Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1728,3,Mod(127,1728)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1728, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1728.127");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1728 = 2^{6} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1728.o (of order \(6\), 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: | \(47.0845896815\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.121550625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} - 4x^{6} - 9x^{5} + 23x^{4} + 18x^{3} - 16x^{2} + 8x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3^{6} \) |
Twist minimal: | no (minimal twist has level 144) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 127.1 | ||
Root | \(2.25820 - 0.369600i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1728.127 |
Dual form | 1728.3.o.d.1279.1 |
$q$-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 \(\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(703\) | \(1217\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.31174 | − | 5.73610i | −0.662348 | − | 1.14722i | −0.979997 | − | 0.199011i | \(-0.936227\pi\) |
0.317650 | − | 0.948208i | \(-0.397106\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −8.46808 | − | 4.88905i | −1.20973 | − | 0.698436i | −0.247027 | − | 0.969009i | \(-0.579454\pi\) |
−0.962700 | + | 0.270573i | \(0.912787\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 10.0623 | + | 5.80948i | 0.914755 | + | 0.528134i | 0.881958 | − | 0.471328i | \(-0.156225\pi\) |
0.0327970 | + | 0.999462i | \(0.489559\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 8.93521 | + | 15.4762i | 0.687324 | + | 1.19048i | 0.972700 | + | 0.232065i | \(0.0745481\pi\) |
−0.285376 | + | 0.958416i | \(0.592119\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.37652 | −0.139796 | −0.0698978 | − | 0.997554i | \(-0.522267\pi\) | ||||
−0.0698978 | + | 0.997554i | \(0.522267\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 14.0337i | 0.738614i | 0.929308 | + | 0.369307i | \(0.120405\pi\) | ||||
−0.929308 | + | 0.369307i | \(0.879595\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 35.9635 | − | 20.7636i | 1.56363 | − | 0.902763i | 0.566747 | − | 0.823892i | \(-0.308202\pi\) |
0.996885 | − | 0.0788718i | \(-0.0251318\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −9.43521 | + | 16.3423i | −0.377409 | + | 0.653691i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.68826 | + | 9.85236i | −0.196147 | + | 0.339737i | −0.947276 | − | 0.320419i | \(-0.896176\pi\) |
0.751129 | + | 0.660156i | \(0.229510\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −18.0334 | + | 10.4116i | −0.581723 | + | 0.335858i | −0.761818 | − | 0.647791i | \(-0.775693\pi\) |
0.180095 | + | 0.983649i | \(0.442360\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 64.7650i | 1.85043i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −35.7409 | −0.965969 | −0.482984 | − | 0.875629i | \(-0.660447\pi\) | ||||
−0.482984 | + | 0.875629i | \(0.660447\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.62957 | + | 4.55456i | 0.0641359 | + | 0.111087i | 0.896310 | − | 0.443427i | \(-0.146238\pi\) |
−0.832174 | + | 0.554514i | \(0.812904\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 54.4939 | + | 31.4621i | 1.26730 | + | 0.731676i | 0.974476 | − | 0.224490i | \(-0.0720716\pi\) |
0.292824 | + | 0.956166i | \(0.405405\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.28568 | − | 2.47434i | −0.0911848 | − | 0.0526456i | 0.453714 | − | 0.891147i | \(-0.350099\pi\) |
−0.544899 | + | 0.838502i | \(0.683432\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 23.3056 | + | 40.3666i | 0.475625 | + | 0.823807i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 75.7409 | 1.42907 | 0.714536 | − | 0.699598i | \(-0.246638\pi\) | ||||
0.714536 | + | 0.699598i | \(0.246638\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 76.9578i | − | 1.39923i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 50.3115 | − | 29.0474i | 0.852738 | − | 0.492328i | −0.00883587 | − | 0.999961i | \(-0.502813\pi\) |
0.861574 | + | 0.507633i | \(0.169479\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.93521 | + | 10.2801i | −0.0972986 | + | 0.168526i | −0.910566 | − | 0.413365i | \(-0.864354\pi\) |
0.813267 | + | 0.581891i | \(0.197687\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 59.1822 | − | 102.507i | 0.910495 | − | 1.57702i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 20.6216 | − | 11.9059i | 0.307785 | − | 0.177700i | −0.338150 | − | 0.941092i | \(-0.609801\pi\) |
0.645935 | + | 0.763393i | \(0.276468\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 46.4758i | − | 0.654589i | −0.944922 | − | 0.327294i | \(-0.893863\pi\) | ||
0.944922 | − | 0.327294i | \(-0.106137\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −104.352 | −1.42948 | −0.714741 | − | 0.699390i | \(-0.753455\pi\) | ||||
−0.714741 | + | 0.699390i | \(0.753455\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −56.8056 | − | 98.3903i | −0.737736 | − | 1.27780i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −18.0334 | − | 10.4116i | −0.228271 | − | 0.131792i | 0.381503 | − | 0.924368i | \(-0.375407\pi\) |
−0.609774 | + | 0.792575i | \(0.708740\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −24.4103 | − | 14.0933i | −0.294100 | − | 0.169799i | 0.345689 | − | 0.938349i | \(-0.387645\pi\) |
−0.639789 | + | 0.768550i | \(0.720978\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.87043 | + | 13.6320i | 0.0925932 | + | 0.160376i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −73.0122 | −0.820362 | −0.410181 | − | 0.912004i | \(-0.634534\pi\) | ||||
−0.410181 | + | 0.912004i | \(0.634534\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 174.739i | − | 1.92021i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 80.4984 | − | 46.4758i | 0.847352 | − | 0.489219i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 71.1113 | − | 123.168i | 0.733106 | − | 1.26978i | −0.222443 | − | 0.974946i | \(-0.571403\pi\) |
