Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1134,2,Mod(865,1134)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1134, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1134.865");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1134 = 2 \cdot 3^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1134.e (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: | \(9.05503558921\) |
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: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 378) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 919.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1134.919 |
Dual form | 1134.2.e.m.865.1 |
$q$-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 \(\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(407\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.500000 | + | 2.59808i | −0.188982 | + | 0.981981i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.00000 | − | 5.19615i | 0.904534 | − | 1.56670i | 0.0829925 | − | 0.996550i | \(-0.473552\pi\) |
0.821541 | − | 0.570149i | \(-0.193114\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.50000 | + | 4.33013i | −0.693375 | + | 1.20096i | 0.277350 | + | 0.960769i | \(0.410544\pi\) |
−0.970725 | + | 0.240192i | \(0.922790\pi\) | |||||||
\(14\) | −0.500000 | + | 2.59808i | −0.133631 | + | 0.694365i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.00000 | + | 5.19615i | 0.727607 | + | 1.26025i | 0.957892 | + | 0.287129i | \(0.0927008\pi\) |
−0.230285 | + | 0.973123i | \(0.573966\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.00000 | − | 3.46410i | 0.458831 | − | 0.794719i | −0.540068 | − | 0.841621i | \(-0.681602\pi\) |
0.998899 | + | 0.0469020i | \(0.0149348\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.00000 | − | 5.19615i | 0.639602 | − | 1.10782i | ||||
\(23\) | 3.00000 | + | 5.19615i | 0.625543 | + | 1.08347i | 0.988436 | + | 0.151642i | \(0.0484560\pi\) |
−0.362892 | + | 0.931831i | \(0.618211\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.50000 | − | 4.33013i | 0.500000 | − | 0.866025i | ||||
\(26\) | −2.50000 | + | 4.33013i | −0.490290 | + | 0.849208i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.500000 | + | 2.59808i | −0.0944911 | + | 0.490990i | ||||
\(29\) | 3.00000 | + | 5.19615i | 0.557086 | + | 0.964901i | 0.997738 | + | 0.0672232i | \(0.0214140\pi\) |
−0.440652 | + | 0.897678i | \(0.645253\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.00000 | −0.179605 | −0.0898027 | − | 0.995960i | \(-0.528624\pi\) | ||||
−0.0898027 | + | 0.995960i | \(0.528624\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.00000 | + | 5.19615i | 0.514496 | + | 0.891133i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.500000 | − | 0.866025i | 0.0821995 | − | 0.142374i | −0.821995 | − | 0.569495i | \(-0.807139\pi\) |
0.904194 | + | 0.427121i | \(0.140472\pi\) | |||||||
\(38\) | 2.00000 | − | 3.46410i | 0.324443 | − | 0.561951i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.00000 | + | 5.19615i | −0.468521 | + | 0.811503i | −0.999353 | − | 0.0359748i | \(-0.988546\pi\) |
0.530831 | + | 0.847477i | \(0.321880\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.500000 | + | 0.866025i | 0.0762493 | + | 0.132068i | 0.901629 | − | 0.432511i | \(-0.142372\pi\) |
−0.825380 | + | 0.564578i | \(0.809039\pi\) | |||||||
\(44\) | 3.00000 | − | 5.19615i | 0.452267 | − | 0.783349i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.00000 | + | 5.19615i | 0.442326 | + | 0.766131i | ||||
\(47\) | 6.00000 | 0.875190 | 0.437595 | − | 0.899172i | \(-0.355830\pi\) | ||||
0.437595 | + | 0.899172i | \(0.355830\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.50000 | − | 2.59808i | −0.928571 | − | 0.371154i | ||||
