.186177i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −8.16025 | + | 14.1340i | −0.515071 | + | 0.892129i | 0.484776 | + | 0.874638i | \(0.338901\pi\) |
−0.999847 | + | 0.0174904i | \(0.994432\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −16.2224 | − | 9.36603i | −1.01990 | − | 0.588837i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −25.8564 | −1.61919 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 11.3038 | + | 6.52628i | 0.705115 | + | 0.407098i | 0.809250 | − | 0.587465i | \(-0.199874\pi\) |
−0.104135 | + | 0.994563i | \(0.533207\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 6.00000i | − | 0.372822i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 11.8301 | − | 6.83013i | 0.729477 | − | 0.421164i | −0.0887539 | − | 0.996054i | \(-0.528288\pi\) |
0.818231 | + | 0.574890i | \(0.194955\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 25.8564i | 1.58835i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 22.3923 | 1.37039 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 10.7321 | + | 18.5885i | 0.654345 | + | 1.13336i | 0.982058 | + | 0.188581i | \(0.0603888\pi\) |
−0.327713 | + | 0.944777i | \(0.606278\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 24.7583 | − | 14.2942i | 1.50396 | − | 0.868313i | 0.503972 | − | 0.863720i | \(-0.331871\pi\) |
0.999989 | − | 0.00459256i | \(-0.00146186\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.50000 | + | 9.52628i | −0.331662 | + | 0.574456i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 4.19615i | − | 0.252122i | −0.992022 | − | 0.126061i | \(-0.959766\pi\) | ||
0.992022 | − | 0.126061i | \(-0.0402336\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −14.8923 | − | 8.59808i | −0.888400 | − | 0.512918i | −0.0149815 | − | 0.999888i | \(-0.504769\pi\) |
−0.873419 | + | 0.486970i | \(0.838102\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.23205 | − | 15.9904i | −0.548788 | − | 0.950529i | −0.998358 | − | 0.0572841i | \(-0.981756\pi\) |
0.449569 | − | 0.893245i | \(-0.351577\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −16.5622 | − | 12.2942i | −0.981059 | − | 0.728247i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.90192 | − | 8.49038i | −0.289351 | − | 0.501171i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.42820 | + | 11.1340i | −0.378130 | + | 0.654940i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.69615 | − | 11.5981i | 0.392535 | − | 0.679891i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4.73205 | −0.276449 | −0.138225 | − | 0.990401i | \(-0.544140\pi\) | ||||
−0.138225 | + | 0.990401i | \(0.544140\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.09808 | − | 1.90192i | 0.0639325 | − | 0.110734i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 23.1962i | 1.34598i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.80385 | − | 2.19615i | 0.219250 | − | 0.126584i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −28.0526 | −1.61158 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −33.3205 | −1.90793 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 11.0885 | − | 6.40192i | 0.632852 | − | 0.365377i | −0.149004 | − | 0.988837i | \(-0.547607\pi\) |
0.781856 | + | 0.623460i | \(0.214273\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 14.1962 | − | 8.19615i | 0.807591 | − | 0.466263i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 18.7321i | 1.06220i | 0.847310 | + | 0.531099i | \(0.178221\pi\) | ||||
−0.847310 | + | 0.531099i | \(0.821779\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.69615 | − | 16.7942i | 0.548059 | − | 0.949266i | −0.450349 | − | 0.892853i | \(-0.648700\pi\) |
0.998408 | − | 0.0564131i | \(-0.0179664\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 15.1244 | − | 26.1962i | 0.849468 | − | 1.47132i | −0.0322149 | − | 0.999481i | \(-0.510256\pi\) |
0.881683 | − | 0.471842i | \(-0.156411\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.90192 | − | 8.49038i | 0.274455 | − | 0.475370i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.80385 | − | 6.58846i | −0.212310 | − | 0.367732i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −21.8564 | + | 9.46410i | −1.21612 | + | 0.526597i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3.80385 | − | 2.19615i | −0.210353 | − | 0.121448i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.12436 | − | 10.6077i | 0.337647 | − | 0.584821i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 31.7321i | 1.74415i | 0.489371 | + | 0.872076i | \(0.337226\pi\) | ||||
−0.489371 | + | 0.872076i | \(0.662774\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 11.6603 | 0.637068 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.89230 | + | 3.40192i | −0.320974 | + | 0.185315i | −0.651827 | − | 0.758368i | \(-0.725997\pi\) |
0.330852 | + | 0.943682i | \(0.392664\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 13.5000 | + | 23.3827i | 0.733219 | + | 1.26997i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −9.80385 | −0.530908 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 15.7128i | − | 0.848412i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −17.1962 | + | 9.92820i | −0.925810 | + | 0.534516i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.23205 | − | 2.13397i | −0.0661400 | − | 0.114558i | 0.831059 | − | 0.556184i | \(-0.187735\pi\) |
