Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [980,2,Mod(361,980)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(980, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("980.361");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 980 = 2^{2} \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 980.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: | \(7.82533939809\) |
Analytic rank: | \(0\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 961.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 980.961 |
Dual form | 980.2.i.e.361.1 |
$q$-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 \(\left(\mathbb{Z}/980\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(197\) | \(491\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) |
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 | 0 | ||||||||
\(3\) | −0.500000 | − | 0.866025i | −0.288675 | − | 0.500000i | 0.684819 | − | 0.728714i | \(-0.259881\pi\) |
−0.973494 | + | 0.228714i | \(0.926548\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.500000 | − | 0.866025i | 0.223607 | − | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | − | 1.73205i | 0.333333 | − | 0.577350i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.500000 | + | 0.866025i | 0.150756 | + | 0.261116i | 0.931505 | − | 0.363727i | \(-0.118496\pi\) |
−0.780750 | + | 0.624844i | \(0.785163\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.00000 | −1.38675 | −0.693375 | − | 0.720577i | \(-0.743877\pi\) | ||||
−0.693375 | + | 0.720577i | \(0.743877\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.500000 | − | 0.866025i | −0.121268 | − | 0.210042i | 0.799000 | − | 0.601331i | \(-0.205363\pi\) |
−0.920268 | + | 0.391289i | \(0.872029\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.00000 | − | 5.19615i | 0.688247 | − | 1.19208i | −0.284157 | − | 0.958778i | \(-0.591714\pi\) |
0.972404 | − | 0.233301i | \(-0.0749529\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.00000 | − | 3.46410i | 0.417029 | − | 0.722315i | −0.578610 | − | 0.815604i | \(-0.696405\pi\) |
0.995639 | + | 0.0932891i | \(0.0297381\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.00000 | −0.962250 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.00000 | 0.557086 | 0.278543 | − | 0.960424i | \(-0.410149\pi\) | ||||
0.278543 | + | 0.960424i | \(0.410149\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.00000 | − | 1.73205i | −0.179605 | − | 0.311086i | 0.762140 | − | 0.647412i | \(-0.224149\pi\) |
−0.941745 | + | 0.336327i | \(0.890815\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.500000 | − | 0.866025i | 0.0870388 | − | 0.150756i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.00000 | + | 6.92820i | −0.657596 | + | 1.13899i | 0.323640 | + | 0.946180i | \(0.395093\pi\) |
−0.981236 | + | 0.192809i | \(0.938240\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.50000 | + | 4.33013i | 0.400320 | + | 0.693375i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10.0000 | −1.56174 | −0.780869 | − | 0.624695i | \(-0.785223\pi\) | ||||
−0.780869 | + | 0.624695i | \(0.785223\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.00000 | −0.304997 | −0.152499 | − | 0.988304i | \(-0.548732\pi\) | ||||
−0.152499 | + | 0.988304i | \(0.548732\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | − | 1.73205i | −0.149071 | − | 0.258199i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.50000 | − | 6.06218i | 0.510527 | − | 0.884260i | −0.489398 | − | 0.872060i | \(-0.662783\pi\) |
0.999926 | − | 0.0121990i | \(-0.00388317\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.500000 | + | 0.866025i | −0.0700140 | + | 0.121268i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.00000 | + | 1.73205i | 0.137361 | + | 0.237915i | 0.926497 | − | 0.376303i | \(-0.122805\pi\) |
−0.789136 | + | 0.614218i | \(0.789471\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.00000 | 0.134840 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.00000 | −0.794719 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.00000 | − | 12.1244i | −0.911322 | − | 1.57846i | −0.812198 | − | 0.583382i | \(-0.801729\pi\) |
−0.0991242 | − | 0.995075i | \(-0.531604\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.00000 | − | 6.92820i | 0.512148 | − | 0.887066i | −0.487753 | − | 0.872982i | \(-0.662183\pi\) |
0.999901 | − | 0.0140840i | \(-0.00448323\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.50000 | + | 4.33013i | −0.310087 | + | 0.537086i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.00000 | − | 12.1244i | −0.855186 | − | 1.48123i | −0.876472 | − | 0.481452i | \(-0.840109\pi\) |
0.0212861 | − | 0.999773i | \(-0.493224\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.00000 | −0.481543 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.00000 | + | 8.66025i | 0.585206 | + | 1.01361i | 0.994850 | + | 0.101361i | \(0.0323196\pi\) |
−0.409644 | + | 0.912245i | \(0.634347\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.500000 | + | 0.866025i | −0.0577350 | + | 0.100000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.50000 | − | 9.52628i | 0.618798 | − | 1.07179i | −0.370907 | − | 0.928670i | \(-0.620953\pi\) |
0.989705 | − | 0.143120i | \(-0.0457135\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.00000 | −0.439057 | −0.219529 | − | 0.975606i | \(-0.570452\pi\) | ||||
−0.219529 | + | 0.975606i | \(0.570452\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.00000 | −0.108465 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.50000 | − | 2.59808i | −0.160817 | − | 0.278543i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.00000 | + | 3.46410i | −0.212000 | + | 0.367194i | −0.952340 | − | 0.305038i | \(-0.901331\pi\) |
0.740341 | + | 0.672232i | \(0.234664\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.00000 | + | 1.73205i | −0.103695 | + | 0.179605i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.00000 | − | 5.19615i | −0.307794 | − | 0.533114i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.00000 | −0.304604 | −0.152302 | − | 0.988334i | \(-0.548669\pi\) | ||||
−0.152302 | + | 0.988334i | \(0.548669\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.00000 | 0.201008 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.00000 | + | 8.66025i | 0.497519 | + | 0.861727i | 0.999996 | − | 0.00286291i | \(-0.000911295\pi\) |
−0.502477 | + | 0.864590i | \(0.667578\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.50000 | − | 6.06218i | 0.344865 | − | 0.597324i | −0.640464 | − | 0.767988i | \(-0.721258\pi\) |
0.985329 | + | 0.170664i | \(0.0545913\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −9.00000 | + | 15.5885i | −0.870063 | + | 1.50699i | −0.00813215 | + | 0.999967i | \(0.502589\pi\) |
−0.861931 | + | 0.507026i | \(0.830745\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.50000 | + | 9.52628i | 0.526804 | + | 0.912452i | 0.999512 | + | 0.0312328i | \(0.00994332\pi\) |