\(50\) | 2.50000 | − | 4.33013i | 0.353553 | − | 0.612372i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.50000 | + | 4.33013i | −0.346688 | + | 0.600481i | ||||
\(53\) | −3.00000 | − | 5.19615i | −0.412082 | − | 0.713746i | 0.583036 | − | 0.812447i | \(-0.301865\pi\) |
−0.995117 | + | 0.0987002i | \(0.968532\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.500000 | + | 2.59808i | −0.0668153 | + | 0.347183i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3.00000 | + | 5.19615i | 0.393919 | + | 0.682288i | ||||
\(59\) | 6.00000 | 0.781133 | 0.390567 | − | 0.920575i | \(-0.372279\pi\) | ||||
0.390567 | + | 0.920575i | \(0.372279\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.00000 | −0.128037 | −0.0640184 | − | 0.997949i | \(-0.520392\pi\) | ||||
−0.0640184 | + | 0.997949i | \(0.520392\pi\) | |||||||
\(62\) | −1.00000 | −0.127000 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.00000 | −0.122169 | −0.0610847 | − | 0.998133i | \(-0.519456\pi\) | ||||
−0.0610847 | + | 0.998133i | \(0.519456\pi\) | |||||||
\(68\) | 3.00000 | + | 5.19615i | 0.363803 | + | 0.630126i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.0000 | −1.42414 | −0.712069 | − | 0.702109i | \(-0.752242\pi\) | ||||
−0.712069 | + | 0.702109i | \(0.752242\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.00000 | − | 1.73205i | −0.117041 | − | 0.202721i | 0.801553 | − | 0.597924i | \(-0.204008\pi\) |
−0.918594 | + | 0.395203i | \(0.870674\pi\) | |||||||
\(74\) | 0.500000 | − | 0.866025i | 0.0581238 | − | 0.100673i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.00000 | − | 3.46410i | 0.229416 | − | 0.397360i | ||||
\(77\) | 12.0000 | + | 10.3923i | 1.36753 | + | 1.18431i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.00000 | −0.112509 | −0.0562544 | − | 0.998416i | \(-0.517916\pi\) | ||||
−0.0562544 | + | 0.998416i | \(0.517916\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −3.00000 | + | 5.19615i | −0.331295 | + | 0.573819i | ||||
\(83\) | 3.00000 | + | 5.19615i | 0.329293 | + | 0.570352i | 0.982372 | − | 0.186938i | \(-0.0598564\pi\) |
−0.653079 | + | 0.757290i | \(0.726523\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0.500000 | + | 0.866025i | 0.0539164 | + | 0.0933859i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.00000 | − | 5.19615i | 0.319801 | − | 0.553912i | ||||
\(89\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −10.0000 | − | 8.66025i | −1.04828 | − | 0.907841i | ||||
\(92\) | 3.00000 | + | 5.19615i | 0.312772 | + | 0.541736i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 6.00000 | 0.618853 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.50000 | − | 14.7224i | −0.863044 | − | 1.49484i | −0.868976 | − | 0.494854i | \(-0.835222\pi\) |
0.00593185 | − | 0.999982i | \(-0.498112\pi\) | |||||||
\(98\) | −6.50000 | − | 2.59808i | −0.656599 | − | 0.262445i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.50000 | − | 4.33013i | 0.250000 | − | 0.433013i | ||||
\(101\) | 6.00000 | − | 10.3923i | 0.597022 | − | 1.03407i | −0.396236 | − | 0.918149i | \(-0.629684\pi\) |
0.993258 | − | 0.115924i | \(-0.0369830\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.50000 | + | 16.4545i | 0.936063 | + | 1.62131i | 0.772728 | + | 0.634738i | \(0.218892\pi\) |
0.163335 | + | 0.986571i | \(0.447775\pi\) | |||||||
\(104\) | −2.50000 | + | 4.33013i | −0.245145 | + | 0.424604i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.00000 | − | 5.19615i | −0.291386 | − | 0.504695i | ||||
\(107\) | 9.00000 | − | 15.5885i | 0.870063 | − | 1.50699i | 0.00813215 | − | 0.999967i | \(-0.497411\pi\) |