0.955549 | − | 0.294831i | \(-0.0952634\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.6761 | − | 23.6876i | 0.135407 | − | 0.234531i | −0.790346 | − | 0.612661i | \(-0.790099\pi\) |
0.925753 | + | 0.378130i | \(0.123433\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 127.021 | − | 73.3358i | 1.23322 | − | 0.711998i | 0.265517 | − | 0.964106i | \(-0.414457\pi\) |
0.967699 | + | 0.252108i | \(0.0811240\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 192.573i | − | 1.79975i | −0.436146 | − | 0.899876i | \(-0.643657\pi\) | ||
0.436146 | − | 0.899876i | \(-0.356343\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.259148 | −0.00237750 | −0.00118875 | − | 0.999999i | \(-0.500378\pi\) | ||||
−0.00118875 | + | 0.999999i | \(0.500378\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 99.4291 | + | 172.216i | 0.879904 | + | 1.52404i | 0.851446 | + | 0.524443i | \(0.175726\pi\) |
0.0284580 | + | 0.999595i | \(0.490940\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −238.204 | − | 137.527i | −2.07134 | − | 1.19589i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 20.1246 | + | 11.6190i | 0.169114 | + | 0.0976382i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.00000 | + | 12.1244i | 0.0578512 | + | 0.100201i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −40.5991 | −0.324793 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 72.2477i | − | 0.568879i | −0.958694 | − | 0.284440i | \(-0.908192\pi\) | ||
0.958694 | − | 0.284440i | \(-0.0918075\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 159.693 | − | 92.1988i | 1.21903 | − | 0.703808i | 0.254320 | − | 0.967120i | \(-0.418148\pi\) |
0.964711 | + | 0.263312i | \(0.0848149\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 68.6113 | − | 118.838i | 0.515874 | − | 0.893520i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 69.8765 | − | 121.030i | 0.510048 | − | 0.883428i | −0.489885 | − | 0.871787i | \(-0.662961\pi\) |
0.999932 | − | 0.0116411i | \(-0.00370557\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 151.722 | − | 87.5967i | 1.09153 | − | 0.630192i | 0.157543 | − | 0.987512i | \(-0.449643\pi\) |
0.933982 | + | 0.357320i | \(0.116309\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 207.636i | 1.45200i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 75.3521 | 0.519670 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 95.5343 | + | 165.470i | 0.641170 | + | 1.11054i | 0.985172 | + | 0.171570i | \(0.0548839\pi\) |
−0.344002 | + | 0.938969i | \(0.611783\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.27360 | + | 3.62206i | 0.0415470 | + | 0.0239872i | 0.520630 | − | 0.853783i | \(-0.325697\pi\) |
−0.479083 | + | 0.877770i | \(0.659031\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 119.444 | + | 68.9609i | 0.770606 | + | 0.444909i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 36.0648 | + | 62.4660i | 0.229712 | + | 0.397873i | 0.957723 | − | 0.287693i | \(-0.0928882\pi\) |
−0.728011 | + | 0.685566i | \(0.759555\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −406.056 | −2.52209 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 112.269i | − | 0.688769i | −0.938829 | − | 0.344384i | \(-0.888088\pi\) | ||
0.938829 | − | 0.344384i | \(-0.111912\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −15.8389 | + | 9.14461i | −0.0948439 | + | 0.0547581i | −0.546672 | − | 0.837347i | \(-0.684105\pi\) |
0.451828 | + | 0.892105i | \(0.350772\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −75.1761 | + | 130.209i | −0.444829 | + | 0.770466i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −146.652 | + | 254.008i | −0.847698 | + | 1.46826i | 0.0355603 | + | 0.999368i | \(0.488678\pi\) |
−0.883258 | + | 0.468888i | \(0.844655\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 159.796 | − | 92.2585i | 0.913122 | − | 0.527191i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 92.9516i | − | 0.519283i | −0.965705 | − | 0.259641i | \(-0.916396\pi\) | ||
0.965705 | − | 0.259641i | \(-0.0836043\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −128.445 | −0.709642 | −0.354821 | − | 0.934934i | \(-0.615458\pi\) | ||||
−0.354821 | + | 0.934934i | \(0.615458\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 118.364 | + | 205.013i | 0.639807 | + | 1.10818i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −23.9133 | − | 13.8064i | −0.127879 | − | 0.0738308i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 260.316 | + | 150.294i | 1.36291 | + | 0.786877i | 0.990011 | − | 0.140994i | \(-0.0450297\pi\) |
0.372901 | + | 0.927871i | \(0.378363\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 19.6296 | + | 33.9994i | 0.101708 | + | 0.176163i | 0.912388 | − | 0.409326i | \(-0.134236\pi\) |
−0.810681 | + | 0.585489i | \(0.800903\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −94.7530 | −0.480980 | −0.240490 | − | 0.970652i | \(-0.577308\pi\) | ||||
−0.240490 | + | 0.970652i | \(0.577308\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 111.360i | 0.559598i | 0.960059 | + | 0.279799i | \(0.0902679\pi\) | ||||
−0.960059 | + | 0.279799i | \(0.909732\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 96.3374 | − | 55.6204i | 0.474568 | − | 0.273992i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 17.4169 | − | 30.1670i | 0.0849606 | − | 0.147156i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −81.5282 | + | 141.211i | −0.390087 | + | 0.675651i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −102.714 | + | 59.3021i | −0.486797 | + | 0.281053i | −0.723245 | − | 0.690592i | \(-0.757350\pi\) |
0.236447 | + | 0.971644i | \(0.424017\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 416.777i | − | 1.93850i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 203.611 | 0.938301 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −21.2348 | − | 36.7797i | −0.0960849 | − | 0.166424i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 21.0153 | + | 12.1332i | 0.0942389 | + | 0.0544089i | 0.546379 | − | 0.837538i | \(-0.316006\pi\) |
−0.452140 | + | 0.891947i | \(0.649339\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 10.0623 | + | 5.80948i | 0.0443273 | + | 0.0255924i | 0.522000 | − | 0.852946i | \(-0.325186\pi\) |