−0.472708 | + | 0.881219i | \(0.656723\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.00000 | 0.759326 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 16.0000 | 1.50515 | 0.752577 | − | 0.658505i | \(-0.228811\pi\) | ||||
0.752577 | + | 0.658505i | \(0.228811\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.00000 | − | 3.46410i | −0.186501 | − | 0.323029i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.00000 | + | 8.66025i | −0.462250 | + | 0.800641i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.00000 | − | 8.66025i | 0.454545 | − | 0.787296i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.00000 | + | 8.66025i | 0.450835 | + | 0.780869i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.00000 | −0.532414 | −0.266207 | − | 0.963916i | \(-0.585770\pi\) | ||||
−0.266207 | + | 0.963916i | \(0.585770\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.00000 | + | 1.73205i | 0.0880451 | + | 0.152499i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.00000 | + | 10.3923i | −0.524222 | + | 0.907980i | 0.475380 | + | 0.879781i | \(0.342311\pi\) |
−0.999602 | + | 0.0281993i | \(0.991023\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.50000 | + | 4.33013i | −0.215166 | + | 0.372678i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −8.00000 | − | 13.8564i | −0.683486 | − | 1.18383i | −0.973910 | − | 0.226935i | \(-0.927130\pi\) |
0.290424 | − | 0.956898i | \(-0.406204\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 16.0000 | 1.35710 | 0.678551 | − | 0.734553i | \(-0.262608\pi\) | ||||
0.678551 | + | 0.734553i | \(0.262608\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.00000 | −0.589506 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.50000 | − | 4.33013i | −0.209061 | − | 0.362103i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.50000 | − | 2.59808i | 0.124568 | − | 0.215758i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 11.0000 | − | 19.0526i | 0.901155 | − | 1.56085i | 0.0751583 | − | 0.997172i | \(-0.476054\pi\) |
0.825997 | − | 0.563675i | \(-0.190613\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.50000 | + | 2.59808i | 0.122068 | + | 0.211428i | 0.920583 | − | 0.390547i | \(-0.127714\pi\) |
−0.798515 | + | 0.601975i | \(0.794381\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.00000 | −0.161690 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.00000 | −0.160644 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.00000 | + | 12.1244i | 0.558661 | + | 0.967629i | 0.997609 | + | 0.0691164i | \(0.0220180\pi\) |
−0.438948 | + | 0.898513i | \(0.644649\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.00000 | − | 1.73205i | 0.0793052 | − | 0.137361i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.00000 | − | 13.8564i | 0.626608 | − | 1.08532i | −0.361619 | − | 0.932326i | \(-0.617776\pi\) |
0.988227 | − | 0.152992i | \(-0.0488907\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.500000 | − | 0.866025i | −0.0389249 | − | 0.0674200i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 21.0000 | 1.62503 | 0.812514 | − | 0.582941i | \(-0.198098\pi\) | ||||
0.812514 | + | 0.582941i | \(0.198098\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.0000 | 0.923077 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.00000 | − | 10.3923i | −0.458831 | − | 0.794719i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −10.5000 | + | 18.1865i | −0.798300 | + | 1.38270i | 0.122422 | + | 0.992478i | \(0.460934\pi\) |
−0.920722 | + | 0.390218i | \(0.872399\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −7.00000 | + | 12.1244i | −0.526152 | + | 0.911322i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 10.0000 | + | 17.3205i | 0.747435 | + | 1.29460i | 0.949048 | + | 0.315130i | \(0.102048\pi\) |
−0.201613 | + | 0.979465i | \(0.564618\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.0000 | 0.743294 | 0.371647 | − | 0.928374i | \(-0.378793\pi\) | ||||
0.371647 | + | 0.928374i | \(0.378793\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.00000 | −0.591377 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.00000 | + | 6.92820i | 0.294086 | + | 0.509372i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.500000 | − | 0.866025i | 0.0365636 | − | 0.0633300i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.50000 | + | 2.59808i | −0.108536 | + | 0.187990i | −0.915177 | − | 0.403051i | \(-0.867950\pi\) |
0.806641 | + | 0.591041i | \(0.201283\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.00000 | + | 10.3923i | 0.431889 | + | 0.748054i | 0.997036 | − | 0.0769360i | \(-0.0245137\pi\) |
−0.565147 | + | 0.824991i | \(0.691180\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 5.00000 | 0.358057 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −18.0000 | −1.28245 | −0.641223 | − | 0.767354i | \(-0.721573\pi\) | ||||
−0.641223 | + | 0.767354i | \(0.721573\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.0000 | + | 19.0526i | 0.779769 | + | 1.35060i | 0.932075 | + | 0.362267i | \(0.117997\pi\) |
−0.152305 | + | 0.988334i | \(0.548670\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.00000 | + | 12.1244i | −0.493742 | + | 0.855186i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.00000 | + | 8.66025i | −0.349215 | + | 0.604858i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.00000 | − | 6.92820i | −0.278019 | − | 0.481543i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.00000 | 0.415029 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.0000 | 1.17033 | 0.585164 | − | 0.810915i | \(-0.301030\pi\) | ||||
0.585164 | + | 0.810915i | \(0.301030\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.00000 | + | 1.73205i | −0.0681994 | + | 0.118125i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.00000 | − | 8.66025i | 0.337869 | − | 0.585206i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.50000 | + | 4.33013i | 0.168168 | + | 0.291276i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 29.0000 | 1.94198 | 0.970992 | − | 0.239113i | \(-0.0768565\pi\) | ||||
0.970992 | + | 0.239113i | \(0.0768565\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.00000 | −0.133333 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.50000 | − | 7.79423i | −0.298675 | − | 0.517321i | 0.677158 | − | 0.735838i | \(-0.263211\pi\) |
−0.975833 | + | 0.218517i | \(0.929878\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.00000 | + | 1.73205i | −0.0660819 | + | 0.114457i | −0.897173 | − | 0.441679i | \(-0.854383\pi\) |
0.831092 | + | 0.556136i | \(0.187717\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.00000 | − | 6.92820i | 0.262049 | − | 0.453882i | −0.704737 | − | 0.709468i | \(-0.748935\pi\) |
0.966786 | + | 0.255586i | \(0.0822686\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.50000 | − | 6.06218i | −0.228315 | − | 0.395453i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −11.0000 | −0.714527 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 13.0000 | 0.840900 | 0.420450 | − | 0.907316i | \(-0.361872\pi\) | ||||