0.861931 | − | 0.507026i | \(-0.169255\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.50000 | − | 4.33013i | −0.239457 | − | 0.414751i | 0.721102 | − | 0.692829i | \(-0.243636\pi\) |
−0.960558 | + | 0.278078i | \(0.910303\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.500000 | + | 2.59808i | −0.0472456 | + | 0.245495i | ||||
\(113\) | 6.00000 | − | 10.3923i | 0.564433 | − | 0.977626i | −0.432670 | − | 0.901553i | \(-0.642428\pi\) |
0.997102 | − | 0.0760733i | \(-0.0242383\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 3.00000 | + | 5.19615i | 0.278543 | + | 0.482451i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 6.00000 | 0.552345 | ||||||||
\(119\) | −15.0000 | + | 5.19615i | −1.37505 | + | 0.476331i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −12.5000 | − | 21.6506i | −1.13636 | − | 1.96824i | ||||
\(122\) | −1.00000 | −0.0905357 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.00000 | −0.0898027 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −13.0000 | −1.15356 | −0.576782 | − | 0.816898i | \(-0.695692\pi\) | ||||
−0.576782 | + | 0.816898i | \(0.695692\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.00000 | − | 10.3923i | −0.524222 | − | 0.907980i | −0.999602 | − | 0.0281993i | \(-0.991023\pi\) |
0.475380 | − | 0.879781i | \(-0.342311\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.00000 | + | 6.92820i | 0.693688 | + | 0.600751i | ||||
\(134\) | −1.00000 | −0.0863868 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.00000 | + | 5.19615i | 0.257248 | + | 0.445566i | ||||
\(137\) | −3.00000 | + | 5.19615i | −0.256307 | + | 0.443937i | −0.965250 | − | 0.261329i | \(-0.915839\pi\) |
0.708942 | + | 0.705266i | \(0.249173\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.50000 | − | 6.06218i | 0.296866 | − | 0.514187i | −0.678551 | − | 0.734553i | \(-0.737392\pi\) |
0.975417 | + | 0.220366i | \(0.0707252\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −12.0000 | −1.00702 | ||||||||
\(143\) | 15.0000 | + | 25.9808i | 1.25436 | + | 2.17262i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −1.00000 | − | 1.73205i | −0.0827606 | − | 0.143346i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.500000 | − | 0.866025i | 0.0410997 | − | 0.0711868i | ||||
\(149\) | −6.00000 | − | 10.3923i | −0.491539 | − | 0.851371i | 0.508413 | − | 0.861113i | \(-0.330232\pi\) |
−0.999953 | + | 0.00974235i | \(0.996899\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.50000 | + | 14.7224i | −0.691720 | + | 1.19809i | 0.279554 | + | 0.960130i | \(0.409814\pi\) |
−0.971274 | + | 0.237964i | \(0.923520\pi\) | |||||||
\(152\) | 2.00000 | − | 3.46410i | 0.162221 | − | 0.280976i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 12.0000 | + | 10.3923i | 0.966988 | + | 0.837436i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −22.0000 | −1.75579 | −0.877896 | − | 0.478852i | \(-0.841053\pi\) | ||||
−0.877896 | + | 0.478852i | \(0.841053\pi\) | |||||||
\(158\) | −1.00000 | −0.0795557 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −15.0000 | + | 5.19615i | −1.18217 | + | 0.409514i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.50000 | + | 9.52628i | −0.430793 | + | 0.746156i | −0.996942 | − | 0.0781474i | \(-0.975100\pi\) |
0.566149 | + | 0.824303i | \(0.308433\pi\) | |||||||
\(164\) | −3.00000 | + | 5.19615i | −0.234261 | + | 0.405751i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.00000 | + | 5.19615i | 0.232845 | + | 0.403300i | ||||
\(167\) | −9.00000 | + | 15.5885i | −0.696441 | + | 1.20627i | 0.273252 | + | 0.961943i | \(0.411901\pi\) |
−0.969693 | + | 0.244328i | \(0.921432\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.00000 | − | 10.3923i | −0.461538 | − | 0.799408i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.500000 | + | 0.866025i | 0.0381246 | + | 0.0660338i | ||||
