Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1755,2,Mod(586,1755)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1755, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1755.586");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1755 = 3^{3} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1755.i (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: | \(14.0137455547\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 585) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 586.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1755.586 |
Dual form | 1755.2.i.b.1171.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1755\mathbb{Z}\right)^\times\).
\(n\) | \(326\) | \(352\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | + | 0.866025i | −0.353553 | + | 0.612372i | −0.986869 | − | 0.161521i | \(-0.948360\pi\) |
0.633316 | + | 0.773893i | \(0.281693\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | −0.500000 | − | 0.866025i | −0.223607 | − | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | + | 1.73205i | −0.377964 | + | 0.654654i | −0.990766 | − | 0.135583i | \(-0.956709\pi\) |
0.612801 | + | 0.790237i | \(0.290043\pi\) | |||||||
\(8\) | −3.00000 | −1.06066 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | −0.500000 | + | 0.866025i | −0.150756 | + | 0.261116i | −0.931505 | − | 0.363727i | \(-0.881504\pi\) |
0.780750 | + | 0.624844i | \(0.214837\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.500000 | + | 0.866025i | 0.138675 | + | 0.240192i | ||||
\(14\) | −1.00000 | − | 1.73205i | −0.267261 | − | 0.462910i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.500000 | − | 0.866025i | 0.125000 | − | 0.216506i | ||||
\(17\) | −2.00000 | −0.485071 | −0.242536 | − | 0.970143i | \(-0.577979\pi\) | ||||
−0.242536 | + | 0.970143i | \(0.577979\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.00000 | −0.688247 | −0.344124 | − | 0.938924i | \(-0.611824\pi\) | ||||
−0.344124 | + | 0.938924i | \(0.611824\pi\) | |||||||
\(20\) | 0.500000 | − | 0.866025i | 0.111803 | − | 0.193649i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.500000 | − | 0.866025i | −0.106600 | − | 0.184637i | ||||
\(23\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | −1.00000 | −0.196116 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.00000 | −0.377964 | ||||||||
\(29\) | 2.50000 | − | 4.33013i | 0.464238 | − | 0.804084i | −0.534928 | − | 0.844897i | \(-0.679661\pi\) |
0.999167 | + | 0.0408130i | \(0.0129948\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.500000 | + | 0.866025i | 0.0898027 | + | 0.155543i | 0.907428 | − | 0.420208i | \(-0.138043\pi\) |
−0.817625 | + | 0.575751i | \(0.804710\pi\) | |||||||
\(32\) | −2.50000 | − | 4.33013i | −0.441942 | − | 0.765466i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.00000 | − | 1.73205i | 0.171499 | − | 0.297044i | ||||
\(35\) | 2.00000 | 0.338062 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.00000 | −0.821995 | −0.410997 | − | 0.911636i | \(-0.634819\pi\) | ||||
−0.410997 | + | 0.911636i | \(0.634819\pi\) | |||||||
\(38\) | 1.50000 | − | 2.59808i | 0.243332 | − | 0.421464i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.50000 | + | 2.59808i | 0.237171 | + | 0.410792i | ||||
\(41\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.00000 | − | 6.92820i | 0.609994 | − | 1.05654i | −0.381246 | − | 0.924473i | \(-0.624505\pi\) |
0.991241 | − | 0.132068i | \(-0.0421616\pi\) | |||||||
\(44\) | −1.00000 | −0.150756 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.00000 | + | 1.73205i | −0.145865 | + | 0.252646i | −0.929695 | − | 0.368329i | \(-0.879930\pi\) |
0.783830 | + | 0.620975i | \(0.213263\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.50000 | + | 2.59808i | 0.214286 | + | 0.371154i | ||||
\(50\) | −0.500000 | − | 0.866025i | −0.0707107 | − | 0.122474i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.500000 | + | 0.866025i | −0.0693375 | + | 0.120096i | ||||
\(53\) | −14.0000 | −1.92305 | −0.961524 | − | 0.274721i | \(-0.911414\pi\) | ||||
−0.961524 | + | 0.274721i | \(0.911414\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.00000 | 0.134840 | ||||||||
\(56\) | 3.00000 | − | 5.19615i | 0.400892 | − | 0.694365i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.50000 | + | 4.33013i | 0.328266 | + | 0.568574i | ||||
\(59\) | −4.50000 | − | 7.79423i | −0.585850 | − | 1.01472i | −0.994769 | − | 0.102151i | \(-0.967427\pi\) |
0.408919 | − | 0.912571i | \(-0.365906\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.500000 | − | 0.866025i | 0.0640184 | − | 0.110883i | −0.832240 | − | 0.554416i | \(-0.812942\pi\) |
0.896258 | + | 0.443533i | \(0.146275\pi\) | |||||||
\(62\) | −1.00000 | −0.127000 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.00000 | 0.875000 | ||||||||
\(65\) | 0.500000 | − | 0.866025i | 0.0620174 | − | 0.107417i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.00000 | − | 12.1244i | −0.855186 | − | 1.48123i | −0.876472 | − | 0.481452i | \(-0.840109\pi\) |
0.0212861 | − | 0.999773i | \(-0.493224\pi\) | |||||||
\(68\) | −1.00000 | − | 1.73205i | −0.121268 | − | 0.210042i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.00000 | + | 1.73205i | −0.119523 | + | 0.207020i | ||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.00000 | 0.702247 | 0.351123 | − | 0.936329i | \(-0.385800\pi\) | ||||
0.351123 | + | 0.936329i | \(0.385800\pi\) | |||||||
\(74\) | 2.50000 | − | 4.33013i | 0.290619 | − | 0.503367i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.50000 | − | 2.59808i | −0.172062 | − | 0.298020i | ||||
\(77\) | −1.00000 | − | 1.73205i | −0.113961 | − | 0.197386i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.00000 | − | 10.3923i | 0.675053 | − | 1.16923i | −0.301401 | − | 0.953498i | \(-0.597454\pi\) |
0.976453 | − | 0.215728i | \(-0.0692125\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.00000 | + | 8.66025i | −0.548821 | + | 0.950586i | 0.449534 | + | 0.893263i | \(0.351590\pi\) |
−0.998356 | + | 0.0573233i | \(0.981743\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.00000 | + | 1.73205i | 0.108465 | + | 0.187867i | ||||
\(86\) | 4.00000 | + | 6.92820i | 0.431331 | + | 0.747087i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.50000 | − | 2.59808i | 0.159901 | − | 0.276956i | ||||
\(89\) | −2.00000 | −0.212000 | −0.106000 | − | 0.994366i | \(-0.533804\pi\) | ||||
−0.106000 | + | 0.994366i | \(0.533804\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.00000 | −0.209657 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.00000 | − | 1.73205i | −0.103142 | − | 0.178647i | ||||
\(95\) | 1.50000 | + | 2.59808i | 0.153897 | + | 0.266557i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.500000 | + | 0.866025i | −0.0507673 | + | 0.0879316i | −0.890292 | − | 0.455389i | \(-0.849500\pi\) |
0.839525 | + | 0.543321i | \(0.182833\pi\) | |||||||
\(98\) | −3.00000 | −0.303046 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.00000 | −0.100000 | ||||||||
\(101\) | 1.50000 | − | 2.59808i | 0.149256 | − | 0.258518i | −0.781697 | − | 0.623658i | \(-0.785646\pi\) |
0.930953 | + | 0.365140i | \(0.118979\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.500000 | + | 0.866025i | 0.0492665 | + | 0.0853320i | 0.889607 | − | 0.456727i | \(-0.150978\pi\) |
−0.840341 | + | 0.542059i | \(0.817645\pi\) | |||||||
\(104\) | −1.50000 | − | 2.59808i | −0.147087 | − | 0.254762i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 7.00000 | − | 12.1244i | 0.679900 | − | 1.17762i | ||||
\(107\) | −19.0000 | −1.83680 | −0.918400 | − | 0.395654i | \(-0.870518\pi\) | ||||
−0.918400 | + | 0.395654i | \(0.870518\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −14.0000 | −1.34096 | −0.670478 | − | 0.741929i | \(-0.733911\pi\) | ||||
−0.670478 | + | 0.741929i | \(0.733911\pi\) | |||||||