0.420450 | + | 0.907316i | \(0.361872\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.00000 | + | 13.8564i | 0.515325 | + | 0.892570i | 0.999842 | + | 0.0177875i | \(0.00566223\pi\) |
−0.484516 | + | 0.874782i | \(0.661004\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −8.00000 | + | 13.8564i | −0.513200 | + | 0.888889i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −15.0000 | + | 25.9808i | −0.954427 | + | 1.65312i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.00000 | + | 3.46410i | 0.126745 | + | 0.219529i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4.00000 | −0.252478 | −0.126239 | − | 0.992000i | \(-0.540291\pi\) | ||||
−0.126239 | + | 0.992000i | \(0.540291\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.00000 | 0.251478 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.500000 | + | 0.866025i | 0.0313112 | + | 0.0542326i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −9.00000 | + | 15.5885i | −0.561405 | + | 0.972381i | 0.435970 | + | 0.899961i | \(0.356405\pi\) |
−0.997374 | + | 0.0724199i | \(0.976928\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.00000 | − | 5.19615i | 0.185695 | − | 0.321634i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −9.00000 | − | 15.5885i | −0.554964 | − | 0.961225i | −0.997906 | − | 0.0646755i | \(-0.979399\pi\) |
0.442943 | − | 0.896550i | \(-0.353935\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.00000 | 0.122859 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.00000 | 0.244796 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.00000 | + | 6.92820i | 0.243884 | + | 0.422420i | 0.961817 | − | 0.273692i | \(-0.0882449\pi\) |
−0.717933 | + | 0.696112i | \(0.754912\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.00000 | − | 13.8564i | 0.485965 | − | 0.841717i | −0.513905 | − | 0.857847i | \(-0.671801\pi\) |
0.999870 | + | 0.0161307i | \(0.00513477\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.500000 | − | 0.866025i | 0.0301511 | − | 0.0522233i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.0000 | − | 17.3205i | −0.600842 | − | 1.04069i | −0.992694 | − | 0.120660i | \(-0.961499\pi\) |
0.391852 | − | 0.920028i | \(-0.371834\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.00000 | −0.239474 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −13.0000 | −0.775515 | −0.387757 | − | 0.921761i | \(-0.626750\pi\) | ||||
−0.387757 | + | 0.921761i | \(0.626750\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.500000 | + | 0.866025i | 0.0297219 | + | 0.0514799i | 0.880504 | − | 0.474039i | \(-0.157204\pi\) |
−0.850782 | + | 0.525519i | \(0.823871\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.00000 | + | 5.19615i | −0.177705 | + | 0.307794i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.00000 | − | 13.8564i | 0.470588 | − | 0.815083i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.50000 | + | 2.59808i | 0.0879316 | + | 0.152302i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9.00000 | 0.525786 | 0.262893 | − | 0.964825i | \(-0.415323\pi\) | ||||
0.262893 | + | 0.964825i | \(0.415323\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −14.0000 | −0.815112 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.50000 | − | 4.33013i | −0.145065 | − | 0.251259i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −10.0000 | + | 17.3205i | −0.578315 | + | 1.00167i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5.00000 | − | 8.66025i | 0.287242 | − | 0.497519i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.00000 | − | 6.92820i | −0.229039 | − | 0.396708i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 23.0000 | 1.31268 | 0.656340 | − | 0.754466i | \(-0.272104\pi\) | ||||
0.656340 | + | 0.754466i | \(0.272104\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7.00000 | −0.398216 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.00000 | − | 12.1244i | −0.396934 | − | 0.687509i | 0.596412 | − | 0.802678i | \(-0.296592\pi\) |
−0.993346 | + | 0.115169i | \(0.963259\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.5000 | − | 21.6506i | 0.706542 | − | 1.22377i | −0.259590 | − | 0.965719i | \(-0.583588\pi\) |
0.966132 | − | 0.258047i | \(-0.0830791\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −9.00000 | + | 15.5885i | −0.505490 | + | 0.875535i | 0.494489 | + | 0.869184i | \(0.335355\pi\) |
−0.999980 | + | 0.00635137i | \(0.997978\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.50000 | + | 2.59808i | 0.0839839 | + | 0.145464i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 18.0000 | 1.00466 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6.00000 | −0.333849 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.50000 | + | 4.33013i | 0.138675 | + | 0.240192i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5.50000 | − | 9.52628i | 0.304151 | − | 0.526804i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.0000 | + | 17.3205i | −0.549650 | + | 0.952021i | 0.448649 | + | 0.893708i | \(0.351905\pi\) |
−0.998298 | + | 0.0583130i | \(0.981428\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 8.00000 | + | 13.8564i | 0.438397 | + | 0.759326i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −14.0000 | −0.764902 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.00000 | −0.435788 | −0.217894 | − | 0.975972i | \(-0.569919\pi\) | ||||
−0.217894 | + | 0.975972i | \(0.569919\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −8.00000 | − | 13.8564i | −0.434500 | − | 0.752577i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.00000 | − | 1.73205i | 0.0541530 | − | 0.0937958i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.00000 | + | 3.46410i | −0.107676 | + | 0.186501i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4.00000 | − | 6.92820i | −0.214731 | − | 0.371925i | 0.738458 | − | 0.674299i | \(-0.235554\pi\) |
−0.953189 | + | 0.302374i | \(0.902221\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −22.0000 | −1.17763 | −0.588817 | − | 0.808267i | \(-0.700406\pi\) | ||||
−0.588817 | + | 0.808267i | \(0.700406\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 25.0000 | 1.33440 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.50000 | − | 7.79423i | −0.239511 | − | 0.414845i | 0.721063 | − | 0.692869i | \(-0.243654\pi\) |
−0.960574 | + | 0.278024i | \(0.910320\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.00000 | − | 6.92820i | 0.211112 | − | 0.365657i | −0.740951 | − | 0.671559i | \(-0.765625\pi\) |
0.952063 | + | 0.305903i | \(0.0989582\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.50000 | − | 14.7224i | −0.447368 | − | 0.774865i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −10.0000 | −0.524864 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10.0000 | 0.523424 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.5000 | + | 19.9186i | 0.600295 | + | 1.03974i | 0.992776 | + | 0.119982i | \(0.0382835\pi\) |