\(173\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 10.0000 | + | 8.66025i | 0.755929 | + | 0.654654i | ||||
\(176\) | 3.00000 | − | 5.19615i | 0.226134 | − | 0.391675i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.0000 | −0.743294 | −0.371647 | − | 0.928374i | \(-0.621207\pi\) | ||||
−0.371647 | + | 0.928374i | \(0.621207\pi\) | |||||||
\(182\) | −10.0000 | − | 8.66025i | −0.741249 | − | 0.641941i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3.00000 | + | 5.19615i | 0.221163 | + | 0.383065i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 36.0000 | 2.63258 | ||||||||
\(188\) | 6.00000 | 0.437595 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.00000 | −0.0719816 | −0.0359908 | − | 0.999352i | \(-0.511459\pi\) | ||||
−0.0359908 | + | 0.999352i | \(0.511459\pi\) | |||||||
\(194\) | −8.50000 | − | 14.7224i | −0.610264 | − | 1.05701i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.50000 | − | 2.59808i | −0.464286 | − | 0.185577i | ||||
\(197\) | 12.0000 | 0.854965 | 0.427482 | − | 0.904024i | \(-0.359401\pi\) | ||||
0.427482 | + | 0.904024i | \(0.359401\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.50000 | − | 9.52628i | −0.389885 | − | 0.675300i | 0.602549 | − | 0.798082i | \(-0.294152\pi\) |
−0.992434 | + | 0.122782i | \(0.960818\pi\) | |||||||
\(200\) | 2.50000 | − | 4.33013i | 0.176777 | − | 0.306186i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 6.00000 | − | 10.3923i | 0.422159 | − | 0.731200i | ||||
\(203\) | −15.0000 | + | 5.19615i | −1.05279 | + | 0.364698i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 9.50000 | + | 16.4545i | 0.661896 | + | 1.14644i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.50000 | + | 4.33013i | −0.173344 | + | 0.300240i | ||||
\(209\) | −12.0000 | − | 20.7846i | −0.830057 | − | 1.43770i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.50000 | − | 11.2583i | 0.447478 | − | 0.775055i | −0.550743 | − | 0.834675i | \(-0.685655\pi\) |
0.998221 | + | 0.0596196i | \(0.0189888\pi\) | |||||||
\(212\) | −3.00000 | − | 5.19615i | −0.206041 | − | 0.356873i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 9.00000 | − | 15.5885i | 0.615227 | − | 1.06561i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.500000 | − | 2.59808i | 0.0339422 | − | 0.176369i | ||||
\(218\) | −2.50000 | − | 4.33013i | −0.169321 | − | 0.293273i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −30.0000 | −2.01802 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.00000 | − | 6.92820i | −0.267860 | − | 0.463947i | 0.700449 | − | 0.713702i | \(-0.252983\pi\) |
−0.968309 | + | 0.249756i | \(0.919650\pi\) | |||||||
\(224\) | −0.500000 | + | 2.59808i | −0.0334077 | + | 0.173591i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 6.00000 | − | 10.3923i | 0.399114 | − | 0.691286i | ||||
\(227\) | −3.00000 | + | 5.19615i | −0.199117 | + | 0.344881i | −0.948242 | − | 0.317547i | \(-0.897141\pi\) |
0.749125 | + | 0.662428i | \(0.230474\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.50000 | − | 4.33013i | −0.165205 | − | 0.286143i | 0.771523 | − | 0.636201i | \(-0.219495\pi\) |
−0.936728 | + | 0.350058i | \(0.886162\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.00000 | + | 5.19615i | 0.196960 | + | 0.341144i | ||||
\(233\) | 12.0000 | − | 20.7846i | 0.786146 | − | 1.36165i | −0.142166 | − | 0.989843i | \(-0.545407\pi\) |
0.928312 | − | 0.371802i | \(-0.121260\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 6.00000 | 0.390567 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −15.0000 | + | 5.19615i | −0.972306 | + | 0.336817i | ||||