−0.477673 | + | 0.878538i | \(0.658519\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.06479 | − | 15.7007i | −0.0395842 | − | 0.0685619i | 0.845555 | − | 0.533889i | \(-0.179270\pi\) |
−0.885139 | + | 0.465327i | \(0.845937\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 219.785 | 0.943283 | 0.471642 | − | 0.881790i | \(-0.343662\pi\) | ||||
0.471642 | + | 0.881790i | \(0.343662\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 32.7775i | 0.139479i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 139.568 | − | 80.5799i | 0.583968 | − | 0.337154i | −0.178740 | − | 0.983896i | \(-0.557202\pi\) |
0.762709 | + | 0.646742i | \(0.223869\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 84.5930 | − | 146.519i | 0.351008 | − | 0.607964i | −0.635418 | − | 0.772168i | \(-0.719172\pi\) |
0.986426 | + | 0.164204i | \(0.0525056\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 154.364 | − | 267.367i | 0.630058 | − | 1.09129i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −217.188 | + | 125.394i | −0.879305 | + | 0.507667i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 219.255i | 0.873524i | 0.899577 | + | 0.436762i | \(0.143875\pi\) | ||||
−0.899577 | + | 0.436762i | \(0.856125\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 482.502 | 1.90712 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −88.7348 | − | 153.693i | −0.345271 | − | 0.598028i | 0.640132 | − | 0.768265i | \(-0.278880\pi\) |
−0.985403 | + | 0.170238i | \(0.945546\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 302.657 | + | 174.739i | 1.16856 | + | 0.674667i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 59.0700 | + | 34.1041i | 0.224601 | + | 0.129673i | 0.608079 | − | 0.793877i | \(-0.291940\pi\) |
−0.383478 | + | 0.923550i | \(0.625274\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −250.834 | − | 434.457i | −0.946543 | − | 1.63946i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −77.7652 | −0.289090 | −0.144545 | − | 0.989498i | \(-0.546172\pi\) | ||||
−0.144545 | + | 0.989498i | \(0.546172\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 447.259i | − | 1.65040i | −0.564840 | − | 0.825201i | \(-0.691062\pi\) | ||
0.564840 | − | 0.825201i | \(-0.308938\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −189.880 | + | 109.627i | −0.690473 | + | 0.398645i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −84.0282 | + | 145.541i | −0.303351 | + | 0.525419i | −0.976893 | − | 0.213730i | \(-0.931439\pi\) |
0.673542 | + | 0.739149i | \(0.264772\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 103.170 | − | 178.696i | 0.367153 | − | 0.635927i | −0.621966 | − | 0.783044i | \(-0.713666\pi\) |
0.989119 | + | 0.147117i | \(0.0469992\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 172.653 | − | 99.6815i | 0.610083 | − | 0.352231i | −0.162915 | − | 0.986640i | \(-0.552090\pi\) |
0.772998 | + | 0.634409i | \(0.218756\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 51.4245i | − | 0.179179i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −283.352 | −0.980457 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 28.5953 | + | 49.5285i | 0.0975948 | + | 0.169039i | 0.910689 | − | 0.413094i | \(-0.135552\pi\) |
−0.813094 | + | 0.582133i | \(0.802218\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −333.237 | − | 192.395i | −1.12962 | − | 0.652185i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 642.684 | + | 371.054i | 2.14944 | + | 1.24098i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −307.639 | − | 532.847i | −1.02206 | − | 1.77026i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 78.6235 | 0.257782 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 276.775i | 0.901549i | 0.892638 | + | 0.450774i | \(0.148852\pi\) | ||||
−0.892638 | + | 0.450774i | \(0.851148\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −21.4284 | + | 12.3717i | −0.0689017 | + | 0.0397804i | −0.534055 | − | 0.845450i | \(-0.679333\pi\) |
0.465153 | + | 0.885230i | \(0.345999\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 32.4070 | − | 56.1306i | 0.103537 | − | 0.179331i | −0.809603 | − | 0.586978i | \(-0.800317\pi\) |
0.913139 | + | 0.407647i | \(0.133651\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 227.300 | − | 393.694i | 0.717033 | − | 1.24194i | −0.245137 | − | 0.969488i | \(-0.578833\pi\) |
0.962170 | − | 0.272450i | \(-0.0878338\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −114.474 | + | 66.0916i | −0.358853 | + | 0.207184i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 33.3513i | − | 0.103255i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −337.223 | −1.03761 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 24.1944 | + | 41.9059i | 0.0735391 | + | 0.127373i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 236.009 | + | 136.260i | 0.713019 | + | 0.411661i | 0.812178 | − | 0.583410i | \(-0.198282\pi\) |
−0.0991592 | + | 0.995072i | \(0.531615\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −136.587 | − | 78.8583i | −0.407721 | − | 0.235398i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 246.945 | + | 427.721i | 0.732775 | + | 1.26920i | 0.955693 | + | 0.294366i | \(0.0951085\pi\) |
−0.222918 | + | 0.974837i | \(0.571558\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −241.944 | −0.709512 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 23.3572i | 0.0680967i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −450.196 | + | 259.921i | −1.29740 | + | 0.749051i | −0.979954 | − | 0.199226i | \(-0.936157\pi\) |
−0.317442 | + | 0.948278i | \(0.602824\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −120.639 | + | 208.954i | −0.345672 | + | 0.598721i | −0.985476 | − | 0.169817i | \(-0.945682\pi\) |
0.639804 | + | 0.768538i | \(0.279016\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 100.463 | − | 174.008i | 0.284599 | − | 0.492940i | −0.687913 | − | 0.725793i | \(-0.741473\pi\) |
0.972512 | + | 0.232853i | \(0.0748063\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −266.590 | + | 153.916i | −0.750957 | + | 0.433565i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 159.654i | − | 0.444719i | −0.974965 | − | 0.222360i | \(-0.928624\pi\) | ||