−0.392481 | + | 0.919760i | \(0.628383\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −10.0000 | + | 17.3205i | −0.520579 | + | 0.901670i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6.00000 | + | 10.3923i | −0.310668 | + | 0.538093i | −0.978507 | − | 0.206213i | \(-0.933886\pi\) |
0.667839 | + | 0.744306i | \(0.267219\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.500000 | + | 0.866025i | 0.0258199 | + | 0.0447214i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −15.0000 | −0.772539 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.00000 | 0.410932 | 0.205466 | − | 0.978664i | \(-0.434129\pi\) | ||||
0.205466 | + | 0.978664i | \(0.434129\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.00000 | + | 5.19615i | 0.153695 | + | 0.266207i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 16.0000 | − | 27.7128i | 0.817562 | − | 1.41606i | −0.0899119 | − | 0.995950i | \(-0.528659\pi\) |
0.907474 | − | 0.420109i | \(-0.138008\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.00000 | + | 3.46410i | −0.101666 | + | 0.176090i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7.50000 | + | 12.9904i | 0.380265 | + | 0.658638i | 0.991100 | − | 0.133120i | \(-0.0424994\pi\) |
−0.610835 | + | 0.791758i | \(0.709166\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.00000 | −0.202289 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 12.0000 | 0.605320 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5.50000 | − | 9.52628i | −0.276735 | − | 0.479319i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11.5000 | − | 19.9186i | 0.577168 | − | 0.999685i | −0.418634 | − | 0.908155i | \(-0.637491\pi\) |
0.995802 | − | 0.0915300i | \(-0.0291757\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.50000 | − | 9.52628i | 0.274657 | − | 0.475720i | −0.695392 | − | 0.718631i | \(-0.744769\pi\) |
0.970049 | + | 0.242911i | \(0.0781024\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.00000 | + | 8.66025i | 0.249068 | + | 0.431398i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −8.00000 | −0.396545 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.00000 | + | 8.66025i | 0.247234 | + | 0.428222i | 0.962757 | − | 0.270367i | \(-0.0871450\pi\) |
−0.715523 | + | 0.698589i | \(0.753812\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −8.00000 | + | 13.8564i | −0.394611 | + | 0.683486i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.00000 | + | 3.46410i | −0.0981761 | + | 0.170046i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −8.00000 | − | 13.8564i | −0.391762 | − | 0.678551i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −18.0000 | −0.879358 | −0.439679 | − | 0.898155i | \(-0.644908\pi\) | ||||
−0.439679 | + | 0.898155i | \(0.644908\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −19.0000 | −0.926003 | −0.463002 | − | 0.886357i | \(-0.653228\pi\) | ||||
−0.463002 | + | 0.886357i | \(0.653228\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −7.00000 | − | 12.1244i | −0.340352 | − | 0.589506i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.500000 | + | 0.866025i | −0.0242536 | + | 0.0420084i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.50000 | + | 4.33013i | −0.120701 | + | 0.209061i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16.5000 | + | 28.5788i | 0.794777 | + | 1.37659i | 0.922981 | + | 0.384846i | \(0.125746\pi\) |
−0.128204 | + | 0.991748i | \(0.540921\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −14.0000 | −0.672797 | −0.336399 | − | 0.941720i | \(-0.609209\pi\) | ||||
−0.336399 | + | 0.941720i | \(0.609209\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.00000 | −0.143839 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −12.0000 | − | 20.7846i | −0.574038 | − | 0.994263i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.0000 | − | 24.2487i | 0.668184 | − | 1.15733i | −0.310228 | − | 0.950662i | \(-0.600405\pi\) |
0.978412 | − | 0.206666i | \(-0.0662612\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 13.0000 | − | 22.5167i | 0.617649 | − | 1.06980i | −0.372265 | − | 0.928126i | \(-0.621419\pi\) |
0.989914 | − | 0.141672i | \(-0.0452479\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.00000 | + | 3.46410i | 0.0948091 | + | 0.164214i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −22.0000 | −1.04056 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9.00000 | −0.424736 | −0.212368 | − | 0.977190i | \(-0.568118\pi\) | ||||
−0.212368 | + | 0.977190i | \(0.568118\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.00000 | − | 8.66025i | −0.235441 | − | 0.407795i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.50000 | − | 2.59808i | 0.0704761 | − | 0.122068i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.00000 | − | 15.5885i | 0.421002 | − | 0.729197i | −0.575036 | − | 0.818128i | \(-0.695012\pi\) |
0.996038 | + | 0.0889312i | \(0.0283451\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.50000 | + | 4.33013i | 0.116690 | + | 0.202113i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12.0000 | −0.558896 | −0.279448 | − | 0.960161i | \(-0.590151\pi\) | ||||
−0.279448 | + | 0.960161i | \(0.590151\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −20.0000 | −0.929479 | −0.464739 | − | 0.885448i | \(-0.653852\pi\) | ||||
−0.464739 | + | 0.885448i | \(0.653852\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.00000 | + | 1.73205i | 0.0463739 | + | 0.0803219i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −9.50000 | + | 16.4545i | −0.439608 | + | 0.761423i | −0.997659 | − | 0.0683836i | \(-0.978216\pi\) |
0.558052 | + | 0.829806i | \(0.311549\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.00000 | − | 12.1244i | 0.322543 | − | 0.558661i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.00000 | − | 1.73205i | −0.0459800 | − | 0.0796398i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.00000 | −0.275299 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.00000 | 0.183147 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8.00000 | + | 13.8564i | 0.365529 | + | 0.633115i | 0.988861 | − | 0.148842i | \(-0.0475547\pi\) |
−0.623332 | + | 0.781958i | \(0.714221\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 20.0000 | − | 34.6410i | 0.911922 | − | 1.57949i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.50000 | + | 2.59808i | −0.0681115 | + | 0.117973i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10.0000 | + | 17.3205i | 0.453143 | + | 0.784867i | 0.998579 | − | 0.0532853i | \(-0.0169693\pi\) |
−0.545436 | + | 0.838152i | \(0.683636\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −16.0000 | −0.723545 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15.0000 | −0.676941 | −0.338470 | − | 0.940977i | \(-0.609909\pi\) | ||||