\(110\) | −0.500000 | + | 0.866025i | −0.0476731 | + | 0.0825723i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.00000 | + | 1.73205i | 0.0944911 | + | 0.163663i | ||||
\(113\) | 5.00000 | + | 8.66025i | 0.470360 | + | 0.814688i | 0.999425 | − | 0.0338931i | \(-0.0107906\pi\) |
−0.529065 | + | 0.848581i | \(0.677457\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 5.00000 | 0.464238 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 9.00000 | 0.828517 | ||||||||
\(119\) | 2.00000 | − | 3.46410i | 0.183340 | − | 0.317554i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.00000 | + | 8.66025i | 0.454545 | + | 0.787296i | ||||
\(122\) | 0.500000 | + | 0.866025i | 0.0452679 | + | 0.0784063i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.500000 | + | 0.866025i | −0.0449013 | + | 0.0777714i | ||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.00000 | −0.709885 | −0.354943 | − | 0.934888i | \(-0.615500\pi\) | ||||
−0.354943 | + | 0.934888i | \(0.615500\pi\) | |||||||
\(128\) | 1.50000 | − | 2.59808i | 0.132583 | − | 0.229640i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.500000 | + | 0.866025i | 0.0438529 | + | 0.0759555i | ||||
\(131\) | −2.00000 | − | 3.46410i | −0.174741 | − | 0.302660i | 0.765331 | − | 0.643637i | \(-0.222575\pi\) |
−0.940072 | + | 0.340977i | \(0.889242\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.00000 | − | 5.19615i | 0.260133 | − | 0.450564i | ||||
\(134\) | 14.0000 | 1.20942 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.00000 | 0.514496 | ||||||||
\(137\) | −2.50000 | + | 4.33013i | −0.213589 | + | 0.369948i | −0.952835 | − | 0.303488i | \(-0.901849\pi\) |
0.739246 | + | 0.673436i | \(0.235182\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.00000 | − | 10.3923i | −0.508913 | − | 0.881464i | −0.999947 | − | 0.0103230i | \(-0.996714\pi\) |
0.491033 | − | 0.871141i | \(-0.336619\pi\) | |||||||
\(140\) | 1.00000 | + | 1.73205i | 0.0845154 | + | 0.146385i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.00000 | −0.0836242 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.00000 | −0.415227 | ||||||||
\(146\) | −3.00000 | + | 5.19615i | −0.248282 | + | 0.430037i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.50000 | − | 4.33013i | −0.205499 | − | 0.355934i | ||||
\(149\) | 3.00000 | + | 5.19615i | 0.245770 | + | 0.425685i | 0.962348 | − | 0.271821i | \(-0.0876260\pi\) |
−0.716578 | + | 0.697507i | \(0.754293\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.00000 | − | 6.92820i | 0.325515 | − | 0.563809i | −0.656101 | − | 0.754673i | \(-0.727796\pi\) |
0.981617 | + | 0.190864i | \(0.0611289\pi\) | |||||||
\(152\) | 9.00000 | 0.729996 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2.00000 | 0.161165 | ||||||||
\(155\) | 0.500000 | − | 0.866025i | 0.0401610 | − | 0.0695608i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.00000 | + | 5.19615i | 0.239426 | + | 0.414698i | 0.960550 | − | 0.278108i | \(-0.0897074\pi\) |
−0.721124 | + | 0.692806i | \(0.756374\pi\) | |||||||
\(158\) | 6.00000 | + | 10.3923i | 0.477334 | + | 0.826767i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.50000 | + | 4.33013i | −0.197642 | + | 0.342327i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.0000 | −0.939913 | −0.469956 | − | 0.882690i | \(-0.655730\pi\) | ||||
−0.469956 | + | 0.882690i | \(0.655730\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −5.00000 | − | 8.66025i | −0.388075 | − | 0.672166i | ||||
\(167\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.500000 | + | 0.866025i | −0.0384615 | + | 0.0666173i | ||||
\(170\) | −2.00000 | −0.153393 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 8.00000 | 0.609994 | ||||||||
\(173\) | 6.00000 | − | 10.3923i | 0.456172 | − | 0.790112i | −0.542583 | − | 0.840002i | \(-0.682554\pi\) |
0.998755 | + | 0.0498898i | \(0.0158870\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.00000 | − | 1.73205i | −0.0755929 | − | 0.130931i | ||||
\(176\) | 0.500000 | + | 0.866025i | 0.0376889 | + | 0.0652791i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.00000 | − | 1.73205i | 0.0749532 | − | 0.129823i | ||||
\(179\) | 18.0000 | 1.34538 | 0.672692 | − | 0.739923i | \(-0.265138\pi\) | ||||
0.672692 | + | 0.739923i | \(0.265138\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.0000 | 1.26360 | 0.631800 | − | 0.775131i | \(-0.282316\pi\) | ||||
0.631800 | + | 0.775131i | \(0.282316\pi\) | |||||||
\(182\) | 1.00000 | − | 1.73205i | 0.0741249 | − | 0.128388i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.50000 | + | 4.33013i | 0.183804 | + | 0.318357i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.00000 | − | 1.73205i | 0.0731272 | − | 0.126660i | ||||
\(188\) | −2.00000 | −0.145865 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −3.00000 | −0.217643 | ||||||||
\(191\) | 9.00000 | − | 15.5885i | 0.651217 | − | 1.12794i | −0.331611 | − | 0.943416i | \(-0.607592\pi\) |
0.982828 | − | 0.184525i | \(-0.0590746\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.50000 | − | 11.2583i | −0.467880 | − | 0.810392i | 0.531446 | − | 0.847092i | \(-0.321649\pi\) |
−0.999326 | + | 0.0366998i | \(0.988315\pi\) | |||||||
\(194\) | −0.500000 | − | 0.866025i | −0.0358979 | − | 0.0621770i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.50000 | + | 2.59808i | −0.107143 | + | 0.185577i | ||||
\(197\) | −15.0000 | −1.06871 | −0.534353 | − | 0.845262i | \(-0.679445\pi\) | ||||
−0.534353 | + | 0.845262i | \(0.679445\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −22.0000 | −1.55954 | −0.779769 | − | 0.626067i | \(-0.784664\pi\) | ||||
−0.779769 | + | 0.626067i | \(0.784664\pi\) | |||||||
\(200\) | 1.50000 | − | 2.59808i | 0.106066 | − | 0.183712i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.50000 | + | 2.59808i | 0.105540 | + | 0.182800i | ||||
\(203\) | 5.00000 | + | 8.66025i | 0.350931 | + | 0.607831i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −1.00000 | −0.0696733 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.00000 | 0.0693375 | ||||||||
\(209\) | 1.50000 | − | 2.59808i | 0.103757 | − | 0.179713i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(212\) | −7.00000 | − | 12.1244i | −0.480762 | − | 0.832704i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 9.50000 | − | 16.4545i | 0.649407 | − | 1.12481i | ||||
\(215\) | −8.00000 | −0.545595 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.00000 | −0.135769 | ||||||||
\(218\) | 7.00000 | − | 12.1244i | 0.474100 | − | 0.821165i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.500000 | + | 0.866025i | 0.0337100 | + | 0.0583874i | ||||
\(221\) | −1.00000 | − | 1.73205i | −0.0672673 | − | 0.116510i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.0000 | − | 22.5167i | 0.870544 | − | 1.50783i | 0.00910984 | − | 0.999959i | \(-0.497100\pi\) |
0.861435 | − | 0.507869i | \(-0.169566\pi\) | |||||||
\(224\) | 10.0000 | 0.668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −10.0000 | −0.665190 | ||||||||
\(227\) | −13.0000 | + | 22.5167i | −0.862840 | + | 1.49448i | 0.00633544 | + | 0.999980i | \(0.497983\pi\) |
−0.869176 | + | 0.494503i | \(0.835350\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.00000 | + | 13.8564i | 0.528655 | + | 0.915657i | 0.999442 | + | 0.0334101i | \(0.0106368\pi\) |
−0.470787 | + | 0.882247i | \(0.656030\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −7.50000 | + | 12.9904i | −0.492399 | + | 0.852860i | ||||
\(233\) | 14.0000 | 0.917170 | 0.458585 | − | 0.888650i | \(-0.348356\pi\) | ||||
0.458585 | + | 0.888650i | \(0.348356\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.00000 | 0.130466 | ||||||||
\(236\) | 4.50000 | − | 7.79423i | 0.292925 | − | 0.507361i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2.00000 | + | 3.46410i | 0.129641 | + | 0.224544i | ||||