0.974965 | − | 0.222360i | \(-0.0713759\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 164.056 | 0.454450 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 345.587 | + | 598.574i | 0.946813 | + | 1.63993i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 320.690 | + | 185.150i | 0.873815 | + | 0.504497i | 0.868614 | − | 0.495489i | \(-0.165011\pi\) |
0.00520064 | + | 0.999986i | \(0.498345\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −641.380 | − | 370.301i | −1.72879 | − | 0.998116i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 163.194 | + | 282.661i | 0.437518 | + | 0.757804i | 0.997497 | − | 0.0707027i | \(-0.0225242\pi\) |
−0.559979 | + | 0.828507i | \(0.689191\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −203.303 | −0.539266 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 348.114i | − | 0.918506i | −0.888305 | − | 0.459253i | \(-0.848117\pi\) | ||
0.888305 | − | 0.459253i | \(-0.151883\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 202.550 | − | 116.942i | 0.528851 | − | 0.305332i | −0.211697 | − | 0.977335i | \(-0.567899\pi\) |
0.740548 | + | 0.672003i | \(0.234566\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −376.251 | + | 651.685i | −0.977275 | + | 1.69269i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 218.806 | − | 378.982i | 0.562482 | − | 0.974248i | −0.434797 | − | 0.900529i | \(-0.643180\pi\) |
0.997279 | − | 0.0737194i | \(-0.0234869\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −85.4682 | + | 49.3451i | −0.218589 | + | 0.126202i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 137.922i | 0.349169i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 324.259 | 0.816774 | 0.408387 | − | 0.912809i | \(-0.366091\pi\) | ||||
0.408387 | + | 0.912809i | \(0.366091\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −197.087 | − | 341.364i | −0.491488 | − | 0.851283i | 0.508463 | − | 0.861084i | \(-0.330214\pi\) |
−0.999952 | + | 0.00980052i | \(0.996880\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −322.265 | − | 186.060i | −0.799664 | − | 0.461686i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −359.635 | − | 207.636i | −0.883625 | − | 0.510161i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.1479 | + | 24.5048i | 0.0345914 | + | 0.0599140i | 0.882803 | − | 0.469744i | \(-0.155654\pi\) |
−0.848211 | + | 0.529658i | \(0.822320\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −568.056 | −1.37544 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 186.693i | 0.449863i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 280.441 | − | 161.913i | 0.669310 | − | 0.386426i | −0.126505 | − | 0.991966i | \(-0.540376\pi\) |
0.795815 | + | 0.605540i | \(0.207043\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −215.676 | + | 373.562i | −0.512295 | + | 0.887320i | 0.487604 | + | 0.873065i | \(0.337871\pi\) |
−0.999898 | + | 0.0142554i | \(0.995462\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 22.4230 | − | 38.8378i | 0.0527600 | − | 0.0913831i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 100.520 | − | 58.0351i | 0.235409 | − | 0.135914i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 345.557i | 0.801757i | 0.916131 | + | 0.400879i | \(0.131295\pi\) | ||||
−0.916131 | + | 0.400879i | \(0.868705\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 369.907 | 0.854289 | 0.427144 | − | 0.904183i | \(-0.359520\pi\) | ||||
0.427144 | + | 0.904183i | \(0.359520\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 291.389 | + | 504.700i | 0.666793 | + | 1.15492i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −358.332 | − | 206.883i | −0.816245 | − | 0.471259i | 0.0328748 | − | 0.999459i | \(-0.489534\pi\) |
−0.849120 | + | 0.528200i | \(0.822867\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −467.339 | − | 269.818i | −1.05494 | − | 0.609070i | −0.130912 | − | 0.991394i | \(-0.541791\pi\) |
−0.924029 | + | 0.382323i | \(0.875124\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 241.797 | + | 418.805i | 0.543365 | + | 0.941135i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 325.056 | 0.723956 | 0.361978 | − | 0.932187i | \(-0.382101\pi\) | ||||
0.361978 | + | 0.932187i | \(0.382101\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 61.1058i | 0.135490i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1002.32 | + | 578.689i | −2.20290 | + | 1.27184i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −309.075 | + | 535.333i | −0.676312 | + | 1.17141i | 0.299771 | + | 0.954011i | \(0.403090\pi\) |
−0.976083 | + | 0.217396i | \(0.930244\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 424.992 | − | 736.107i | 0.921891 | − | 1.59676i | 0.125404 | − | 0.992106i | \(-0.459977\pi\) |
0.796487 | − | 0.604656i | \(-0.206689\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 706.453 | − | 407.871i | 1.52582 | − | 0.880930i | 0.526285 | − | 0.850309i | \(-0.323585\pi\) |
0.999531 | − | 0.0306215i | \(-0.00974865\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 378.909i | − | 0.811368i | −0.914013 | − | 0.405684i | \(-0.867033\pi\) | ||
0.914013 | − | 0.405684i | \(-0.132967\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −232.834 | −0.496447 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 365.556 | + | 633.162i | 0.772846 | + | 1.33861i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −229.342 | − | 132.411i | −0.482825 | − | 0.278759i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −297.958 | − | 172.026i | −0.622041 | − | 0.359136i | 0.155622 | − | 0.987817i | \(-0.450262\pi\) |
−0.777663 | + | 0.628681i | \(0.783595\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −319.352 | − | 553.134i | −0.663934 | − | 1.14997i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −942.008 | −1.94228 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 587.595i | 1.20656i | 0.797529 | + | 0.603281i | \(0.206140\pi\) | ||||
−0.797529 | + | 0.603281i | \(0.793860\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 430.072 | − | 248.302i | 0.875909 | − | 0.505707i | 0.00660193 | − | 0.999978i | \(-0.497899\pi\) |