−0.338470 | + | 0.940977i | \(0.609909\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.50000 | − | 2.59808i | −0.0675566 | − | 0.117011i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.00000 | − | 1.73205i | 0.0449467 | − | 0.0778499i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.50000 | − | 4.33013i | 0.111915 | − | 0.193843i | −0.804627 | − | 0.593780i | \(-0.797635\pi\) |
0.916542 | + | 0.399937i | \(0.130968\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −10.5000 | − | 18.1865i | −0.469105 | − | 0.812514i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −9.00000 | −0.401290 | −0.200645 | − | 0.979664i | \(-0.564304\pi\) | ||||
−0.200645 | + | 0.979664i | \(0.564304\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.0000 | 0.444994 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −6.00000 | − | 10.3923i | −0.266469 | − | 0.461538i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 12.0000 | − | 20.7846i | 0.531891 | − | 0.921262i | −0.467416 | − | 0.884037i | \(-0.654815\pi\) |
0.999307 | − | 0.0372243i | \(-0.0118516\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −15.0000 | + | 25.9808i | −0.662266 | + | 1.14708i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.50000 | − | 6.06218i | −0.154228 | − | 0.267131i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.00000 | 0.307860 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 21.0000 | 0.921798 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −15.0000 | − | 25.9808i | −0.657162 | − | 1.13824i | −0.981347 | − | 0.192244i | \(-0.938423\pi\) |
0.324185 | − | 0.945994i | \(-0.394910\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8.00000 | + | 13.8564i | −0.349816 | + | 0.605898i | −0.986216 | − | 0.165460i | \(-0.947089\pi\) |
0.636401 | + | 0.771358i | \(0.280422\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.00000 | + | 1.73205i | −0.0435607 | + | 0.0754493i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.50000 | + | 6.06218i | 0.152174 | + | 0.263573i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −28.0000 | −1.21510 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 50.0000 | 2.16574 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.00000 | + | 15.5885i | 0.389104 | + | 0.673948i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 10.0000 | − | 17.3205i | 0.431532 | − | 0.747435i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.5000 | − | 21.6506i | 0.537417 | − | 0.930834i | −0.461625 | − | 0.887075i | \(-0.652733\pi\) |
0.999042 | − | 0.0437584i | \(-0.0139332\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −5.00000 | − | 8.66025i | −0.214571 | − | 0.371647i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 11.0000 | 0.471188 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.0000 | 0.684111 | 0.342055 | − | 0.939680i | \(-0.388877\pi\) | ||||
0.342055 | + | 0.939680i | \(0.388877\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −8.00000 | − | 13.8564i | −0.341432 | − | 0.591377i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.00000 | − | 15.5885i | 0.383413 | − | 0.664091i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4.00000 | − | 6.92820i | 0.169791 | − | 0.294086i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6.00000 | + | 10.3923i | 0.254228 | + | 0.440336i | 0.964686 | − | 0.263404i | \(-0.0848453\pi\) |
−0.710457 | + | 0.703740i | \(0.751512\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 10.0000 | 0.422955 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.00000 | −0.0422200 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −6.00000 | − | 10.3923i | −0.252870 | − | 0.437983i | 0.711445 | − | 0.702742i | \(-0.248041\pi\) |
−0.964315 | + | 0.264758i | \(0.914708\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.00000 | − | 13.8564i | 0.336563 | − | 0.582943i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.00000 | + | 8.66025i | −0.209611 | + | 0.363057i | −0.951592 | − | 0.307364i | \(-0.900553\pi\) |
0.741981 | + | 0.670421i | \(0.233886\pi\) | |||||||
\(570\) | 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 | 0 | ||||||||
\(573\) | 3.00000 | 0.125327 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.00000 | −0.166812 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.50000 | − | 9.52628i | −0.228968 | − | 0.396584i | 0.728535 | − | 0.685009i | \(-0.240202\pi\) |
−0.957503 | + | 0.288425i | \(0.906868\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 6.00000 | − | 10.3923i | 0.249351 | − | 0.431889i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.00000 | + | 1.73205i | −0.0414158 | + | 0.0717342i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 5.00000 | + | 8.66025i | 0.206725 | + | 0.358057i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −44.0000 | −1.81607 | −0.908037 | − | 0.418890i | \(-0.862419\pi\) | ||||
−0.908037 | + | 0.418890i | \(0.862419\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −12.0000 | −0.494451 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9.00000 | + | 15.5885i | 0.370211 | + | 0.641223i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −11.5000 | + | 19.9186i | −0.472248 | + | 0.817958i | −0.999496 | − | 0.0317536i | \(-0.989891\pi\) |
0.527247 | + | 0.849712i | \(0.323224\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 11.0000 | − | 19.0526i | 0.450200 | − | 0.779769i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −17.5000 | − | 30.3109i | −0.715031 | − | 1.23847i | −0.962948 | − | 0.269688i | \(-0.913079\pi\) |
0.247917 | − | 0.968781i | \(-0.420254\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22.0000 | −0.897399 | −0.448699 | − | 0.893683i | \(-0.648113\pi\) | ||||
−0.448699 | + | 0.893683i | \(0.648113\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −28.0000 | −1.14025 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −5.00000 | − | 8.66025i | −0.203279 | − | 0.352089i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14.5000 | − | 25.1147i | 0.588537 | − | 1.01938i | −0.405887 | − | 0.913923i | \(-0.633038\pi\) |
0.994424 | − | 0.105453i | \(-0.0336291\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −17.5000 | + | 30.3109i | −0.707974 | + | 1.22625i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13.0000 | + | 22.5167i | 0.525065 | + | 0.909439i | 0.999574 | + | 0.0291886i | \(0.00929235\pi\) |
−0.474509 | + | 0.880251i | \(0.657374\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 10.0000 | 0.403239 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −12.0000 | −0.483102 | −0.241551 | − | 0.970388i | \(-0.577656\pi\) | ||||
−0.241551 | + | 0.970388i | \(0.577656\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −10.0000 | + | 17.3205i | −0.401286 | + | 0.695048i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.00000 | − | 5.19615i | −0.119808 | − | 0.207514i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 8.00000 | 0.318981 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 31.0000 | 1.23409 | 0.617045 | − | 0.786928i | \(-0.288330\pi\) | ||||