−0.897199 | + | 0.441626i | \(0.854402\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 34.6410i | 1.85429i | 0.374701 | + | 0.927146i | \(0.377745\pi\) | ||||
−0.374701 | + | 0.927146i | \(0.622255\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 25.7846 | 1.37238 | 0.686188 | − | 0.727424i | \(-0.259283\pi\) | ||||
0.686188 | + | 0.727424i | \(0.259283\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.00000 | + | 3.46410i | 0.318447 | + | 0.183855i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6.00000 | + | 10.3923i | −0.317554 | + | 0.550019i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.02628 | − | 1.16987i | 0.106943 | − | 0.0617435i | −0.445575 | − | 0.895245i | \(-0.647001\pi\) |
0.552517 | + | 0.833501i | \(0.313667\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.5000 | − | 4.33013i | −0.973684 | − | 0.227901i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −13.3923 | + | 7.73205i | −0.702914 | + | 0.405827i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 11.8301 | + | 6.83013i | 0.619217 | + | 0.357505i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −24.7583 | − | 14.2942i | −1.29237 | − | 0.746153i | −0.313300 | − | 0.949654i | \(-0.601434\pi\) |
−0.979075 | + | 0.203502i | \(0.934768\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 10.3923 | + | 6.00000i | 0.539542 | + | 0.311504i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.92820 | 0.358729 | 0.179364 | − | 0.983783i | \(-0.442596\pi\) | ||||
0.179364 | + | 0.983783i | \(0.442596\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −6.00000 | − | 10.3923i | −0.309839 | − | 0.536656i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 17.3205i | − | 0.889695i | −0.895606 | − | 0.444847i | \(-0.853258\pi\) | ||
0.895606 | − | 0.444847i | \(-0.146742\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.39230i | 0.225025i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8.36603 | + | 14.4904i | 0.427484 | + | 0.740424i | 0.996649 | − | 0.0817995i | \(-0.0260667\pi\) |
−0.569165 | + | 0.822223i | \(0.692733\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.73205 | + | 13.3923i | 0.394062 | + | 0.682535i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 22.0526 | + | 12.7321i | 1.11811 | + | 0.645541i | 0.940918 | − | 0.338636i | \(-0.109965\pi\) |
0.177192 | + | 0.984176i | \(0.443299\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 22.9282i | 1.15953i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.89230 | − | 1.66987i | −0.145897 | − | 0.0842339i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 38.7846 | + | 22.3923i | 1.95147 | + | 1.12668i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −30.0788 | + | 17.3660i | −1.50961 | + | 0.871576i | −0.509676 | + | 0.860366i | \(0.670235\pi\) |
−0.999937 | + | 0.0112097i | \(0.996432\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −8.78461 | + | 3.80385i | −0.439781 | + | 0.190431i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 17.0885 | − | 9.86603i | 0.853357 | − | 0.492686i | −0.00842522 | − | 0.999965i | \(-0.502682\pi\) |
0.861782 | + | 0.507279i | \(0.169349\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 21.2942 | + | 12.2942i | 1.05812 | + | 0.610905i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −21.1244 | −1.04710 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −14.3038 | − | 8.25833i | −0.707280 | − | 0.408348i | 0.102773 | − | 0.994705i | \(-0.467228\pi\) |
−0.810053 | + | 0.586357i | \(0.800562\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 31.0526i | − | 1.53171i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.509619 | − | 0.882686i | −0.0250767 | − | 0.0434341i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.02628 | − | 4.63397i | 0.393995 | − | 0.227473i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 9.33975i | 0.457369i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 35.1769 | 1.71850 | 0.859252 | − | 0.511552i | \(-0.170929\pi\) | ||||
0.859252 | + | 0.511552i | \(0.170929\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.09808 | − | 1.90192i | −0.0535170 | − | 0.0926941i | 0.838026 | − | 0.545631i | \(-0.183710\pi\) |
−0.891543 | + | 0.452936i | \(0.850376\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 13.4641 | 0.653105 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.73205 | + | 13.3923i | −0.374180 | + | 0.648099i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10.7321 | − | 18.5885i | 0.516945 | − | 0.895374i | −0.482862 | − | 0.875697i | \(-0.660403\pi\) |
0.999806 | − | 0.0196778i | \(-0.00626406\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.80385 | − | 3.92820i | −0.326972 | − | 0.188777i | 0.327524 | − | 0.944843i | \(-0.393786\pi\) |
−0.654496 | + | 0.756065i | \(0.727119\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5.19615 | − | 9.00000i | −0.249136 | − | 0.431517i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −10.9019 | + | 14.6865i | −0.521510 | + | 0.702552i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.29423 | + | 16.0981i | 0.443589 | + | 0.768319i | 0.997953 | − | 0.0639555i | \(-0.0203716\pi\) |