0.869307 | + | 0.494272i | \(0.164565\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 13.5183 | − | 23.4144i | 0.0274205 | − | 0.0474937i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −227.223 | + | 393.561i | −0.457188 | + | 0.791873i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 30.1869 | − | 17.4284i | 0.0604948 | − | 0.0349267i | −0.469448 | − | 0.882960i | \(-0.655547\pi\) |
0.529942 | + | 0.848034i | \(0.322214\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 630.866i | 1.25421i | 0.778936 | + | 0.627104i | \(0.215760\pi\) | ||||
−0.778936 | + | 0.627104i | \(0.784240\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −181.166 | −0.358745 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −41.0282 | − | 71.0629i | −0.0806055 | − | 0.139613i | 0.822905 | − | 0.568179i | \(-0.192352\pi\) |
−0.903510 | + | 0.428567i | \(0.859019\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 883.663 | + | 510.183i | 1.72928 | + | 0.998401i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −841.322 | − | 485.738i | −1.63364 | − | 0.943180i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −28.7492 | − | 49.7952i | −0.0556078 | − | 0.0963156i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −562.797 | −1.08023 | −0.540113 | − | 0.841593i | \(-0.681618\pi\) | ||||
−0.540113 | + | 0.841593i | \(0.681618\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 909.721i | 1.73943i | 0.493555 | + | 0.869714i | \(0.335697\pi\) | ||||
−0.493555 | + | 0.869714i | \(0.664303\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 42.8568 | − | 24.7434i | 0.0813223 | − | 0.0469514i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 597.751 | − | 1035.33i | 1.12996 | − | 1.95715i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −46.9916 | + | 81.3918i | −0.0881644 | + | 0.152705i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1104.62 | + | 637.753i | −2.06471 | + | 1.19206i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 541.574i | 1.00478i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −468.259 | −0.865544 | −0.432772 | − | 0.901503i | \(-0.642464\pi\) | ||||
−0.432772 | + | 0.901503i | \(0.642464\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.858229 | + | 1.48650i | 0.00157473 | + | 0.00272752i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −271.063 | − | 156.498i | −0.495544 | − | 0.286102i | 0.231328 | − | 0.972876i | \(-0.425693\pi\) |
−0.726872 | + | 0.686773i | \(0.759026\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −138.265 | − | 79.8271i | −0.250934 | − | 0.144877i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 101.806 | + | 176.333i | 0.184097 | + | 0.318865i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 382.841 | 0.687328 | 0.343664 | − | 0.939093i | \(-0.388332\pi\) | ||||
0.343664 | + | 0.939093i | \(0.388332\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1124.48i | 2.01160i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −518.767 | + | 299.510i | −0.921434 | + | 0.531990i | −0.884092 | − | 0.467313i | \(-0.845222\pi\) |
−0.0373414 | + | 0.999303i | \(0.511889\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 658.566 | − | 1140.67i | 1.16560 | − | 2.01889i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 422.087 | − | 731.076i | 0.741805 | − | 1.28484i | −0.209868 | − | 0.977730i | \(-0.567303\pi\) |
0.951673 | − | 0.307114i | \(-0.0993632\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −672.354 | + | 388.184i | −1.17750 | + | 0.679832i | −0.955436 | − | 0.295200i | \(-0.904614\pi\) |
−0.222067 | + | 0.975031i | \(0.571281\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 783.634i | 1.36284i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −487.316 | −0.844568 | −0.422284 | − | 0.906464i | \(-0.638771\pi\) | ||||
−0.422284 | + | 0.906464i | \(0.638771\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 137.806 | + | 238.686i | 0.237187 | + | 0.410820i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 762.128 | + | 440.015i | 1.30725 | + | 0.754742i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 487.463 | + | 281.437i | 0.830432 | + | 0.479450i | 0.854001 | − | 0.520272i | \(-0.174170\pi\) |
−0.0235687 | + | 0.999722i | \(0.507503\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −146.113 | − | 253.075i | −0.248069 | − | 0.429669i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 316.915 | 0.534426 | 0.267213 | − | 0.963637i | \(-0.413897\pi\) | ||||
0.267213 | + | 0.963637i | \(0.413897\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 153.916i | − | 0.258682i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 76.5870 | − | 44.2175i | 0.127858 | − | 0.0738189i | −0.434707 | − | 0.900572i | \(-0.643148\pi\) |
0.562565 | + | 0.826753i | \(0.309815\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 55.9085 | − | 96.8364i | 0.0930258 | − | 0.161125i | −0.815757 | − | 0.578395i | \(-0.803679\pi\) |
0.908783 | + | 0.417269i | \(0.137013\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 46.3643 | − | 80.3054i | 0.0766353 | − | 0.132736i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 596.058 | − | 344.134i | 0.981973 | − | 0.566942i | 0.0791078 | − | 0.996866i | \(-0.474793\pi\) |
0.902865 | + | 0.429924i | \(0.141460\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 88.4351i | − | 0.144738i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1021.67 | 1.66667 | 0.833334 | − | 0.552770i | \(-0.186429\pi\) | ||||
0.833334 | + | 0.552770i | \(0.186429\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −381.884 | − | 661.443i | −0.618937 | − | 1.07203i | −0.989680 | − | 0.143295i | \(-0.954230\pi\) |
0.370743 | − | 0.928735i | \(-0.379103\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 661.382 | + | 381.849i | 1.06847 | + | 0.616880i | 0.927763 | − | 0.373171i | \(-0.121730\pi\) |
0.140706 | + | 0.990051i | \(0.455063\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 618.273 | + | 356.960i | 0.992413 | + | 0.572970i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 370.334 | + | 641.437i | 0.592534 | + | 1.02630i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 84.9390 | 0.135038 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 166.586i | 0.264002i | 0.991250 | + | 0.132001i | \(0.0421403\pi\) | ||||