\(239\) | 12.0000 | − | 20.7846i | 0.776215 | − | 1.34444i | −0.157893 | − | 0.987456i | \(-0.550470\pi\) |
0.934109 | − | 0.356988i | \(-0.116196\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.50000 | + | 14.7224i | −0.547533 | + | 0.948355i | 0.450910 | + | 0.892570i | \(0.351100\pi\) |
−0.998443 | + | 0.0557856i | \(0.982234\pi\) | |||||||
\(242\) | −12.5000 | − | 21.6506i | −0.803530 | − | 1.39176i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1.00000 | −0.0640184 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 10.0000 | + | 17.3205i | 0.636285 | + | 1.10208i | ||||
\(248\) | −1.00000 | −0.0635001 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −18.0000 | −1.13615 | −0.568075 | − | 0.822977i | \(-0.692312\pi\) | ||||
−0.568075 | + | 0.822977i | \(0.692312\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 36.0000 | 2.26330 | ||||||||
\(254\) | −13.0000 | −0.815693 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −3.00000 | − | 5.19615i | −0.187135 | − | 0.324127i | 0.757159 | − | 0.653231i | \(-0.226587\pi\) |
−0.944294 | + | 0.329104i | \(0.893253\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.00000 | + | 1.73205i | 0.124274 | + | 0.107624i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −6.00000 | − | 10.3923i | −0.370681 | − | 0.642039i | ||||
\(263\) | 3.00000 | − | 5.19615i | 0.184988 | − | 0.320408i | −0.758585 | − | 0.651575i | \(-0.774109\pi\) |
0.943572 | + | 0.331166i | \(0.107442\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 8.00000 | + | 6.92820i | 0.490511 | + | 0.424795i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.00000 | −0.0610847 | ||||||||
\(269\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.50000 | − | 6.06218i | 0.212610 | − | 0.368251i | −0.739921 | − | 0.672694i | \(-0.765137\pi\) |
0.952531 | + | 0.304443i | \(0.0984703\pi\) | |||||||
\(272\) | 3.00000 | + | 5.19615i | 0.181902 | + | 0.315063i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3.00000 | + | 5.19615i | −0.181237 | + | 0.313911i | ||||
\(275\) | −15.0000 | − | 25.9808i | −0.904534 | − | 1.56670i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.50000 | + | 14.7224i | −0.510716 | + | 0.884585i | 0.489207 | + | 0.872167i | \(0.337286\pi\) |
−0.999923 | + | 0.0124177i | \(0.996047\pi\) | |||||||
\(278\) | 3.50000 | − | 6.06218i | 0.209916 | − | 0.363585i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.00000 | + | 10.3923i | 0.357930 | + | 0.619953i | 0.987615 | − | 0.156898i | \(-0.0501493\pi\) |
−0.629685 | + | 0.776851i | \(0.716816\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −13.0000 | −0.772770 | −0.386385 | − | 0.922338i | \(-0.626276\pi\) | ||||
−0.386385 | + | 0.922338i | \(0.626276\pi\) | |||||||
\(284\) | −12.0000 | −0.712069 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 15.0000 | + | 25.9808i | 0.886969 | + | 1.53627i | ||||
\(287\) | −12.0000 | − | 10.3923i | −0.708338 | − | 0.613438i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.50000 | + | 16.4545i | −0.558824 | + | 0.967911i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.00000 | − | 1.73205i | −0.0585206 | − | 0.101361i | ||||
\(293\) | 9.00000 | − | 15.5885i | 0.525786 | − | 0.910687i | −0.473763 | − | 0.880652i | \(-0.657105\pi\) |
0.999549 | − | 0.0300351i | \(-0.00956192\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0.500000 | − | 0.866025i | 0.0290619 | − | 0.0503367i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −6.00000 | − | 10.3923i | −0.347571 | − | 0.602010i | ||||
\(299\) | −30.0000 | −1.73494 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.50000 | + | 0.866025i | −0.144098 | + | 0.0499169i | ||||