−0.554363 | + | 0.832275i | \(0.687038\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.23205 | − | 2.13397i | 0.0585365 | − | 0.101388i | −0.835272 | − | 0.549837i | \(-0.814690\pi\) |
0.893809 | + | 0.448449i | \(0.148023\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −35.3205 | −1.67435 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −8.36603 | + | 14.4904i | −0.395699 | + | 0.685372i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10.5167i | 0.496312i | 0.968720 | + | 0.248156i | \(0.0798245\pi\) | ||||
−0.968720 | + | 0.248156i | \(0.920175\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −29.8923 | + | 17.2583i | −1.40757 | + | 0.812663i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 25.0981 | − | 14.4904i | 1.17921 | − | 0.680817i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −24.1769 | −1.13095 | −0.565474 | − | 0.824766i | \(-0.691307\pi\) | ||||
−0.565474 | + | 0.824766i | \(0.691307\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 24.5885 | − | 14.1962i | 1.14769 | − | 0.662620i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 11.6603 | − | 6.73205i | 0.543072 | − | 0.313543i | −0.203251 | − | 0.979127i | \(-0.565151\pi\) |
0.746323 | + | 0.665584i | \(0.231817\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.7846i | 0.780047i | 0.920805 | + | 0.390023i | \(0.127533\pi\) | ||||
−0.920805 | + | 0.390023i | \(0.872467\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −5.19615 | + | 9.00000i | −0.240966 | + | 0.417365i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −4.46410 | −0.206574 | −0.103287 | − | 0.994652i | \(-0.532936\pi\) | ||||
−0.103287 | + | 0.994652i | \(0.532936\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.70577 | − | 4.68653i | 0.124941 | − | 0.216404i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.339746 | + | 0.588457i | −0.0156547 | + | 0.0271147i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7.73205 | − | 13.3923i | −0.355520 | − | 0.615779i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.62436 | + | 6.40192i | 0.395713 | + | 0.293740i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 25.2679 | + | 14.5885i | 1.15452 | + | 0.666564i | 0.949985 | − | 0.312295i | \(-0.101098\pi\) |
0.204537 | + | 0.978859i | \(0.434431\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 9.21539i | 0.419315i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −10.5622 | + | 18.2942i | −0.479604 | + | 0.830698i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −33.1244 | −1.50101 | −0.750504 | − | 0.660866i | \(-0.770189\pi\) | ||||
−0.750504 | + | 0.660866i | \(0.770189\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 14.0885 | − | 8.13397i | 0.637102 | − | 0.367831i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −11.5885 | − | 20.0718i | −0.522980 | − | 0.905828i | −0.999642 | − | 0.0267412i | \(-0.991487\pi\) |
0.476663 | − | 0.879086i | \(-0.341846\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −12.0000 | −0.540453 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.78461 | − | 1.60770i | 0.124907 | − | 0.0721150i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −15.0885 | − | 26.1340i | −0.675452 | − | 1.16992i | −0.976337 | − | 0.216257i | \(-0.930615\pi\) |
0.300884 | − | 0.953661i | \(-0.402718\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8.78461i | 0.392467i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 25.4378 | + | 14.6865i | 1.13422 | + | 0.654840i | 0.944992 | − | 0.327094i | \(-0.106069\pi\) |
0.189225 | + | 0.981934i | \(0.439403\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 44.2487 | 1.96904 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −19.5000 | − | 11.2583i | −0.866025 | − | 0.500000i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 13.8564 | − | 24.0000i | 0.614174 | − | 1.06378i | −0.376354 | − | 0.926476i | \(-0.622822\pi\) |
0.990529 | − | 0.137305i | \(-0.0438442\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.49038 | − | 3.16987i | 0.242880 | − | 0.140227i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 22.5000 | + | 2.59808i | 0.993399 | + | 0.114708i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −22.3923 | + | 12.9282i | −0.986723 | + | 0.569685i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −37.3468 | − | 21.5622i | −1.64251 | − | 0.948303i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 38.7846 | + | 22.3923i | 1.70246 | + | 0.982913i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 19.0526i | − | 0.834708i | −0.908744 | − | 0.417354i | \(-0.862958\pi\) | ||
0.908744 | − | 0.417354i | \(-0.137042\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −16.9808 | − | 9.80385i | −0.742517 | − | 0.428692i | 0.0804668 | − | 0.996757i | \(-0.474359\pi\) |