\(239\) | 7.50000 | + | 12.9904i | 0.485135 | + | 0.840278i | 0.999854 | − | 0.0170808i | \(-0.00543724\pi\) |
−0.514719 | + | 0.857359i | \(0.672104\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.00000 | + | 8.66025i | −0.322078 | + | 0.557856i | −0.980917 | − | 0.194429i | \(-0.937715\pi\) |
0.658838 | + | 0.752285i | \(0.271048\pi\) | |||||||
\(242\) | −10.0000 | −0.642824 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.00000 | 0.0640184 | ||||||||
\(245\) | 1.50000 | − | 2.59808i | 0.0958315 | − | 0.165985i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.50000 | − | 2.59808i | −0.0954427 | − | 0.165312i | ||||
\(248\) | −1.50000 | − | 2.59808i | −0.0952501 | − | 0.164978i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −0.500000 | + | 0.866025i | −0.0316228 | + | 0.0547723i | ||||
\(251\) | −12.0000 | −0.757433 | −0.378717 | − | 0.925513i | \(-0.623635\pi\) | ||||
−0.378717 | + | 0.925513i | \(0.623635\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 4.00000 | − | 6.92820i | 0.250982 | − | 0.434714i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 8.50000 | + | 14.7224i | 0.531250 | + | 0.920152i | ||||
\(257\) | −14.0000 | − | 24.2487i | −0.873296 | − | 1.51259i | −0.858567 | − | 0.512702i | \(-0.828645\pi\) |
−0.0147291 | − | 0.999892i | \(-0.504689\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.00000 | − | 8.66025i | 0.310685 | − | 0.538122i | ||||
\(260\) | 1.00000 | 0.0620174 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 4.00000 | 0.247121 | ||||||||
\(263\) | −8.00000 | + | 13.8564i | −0.493301 | + | 0.854423i | −0.999970 | − | 0.00771799i | \(-0.997543\pi\) |
0.506669 | + | 0.862141i | \(0.330877\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.00000 | + | 12.1244i | 0.430007 | + | 0.744793i | ||||
\(266\) | 3.00000 | + | 5.19615i | 0.183942 | + | 0.318597i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 7.00000 | − | 12.1244i | 0.427593 | − | 0.740613i | ||||
\(269\) | −3.00000 | −0.182913 | −0.0914566 | − | 0.995809i | \(-0.529152\pi\) | ||||
−0.0914566 | + | 0.995809i | \(0.529152\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.00000 | −0.425220 | −0.212610 | − | 0.977137i | \(-0.568196\pi\) | ||||
−0.212610 | + | 0.977137i | \(0.568196\pi\) | |||||||
\(272\) | −1.00000 | + | 1.73205i | −0.0606339 | + | 0.105021i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.50000 | − | 4.33013i | −0.151031 | − | 0.261593i | ||||
\(275\) | −0.500000 | − | 0.866025i | −0.0301511 | − | 0.0522233i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.00000 | + | 8.66025i | −0.300421 | + | 0.520344i | −0.976231 | − | 0.216731i | \(-0.930460\pi\) |
0.675810 | + | 0.737075i | \(0.263794\pi\) | |||||||
\(278\) | 12.0000 | 0.719712 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −6.00000 | −0.358569 | ||||||||
\(281\) | −6.00000 | + | 10.3923i | −0.357930 | + | 0.619953i | −0.987615 | − | 0.156898i | \(-0.949851\pi\) |
0.629685 | + | 0.776851i | \(0.283184\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.5000 | + | 21.6506i | 0.743048 | + | 1.28700i | 0.951101 | + | 0.308879i | \(0.0999539\pi\) |
−0.208053 | + | 0.978117i | \(0.566713\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.500000 | − | 0.866025i | 0.0295656 | − | 0.0512092i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.0000 | −0.764706 | ||||||||
\(290\) | 2.50000 | − | 4.33013i | 0.146805 | − | 0.254274i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 3.00000 | + | 5.19615i | 0.175562 | + | 0.304082i | ||||
\(293\) | 0.500000 | + | 0.866025i | 0.0292103 | + | 0.0505937i | 0.880261 | − | 0.474490i | \(-0.157367\pi\) |
−0.851051 | + | 0.525084i | \(0.824034\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.50000 | + | 7.79423i | −0.262000 | + | 0.453798i | ||||
\(296\) | 15.0000 | 0.871857 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −6.00000 | −0.347571 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.00000 | + | 13.8564i | 0.461112 | + | 0.798670i | ||||
\(302\) | 4.00000 | + | 6.92820i | 0.230174 | + | 0.398673i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.50000 | + | 2.59808i | −0.0860309 | + | 0.149010i | ||||
\(305\) | −1.00000 | −0.0572598 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.00000 | 0.114146 | 0.0570730 | − | 0.998370i | \(-0.481823\pi\) | ||||
0.0570730 | + | 0.998370i | \(0.481823\pi\) | |||||||
\(308\) | 1.00000 | − | 1.73205i | 0.0569803 | − | 0.0986928i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0.500000 | + | 0.866025i | 0.0283981 | + | 0.0491869i | ||||
\(311\) | −2.00000 | − | 3.46410i | −0.113410 | − | 0.196431i | 0.803733 | − | 0.594990i | \(-0.202844\pi\) |
−0.917143 | + | 0.398559i | \(0.869511\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.0000 | − | 24.2487i | 0.791327 | − | 1.37062i | −0.133819 | − | 0.991006i | \(-0.542724\pi\) |
0.925146 | − | 0.379612i | \(-0.123943\pi\) | |||||||
\(314\) | −6.00000 | −0.338600 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 12.0000 | 0.675053 | ||||||||
\(317\) | −13.5000 | + | 23.3827i | −0.758236 | + | 1.31330i | 0.185514 | + | 0.982642i | \(0.440605\pi\) |
−0.943750 | + | 0.330661i | \(0.892728\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.50000 | + | 4.33013i | 0.139973 | + | 0.242441i | ||||
\(320\) | −3.50000 | − | 6.06218i | −0.195656 | − | 0.338886i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.00000 | 0.333849 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.00000 | −0.0554700 | ||||||||
\(326\) | 6.00000 | − | 10.3923i | 0.332309 | − | 0.575577i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.00000 | − | 3.46410i | −0.110264 | − | 0.190982i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.5000 | + | 23.3827i | −0.742027 | + | 1.28523i | 0.209544 | + | 0.977799i | \(0.432802\pi\) |
−0.951571 | + | 0.307429i | \(0.900531\pi\) | |||||||
\(332\) | −10.0000 | −0.548821 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −7.00000 | + | 12.1244i | −0.382451 | + | 0.662424i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.0000 | + | 19.0526i | 0.599208 | + | 1.03786i | 0.992938 | + | 0.118633i | \(0.0378512\pi\) |
−0.393730 | + | 0.919226i | \(0.628816\pi\) | |||||||
\(338\) | −0.500000 | − | 0.866025i | −0.0271964 | − | 0.0471056i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1.00000 | + | 1.73205i | −0.0542326 | + | 0.0939336i | ||||
\(341\) | −1.00000 | −0.0541530 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −20.0000 | −1.07990 | ||||||||
\(344\) | −12.0000 | + | 20.7846i | −0.646997 | + | 1.12063i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 6.00000 | + | 10.3923i | 0.322562 | + | 0.558694i | ||||
\(347\) | 8.50000 | + | 14.7224i | 0.456304 | + | 0.790342i | 0.998762 | − | 0.0497412i | \(-0.0158397\pi\) |
−0.542458 | + | 0.840083i | \(0.682506\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.00000 | + | 10.3923i | −0.321173 | + | 0.556287i | −0.980730 | − | 0.195367i | \(-0.937410\pi\) |
0.659558 | + | 0.751654i | \(0.270744\pi\) | |||||||
\(350\) | 2.00000 | 0.106904 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 5.00000 | 0.266501 | ||||||||
\(353\) | −1.50000 | + | 2.59808i | −0.0798369 | + | 0.138282i | −0.903179 | − | 0.429263i | \(-0.858773\pi\) |
0.823343 | + | 0.567545i | \(0.192107\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1.00000 | − | 1.73205i | −0.0529999 | − | 0.0917985i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −9.00000 | + | 15.5885i | −0.475665 | + | 0.823876i | ||||
\(359\) | 31.0000 | 1.63612 | 0.818059 | − | 0.575135i | \(-0.195050\pi\) | ||||
0.818059 | + | 0.575135i | \(0.195050\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −10.0000 | −0.526316 | ||||||||
\(362\) | −8.50000 | + | 14.7224i | −0.446750 | + | 0.773794i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.00000 | − | 1.73205i | −0.0524142 | − | 0.0907841i | ||||