\(302\) | −8.50000 | + | 14.7224i | −0.489120 | + | 0.847181i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.00000 | − | 3.46410i | 0.114708 | − | 0.198680i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 17.0000 | 0.970241 | 0.485121 | − | 0.874447i | \(-0.338776\pi\) | ||||
0.485121 | + | 0.874447i | \(0.338776\pi\) | |||||||
\(308\) | 12.0000 | + | 10.3923i | 0.683763 | + | 0.592157i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.0000 | 0.680458 | 0.340229 | − | 0.940343i | \(-0.389495\pi\) | ||||
0.340229 | + | 0.940343i | \(0.389495\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −22.0000 | −1.24351 | −0.621757 | − | 0.783210i | \(-0.713581\pi\) | ||||
−0.621757 | + | 0.783210i | \(0.713581\pi\) | |||||||
\(314\) | −22.0000 | −1.24153 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.00000 | −0.0562544 | ||||||||
\(317\) | −18.0000 | −1.01098 | −0.505490 | − | 0.862832i | \(-0.668688\pi\) | ||||
−0.505490 | + | 0.862832i | \(0.668688\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 36.0000 | 2.01561 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −15.0000 | + | 5.19615i | −0.835917 | + | 0.289570i | ||||
\(323\) | 24.0000 | 1.33540 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 12.5000 | + | 21.6506i | 0.693375 | + | 1.20096i | ||||
\(326\) | −5.50000 | + | 9.52628i | −0.304617 | + | 0.527612i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −3.00000 | + | 5.19615i | −0.165647 | + | 0.286910i | ||||
\(329\) | −3.00000 | + | 15.5885i | −0.165395 | + | 0.859419i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 20.0000 | 1.09930 | 0.549650 | − | 0.835395i | \(-0.314761\pi\) | ||||
0.549650 | + | 0.835395i | \(0.314761\pi\) | |||||||
\(332\) | 3.00000 | + | 5.19615i | 0.164646 | + | 0.285176i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −9.00000 | + | 15.5885i | −0.492458 | + | 0.852962i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.00000 | + | 1.73205i | −0.0544735 | + | 0.0943508i | −0.891976 | − | 0.452082i | \(-0.850681\pi\) |
0.837503 | + | 0.546433i | \(0.184015\pi\) | |||||||
\(338\) | −6.00000 | − | 10.3923i | −0.326357 | − | 0.565267i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.00000 | + | 5.19615i | −0.162459 | + | 0.281387i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.0000 | − | 15.5885i | 0.539949 | − | 0.841698i | ||||
\(344\) | 0.500000 | + | 0.866025i | 0.0269582 | + | 0.0466930i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 24.0000 | 1.28839 | 0.644194 | − | 0.764862i | \(-0.277193\pi\) | ||||
0.644194 | + | 0.764862i | \(0.277193\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.500000 | + | 0.866025i | 0.0267644 | + | 0.0463573i | 0.879097 | − | 0.476642i | \(-0.158146\pi\) |
−0.852333 | + | 0.523000i | \(0.824813\pi\) | |||||||
\(350\) | 10.0000 | + | 8.66025i | 0.534522 | + | 0.462910i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.00000 | − | 5.19615i | 0.159901 | − | 0.276956i | ||||
\(353\) | −18.0000 | + | 31.1769i | −0.958043 | + | 1.65938i | −0.230799 | + | 0.973002i | \(0.574134\pi\) |
−0.727245 | + | 0.686378i | \(0.759200\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3.00000 | − | 5.19615i | 0.158334 | − | 0.274242i | −0.775934 | − | 0.630814i | \(-0.782721\pi\) |
0.934268 | + | 0.356572i | \(0.116054\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.50000 | + | 2.59808i | 0.0789474 | + | 0.136741i | ||||
\(362\) | −10.0000 | −0.525588 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −10.0000 | − | 8.66025i | −0.524142 | − | 0.453921i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.0000 | − | 24.2487i | 0.730794 | − | 1.26577i | −0.225750 | − | 0.974185i | \(-0.572483\pi\) |
0.956544 | − | 0.291587i | \(-0.0941834\pi\) | |||||||