−0.822984 | + | 0.568065i | \(0.807692\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 5.41154 | 0.236179 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.00000 | + | 10.3923i | 0.261364 | + | 0.452696i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.69615 | − | 4.66987i | −0.117224 | − | 0.203038i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.00000 | + | 10.3923i | 0.259403 | + | 0.449299i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −4.50000 | − | 7.79423i | −0.194189 | − | 0.336346i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −24.0718 | −1.03685 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.588457 | + | 0.339746i | 0.0252998 | + | 0.0146068i | 0.512597 | − | 0.858630i | \(-0.328684\pi\) |
−0.487297 | + | 0.873236i | \(0.662017\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 8.19615i | 0.351731i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.00000 | + | 3.46410i | 0.257012 | + | 0.148386i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14.1962 | − | 8.19615i | −0.606984 | − | 0.350442i | 0.164800 | − | 0.986327i | \(-0.447302\pi\) |
−0.771784 | + | 0.635885i | \(0.780635\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.68653 | − | 5.70577i | −0.327457 | − | 0.243074i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 18.0000 | − | 10.3923i | 0.765438 | − | 0.441926i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −11.1962 | + | 19.3923i | −0.475250 | + | 0.823157i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 8.53590 | + | 4.92820i | 0.361678 | + | 0.208815i | 0.669816 | − | 0.742527i | \(-0.266373\pi\) |
−0.308139 | + | 0.951341i | \(0.599706\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 36.5885 | + | 21.1244i | 1.54477 | + | 0.891871i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 35.1962i | 1.48334i | 0.670764 | + | 0.741670i | \(0.265966\pi\) | ||||
−0.670764 | + | 0.741670i | \(0.734034\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −21.2942 | − | 36.8827i | −0.895855 | − | 1.55167i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 9.88269 | − | 5.70577i | 0.415034 | − | 0.239620i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0.928203i | 0.0389123i | 0.999811 | + | 0.0194562i | \(0.00619348\pi\) | ||||
−0.999811 | + | 0.0194562i | \(0.993807\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.60770 | −0.192826 | −0.0964130 | − | 0.995341i | \(-0.530737\pi\) | ||||
−0.0964130 | + | 0.995341i | \(0.530737\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 15.4641 | + | 26.7846i | 0.646022 | + | 1.11894i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.95448 | − | 5.16987i | 0.373428 | − | 0.215599i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10.8564 | 0.451958 | 0.225979 | − | 0.974132i | \(-0.427442\pi\) | ||||
0.225979 | + | 0.974132i | \(0.427442\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 21.5885 | − | 37.3923i | 0.897186 | − | 1.55397i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 4.30127i | − | 0.178447i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 21.1244 | − | 36.5885i | 0.874881 | − | 1.51534i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.26795 | + | 3.92820i | 0.0936083 | + | 0.162134i | 0.909027 | − | 0.416737i | \(-0.136827\pi\) |
−0.815419 | + | 0.578872i | \(0.803493\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.09808 | + | 9.50962i | −0.0452454 | + | 0.391837i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.75833 | − | 11.7058i | −0.278001 | − | 0.481511i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 20.6962 | − | 35.8468i | 0.849889 | − | 1.47205i | −0.0314175 | − | 0.999506i | \(-0.510002\pi\) |
0.881307 | − | 0.472545i | \(-0.156665\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 9.46410 | − | 16.3923i | 0.387990 | − | 0.672019i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −21.4641 | −0.878467 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3.29423 | + | 5.70577i | −0.134599 | + | 0.233131i | −0.925444 | − | 0.378884i | \(-0.876308\pi\) |
0.790845 | + | 0.612016i | \(0.209641\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 13.7321i | − | 0.560142i | −0.959979 | − | 0.280071i | \(-0.909642\pi\) | ||
0.959979 | − | 0.280071i | \(-0.0903580\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 21.1244 | − | 12.1962i | 0.858827 | − | 0.495844i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −42.5885 | −1.72861 | −0.864306 | − | 0.502966i | \(-0.832242\pi\) | ||||
−0.864306 | + | 0.502966i | \(0.832242\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4.82309 | −0.195441 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 17.3205 | − | 10.0000i | 0.699569 | − | 0.403896i | −0.107618 | − | 0.994192i | \(-0.534322\pi\) |
0.807187 | + | 0.590296i | \(0.200989\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 36.5885i | 1.47539i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5.16025 | − | 8.93782i | 0.207744 | − | 0.359823i | −0.743260 | − | 0.669003i | \(-0.766721\pi\) |
0.951004 | + | 0.309180i | \(0.100055\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −30.3923 | −1.22157 | −0.610785 | − | 0.791797i | \(-0.709146\pi\) | ||||
−0.610785 | + | 0.791797i | \(0.709146\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 10.9019 | − | 18.8827i | 0.437479 | − | 0.757736i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −8.19615 | + | 14.1962i | −0.328372 | + | 0.568757i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15.6244 | + | 27.0622i | 0.624974 | + | 1.08249i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 13.3923 | + | 30.9282i | 0.534837 | + | 1.23515i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 12.9282 | + | 22.3923i | 0.515481 | + | 0.892840i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −32.2750 | − | 18.6340i | −1.28485 | − | 0.741807i | −0.307117 | − | 0.951672i | \(-0.599364\pi\) |