\(365\) | −3.00000 | − | 5.19615i | −0.157027 | − | 0.271979i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −12.5000 | + | 21.6506i | −0.652495 | + | 1.13015i | 0.330021 | + | 0.943974i | \(0.392944\pi\) |
−0.982516 | + | 0.186180i | \(0.940389\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −5.00000 | −0.259938 | ||||||||
\(371\) | 14.0000 | − | 24.2487i | 0.726844 | − | 1.25893i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.0000 | + | 17.3205i | 0.517780 | + | 0.896822i | 0.999787 | + | 0.0206542i | \(0.00657489\pi\) |
−0.482006 | + | 0.876168i | \(0.660092\pi\) | |||||||
\(374\) | 1.00000 | + | 1.73205i | 0.0517088 | + | 0.0895622i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.00000 | − | 5.19615i | 0.154713 | − | 0.267971i | ||||
\(377\) | 5.00000 | 0.257513 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −23.0000 | −1.18143 | −0.590715 | − | 0.806880i | \(-0.701154\pi\) | ||||
−0.590715 | + | 0.806880i | \(0.701154\pi\) | |||||||
\(380\) | −1.50000 | + | 2.59808i | −0.0769484 | + | 0.133278i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 9.00000 | + | 15.5885i | 0.460480 | + | 0.797575i | ||||
\(383\) | −6.00000 | − | 10.3923i | −0.306586 | − | 0.531022i | 0.671027 | − | 0.741433i | \(-0.265853\pi\) |
−0.977613 | + | 0.210411i | \(0.932520\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.00000 | + | 1.73205i | −0.0509647 | + | 0.0882735i | ||||
\(386\) | 13.0000 | 0.661683 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1.00000 | −0.0507673 | ||||||||
\(389\) | −11.0000 | + | 19.0526i | −0.557722 | + | 0.966003i | 0.439964 | + | 0.898015i | \(0.354991\pi\) |
−0.997686 | + | 0.0679877i | \(0.978342\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −4.50000 | − | 7.79423i | −0.227284 | − | 0.393668i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 7.50000 | − | 12.9904i | 0.377845 | − | 0.654446i | ||||
\(395\) | −12.0000 | −0.603786 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −30.0000 | −1.50566 | −0.752828 | − | 0.658217i | \(-0.771311\pi\) | ||||
−0.752828 | + | 0.658217i | \(0.771311\pi\) | |||||||
\(398\) | 11.0000 | − | 19.0526i | 0.551380 | − | 0.955018i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.500000 | + | 0.866025i | 0.0250000 | + | 0.0433013i | ||||
\(401\) | 14.0000 | + | 24.2487i | 0.699127 | + | 1.21092i | 0.968770 | + | 0.247962i | \(0.0797610\pi\) |
−0.269643 | + | 0.962960i | \(0.586906\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.500000 | + | 0.866025i | −0.0249068 | + | 0.0431398i | ||||
\(404\) | 3.00000 | 0.149256 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −10.0000 | −0.496292 | ||||||||
\(407\) | 2.50000 | − | 4.33013i | 0.123920 | − | 0.214636i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −0.500000 | + | 0.866025i | −0.0246332 | + | 0.0426660i | ||||
\(413\) | 18.0000 | 0.885722 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 10.0000 | 0.490881 | ||||||||
\(416\) | 2.50000 | − | 4.33013i | 0.122573 | − | 0.212302i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.50000 | + | 2.59808i | 0.0733674 | + | 0.127076i | ||||
\(419\) | 10.0000 | + | 17.3205i | 0.488532 | + | 0.846162i | 0.999913 | − | 0.0131919i | \(-0.00419923\pi\) |
−0.511381 | + | 0.859354i | \(0.670866\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.00000 | + | 8.66025i | −0.243685 | + | 0.422075i | −0.961761 | − | 0.273890i | \(-0.911690\pi\) |
0.718076 | + | 0.695965i | \(0.245023\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 42.0000 | 2.03970 | ||||||||
\(425\) | 1.00000 | − | 1.73205i | 0.0485071 | − | 0.0840168i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.00000 | + | 1.73205i | 0.0483934 | + | 0.0838198i | ||||
\(428\) | −9.50000 | − | 16.4545i | −0.459200 | − | 0.795357i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4.00000 | − | 6.92820i | 0.192897 | − | 0.334108i | ||||
\(431\) | −17.0000 | −0.818861 | −0.409431 | − | 0.912341i | \(-0.634273\pi\) | ||||
−0.409431 | + | 0.912341i | \(0.634273\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −38.0000 | −1.82616 | −0.913082 | − | 0.407777i | \(-0.866304\pi\) | ||||
−0.913082 | + | 0.407777i | \(0.866304\pi\) | |||||||
\(434\) | 1.00000 | − | 1.73205i | 0.0480015 | − | 0.0831411i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −7.00000 | − | 12.1244i | −0.335239 | − | 0.580651i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(440\) | −3.00000 | −0.143019 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.00000 | 0.0951303 | ||||||||
\(443\) | −3.50000 | + | 6.06218i | −0.166290 | + | 0.288023i | −0.937113 | − | 0.349027i | \(-0.886512\pi\) |
0.770823 | + | 0.637050i | \(0.219845\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.00000 | + | 1.73205i | 0.0474045 | + | 0.0821071i | ||||
\(446\) | 13.0000 | + | 22.5167i | 0.615568 | + | 1.06619i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −7.00000 | + | 12.1244i | −0.330719 | + | 0.572822i | ||||
\(449\) | 30.0000 | 1.41579 | 0.707894 | − | 0.706319i | \(-0.249646\pi\) | ||||
0.707894 | + | 0.706319i | \(0.249646\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −5.00000 | + | 8.66025i | −0.235180 | + | 0.407344i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −13.0000 | − | 22.5167i | −0.610120 | − | 1.05676i | ||||
\(455\) | 1.00000 | + | 1.73205i | 0.0468807 | + | 0.0811998i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −13.0000 | + | 22.5167i | −0.608114 | + | 1.05328i | 0.383437 | + | 0.923567i | \(0.374740\pi\) |
−0.991551 | + | 0.129718i | \(0.958593\pi\) | |||||||
\(458\) | −16.0000 | −0.747631 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −13.0000 | + | 22.5167i | −0.605470 | + | 1.04871i | 0.386507 | + | 0.922287i | \(0.373682\pi\) |
−0.991977 | + | 0.126419i | \(0.959652\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.00000 | + | 5.19615i | 0.139422 | + | 0.241486i | 0.927278 | − | 0.374374i | \(-0.122142\pi\) |
−0.787856 | + | 0.615859i | \(0.788809\pi\) | |||||||
\(464\) | −2.50000 | − | 4.33013i | −0.116060 | − | 0.201021i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −7.00000 | + | 12.1244i | −0.324269 | + | 0.561650i | ||||
\(467\) | 28.0000 | 1.29569 | 0.647843 | − | 0.761774i | \(-0.275671\pi\) | ||||
0.647843 | + | 0.761774i | \(0.275671\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 28.0000 | 1.29292 | ||||||||
\(470\) | −1.00000 | + | 1.73205i | −0.0461266 | + | 0.0798935i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 13.5000 | + | 23.3827i | 0.621388 | + | 1.07628i | ||||
\(473\) | 4.00000 | + | 6.92820i | 0.183920 | + | 0.318559i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.50000 | − | 2.59808i | 0.0688247 | − | 0.119208i | ||||
\(476\) | 4.00000 | 0.183340 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −15.0000 | −0.686084 | ||||||||
\(479\) | 7.50000 | − | 12.9904i | 0.342684 | − | 0.593546i | −0.642246 | − | 0.766498i | \(-0.721997\pi\) |
0.984930 | + | 0.172953i | \(0.0553307\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.50000 | − | 4.33013i | −0.113990 | − | 0.197437i | ||||
\(482\) | −5.00000 | − | 8.66025i | −0.227744 | − | 0.394464i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5.00000 | + | 8.66025i | −0.227273 | + | 0.393648i | ||||
\(485\) | 1.00000 | 0.0454077 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −34.0000 | −1.54069 | −0.770344 | − | 0.637629i | \(-0.779915\pi\) | ||||
−0.770344 | + | 0.637629i | \(0.779915\pi\) | |||||||
\(488\) | −1.50000 | + | 2.59808i | −0.0679018 | + | 0.117609i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.50000 | + | 2.59808i | 0.0677631 | + | 0.117369i | ||||
\(491\) | −3.00000 | − | 5.19615i | −0.135388 | − | 0.234499i | 0.790358 | − | 0.612646i | \(-0.209895\pi\) |