0.617045 | + | 0.786928i | \(0.288330\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −8.50000 | − | 14.7224i | −0.337845 | − | 0.585164i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3.00000 | + | 5.19615i | −0.119051 | + | 0.206203i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9.00000 | + | 15.5885i | 0.355479 | + | 0.615707i | 0.987200 | − | 0.159489i | \(-0.0509845\pi\) |
−0.631721 | + | 0.775196i | \(0.717651\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −15.0000 | −0.591542 | −0.295771 | − | 0.955259i | \(-0.595577\pi\) | ||||
−0.295771 | + | 0.955259i | \(0.595577\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.00000 | 0.0787499 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 14.0000 | + | 24.2487i | 0.550397 | + | 0.953315i | 0.998246 | + | 0.0592060i | \(0.0188569\pi\) |
−0.447849 | + | 0.894109i | \(0.647810\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.00000 | − | 12.1244i | 0.274774 | − | 0.475923i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −7.00000 | + | 12.1244i | −0.273931 | + | 0.474463i | −0.969865 | − | 0.243643i | \(-0.921657\pi\) |
0.695934 | + | 0.718106i | \(0.254991\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.00000 | + | 10.3923i | 0.234439 | + | 0.406061i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 20.0000 | 0.780274 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −37.0000 | −1.44132 | −0.720658 | − | 0.693291i | \(-0.756160\pi\) | ||||
−0.720658 | + | 0.693291i | \(0.756160\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.00000 | + | 3.46410i | 0.0777910 | + | 0.134738i | 0.902297 | − | 0.431116i | \(-0.141880\pi\) |
−0.824506 | + | 0.565854i | \(0.808547\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.50000 | − | 4.33013i | 0.0970920 | − | 0.168168i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.00000 | − | 10.3923i | 0.232321 | − | 0.402392i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −14.5000 | − | 25.1147i | −0.560602 | − | 0.970992i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 8.00000 | 0.308837 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.00000 | 0.154189 | 0.0770943 | − | 0.997024i | \(-0.475436\pi\) | ||||
0.0770943 | + | 0.997024i | \(0.475436\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.50000 | + | 4.33013i | 0.0962250 | + | 0.166667i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −15.5000 | + | 26.8468i | −0.595713 | + | 1.03181i | 0.397732 | + | 0.917501i | \(0.369797\pi\) |
−0.993446 | + | 0.114304i | \(0.963536\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.50000 | + | 7.79423i | −0.172440 | + | 0.298675i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −24.0000 | − | 41.5692i | −0.918334 | − | 1.59060i | −0.801945 | − | 0.597398i | \(-0.796201\pi\) |
−0.116390 | − | 0.993204i | \(-0.537132\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −16.0000 | −0.611329 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.00000 | 0.0763048 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −5.00000 | − | 8.66025i | −0.190485 | − | 0.329929i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14.0000 | + | 24.2487i | −0.532585 | + | 0.922464i | 0.466691 | + | 0.884420i | \(0.345446\pi\) |
−0.999276 | + | 0.0380440i | \(0.987887\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 8.00000 | − | 13.8564i | 0.303457 | − | 0.525603i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.00000 | + | 8.66025i | 0.189389 | + | 0.328031i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −8.00000 | −0.302588 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −29.0000 | −1.09531 | −0.547657 | − | 0.836703i | \(-0.684480\pi\) | ||||
−0.547657 | + | 0.836703i | \(0.684480\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 24.0000 | + | 41.5692i | 0.905177 | + | 1.56781i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3.50000 | + | 6.06218i | −0.131818 | + | 0.228315i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −13.5000 | + | 23.3827i | −0.507003 | + | 0.878155i | 0.492964 | + | 0.870050i | \(0.335913\pi\) |
−0.999967 | + | 0.00810550i | \(0.997420\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −11.0000 | − | 19.0526i | −0.412532 | − | 0.714527i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −8.00000 | −0.299602 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.00000 | −0.186989 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −6.50000 | − | 11.2583i | −0.242747 | − | 0.420450i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −6.00000 | + | 10.3923i | −0.223762 | + | 0.387568i | −0.955947 | − | 0.293538i | \(-0.905167\pi\) |
0.732185 | + | 0.681106i | \(0.238501\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 8.00000 | − | 13.8564i | 0.297523 | − | 0.515325i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.50000 | − | 2.59808i | −0.0557086 | − | 0.0964901i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16.0000 | 0.593407 | 0.296704 | − | 0.954970i | \(-0.404113\pi\) | ||||
0.296704 | + | 0.954970i | \(0.404113\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13.0000 | 0.481481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.00000 | + | 1.73205i | 0.0369863 | + | 0.0640622i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 16.5000 | − | 28.5788i | 0.609441 | − | 1.05558i | −0.381891 | − | 0.924207i | \(-0.624727\pi\) |
0.991333 | − | 0.131376i | \(-0.0419396\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 7.00000 | − | 12.1244i | 0.257848 | − | 0.446606i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.50000 | − | 2.59808i | −0.0551784 | − | 0.0955718i | 0.837117 | − | 0.547024i | \(-0.184239\pi\) |
−0.892295 | + | 0.451452i | \(0.850906\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 30.0000 | 1.10208 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −18.0000 | −0.660356 | −0.330178 | − | 0.943919i | \(-0.607109\pi\) | ||||
−0.330178 | + | 0.943919i | \(0.607109\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −11.0000 | − | 19.0526i | −0.403009 | − | 0.698032i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −4.00000 | + | 6.92820i | −0.146352 | + | 0.253490i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6.50000 | + | 11.2583i | −0.237188 | + | 0.410822i | −0.959906 | − | 0.280321i | \(-0.909559\pi\) |
0.722718 | + | 0.691143i | \(0.242893\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.00000 | + | 3.46410i | 0.0728841 | + | 0.126239i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.00000 | 0.109181 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 16.0000 | 0.581530 | 0.290765 | − | 0.956795i | \(-0.406090\pi\) | ||||
0.290765 | + | 0.956795i | \(0.406090\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.00000 | − | 3.46410i | −0.0725954 | − | 0.125739i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6.00000 | − | 10.3923i | 0.217500 | − | 0.376721i | −0.736543 | − | 0.676391i | \(-0.763543\pi\) |