−0.991250 | + | 0.132001i | \(0.957860\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −414.420 | + | 239.265i | −0.652629 | + | 0.376796i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −416.482 | + | 721.367i | −0.653817 | + | 1.13245i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 102.136 | − | 176.904i | 0.159338 | − | 0.275982i | −0.775292 | − | 0.631603i | \(-0.782397\pi\) |
0.934630 | + | 0.355621i | \(0.115731\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −826.974 | + | 477.454i | −1.28612 | + | 0.742541i | −0.977960 | − | 0.208794i | \(-0.933046\pi\) |
−0.308159 | + | 0.951335i | \(0.599713\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 424.736i | 0.656470i | 0.944596 | + | 0.328235i | \(0.106454\pi\) | ||||
−0.944596 | + | 0.328235i | \(0.893546\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 675.000 | 1.04006 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 307.178 | + | 532.047i | 0.470410 | + | 0.814774i | 0.999427 | − | 0.0338373i | \(-0.0107728\pi\) |
−0.529018 | + | 0.848611i | \(0.677439\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1057.72 | − | 610.677i | −1.61484 | − | 0.932331i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 843.930 | + | 487.243i | 1.28062 | + | 0.739367i | 0.976962 | − | 0.213413i | \(-0.0684580\pi\) |
0.303660 | + | 0.952780i | \(0.401791\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −274.380 | − | 475.241i | −0.415099 | − | 0.718972i | 0.580340 | − | 0.814374i | \(-0.302920\pi\) |
−0.995439 | + | 0.0954020i | \(0.969586\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −908.890 | −1.36675 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 472.434i | 0.708297i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −119.444 | + | 68.9609i | −0.178009 | + | 0.102773i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 186.992 | − | 323.879i | 0.277848 | − | 0.481247i | −0.693002 | − | 0.720936i | \(-0.743712\pi\) |
0.970850 | + | 0.239689i | \(0.0770456\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 120.972 | − | 209.529i | 0.178688 | − | 0.309497i | −0.762743 | − | 0.646701i | \(-0.776148\pi\) |
0.941431 | + | 0.337205i | \(0.109481\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1204.35 | + | 695.333i | −1.77372 | + | 1.02405i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 524.358i | 0.767728i | 0.923390 | + | 0.383864i | \(0.125407\pi\) | ||||
−0.923390 | + | 0.383864i | \(0.874593\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −925.651 | −1.35132 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 676.761 | + | 1172.18i | 0.982236 | + | 1.70128i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 306.568 | + | 176.997i | 0.443658 | + | 0.256146i | 0.705148 | − | 0.709060i | \(-0.250880\pi\) |
−0.261490 | + | 0.965206i | \(0.584214\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1004.93 | − | 580.195i | −1.44594 | − | 0.834813i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.24925 | − | 10.8240i | −0.00896592 | − | 0.0155294i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −621.287 | −0.886286 | −0.443143 | − | 0.896451i | \(-0.646137\pi\) | ||||
−0.443143 | + | 0.896451i | \(0.646137\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 501.575i | − | 0.713478i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −231.620 | + | 133.726i | −0.327610 | + | 0.189146i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 393.992 | − | 682.413i | 0.555700 | − | 0.962501i | −0.442148 | − | 0.896942i | \(-0.645783\pi\) |
0.997849 | − | 0.0655594i | \(-0.0208832\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −432.364 | + | 748.876i | −0.606400 | + | 1.05032i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1191.02 | − | 687.635i | 1.66576 | − | 0.961727i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 1248.82i | − | 1.73689i | −0.495785 | − | 0.868445i | \(-0.665119\pi\) | ||
0.495785 | − | 0.868445i | \(-0.334881\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1434.17 | −1.98914 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −107.340 | − | 185.918i | −0.148055 | − | 0.256439i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −634.487 | − | 366.321i | −0.872746 | − | 0.503880i | −0.00448649 | − | 0.999990i | \(-0.501428\pi\) |
−0.868260 | + | 0.496110i | \(0.834761\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −129.506 | − | 74.7704i | −0.177163 | − | 0.102285i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −182.361 | − | 315.858i | −0.248787 | − | 0.430911i | 0.714403 | − | 0.699735i | \(-0.246698\pi\) |
−0.963189 | + | 0.268824i | \(0.913365\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 276.668 | 0.375397 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1162.07i | 1.57248i | 0.617918 | + | 0.786242i | \(0.287976\pi\) | ||||
−0.617918 | + | 0.786242i | \(0.712024\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 156.711 | − | 90.4773i | 0.210917 | − | 0.121773i | −0.390821 | − | 0.920467i | \(-0.627809\pi\) |
0.601737 | + | 0.798694i | \(0.294475\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 632.769 | − | 1095.99i | 0.849354 | − | 1.47113i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −941.502 | + | 1630.73i | −1.25701 | + | 2.17721i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 152.903 | − | 88.2786i | 0.203599 | − | 0.117548i | −0.394734 | − | 0.918795i | \(-0.629163\pi\) |
0.598333 | + | 0.801247i | \(0.295830\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 47.9813i | − | 0.0635514i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −146.665 | −0.193745 | −0.0968723 | − | 0.995297i | \(-0.530884\pi\) | ||||
−0.0968723 | + | 0.995297i | \(0.530884\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 403.405 | + | 698.717i | 0.530098 | + | 0.918157i | 0.999383 | + | 0.0351104i | \(0.0111783\pi\) |