−0.925746 | + | 0.378147i | \(0.876561\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.00000 | + | 8.66025i | −0.225189 | + | 0.390038i | ||||
\(494\) | 3.00000 | 0.134976 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.00000 | 0.0449013 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −14.0000 | − | 24.2487i | −0.626726 | − | 1.08552i | −0.988204 | − | 0.153141i | \(-0.951061\pi\) |
0.361478 | − | 0.932381i | \(-0.382272\pi\) | |||||||
\(500\) | 0.500000 | + | 0.866025i | 0.0223607 | + | 0.0387298i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 6.00000 | − | 10.3923i | 0.267793 | − | 0.463831i | ||||
\(503\) | 9.00000 | 0.401290 | 0.200645 | − | 0.979664i | \(-0.435696\pi\) | ||||
0.200645 | + | 0.979664i | \(0.435696\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.00000 | −0.133498 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −4.00000 | − | 6.92820i | −0.177471 | − | 0.307389i | ||||
\(509\) | −12.0000 | − | 20.7846i | −0.531891 | − | 0.921262i | −0.999307 | − | 0.0372243i | \(-0.988148\pi\) |
0.467416 | − | 0.884037i | \(-0.345185\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.00000 | + | 10.3923i | −0.265424 | + | 0.459728i | ||||
\(512\) | −11.0000 | −0.486136 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 28.0000 | 1.23503 | ||||||||
\(515\) | 0.500000 | − | 0.866025i | 0.0220326 | − | 0.0381616i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.00000 | − | 1.73205i | −0.0439799 | − | 0.0761755i | ||||
\(518\) | 5.00000 | + | 8.66025i | 0.219687 | + | 0.380510i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.50000 | + | 2.59808i | −0.0657794 | + | 0.113933i | ||||
\(521\) | −6.00000 | −0.262865 | −0.131432 | − | 0.991325i | \(-0.541958\pi\) | ||||
−0.131432 | + | 0.991325i | \(0.541958\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −15.0000 | −0.655904 | −0.327952 | − | 0.944694i | \(-0.606358\pi\) | ||||
−0.327952 | + | 0.944694i | \(0.606358\pi\) | |||||||
\(524\) | 2.00000 | − | 3.46410i | 0.0873704 | − | 0.151330i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.00000 | − | 13.8564i | −0.348817 | − | 0.604168i | ||||
\(527\) | −1.00000 | − | 1.73205i | −0.0435607 | − | 0.0754493i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.5000 | − | 19.9186i | 0.500000 | − | 0.866025i | ||||
\(530\) | −14.0000 | −0.608121 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 6.00000 | 0.260133 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.50000 | + | 16.4545i | 0.410721 | + | 0.711389i | ||||
\(536\) | 21.0000 | + | 36.3731i | 0.907062 | + | 1.57108i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1.50000 | − | 2.59808i | 0.0646696 | − | 0.112011i | ||||
\(539\) | −3.00000 | −0.129219 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 32.0000 | 1.37579 | 0.687894 | − | 0.725811i | \(-0.258536\pi\) | ||||
0.687894 | + | 0.725811i | \(0.258536\pi\) | |||||||
\(542\) | 3.50000 | − | 6.06218i | 0.150338 | − | 0.260393i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 5.00000 | + | 8.66025i | 0.214373 | + | 0.371305i | ||||
\(545\) | 7.00000 | + | 12.1244i | 0.299847 | + | 0.519350i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.50000 | − | 12.9904i | 0.320677 | − | 0.555429i | −0.659951 | − | 0.751309i | \(-0.729423\pi\) |
0.980628 | + | 0.195880i | \(0.0627563\pi\) | |||||||
\(548\) | −5.00000 | −0.213589 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1.00000 | 0.0426401 | ||||||||
\(551\) | −7.50000 | + | 12.9904i | −0.319511 | + | 0.553409i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12.0000 | + | 20.7846i | 0.510292 | + | 0.883852i | ||||
\(554\) | −5.00000 | − | 8.66025i | −0.212430 | − | 0.367939i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6.00000 | − | 10.3923i | 0.254457 | − | 0.440732i | ||||
\(557\) | 5.00000 | 0.211857 | 0.105928 | − | 0.994374i | \(-0.466219\pi\) | ||||
0.105928 | + | 0.994374i | \(0.466219\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.00000 | 0.338364 | ||||||||
\(560\) | 1.00000 | − | 1.73205i | 0.0422577 | − | 0.0731925i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −6.00000 | − | 10.3923i | −0.253095 | − | 0.438373i | ||||
\(563\) | −9.50000 | − | 16.4545i | −0.400377 | − | 0.693474i | 0.593394 | − | 0.804912i | \(-0.297788\pi\) |
−0.993771 | + | 0.111438i | \(0.964454\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.00000 | − | 8.66025i | 0.210352 | − | 0.364340i | ||||
\(566\) | −25.0000 | −1.05083 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.50000 | + | 9.52628i | −0.230572 | + | 0.399362i | −0.957977 | − | 0.286846i | \(-0.907393\pi\) |
0.727405 | + | 0.686209i | \(0.240726\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.00000 | − | 10.3923i | −0.251092 | − | 0.434904i | 0.712735 | − | 0.701434i | \(-0.247456\pi\) |
−0.963827 | + | 0.266529i | \(0.914123\pi\) | |||||||
\(572\) | −0.500000 | − | 0.866025i | −0.0209061 | − | 0.0362103i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11.0000 | 0.457936 | 0.228968 | − | 0.973434i | \(-0.426465\pi\) | ||||
0.228968 | + | 0.973434i | \(0.426465\pi\) | |||||||
\(578\) | 6.50000 | − | 11.2583i | 0.270364 | − | 0.468285i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −2.50000 | − | 4.33013i | −0.103807 | − | 0.179799i | ||||
\(581\) | −10.0000 | − | 17.3205i | −0.414870 | − | 0.718576i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.00000 | − | 12.1244i | 0.289910 | − | 0.502140i | ||||
\(584\) | −18.0000 | −0.744845 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.00000 | −0.0413096 | ||||||||
\(587\) | −7.00000 | + | 12.1244i | −0.288921 | + | 0.500426i | −0.973552 | − | 0.228464i | \(-0.926630\pi\) |
0.684632 | + | 0.728889i | \(0.259963\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.50000 | − | 2.59808i | −0.0618064 | − | 0.107052i | ||||
\(590\) | −4.50000 | − | 7.79423i | −0.185262 | − | 0.320883i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2.50000 | + | 4.33013i | −0.102749 | + | 0.177967i | ||||
\(593\) | 31.0000 | 1.27302 | 0.636509 | − | 0.771270i | \(-0.280378\pi\) | ||||
0.636509 | + | 0.771270i | \(0.280378\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.00000 | −0.163984 | ||||||||
\(596\) | −3.00000 | + | 5.19615i | −0.122885 | + | 0.212843i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 7.00000 | + | 12.1244i | 0.286012 | + | 0.495388i | 0.972854 | − | 0.231419i | \(-0.0743369\pi\) |
−0.686842 | + | 0.726807i | \(0.741004\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.50000 | − | 14.7224i | 0.346722 | − | 0.600541i | −0.638943 | − | 0.769254i | \(-0.720628\pi\) |
0.985665 | + | 0.168714i | \(0.0539613\pi\) | |||||||
\(602\) | −16.0000 | −0.652111 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 8.00000 | 0.325515 | ||||||||
\(605\) | 5.00000 | − | 8.66025i | 0.203279 | − | 0.352089i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.00000 | + | 6.92820i | 0.162355 | + | 0.281207i | 0.935713 | − | 0.352763i | \(-0.114758\pi\) |
−0.773358 | + | 0.633970i | \(0.781424\pi\) | |||||||
\(608\) | 7.50000 | + | 12.9904i | 0.304165 | + | 0.526830i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.500000 | − | 0.866025i | 0.0202444 | − | 0.0350643i | ||||
\(611\) | −2.00000 | −0.0809113 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 30.0000 | 1.21169 | 0.605844 | − | 0.795583i | \(-0.292835\pi\) | ||||
0.605844 | + | 0.795583i | \(0.292835\pi\) | |||||||
\(614\) | −1.00000 | + | 1.73205i | −0.0403567 | + | 0.0698999i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.00000 | + | 5.19615i | 0.120873 | + | 0.209359i | ||||
\(617\) | 4.50000 | + | 7.79423i | 0.181163 | + | 0.313784i | 0.942277 | − | 0.334835i | \(-0.108680\pi\) |
−0.761114 | + | 0.648618i | \(0.775347\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.50000 | − | 9.52628i | 0.221064 | − | 0.382893i | −0.734068 | − | 0.679076i | \(-0.762380\pi\) |