−0.977730 | + | 0.209865i | \(0.932698\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −15.0000 | + | 25.9808i | −0.596196 | + | 1.03264i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 6.92820i | − | 0.274937i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 31.5000 | − | 18.1865i | 1.24418 | − | 0.718325i | 0.274234 | − | 0.961663i | \(-0.411576\pi\) |
0.969942 | + | 0.243338i | \(0.0782425\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −19.9641 | − | 34.5788i | −0.787307 | − | 1.36366i | −0.927611 | − | 0.373548i | \(-0.878141\pi\) |
0.140304 | − | 0.990109i | \(-0.455192\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −16.3923 | −0.645446 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 33.8564i | 1.33103i | 0.746383 | + | 0.665516i | \(0.231789\pi\) | ||||
−0.746383 | + | 0.665516i | \(0.768211\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.10770 | + | 1.79423i | −0.121988 | + | 0.0704296i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.41154 | + | 4.17691i | 0.0945158 | + | 0.163706i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 3.32051i | − | 0.129942i | −0.997887 | − | 0.0649708i | \(-0.979305\pi\) | ||
0.997887 | − | 0.0649708i | \(-0.0206954\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.56218 | + | 2.63397i | 0.178259 | + | 0.102918i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −33.3731 | − | 19.2679i | −1.30003 | − | 0.750573i | −0.319621 | − | 0.947545i | \(-0.603556\pi\) |
−0.980409 | + | 0.196973i | \(0.936889\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −18.7583 | + | 32.4904i | −0.729614 | + | 1.26373i | 0.227432 | + | 0.973794i | \(0.426967\pi\) |
−0.957046 | + | 0.289935i | \(0.906366\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 13.8564 | − | 6.00000i | 0.537328 | − | 0.232670i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.98076 | + | 4.60770i | −0.309016 | + | 0.178411i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 38.2750 | + | 22.0981i | 1.47980 | + | 0.854361i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 47.1506 | + | 27.2224i | 1.82023 | + | 1.05091i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.928203i | 0.0357796i | 0.999840 | + | 0.0178898i | \(0.00569480\pi\) | ||||
−0.999840 | + | 0.0178898i | \(0.994305\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −11.0885 | − | 6.40192i | −0.426795 | − | 0.246410i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.21539 | 0.123577 | 0.0617887 | − | 0.998089i | \(-0.480319\pi\) | ||||
0.0617887 | + | 0.998089i | \(0.480319\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.90192 | + | 8.49038i | 0.188119 | + | 0.325831i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 15.6962 | + | 27.1865i | 0.601478 | + | 1.04179i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 51.0333i | 1.95274i | 0.216115 | + | 0.976368i | \(0.430661\pi\) | ||||
−0.216115 | + | 0.976368i | \(0.569339\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 48.9808i | 1.87146i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −11.0718 | − | 19.1769i | −0.422415 | − | 0.731645i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −17.3205 | −0.658903 | −0.329452 | − | 0.944172i | \(-0.606864\pi\) | ||||
−0.329452 | + | 0.944172i | \(0.606864\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 14.7321i | − | 0.558819i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 36.5885 | + | 21.1244i | 1.38589 | + | 0.800142i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 10.2846 | + | 5.93782i | 0.389000 | + | 0.224589i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 24.4186 | − | 14.0981i | 0.922277 | − | 0.532477i | 0.0379164 | − | 0.999281i | \(-0.487928\pi\) |
0.884361 | + | 0.466804i | \(0.154595\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.36603 | + | 20.4904i | −0.0892363 | + | 0.772809i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −39.5885 | + | 22.8564i | −1.49099 | + | 0.860822i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 10.2679 | − | 17.7846i | 0.386166 | − | 0.668859i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 31.6865 | + | 18.2942i | 1.19001 | + | 0.687054i | 0.958309 | − | 0.285732i | \(-0.0922368\pi\) |
0.231703 | + | 0.972787i | \(0.425570\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 7.98076 | + | 4.60770i | 0.298882 | + | 0.172560i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −5.07180 | − | 8.78461i | −0.189410 | − | 0.328067i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 19.8564 | − | 11.4641i | 0.740519 | − | 0.427539i | −0.0817390 | − | 0.996654i | \(-0.526047\pi\) |
0.822258 | + | 0.569115i | \(0.192714\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12.0000i | 0.446903i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 44.5692 | 1.65755 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.70577 | + | 4.68653i | 0.100490 | + | 0.174053i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −0.679492 | + | 0.392305i | −0.0252010 | + | 0.0145498i | −0.512548 | − | 0.858659i | \(-0.671298\pi\) |