0.954043 | + | 0.299670i | \(0.0968765\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.00000 | + | 1.73205i | −0.0361551 | + | 0.0626224i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 35.0000 | + | 60.6218i | 1.26378 | + | 2.18893i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 50.0000 | 1.80305 | 0.901523 | − | 0.432731i | \(-0.142450\pi\) | ||||
0.901523 | + | 0.432731i | \(0.142450\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 18.0000 | 0.648254 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 10.5000 | + | 18.1865i | 0.377659 | + | 0.654124i | 0.990721 | − | 0.135910i | \(-0.0433959\pi\) |
−0.613062 | + | 0.790034i | \(0.710063\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.00000 | + | 1.73205i | −0.0359211 | + | 0.0622171i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −30.0000 | + | 51.9615i | −1.07486 | + | 1.86171i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −15.0000 | −0.536056 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 14.0000 | 0.499681 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.50000 | + | 2.59808i | 0.0534692 | + | 0.0926114i | 0.891521 | − | 0.452979i | \(-0.149639\pi\) |
−0.838052 | + | 0.545590i | \(0.816305\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −9.00000 | + | 15.5885i | −0.320408 | + | 0.554964i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −20.0000 | + | 34.6410i | −0.710221 | + | 1.23014i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.00000 | − | 1.73205i | −0.0354663 | − | 0.0614295i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 37.0000 | 1.31061 | 0.655304 | − | 0.755366i | \(-0.272541\pi\) | ||||
0.655304 | + | 0.755366i | \(0.272541\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7.00000 | −0.247642 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.00000 | + | 6.92820i | 0.141333 | + | 0.244796i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −5.00000 | + | 8.66025i | −0.176446 | + | 0.305614i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 4.00000 | − | 6.92820i | 0.140807 | − | 0.243884i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.50000 | − | 4.33013i | −0.0878953 | − | 0.152239i | 0.818726 | − | 0.574184i | \(-0.194681\pi\) |
−0.906621 | + | 0.421945i | \(0.861347\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 16.0000 | 0.561836 | 0.280918 | − | 0.959732i | \(-0.409361\pi\) | ||||
0.280918 | + | 0.959732i | \(0.409361\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −16.0000 | −0.561144 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8.00000 | − | 13.8564i | −0.280228 | − | 0.485369i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.00000 | + | 10.3923i | −0.209913 | + | 0.363581i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.50000 | − | 2.59808i | 0.0523504 | − | 0.0906735i | −0.838663 | − | 0.544651i | \(-0.816662\pi\) |
0.891013 | + | 0.453978i | \(0.149995\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7.00000 | − | 12.1244i | −0.244005 | − | 0.422628i | 0.717847 | − | 0.696201i | \(-0.245128\pi\) |
−0.961851 | + | 0.273573i | \(0.911795\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.00000 | −0.0348155 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 32.0000 | 1.11275 | 0.556375 | − | 0.830932i | \(-0.312192\pi\) | ||||
0.556375 | + | 0.830932i | \(0.312192\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −23.0000 | − | 39.8372i | −0.798823 | − | 1.38360i | −0.920383 | − | 0.391018i | \(-0.872123\pi\) |
0.121560 | − | 0.992584i | \(-0.461210\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −10.0000 | + | 17.3205i | −0.346896 | + | 0.600842i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 10.5000 | − | 18.1865i | 0.363367 | − | 0.629371i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5.00000 | + | 8.66025i | 0.172825 | + | 0.299342i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.0000 | −0.689655 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 6.50000 | + | 11.2583i | 0.223872 | + | 0.387757i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 6.00000 | − | 10.3923i | 0.206406 | − | 0.357506i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0.500000 | − | 0.866025i | 0.0171600 | − | 0.0297219i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 16.0000 | + | 27.7128i | 0.548473 | + | 0.949983i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 46.0000 | 1.57501 | 0.787505 | − | 0.616308i | \(-0.211372\pi\) | ||||
0.787505 | + | 0.616308i | \(0.211372\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −12.0000 | −0.410391 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 21.0000 | + | 36.3731i | 0.717346 | + | 1.24248i | 0.962048 | + | 0.272882i | \(0.0879768\pi\) |
−0.244701 | + | 0.969599i | \(0.578690\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −26.0000 | + | 45.0333i | −0.887109 | + | 1.53652i | −0.0438309 | + | 0.999039i | \(0.513956\pi\) |
−0.843278 | + | 0.537478i | \(0.819377\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 15.0000 | − | 25.9808i | 0.510606 | − | 0.884395i | −0.489319 | − | 0.872105i | \(-0.662754\pi\) |
0.999924 | − | 0.0122903i | \(-0.00391222\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 10.5000 | + | 18.1865i | 0.357011 | + | 0.618361i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −16.0000 | −0.543388 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 11.0000 | 0.373149 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 35.0000 | + | 60.6218i | 1.18593 | + | 2.05409i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.00000 | + | 5.19615i | −0.101535 | + | 0.175863i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 27.0000 | − | 46.7654i | 0.911725 | − | 1.57915i | 0.100099 | − | 0.994977i | \(-0.468084\pi\) |
0.811626 | − | 0.584177i | \(-0.198583\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −4.50000 | − | 7.79423i | −0.151781 | − | 0.262893i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 16.0000 | 0.539054 | 0.269527 | − | 0.962993i | \(-0.413133\pi\) | ||||
0.269527 | + | 0.962993i | \(0.413133\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −56.0000 | −1.88455 | −0.942275 | − | 0.334840i | \(-0.891318\pi\) | ||||
−0.942275 | + | 0.334840i | \(0.891318\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 7.00000 | + | 12.1244i | 0.235302 | + | 0.407556i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −4.00000 | + | 6.92820i | −0.134307 | + | 0.232626i | −0.925332 | − | 0.379157i | \(-0.876214\pi\) |