0.955131 | + | 0.296183i | \(0.0957138\pi\) | |||||||
\(620\) | 1.00000 | 0.0401610 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 4.00000 | 0.160385 | ||||||||
\(623\) | 2.00000 | − | 3.46410i | 0.0801283 | − | 0.138786i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 14.0000 | + | 24.2487i | 0.559553 | + | 0.969173i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −3.00000 | + | 5.19615i | −0.119713 | + | 0.207349i | ||||
\(629\) | 10.0000 | 0.398726 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.00000 | −0.199047 | −0.0995234 | − | 0.995035i | \(-0.531732\pi\) | ||||
−0.0995234 | + | 0.995035i | \(0.531732\pi\) | |||||||
\(632\) | −18.0000 | + | 31.1769i | −0.716002 | + | 1.24015i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −13.5000 | − | 23.3827i | −0.536153 | − | 0.928645i | ||||
\(635\) | 4.00000 | + | 6.92820i | 0.158735 | + | 0.274937i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.50000 | + | 2.59808i | −0.0594322 | + | 0.102940i | ||||
\(638\) | −5.00000 | −0.197952 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −3.00000 | −0.118585 | ||||||||
\(641\) | 8.50000 | − | 14.7224i | 0.335730 | − | 0.581501i | −0.647895 | − | 0.761730i | \(-0.724350\pi\) |
0.983625 | + | 0.180229i | \(0.0576838\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −16.0000 | − | 27.7128i | −0.630978 | − | 1.09289i | −0.987352 | − | 0.158543i | \(-0.949320\pi\) |
0.356374 | − | 0.934344i | \(-0.384013\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.00000 | + | 5.19615i | −0.118033 | + | 0.204440i | ||||
\(647\) | −41.0000 | −1.61188 | −0.805938 | − | 0.592000i | \(-0.798339\pi\) | ||||
−0.805938 | + | 0.592000i | \(0.798339\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9.00000 | 0.353281 | ||||||||
\(650\) | 0.500000 | − | 0.866025i | 0.0196116 | − | 0.0339683i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −6.00000 | − | 10.3923i | −0.234978 | − | 0.406994i | ||||
\(653\) | 24.0000 | + | 41.5692i | 0.939193 | + | 1.62673i | 0.766982 | + | 0.641669i | \(0.221758\pi\) |
0.172211 | + | 0.985060i | \(0.444909\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.00000 | + | 3.46410i | −0.0781465 | + | 0.135354i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 4.00000 | 0.155936 | ||||||||
\(659\) | −18.0000 | + | 31.1769i | −0.701180 | + | 1.21448i | 0.266872 | + | 0.963732i | \(0.414010\pi\) |
−0.968052 | + | 0.250748i | \(0.919323\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −19.0000 | − | 32.9090i | −0.739014 | − | 1.28001i | −0.952940 | − | 0.303160i | \(-0.901958\pi\) |
0.213925 | − | 0.976850i | \(-0.431375\pi\) | |||||||
\(662\) | −13.5000 | − | 23.3827i | −0.524692 | − | 0.908794i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 15.0000 | − | 25.9808i | 0.582113 | − | 1.00825i | ||||
\(665\) | −6.00000 | −0.232670 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −7.00000 | − | 12.1244i | −0.270434 | − | 0.468405i | ||||
\(671\) | 0.500000 | + | 0.866025i | 0.0193023 | + | 0.0334325i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12.0000 | + | 20.7846i | −0.462566 | + | 0.801188i | −0.999088 | − | 0.0426985i | \(-0.986405\pi\) |
0.536522 | + | 0.843886i | \(0.319738\pi\) | |||||||
\(674\) | −22.0000 | −0.847408 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.00000 | −0.0384615 | ||||||||
\(677\) | 3.00000 | − | 5.19615i | 0.115299 | − | 0.199704i | −0.802600 | − | 0.596518i | \(-0.796551\pi\) |
0.917899 | + | 0.396813i | \(0.129884\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.00000 | − | 1.73205i | −0.0383765 | − | 0.0664700i | ||||
\(680\) | −3.00000 | − | 5.19615i | −0.115045 | − | 0.199263i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0.500000 | − | 0.866025i | 0.0191460 | − | 0.0331618i | ||||
\(683\) | 20.0000 | 0.765279 | 0.382639 | − | 0.923898i | \(-0.375015\pi\) | ||||
0.382639 | + | 0.923898i | \(0.375015\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.00000 | 0.191040 | ||||||||
\(686\) | 10.0000 | − | 17.3205i | 0.381802 | − | 0.661300i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −4.00000 | − | 6.92820i | −0.152499 | − | 0.264135i | ||||
\(689\) | −7.00000 | − | 12.1244i | −0.266679 | − | 0.461901i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.500000 | + | 0.866025i | −0.0190209 | + | 0.0329452i | −0.875379 | − | 0.483437i | \(-0.839388\pi\) |
0.856358 | + | 0.516382i | \(0.172722\pi\) | |||||||
\(692\) | 12.0000 | 0.456172 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −17.0000 | −0.645311 | ||||||||
\(695\) | −6.00000 | + | 10.3923i | −0.227593 | + | 0.394203i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −6.00000 | − | 10.3923i | −0.227103 | − | 0.393355i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.00000 | − | 1.73205i | 0.0377964 | − | 0.0654654i | ||||
\(701\) | 5.00000 | 0.188847 | 0.0944237 | − | 0.995532i | \(-0.469899\pi\) | ||||
0.0944237 | + | 0.995532i | \(0.469899\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 15.0000 | 0.565736 | ||||||||
\(704\) | −3.50000 | + | 6.06218i | −0.131911 | + | 0.228477i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.50000 | − | 2.59808i | −0.0564532 | − | 0.0977799i | ||||
\(707\) | 3.00000 | + | 5.19615i | 0.112827 | + | 0.195421i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.00000 | + | 3.46410i | −0.0751116 | + | 0.130097i | −0.901135 | − | 0.433539i | \(-0.857265\pi\) |
0.826023 | + | 0.563636i | \(0.190598\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 6.00000 | 0.224860 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.500000 | + | 0.866025i | 0.0186989 | + | 0.0323875i | ||||
\(716\) | 9.00000 | + | 15.5885i | 0.336346 | + | 0.582568i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −15.5000 | + | 26.8468i | −0.578455 | + | 1.00191i | ||||
\(719\) | 2.00000 | 0.0745874 | 0.0372937 | − | 0.999304i | \(-0.488126\pi\) | ||||
0.0372937 | + | 0.999304i | \(0.488126\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.00000 | −0.0744839 | ||||||||
\(722\) | 5.00000 | − | 8.66025i | 0.186081 | − | 0.322301i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 8.50000 | + | 14.7224i | 0.315900 | + | 0.547155i | ||||
\(725\) | 2.50000 | + | 4.33013i | 0.0928477 | + | 0.160817i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −24.0000 | + | 41.5692i | −0.890111 | + | 1.54172i | −0.0503692 | + | 0.998731i | \(0.516040\pi\) |
−0.839742 | + | 0.542986i | \(0.817294\pi\) | |||||||
\(728\) | 6.00000 | 0.222375 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 6.00000 | 0.222070 | ||||||||
\(731\) | −8.00000 | + | 13.8564i | −0.295891 | + | 0.512498i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −6.50000 | − | 11.2583i | −0.240083 | − | 0.415836i | 0.720655 | − | 0.693294i | \(-0.243841\pi\) |
−0.960738 | + | 0.277458i | \(0.910508\pi\) | |||||||
\(734\) | −12.5000 | − | 21.6506i | −0.461383 | − | 0.799140i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 14.0000 | 0.515697 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.00000 | 0.331070 | 0.165535 | − | 0.986204i | \(-0.447065\pi\) | ||||
0.165535 | + | 0.986204i | \(0.447065\pi\) | |||||||
\(740\) | −2.50000 | + | 4.33013i | −0.0919018 | + | 0.159179i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 14.0000 | + | 24.2487i | 0.513956 | + | 0.890198i | ||||
\(743\) | −24.0000 | − | 41.5692i | −0.880475 | − | 1.52503i | −0.850814 | − | 0.525467i | \(-0.823891\pi\) |
−0.0296605 | − | 0.999560i | \(-0.509443\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.00000 | − | 5.19615i | 0.109911 | − | 0.190372i | ||||
\(746\) | −20.0000 | −0.732252 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 2.00000 | 0.0731272 | ||||||||