0.487347 | + | 0.873209i | \(0.337965\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −9.46410 | + | 16.3923i | −0.350042 | + | 0.606291i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 24.5885i | − | 0.908195i | −0.890952 | − | 0.454098i | \(-0.849962\pi\) | ||
0.890952 | − | 0.454098i | \(-0.150038\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −12.7583 | + | 22.0981i | −0.470598 | + | 0.815100i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −16.5000 | − | 9.52628i | −0.607785 | − | 0.350905i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 21.8923 | + | 37.9186i | 0.805321 | + | 1.39486i | 0.916074 | + | 0.401010i | \(0.131341\pi\) |
−0.110752 | + | 0.993848i | \(0.535326\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4.22243 | − | 7.31347i | −0.154906 | − | 0.268305i | 0.778119 | − | 0.628117i | \(-0.216174\pi\) |
−0.933025 | + | 0.359812i | \(0.882841\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 13.1962 | − | 22.8564i | 0.483470 | − | 0.837394i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.56922 | 0.203495 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.928203 | − | 1.60770i | 0.0338706 | − | 0.0586656i | −0.848593 | − | 0.529046i | \(-0.822550\pi\) |
0.882464 | + | 0.470380i | \(0.155883\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 28.2679i | − | 1.03014i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −39.5885 | + | 22.8564i | −1.44077 | + | 0.831830i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 14.5359 | − | 8.39230i | 0.528316 | − | 0.305024i | −0.212014 | − | 0.977267i | \(-0.568002\pi\) |
0.740331 | + | 0.672243i | \(0.234669\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 32.4449 | 1.17767 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6.85641 | −0.248545 | −0.124272 | − | 0.992248i | \(-0.539660\pi\) | ||||
−0.124272 | + | 0.992248i | \(0.539660\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.78461 | − | 1.60770i | 0.100810 | − | 0.0582025i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 21.1244 | − | 36.5885i | 0.761764 | − | 1.31941i | −0.180177 | − | 0.983634i | \(-0.557667\pi\) |
0.941941 | − | 0.335779i | \(-0.109000\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −22.6077 | −0.814196 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −12.7583 | + | 22.0981i | −0.458885 | + | 0.794813i | −0.998902 | − | 0.0468415i | \(-0.985084\pi\) |
0.540017 | + | 0.841654i | \(0.318418\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.70577 | − | 4.68653i | 0.0971942 | − | 0.168345i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 5.19615 | + | 9.00000i | 0.186411 | + | 0.322873i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 13.3923 | + | 30.9282i | 0.479829 | + | 1.10812i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.66025 | − | 9.80385i | −0.202540 | − | 0.350809i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 9.88269 | + | 5.70577i | 0.353178 | + | 0.203908i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.535898 | − | 0.928203i | 0.0191270 | − | 0.0331290i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 30.8038i | 1.09804i | 0.835810 | + | 0.549019i | \(0.184999\pi\) | ||||
−0.835810 | + | 0.549019i | \(0.815001\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −11.8301 | + | 20.4904i | −0.421164 | + | 0.729477i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −19.7654 | −0.702776 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −22.3923 | − | 38.7846i | −0.794173 | − | 1.37555i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −28.7321 | −1.01774 | −0.508871 | − | 0.860843i | \(-0.669937\pi\) | ||||
−0.508871 | + | 0.860843i | \(0.669937\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 52.7846i | 1.86739i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −11.1603 | − | 19.3301i | −0.393837 | − | 0.682145i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 14.5359i | − | 0.512323i | ||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −32.1962 | − | 18.5885i | −1.13336 | − | 0.654345i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −0.320508 | −0.0112685 | −0.00563423 | − | 0.999984i | \(-0.501793\pi\) | ||||
−0.00563423 | + | 0.999984i | \(0.501793\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 40.9808 | + | 23.6603i | 1.43903 | + | 0.830824i | 0.997782 | − | 0.0665619i | \(-0.0212030\pi\) |
0.441247 | + | 0.897386i | \(0.354536\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −24.7583 | + | 42.8827i | −0.868313 | + | 1.50396i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −22.2224 | + | 12.8301i | −0.778418 | + | 0.449420i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −13.8564 | + | 6.00000i | −0.484774 | + | 0.209913i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −36.8372 | − | 21.2679i | −1.28563 | − | 0.742257i | −0.307755 | − | 0.951466i | \(-0.599578\pi\) |
−0.977871 | + | 0.209209i | \(0.932911\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −46.9808 | − | 27.1244i | −1.63765 | − | 0.945496i | −0.981641 | − | 0.190740i | \(-0.938911\pi\) |