−0.469285 | + | 0.883047i | \(0.655488\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.19448 | + | 1.26699i | 0.00287613 | + | 0.00166053i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 899.088 | + | 519.089i | 1.17221 | + | 0.676778i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −275.566 | − | 477.295i | −0.358344 | − | 0.620669i | 0.629341 | − | 0.777130i | \(-0.283325\pi\) |
−0.987684 | + | 0.156460i | \(0.949992\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 856.915 | 1.10856 | 0.554279 | − | 0.832331i | \(-0.312994\pi\) | ||||
0.554279 | + | 0.832331i | \(0.312994\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 392.942i | − | 0.507023i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −63.9171 | + | 36.9025i | −0.0820502 | + | 0.0473717i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 270.000 | − | 467.654i | 0.345711 | − | 0.598788i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 238.874 | − | 413.742i | 0.304298 | − | 0.527060i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −466.532 | + | 269.352i | −0.592798 | + | 0.342252i | −0.766203 | − | 0.642598i | \(-0.777856\pi\) |
0.173405 | + | 0.984851i | \(0.444523\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 1944.46i | − | 2.45823i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −212.130 | −0.267503 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −674.153 | − | 1167.67i | −0.845863 | − | 1.46508i | −0.884869 | − | 0.465840i | \(-0.845752\pi\) |
0.0390058 | − | 0.999239i | \(-0.487581\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 10.1850 | + | 5.88033i | 0.0127472 | + | 0.00735962i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1050.02 | − | 606.231i | −1.30763 | − | 0.754958i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1344.75 | + | 2329.18i | 1.67050 | + | 2.89339i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1163.88 | −1.43867 | −0.719334 | − | 0.694664i | \(-0.755553\pi\) | ||||
−0.719334 | + | 0.694664i | \(0.755553\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 627.878i | − | 0.774202i | −0.922037 | − | 0.387101i | \(-0.873476\pi\) | ||
0.922037 | − | 0.387101i | \(-0.126524\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −643.988 | + | 371.806i | −0.790169 | + | 0.456204i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −441.528 | + | 764.749i | −0.540426 | + | 0.936046i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −32.1822 | + | 55.7411i | −0.0391987 | + | 0.0678942i | −0.884959 | − | 0.465669i | \(-0.845814\pi\) |
0.845760 | + | 0.533563i | \(0.179147\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 817.183 | − | 471.801i | 0.992932 | − | 0.573269i | 0.0867825 | − | 0.996227i | \(-0.472341\pi\) |
0.906149 | + | 0.422958i | \(0.139008\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 571.482i | 0.691031i | 0.938413 | + | 0.345515i | \(0.112296\pi\) | ||||
−0.938413 | + | 0.345515i | \(0.887704\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 519.555 | 0.626725 | 0.313362 | − | 0.949634i | \(-0.398545\pi\) | ||||
0.313362 | + | 0.949634i | \(0.398545\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −55.3864 | − | 95.9321i | −0.0664903 | − | 0.115165i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 104.909 | + | 60.5691i | 0.125639 | + | 0.0725378i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1039.96 | − | 600.422i | −1.23952 | − | 0.715640i | −0.270527 | − | 0.962712i | \(-0.587198\pi\) |
−0.968997 | + | 0.247073i | \(0.920531\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 355.787 | + | 616.242i | 0.423053 | + | 0.732749i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 995.854 | 1.17853 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 136.893i | − | 0.161622i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1285.37 | + | 742.107i | −1.51042 | + | 0.872041i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −299.583 | + | 518.893i | −0.351211 | + | 0.608315i | −0.986462 | − | 0.163990i | \(-0.947563\pi\) |
0.635251 | + | 0.772306i | \(0.280897\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 345.664 | − | 598.707i | 0.403342 | − | 0.698608i | −0.590785 | − | 0.806829i | \(-0.701182\pi\) |
0.994127 | + | 0.108221i | \(0.0345153\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1215.72 | − | 701.896i | 1.41527 | − | 0.817108i | 0.419394 | − | 0.907805i | \(-0.362243\pi\) |
0.995879 | + | 0.0906967i | \(0.0289094\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 253.038i | 0.293207i | 0.989195 | + | 0.146604i | \(0.0468342\pi\) | ||||
−0.989195 | + | 0.146604i | \(0.953166\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1942.69 | 2.24588 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −120.972 | − | 209.529i | −0.139208 | − | 0.241115i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 368.517 | + | 212.763i | 0.423096 | + | 0.244275i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 343.796 | + | 198.491i | 0.392910 | + | 0.226847i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −53.9352 | − | 93.4185i | −0.0614997 | − | 0.106521i | 0.833636 | − | 0.552314i | \(-0.186255\pi\) |
−0.895136 | + | 0.445793i | \(0.852922\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 119.927 | 0.136126 | 0.0680629 | − | 0.997681i | \(-0.478318\pi\) | ||||
0.0680629 | + | 0.997681i | \(0.478318\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 306.661i | − | 0.347295i | −0.984808 | − | 0.173647i | \(-0.944445\pi\) | ||
0.984808 | − | 0.173647i | \(-0.0555553\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 680.325 | − | 392.786i | 0.766996 | − | 0.442825i | −0.0648060 | − | 0.997898i | \(-0.520643\pi\) |
0.831802 | + | 0.555073i | \(0.187310\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −353.223 | + | 611.799i | −0.397326 | + | 0.688188i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 34.7241 | − | 60.1438i | 0.0388847 | − | 0.0673503i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −533.179 | + | 307.831i | −0.595731 | + | 0.343946i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 236.896i | − | 0.263510i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −180.000 | −0.199778 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 425.377 | + | 736.774i | 0.470029 | + | 0.814115i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1055.14 | + | 609.182i | 1.16332 | + | 0.671646i | 0.952098 | − | 0.305792i | \(-0.0989211\pi\) |