\(749\) | 19.0000 | − | 32.9090i | 0.694245 | − | 1.20247i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.00000 | − | 1.73205i | −0.0364905 | − | 0.0632034i | 0.847203 | − | 0.531269i | \(-0.178285\pi\) |
−0.883694 | + | 0.468065i | \(0.844951\pi\) | |||||||
\(752\) | 1.00000 | + | 1.73205i | 0.0364662 | + | 0.0631614i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −2.50000 | + | 4.33013i | −0.0910446 | + | 0.157694i | ||||
\(755\) | −8.00000 | −0.291150 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −16.0000 | −0.581530 | −0.290765 | − | 0.956795i | \(-0.593910\pi\) | ||||
−0.290765 | + | 0.956795i | \(0.593910\pi\) | |||||||
\(758\) | 11.5000 | − | 19.9186i | 0.417699 | − | 0.723476i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −4.50000 | − | 7.79423i | −0.163232 | − | 0.282726i | ||||
\(761\) | −18.0000 | − | 31.1769i | −0.652499 | − | 1.13016i | −0.982514 | − | 0.186187i | \(-0.940387\pi\) |
0.330015 | − | 0.943976i | \(-0.392946\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 14.0000 | − | 24.2487i | 0.506834 | − | 0.877862i | ||||
\(764\) | 18.0000 | 0.651217 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 12.0000 | 0.433578 | ||||||||
\(767\) | 4.50000 | − | 7.79423i | 0.162486 | − | 0.281433i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 20.0000 | + | 34.6410i | 0.721218 | + | 1.24919i | 0.960512 | + | 0.278240i | \(0.0897509\pi\) |
−0.239293 | + | 0.970947i | \(0.576916\pi\) | |||||||
\(770\) | −1.00000 | − | 1.73205i | −0.0360375 | − | 0.0624188i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 6.50000 | − | 11.2583i | 0.233940 | − | 0.405196i | ||||
\(773\) | −31.0000 | −1.11499 | −0.557496 | − | 0.830179i | \(-0.688238\pi\) | ||||
−0.557496 | + | 0.830179i | \(0.688238\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.00000 | −0.0359211 | ||||||||
\(776\) | 1.50000 | − | 2.59808i | 0.0538469 | − | 0.0932655i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −11.0000 | − | 19.0526i | −0.394369 | − | 0.683067i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 3.00000 | 0.107143 | ||||||||
\(785\) | 3.00000 | − | 5.19615i | 0.107075 | − | 0.185459i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −19.0000 | − | 32.9090i | −0.677277 | − | 1.17308i | −0.975798 | − | 0.218675i | \(-0.929827\pi\) |
0.298521 | − | 0.954403i | \(-0.403507\pi\) | |||||||
\(788\) | −7.50000 | − | 12.9904i | −0.267176 | − | 0.462763i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 6.00000 | − | 10.3923i | 0.213470 | − | 0.369742i | ||||
\(791\) | −20.0000 | −0.711118 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.00000 | 0.0355110 | ||||||||
\(794\) | 15.0000 | − | 25.9808i | 0.532330 | − | 0.922023i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −11.0000 | − | 19.0526i | −0.389885 | − | 0.675300i | ||||
\(797\) | −21.0000 | − | 36.3731i | −0.743858 | − | 1.28840i | −0.950726 | − | 0.310031i | \(-0.899660\pi\) |
0.206868 | − | 0.978369i | \(-0.433673\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.00000 | − | 3.46410i | 0.0707549 | − | 0.122551i | ||||
\(800\) | 5.00000 | 0.176777 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −28.0000 | −0.988714 | ||||||||
\(803\) | −3.00000 | + | 5.19615i | −0.105868 | + | 0.183368i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.500000 | − | 0.866025i | −0.0176117 | − | 0.0305044i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −4.50000 | + | 7.79423i | −0.158309 | + | 0.274200i | ||||
\(809\) | 5.00000 | 0.175791 | 0.0878953 | − | 0.996130i | \(-0.471986\pi\) | ||||
0.0878953 | + | 0.996130i | \(0.471986\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −36.0000 | −1.26413 | −0.632065 | − | 0.774915i | \(-0.717793\pi\) | ||||
−0.632065 | + | 0.774915i | \(0.717793\pi\) | |||||||
\(812\) | −5.00000 | + | 8.66025i | −0.175466 | + | 0.303915i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 2.50000 | + | 4.33013i | 0.0876250 | + | 0.151771i | ||||
\(815\) | 6.00000 | + | 10.3923i | 0.210171 | + | 0.364027i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −12.0000 | + | 20.7846i | −0.419827 | + | 0.727161i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 16.0000 | − | 27.7128i | 0.558404 | − | 0.967184i | −0.439226 | − | 0.898377i | \(-0.644747\pi\) |
0.997630 | − | 0.0688073i | \(-0.0219194\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5.50000 | − | 9.52628i | −0.191718 | − | 0.332065i | 0.754102 | − | 0.656758i | \(-0.228073\pi\) |
−0.945820 | + | 0.324692i | \(0.894739\pi\) | |||||||
\(824\) | −1.50000 | − | 2.59808i | −0.0522550 | − | 0.0905083i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −9.00000 | + | 15.5885i | −0.313150 | + | 0.542392i | ||||
\(827\) | 44.0000 | 1.53003 | 0.765015 | − | 0.644013i | \(-0.222732\pi\) | ||||
0.765015 | + | 0.644013i | \(0.222732\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 34.0000 | 1.18087 | 0.590434 | − | 0.807086i | \(-0.298956\pi\) | ||||
0.590434 | + | 0.807086i | \(0.298956\pi\) | |||||||
\(830\) | −5.00000 | + | 8.66025i | −0.173553 | + | 0.300602i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3.50000 | + | 6.06218i | 0.121341 | + | 0.210168i | ||||
\(833\) | −3.00000 | − | 5.19615i | −0.103944 | − | 0.180036i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 3.00000 | 0.103757 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −20.0000 | −0.690889 | ||||||||
\(839\) | 2.50000 | − | 4.33013i | 0.0863096 | − | 0.149493i | −0.819639 | − | 0.572880i | \(-0.805826\pi\) |
0.905949 | + | 0.423388i | \(0.139159\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.00000 | + | 3.46410i | 0.0689655 | + | 0.119452i | ||||
\(842\) | −5.00000 | − | 8.66025i | −0.172311 | − | 0.298452i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.00000 | 0.0344010 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −20.0000 | −0.687208 | ||||||||
\(848\) | −7.00000 | + | 12.1244i | −0.240381 | + | 0.416352i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.00000 | + | 1.73205i | 0.0342997 | + | 0.0594089i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 27.0000 | − | 46.7654i | 0.924462 | − | 1.60122i | 0.132039 | − | 0.991245i | \(-0.457848\pi\) |
0.792424 | − | 0.609971i | \(-0.208819\pi\) | |||||||
\(854\) | −2.00000 | −0.0684386 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 57.0000 | 1.94822 | ||||||||
\(857\) | 12.0000 | − | 20.7846i | 0.409912 | − | 0.709989i | −0.584967 | − | 0.811057i | \(-0.698893\pi\) |
0.994880 | + | 0.101068i | \(0.0322260\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −14.0000 | − | 24.2487i | −0.477674 | − | 0.827355i | 0.521999 | − | 0.852946i | \(-0.325187\pi\) |
−0.999672 | + | 0.0255910i | \(0.991853\pi\) | |||||||
\(860\) | −4.00000 | − | 6.92820i | −0.136399 | − | 0.236250i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 8.50000 | − | 14.7224i | 0.289511 | − | 0.501448i | ||||
\(863\) | 30.0000 | 1.02121 | 0.510606 | − | 0.859815i | \(-0.329421\pi\) | ||||
0.510606 | + | 0.859815i | \(0.329421\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −12.0000 | −0.408012 | ||||||||
\(866\) | 19.0000 | − | 32.9090i | 0.645646 | − | 1.11829i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.00000 | − | 1.73205i | −0.0339422 | − | 0.0587896i | ||||
\(869\) | 6.00000 | + | 10.3923i | 0.203536 | + | 0.352535i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.00000 | − | 12.1244i | 0.237186 | − | 0.410818i | ||||
\(872\) | 42.0000 | 1.42230 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.00000 | + | 1.73205i | −0.0338062 | + | 0.0585540i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7.50000 | − | 12.9904i | −0.253257 | − | 0.438654i | 0.711164 | − | 0.703027i | \(-0.248168\pi\) |
−0.964421 | + | 0.264373i | \(0.914835\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0.500000 | − | 0.866025i | 0.0168550 | − | 0.0291937i | ||||