−0.656006 | − | 0.754756i | \(-0.727755\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 19.0526i | − | 0.663325i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −27.6962 | − | 15.9904i | −0.963090 | − | 0.556040i | −0.0659670 | − | 0.997822i | \(-0.521013\pi\) |
−0.897123 | + | 0.441782i | \(0.854347\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 40.3923 | 1.40288 | 0.701441 | − | 0.712727i | \(-0.252540\pi\) | ||||
0.701441 | + | 0.712727i | \(0.252540\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.63397 | + | 6.29423i | 0.126061 | + | 0.218344i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 14.7321 | + | 25.5167i | 0.510435 | + | 0.884100i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 13.8564i | − | 0.479521i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 11.4115i | − | 0.394441i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 10.9019 | + | 18.8827i | 0.376376 | + | 0.651903i | 0.990532 | − | 0.137282i | \(-0.0438367\pi\) |
−0.614156 | + | 0.789185i | \(0.710503\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.0885 | + | 20.9378i | 0.416843 | + | 0.721994i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 29.7846 | 1.02584 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 30.7583 | + | 17.7583i | 1.05812 | + | 0.610905i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 11.3205i | − | 0.388977i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 27.6962 | + | 15.9904i | 0.950529 | + | 0.548788i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 17.1962 | + | 9.92820i | 0.589477 | + | 0.340334i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 13.1769 | − | 7.60770i | 0.451169 | − | 0.260483i | −0.257155 | − | 0.966370i | \(-0.582785\pi\) |
0.708324 | + | 0.705888i | \(0.249452\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −4.50000 | + | 2.59808i | −0.153717 | + | 0.0887486i | −0.574886 | − | 0.818234i | \(-0.694953\pi\) |
0.421168 | + | 0.906982i | \(0.361620\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.69615 | − | 13.3301i | 0.262589 | − | 0.454818i | −0.704340 | − | 0.709863i | \(-0.748757\pi\) |
0.966929 | + | 0.255045i | \(0.0820902\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 14.7058 | + | 8.49038i | 0.501171 | + | 0.289351i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −8.44486 | −0.287467 | −0.143733 | − | 0.989616i | \(-0.545911\pi\) | ||||
−0.143733 | + | 0.989616i | \(0.545911\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −61.1769 | − | 35.3205i | −2.08008 | − | 1.20093i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 22.2679i | − | 0.756259i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −36.5885 | − | 63.3731i | −1.24118 | − | 2.14978i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 8.78461 | 0.296974 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 16.5622 | + | 28.6865i | 0.559265 | + | 0.968675i | 0.997558 | + | 0.0698432i | \(0.0222499\pi\) |
−0.438293 | + | 0.898832i | \(0.644417\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 7.09808 | − | 4.09808i | 0.239412 | − | 0.138225i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −19.5359 | −0.658181 | −0.329091 | − | 0.944298i | \(-0.606742\pi\) | ||||
−0.329091 | + | 0.944298i | \(0.606742\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.50000 | + | 6.06218i | −0.117784 | + | 0.204009i | −0.918889 | − | 0.394515i | \(-0.870912\pi\) |
0.801105 | + | 0.598524i | \(0.204246\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.80385i | 0.127865i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 24.2487 | − | 42.0000i | 0.814192 | − | 1.41022i | −0.0957146 | − | 0.995409i | \(-0.530514\pi\) |
0.909907 | − | 0.414813i | \(-0.136153\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.78461 | − | 1.60770i | −0.0933928 | − | 0.0539204i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −20.0885 | − | 34.7942i | −0.672989 | − | 1.16565i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −25.0981 | + | 33.8109i | −0.839875 | + | 1.13144i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.09808 | + | 12.2942i | 0.237263 | + | 0.410951i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.41154 | + | 4.17691i | −0.0804295 | + | 0.139308i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −51.7128 | −1.72280 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3.80385 | + | 6.58846i | −0.126584 | + | 0.219250i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 12.9282i | − | 0.429748i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 46.5000 | − | 26.8468i | 1.54401 | − | 0.891433i | 0.545427 | − | 0.838158i | \(-0.316367\pi\) |
0.998580 | − | 0.0532748i | \(-0.0169659\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 49.5167 | 1.64056 | 0.820280 | − | 0.571962i | \(-0.193818\pi\) | ||||
0.820280 | + | 0.571962i | \(0.193818\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −15.1436 | −0.501180 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 49.9808 | − | 28.8564i | 1.65231 | − | 0.953963i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.11731 | − | 1.22243i | 0.0699199 | − | 0.0403683i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 8.78461i | − | 0.289778i | −0.989448 | − | 0.144889i | \(-0.953718\pi\) | ||