0.211226 | + | 0.977437i | \(0.432254\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 760.824 | + | 439.262i | 0.835152 | + | 0.482175i | 0.855614 | − | 0.517615i | \(-0.173180\pi\) |
−0.0204612 | + | 0.999791i | \(0.506513\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −163.749 | − | 283.622i | −0.179353 | − | 0.310648i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1803.06 | −1.96626 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 1036.67i | − | 1.12804i | −0.825760 | − | 0.564022i | \(-0.809253\pi\) | ||
0.825760 | − | 0.564022i | \(-0.190747\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 719.271 | − | 415.271i | 0.779275 | − | 0.449915i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 337.223 | − | 584.087i | 0.364565 | − | 0.631445i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 124.911 | − | 216.352i | 0.134457 | − | 0.232887i | −0.790933 | − | 0.611903i | \(-0.790404\pi\) |
0.925390 | + | 0.379016i | \(0.123738\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −566.490 | + | 327.063i | −0.608475 | + | 0.351303i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 182.892i | 0.195607i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 190.744 | 0.203569 | 0.101784 | − | 0.994806i | \(-0.467545\pi\) | ||||
0.101784 | + | 0.994806i | \(0.467545\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −141.150 | − | 244.479i | −0.150000 | − | 0.259808i | 0.781227 | − | 0.624247i | \(-0.214594\pi\) |
−0.931227 | + | 0.364439i | \(0.881261\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 189.138 | + | 109.199i | 0.200570 | + | 0.115799i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 573.926 | + | 331.356i | 0.606046 | + | 0.349901i | 0.771416 | − | 0.636331i | \(-0.219549\pi\) |
−0.165370 | + | 0.986232i | \(0.552882\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −932.409 | − | 1614.98i | −0.982517 | − | 1.70177i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1166.70 | −1.22424 | −0.612119 | − | 0.790765i | \(-0.709683\pi\) | ||||
−0.612119 | + | 0.790765i | \(0.709683\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 1990.93i | − | 2.08475i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1183.44 | + | 683.260i | −1.23404 | + | 0.712471i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −263.697 | + | 456.737i | −0.274399 | + | 0.475273i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 130.016 | − | 225.194i | 0.134732 | − | 0.233362i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1010.52 | − | 583.422i | 1.04500 | − | 0.603332i | 0.123756 | − | 0.992313i | \(-0.460506\pi\) |
0.921246 | + | 0.388981i | \(0.127173\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 1481.20i | − | 1.52544i | −0.646728 | − | 0.762721i | \(-0.723863\pi\) | ||
0.646728 | − | 0.762721i | \(-0.276137\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1713.06 | −1.76060 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −592.779 | − | 1026.72i | −0.606734 | − | 1.05089i | −0.991775 | − | 0.127994i | \(-0.959146\pi\) |
0.385041 | − | 0.922899i | \(-0.374187\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −734.671 | − | 424.163i | −0.750430 | − | 0.433261i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −56.0882 | − | 32.3825i | −0.0570581 | − | 0.0329425i | 0.471200 | − | 0.882027i | \(-0.343821\pi\) |
−0.528258 | + | 0.849084i | \(0.677154\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 313.797 | + | 543.513i | 0.318576 | + | 0.551790i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2613.06 | 2.64212 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 1394.27i | − | 1.40694i | −0.710727 | − | 0.703468i | \(-0.751634\pi\) | ||
0.710727 | − | 0.703468i | \(-0.248366\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 638.772 | − | 368.795i | 0.641982 | − | 0.370649i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −487.271 | + | 843.977i | −0.488737 | + | 0.846517i | −0.999916 | − | 0.0129572i | \(-0.995875\pi\) |
0.511179 | + | 0.859474i | \(0.329209\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1728.3.o.d.127.1 | 8 | ||
3.2 | odd | 2 | 576.3.o.e.511.3 | 8 | |||
4.3 | odd | 2 | inner | 1728.3.o.d.127.2 | 8 | ||
8.3 | odd | 2 | 432.3.o.c.127.4 | 8 | |||
8.5 | even | 2 | 432.3.o.c.127.3 | 8 | |||
9.4 | even | 3 | inner | 1728.3.o.d.1279.2 | 8 | ||
9.5 | odd | 6 | 576.3.o.e.319.2 | 8 | |||
12.11 | even | 2 | 576.3.o.e.511.2 | 8 | |||
24.5 | odd | 2 | 144.3.o.b.79.2 | yes | 8 | ||
24.11 | even | 2 | 144.3.o.b.79.3 | yes | 8 | ||
36.23 | even | 6 | 576.3.o.e.319.3 | 8 | |||
36.31 | odd | 6 | inner | 1728.3.o.d.1279.1 | 8 | ||
72.5 | odd | 6 | 144.3.o.b.31.3 | yes | 8 | ||
72.11 | even | 6 | 1296.3.g.h.1135.3 | 4 | |||
72.13 | even | 6 | 432.3.o.c.415.4 | 8 | |||
72.29 | odd | 6 | 1296.3.g.h.1135.4 | 4 | |||
72.43 | odd | 6 | 1296.3.g.d.1135.1 | 4 | |||
72.59 | even | 6 | 144.3.o.b.31.2 | ✓ | 8 | ||
72.61 | even | 6 | 1296.3.g.d.1135.2 | 4 | |||
72.67 | odd | 6 | 432.3.o.c.415.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
144.3.o.b.31.2 | ✓ | 8 | 72.59 | even | 6 | ||
144.3.o.b.31.3 | yes | 8 | 72.5 | odd | 6 | ||
144.3.o.b.79.2 | yes | 8 | 24.5 | odd | 2 | ||
144.3.o.b.79.3 | yes | 8 | 24.11 | even | 2 | ||
432.3.o.c.127.3 | 8 | 8.5 | even | 2 | |||
432.3.o.c.127.4 | 8 | 8.3 | odd | 2 | |||
432.3.o.c.415.3 | 8 | 72.67 | odd | 6 | |||
432.3.o.c.415.4 | 8 | 72.13 | even | 6 | |||
576.3.o.e.319.2 | 8 | 9.5 | odd | 6 | |||
576.3.o.e.319.3 | 8 | 36.23 | even | 6 | |||
576.3.o.e.511.2 | 8 | 12.11 | even | 2 | |||
576.3.o.e.511.3 | 8 | 3.2 | odd | 2 | |||
1296.3.g.d.1135.1 | 4 | 72.43 | odd | 6 | |||
1296.3.g.d.1135.2 | 4 | 72.61 | even | 6 | |||
1296.3.g.h.1135.3 | 4 | 72.11 | even | 6 | |||
1296.3.g.h.1135.4 | 4 | 72.29 | odd | 6 | |||
1728.3.o.d.127.1 | 8 | 1.1 | even | 1 | trivial | ||
1728.3.o.d.127.2 | 8 | 4.3 | odd | 2 | inner | ||
1728.3.o.d.1279.1 | 8 | 36.31 | odd | 6 | inner | ||
1728.3.o.d.1279.2 | 8 | 9.4 | even | 3 | inner |