\(881\) | −23.0000 | −0.774890 | −0.387445 | − | 0.921893i | \(-0.626642\pi\) | ||||
−0.387445 | + | 0.921893i | \(0.626642\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 47.0000 | 1.58168 | 0.790838 | − | 0.612026i | \(-0.209645\pi\) | ||||
0.790838 | + | 0.612026i | \(0.209645\pi\) | |||||||
\(884\) | 1.00000 | − | 1.73205i | 0.0336336 | − | 0.0582552i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −3.50000 | − | 6.06218i | −0.117585 | − | 0.203663i | ||||
\(887\) | −11.5000 | − | 19.9186i | −0.386132 | − | 0.668801i | 0.605793 | − | 0.795622i | \(-0.292856\pi\) |
−0.991926 | + | 0.126821i | \(0.959522\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.00000 | − | 13.8564i | 0.268311 | − | 0.464729i | ||||
\(890\) | −2.00000 | −0.0670402 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 26.0000 | 0.870544 | ||||||||
\(893\) | 3.00000 | − | 5.19615i | 0.100391 | − | 0.173883i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −9.00000 | − | 15.5885i | −0.300837 | − | 0.521065i | ||||
\(896\) | 3.00000 | + | 5.19615i | 0.100223 | + | 0.173591i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −15.0000 | + | 25.9808i | −0.500556 | + | 0.866989i | ||||
\(899\) | 5.00000 | 0.166759 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 28.0000 | 0.932815 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −15.0000 | − | 25.9808i | −0.498893 | − | 0.864107i | ||||
\(905\) | −8.50000 | − | 14.7224i | −0.282550 | − | 0.489390i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0.500000 | − | 0.866025i | 0.0166022 | − | 0.0287559i | −0.857605 | − | 0.514309i | \(-0.828048\pi\) |
0.874207 | + | 0.485553i | \(0.161382\pi\) | |||||||
\(908\) | −26.0000 | −0.862840 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −2.00000 | −0.0662994 | ||||||||
\(911\) | 21.0000 | − | 36.3731i | 0.695761 | − | 1.20509i | −0.274162 | − | 0.961683i | \(-0.588401\pi\) |
0.969923 | − | 0.243410i | \(-0.0782661\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5.00000 | − | 8.66025i | −0.165476 | − | 0.286613i | ||||
\(914\) | −13.0000 | − | 22.5167i | −0.430002 | − | 0.744785i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −8.00000 | + | 13.8564i | −0.264327 | + | 0.457829i | ||||
\(917\) | 8.00000 | 0.264183 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 38.0000 | 1.25350 | 0.626752 | − | 0.779219i | \(-0.284384\pi\) | ||||
0.626752 | + | 0.779219i | \(0.284384\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −13.0000 | − | 22.5167i | −0.428132 | − | 0.741547i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.50000 | − | 4.33013i | 0.0821995 | − | 0.142374i | ||||
\(926\) | −6.00000 | −0.197172 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −25.0000 | −0.820665 | ||||||||
\(929\) | −28.0000 | + | 48.4974i | −0.918650 | + | 1.59115i | −0.117183 | + | 0.993110i | \(0.537386\pi\) |
−0.801467 | + | 0.598038i | \(0.795947\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.50000 | − | 7.79423i | −0.147482 | − | 0.255446i | ||||
\(932\) | 7.00000 | + | 12.1244i | 0.229293 | + | 0.397146i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −14.0000 | + | 24.2487i | −0.458094 | + | 0.793442i | ||||
\(935\) | −2.00000 | −0.0654070 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 60.0000 | 1.96011 | 0.980057 | − | 0.198715i | \(-0.0636769\pi\) | ||||
0.980057 | + | 0.198715i | \(0.0636769\pi\) | |||||||
\(938\) | −14.0000 | + | 24.2487i | −0.457116 | + | 0.791748i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1.00000 | + | 1.73205i | 0.0326164 | + | 0.0564933i | ||||
\(941\) | −18.0000 | − | 31.1769i | −0.586783 | − | 1.01634i | −0.994651 | − | 0.103297i | \(-0.967061\pi\) |
0.407867 | − | 0.913041i | \(-0.366273\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −9.00000 | −0.292925 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8.00000 | −0.260102 | ||||||||
\(947\) | 12.0000 | − | 20.7846i | 0.389948 | − | 0.675409i | −0.602494 | − | 0.798123i | \(-0.705826\pi\) |
0.992442 | + | 0.122714i | \(0.0391598\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.00000 | + | 5.19615i | 0.0973841 | + | 0.168674i | ||||
\(950\) | 1.50000 | + | 2.59808i | 0.0486664 | + | 0.0842927i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −6.00000 | + | 10.3923i | −0.194461 | + | 0.336817i | ||||
\(953\) | 48.0000 | 1.55487 | 0.777436 | − | 0.628962i | \(-0.216520\pi\) | ||||
0.777436 | + | 0.628962i | \(0.216520\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −18.0000 | −0.582466 | ||||||||
\(956\) | −7.50000 | + | 12.9904i | −0.242567 | + | 0.420139i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 7.50000 | + | 12.9904i | 0.242314 | + | 0.419700i | ||||
\(959\) | −5.00000 | − | 8.66025i | −0.161458 | − | 0.279654i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.0000 | − | 25.9808i | 0.483871 | − | 0.838089i | ||||
\(962\) | 5.00000 | 0.161206 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −10.0000 | −0.322078 | ||||||||
\(965\) | −6.50000 | + | 11.2583i | −0.209242 | + | 0.362418i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 25.0000 | + | 43.3013i | 0.803946 | + | 1.39247i | 0.917000 | + | 0.398886i | \(0.130603\pi\) |
−0.113055 | + | 0.993589i | \(0.536064\pi\) | |||||||
\(968\) | −15.0000 | − | 25.9808i | −0.482118 | − | 0.835053i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −0.500000 | + | 0.866025i | −0.0160540 | + | 0.0278064i | ||||
\(971\) | −50.0000 | −1.60458 | −0.802288 | − | 0.596937i | \(-0.796384\pi\) | ||||
−0.802288 | + | 0.596937i | \(0.796384\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 24.0000 | 0.769405 | ||||||||
\(974\) | 17.0000 | − | 29.4449i | 0.544715 | − | 0.943474i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.500000 | − | 0.866025i | −0.0160046 | − | 0.0277208i | ||||
\(977\) | −4.50000 | − | 7.79423i | −0.143968 | − | 0.249359i | 0.785020 | − | 0.619471i | \(-0.212653\pi\) |
−0.928987 | + | 0.370111i | \(0.879319\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.00000 | − | 1.73205i | 0.0319601 | − | 0.0553566i | ||||
\(980\) | 3.00000 | 0.0958315 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 6.00000 | 0.191468 | ||||||||
\(983\) | −2.00000 | + | 3.46410i | −0.0637901 | + | 0.110488i | −0.896157 | − | 0.443738i | \(-0.853652\pi\) |
0.832367 | + | 0.554226i | \(0.186985\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7.50000 | + | 12.9904i | 0.238970 | + | 0.413908i | ||||
\(986\) | −5.00000 | − | 8.66025i | −0.159232 | − | 0.275799i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.50000 | − | 2.59808i | 0.0477214 | − | 0.0826558i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −18.0000 | −0.571789 | −0.285894 | − | 0.958261i | \(-0.592291\pi\) | ||||
−0.285894 | + | 0.958261i | \(0.592291\pi\) | |||||||
\(992\) | 2.50000 | − | 4.33013i | 0.0793751 | − | 0.137482i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 11.0000 | + | 19.0526i | 0.348723 | + | 0.604007i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 20.0000 | − | 34.6410i | 0.633406 | − | 1.09709i | −0.353444 | − | 0.935456i | \(-0.614990\pi\) |
0.986850 | − | 0.161636i | \(-0.0516771\pi\) | |||||||
\(998\) | 28.0000 | 0.886325 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1755.2.i.b.586.1 | 2 | ||
3.2 | odd | 2 | 585.2.i.b.196.1 | ✓ | 2 | ||
9.2 | odd | 6 | 5265.2.a.e.1.1 | 1 | |||
9.4 | even | 3 | inner | 1755.2.i.b.1171.1 | 2 | ||
9.5 | odd | 6 | 585.2.i.b.391.1 | yes | 2 | ||
9.7 | even | 3 | 5265.2.a.m.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
585.2.i.b.196.1 | ✓ | 2 | 3.2 | odd | 2 | ||
585.2.i.b.391.1 | yes | 2 | 9.5 | odd | 6 | ||
1755.2.i.b.586.1 | 2 | 1.1 | even | 1 | trivial | ||
1755.2.i.b.1171.1 | 2 | 9.4 | even | 3 | inner | ||
5265.2.a.e.1.1 | 1 | 9.2 | odd | 6 | |||
5265.2.a.m.1.1 | 1 | 9.7 | even | 3 |