0.989448 | − | 0.144889i | \(-0.0462824\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −11.0885 | + | 19.2058i | −0.365377 | + | 0.632852i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.83013 | − | 10.0981i | 0.191693 | − | 0.332023i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −19.0885 | − | 33.0622i | −0.626272 | − | 1.08473i | −0.988293 | − | 0.152565i | \(-0.951247\pi\) |
0.362021 | − | 0.932170i | \(-0.382087\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.69615 | + | 23.3494i | −0.0883628 | + | 0.765245i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −16.2224 | − | 28.0981i | −0.531099 | − | 0.919890i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −57.7128 | − | 33.3205i | −1.88741 | − | 1.08970i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −24.8923 | + | 43.1147i | −0.813196 | + | 1.40850i | 0.0974198 | + | 0.995243i | \(0.468941\pi\) |
−0.910616 | + | 0.413254i | \(0.864392\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 33.5885i | 1.09612i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 19.5167 | − | 33.8038i | 0.636225 | − | 1.10197i | −0.350029 | − | 0.936739i | \(-0.613828\pi\) |
0.986254 | − | 0.165235i | \(-0.0528383\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 32.4449 | 1.05655 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −15.5885 | + | 9.00000i | −0.507093 | + | 0.292770i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.80385 | + | 4.85641i | 0.0911128 | + | 0.157812i | 0.907980 | − | 0.419014i | \(-0.137624\pi\) |
−0.816867 | + | 0.576826i | \(0.804291\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 52.3923i | 1.69894i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 14.3038 | − | 8.25833i | 0.463347 | − | 0.267514i | −0.250104 | − | 0.968219i | \(-0.580465\pi\) |
0.713451 | + | 0.700706i | \(0.247131\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −24.3923 | − | 42.2487i | −0.789316 | − | 1.36714i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 16.9808i | 0.548910i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 19.6865 | + | 11.3660i | 0.635711 | + | 0.367028i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26.1769 | −0.844417 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −34.0526 | + | 58.9808i | −1.09619 | + | 1.89866i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10.3923 | − | 6.00000i | 0.334194 | − | 0.192947i | −0.323508 | − | 0.946226i | \(-0.604862\pi\) |
0.657702 | + | 0.753279i | \(0.271529\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 24.5885 | − | 33.1244i | 0.789895 | − | 1.06411i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 9.10770 | − | 5.25833i | 0.292280 | − | 0.168748i | −0.346690 | − | 0.937980i | \(-0.612694\pi\) |
0.638970 | + | 0.769232i | \(0.279361\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.92116 | − | 3.41858i | −0.189824 | − | 0.109595i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 16.2679i | 0.520458i | 0.965547 | + | 0.260229i | \(0.0837980\pi\) | ||||
−0.965547 | + | 0.260229i | \(0.916202\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 49.9808 | + | 28.8564i | 1.59739 | + | 0.922255i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 12.5885 | + | 21.8038i | 0.401509 | + | 0.695435i | 0.993908 | − | 0.110210i | \(-0.0351524\pi\) |
−0.592399 | + | 0.805645i | \(0.701819\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 10.6603 | + | 18.4641i | 0.339664 | + | 0.588315i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 21.2154i | 0.675293i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 14.5359i | 0.462215i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16.0526 | + | 27.8038i | 0.509926 | + | 0.883218i | 0.999934 | + | 0.0115001i | \(0.00366069\pi\) |
−0.490008 | + | 0.871718i | \(0.663006\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −27.4808 | − | 47.5981i | −0.872076 | − | 1.51048i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 33.8564 | 1.07332 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −10.5622 | − | 6.09808i | −0.334508 | − | 0.193128i | 0.323333 | − | 0.946285i | \(-0.395197\pi\) |
−0.657841 | + | 0.753157i | \(0.728530\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 24.5885i | − | 0.777944i |
(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 | 1216.2.s.b.31.2 | yes | 4 | |
4.3 | odd | 2 | 1216.2.s.f.31.2 | yes | 4 | ||
8.3 | odd | 2 | 1216.2.s.a.31.1 | ✓ | 4 | ||
8.5 | even | 2 | 1216.2.s.e.31.1 | yes | 4 | ||
19.8 | odd | 6 | 1216.2.s.a.863.1 | yes | 4 | ||
76.27 | even | 6 | 1216.2.s.e.863.1 | yes | 4 | ||
152.27 | even | 6 | inner | 1216.2.s.b.863.2 | yes | 4 | |
152.141 | odd | 6 | 1216.2.s.f.863.2 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1216.2.s.a.31.1 | ✓ | 4 | 8.3 | odd | 2 | ||
1216.2.s.a.863.1 | yes | 4 | 19.8 | odd | 6 | ||
1216.2.s.b.31.2 | yes | 4 | 1.1 | even | 1 | trivial | |
1216.2.s.b.863.2 | yes | 4 | 152.27 | even | 6 | inner | |
1216.2.s.e.31.1 | yes | 4 | 8.5 | even | 2 | ||
1216.2.s.e.863.1 | yes | 4 | 76.27 | even | 6 | ||
1216.2.s.f.31.2 | yes | 4 | 4.3 | odd | 2 | ||
1216.2.s.f.863.2 | yes | 4 | 152.141 | odd | 6 |