0.791026 | + | 0.611783i | \(0.209547\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.500000 | − | 0.866025i | 0.0167506 | − | 0.0290129i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −21.0000 | − | 36.3731i | −0.702738 | − | 1.21718i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 20.0000 | 0.668526 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 20.0000 | 0.667781 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.00000 | − | 5.19615i | −0.100056 | − | 0.173301i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.00000 | − | 1.73205i | 0.0333148 | − | 0.0577030i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 5.00000 | − | 8.66025i | 0.166206 | − | 0.287877i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −8.00000 | − | 13.8564i | −0.265636 | − | 0.460094i | 0.702094 | − | 0.712084i | \(-0.252248\pi\) |
−0.967730 | + | 0.251990i | \(0.918915\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 20.0000 | 0.663358 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 16.0000 | 0.530104 | 0.265052 | − | 0.964234i | \(-0.414611\pi\) | ||||
0.265052 | + | 0.964234i | \(0.414611\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.00000 | − | 3.46410i | −0.0661903 | − | 0.114645i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −4.00000 | + | 6.92820i | −0.132236 | + | 0.229039i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −14.5000 | + | 25.1147i | −0.478311 | + | 0.828459i | −0.999691 | − | 0.0248659i | \(-0.992084\pi\) |
0.521380 | + | 0.853325i | \(0.325417\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −11.5000 | − | 19.9186i | −0.378938 | − | 0.656340i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.00000 | 0.263038 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −7.00000 | − | 12.1244i | −0.229910 | − | 0.398216i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −9.00000 | + | 15.5885i | −0.295280 | + | 0.511441i | −0.975050 | − | 0.221985i | \(-0.928746\pi\) |
0.679770 | + | 0.733426i | \(0.262080\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −7.00000 | + | 12.1244i | −0.229170 | + | 0.396934i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.500000 | − | 0.866025i | −0.0163517 | − | 0.0283221i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9.00000 | 0.294017 | 0.147009 | − | 0.989135i | \(-0.453036\pi\) | ||||
0.147009 | + | 0.989135i | \(0.453036\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −25.0000 | −0.815844 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −20.0000 | − | 34.6410i | −0.651981 | − | 1.12926i | −0.982641 | − | 0.185515i | \(-0.940605\pi\) |
0.330660 | − | 0.943750i | \(-0.392729\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −20.0000 | + | 34.6410i | −0.651290 | + | 1.12807i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 27.0000 | − | 46.7654i | 0.877382 | − | 1.51967i | 0.0231788 | − | 0.999731i | \(-0.492621\pi\) |
0.854203 | − | 0.519939i | \(-0.174045\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −25.0000 | − | 43.3013i | −0.811534 | − | 1.40562i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 18.0000 | 0.583690 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 50.0000 | 1.61966 | 0.809829 | − | 0.586665i | \(-0.199560\pi\) | ||||
0.809829 | + | 0.586665i | \(0.199560\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.50000 | + | 2.59808i | 0.0485389 | + | 0.0840718i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.50000 | − | 2.59808i | 0.0484881 | − | 0.0839839i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.5000 | − | 23.3827i | 0.435484 | − | 0.754280i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 18.0000 | + | 31.1769i | 0.580042 | + | 1.00466i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 12.0000 | 0.386294 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 14.0000 | 0.450210 | 0.225105 | − | 0.974335i | \(-0.427728\pi\) | ||||
0.225105 | + | 0.974335i | \(0.427728\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.00000 | + | 5.19615i | 0.0963739 | + | 0.166924i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.00000 | + | 1.73205i | −0.0320915 | + | 0.0555842i | −0.881625 | − | 0.471950i | \(-0.843550\pi\) |
0.849534 | + | 0.527535i | \(0.176883\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.50000 | − | 4.33013i | 0.0800641 | − | 0.138675i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 27.0000 | + | 46.7654i | 0.863807 | + | 1.49616i | 0.868227 | + | 0.496167i | \(0.165259\pi\) |
−0.00442082 | + | 0.999990i | \(0.501407\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.00000 | −0.127841 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 22.0000 | 0.702406 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 26.5000 | + | 45.8993i | 0.845219 | + | 1.46396i | 0.885431 | + | 0.464771i | \(0.153863\pi\) |
−0.0402124 | + | 0.999191i | \(0.512803\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9.00000 | + | 15.5885i | −0.286764 | + | 0.496690i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.00000 | + | 6.92820i | −0.127193 | + | 0.220304i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −6.00000 | − | 10.3923i | −0.190596 | − | 0.330122i | 0.754852 | − | 0.655895i | \(-0.227709\pi\) |
−0.945448 | + | 0.325773i | \(0.894375\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 20.0000 | 0.634681 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 22.0000 | 0.697447 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.50000 | + | 2.59808i | 0.0475055 | + | 0.0822819i | 0.888800 | − | 0.458295i | \(-0.151540\pi\) |
−0.841295 | + | 0.540576i | \(0.818206\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 20.0000 | − | 34.6410i | 0.632772 | − | 1.09599i |
(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 | 980.2.i.e.961.1 | 2 | ||
7.2 | even | 3 | 980.2.a.f.1.1 | yes | 1 | ||
7.3 | odd | 6 | 980.2.i.g.361.1 | 2 | |||
7.4 | even | 3 | inner | 980.2.i.e.361.1 | 2 | ||
7.5 | odd | 6 | 980.2.a.d.1.1 | ✓ | 1 | ||
7.6 | odd | 2 | 980.2.i.g.961.1 | 2 | |||
21.2 | odd | 6 | 8820.2.a.v.1.1 | 1 | |||
21.5 | even | 6 | 8820.2.a.i.1.1 | 1 | |||
28.19 | even | 6 | 3920.2.a.z.1.1 | 1 | |||
28.23 | odd | 6 | 3920.2.a.n.1.1 | 1 | |||
35.2 | odd | 12 | 4900.2.e.k.2549.1 | 2 | |||
35.9 | even | 6 | 4900.2.a.h.1.1 | 1 | |||
35.12 | even | 12 | 4900.2.e.j.2549.2 | 2 | |||
35.19 | odd | 6 | 4900.2.a.o.1.1 | 1 | |||
35.23 | odd | 12 | 4900.2.e.k.2549.2 | 2 | |||
35.33 | even | 12 | 4900.2.e.j.2549.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
980.2.a.d.1.1 | ✓ | 1 | 7.5 | odd | 6 | ||
980.2.a.f.1.1 | yes | 1 | 7.2 | even | 3 | ||
980.2.i.e.361.1 | 2 | 7.4 | even | 3 | inner | ||
980.2.i.e.961.1 | 2 | 1.1 | even | 1 | trivial | ||
980.2.i.g.361.1 | 2 | 7.3 | odd | 6 | |||
980.2.i.g.961.1 | 2 | 7.6 | odd | 2 | |||
3920.2.a.n.1.1 | 1 | 28.23 | odd | 6 | |||
3920.2.a.z.1.1 | 1 | 28.19 | even | 6 | |||
4900.2.a.h.1.1 | 1 | 35.9 | even | 6 | |||
4900.2.a.o.1.1 | 1 | 35.19 | odd | 6 | |||
4900.2.e.j.2549.1 | 2 | 35.33 | even | 12 | |||
4900.2.e.j.2549.2 | 2 | 35.12 | even | 12 | |||
4900.2.e.k.2549.1 | 2 | 35.2 | odd | 12 | |||
4900.2.e.k.2549.2 | 2 | 35.23 | odd | 12 | |||
8820.2.a.i.1.1 | 1 | 21.5 | even | 6 | |||
8820.2.a.v.1.1 | 1 | 21.2 | odd | 6 |