\(368\) | 3.00000 | + | 5.19615i | 0.156386 | + | 0.270868i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 15.0000 | − | 5.19615i | 0.778761 | − | 0.269771i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −13.0000 | − | 22.5167i | −0.673114 | − | 1.16587i | −0.977016 | − | 0.213165i | \(-0.931623\pi\) |
0.303902 | − | 0.952703i | \(-0.401711\pi\) | |||||||
\(374\) | 36.0000 | 1.86152 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6.00000 | 0.309426 | ||||||||
\(377\) | −30.0000 | −1.54508 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.00000 | −0.0513665 | −0.0256833 | − | 0.999670i | \(-0.508176\pi\) | ||||
−0.0256833 | + | 0.999670i | \(0.508176\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.00000 | + | 5.19615i | 0.153293 | + | 0.265511i | 0.932436 | − | 0.361335i | \(-0.117679\pi\) |
−0.779143 | + | 0.626846i | \(0.784346\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.00000 | −0.0508987 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −8.50000 | − | 14.7224i | −0.431522 | − | 0.747418i | ||||
\(389\) | −6.00000 | + | 10.3923i | −0.304212 | + | 0.526911i | −0.977086 | − | 0.212847i | \(-0.931726\pi\) |
0.672874 | + | 0.739758i | \(0.265060\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −18.0000 | + | 31.1769i | −0.910299 | + | 1.57668i | ||||
\(392\) | −6.50000 | − | 2.59808i | −0.328300 | − | 0.131223i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 12.0000 | 0.604551 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.50000 | − | 11.2583i | 0.326226 | − | 0.565039i | −0.655534 | − | 0.755166i | \(-0.727556\pi\) |
0.981760 | + | 0.190126i | \(0.0608897\pi\) | |||||||
\(398\) | −5.50000 | − | 9.52628i | −0.275690 | − | 0.477509i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.50000 | − | 4.33013i | 0.125000 | − | 0.216506i | ||||
\(401\) | −3.00000 | − | 5.19615i | −0.149813 | − | 0.259483i | 0.781345 | − | 0.624099i | \(-0.214534\pi\) |
−0.931158 | + | 0.364615i | \(0.881200\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.50000 | − | 4.33013i | 0.124534 | − | 0.215699i | ||||
\(404\) | 6.00000 | − | 10.3923i | 0.298511 | − | 0.517036i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −15.0000 | + | 5.19615i | −0.744438 | + | 0.257881i | ||||
\(407\) | −3.00000 | − | 5.19615i | −0.148704 | − | 0.257564i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 29.0000 | 1.43396 | 0.716979 | − | 0.697095i | \(-0.245524\pi\) | ||||
0.716979 | + | 0.697095i | \(0.245524\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 9.50000 | + | 16.4545i | 0.468031 | + | 0.810654i | ||||
\(413\) | −3.00000 | + | 15.5885i | −0.147620 | + | 0.767058i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2.50000 | + | 4.33013i | −0.122573 | + | 0.212302i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −12.0000 | − | 20.7846i | −0.586939 | − | 1.01661i | ||||
\(419\) | −12.0000 | + | 20.7846i | −0.586238 | + | 1.01539i | 0.408481 | + | 0.912767i | \(0.366058\pi\) |
−0.994720 | + | 0.102628i | \(0.967275\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.00000 | − | 12.1244i | −0.341159 | − | 0.590905i | 0.643489 | − | 0.765455i | \(-0.277486\pi\) |
−0.984648 | + | 0.174550i | \(0.944153\pi\) | |||||||
\(422\) | 6.50000 | − | 11.2583i | 0.316415 | − | 0.548047i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3.00000 | − | 5.19615i | −0.145693 | − | 0.252347i | ||||
\(425\) | 30.0000 | 1.45521 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.500000 | − | 2.59808i | 0.0241967 | − | 0.125730i | ||||
\(428\) | 9.00000 | − | 15.5885i | 0.435031 | − | 0.753497i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9.00000 | − | 15.5885i | −0.433515 | − | 0.750870i | 0.563658 | − | 0.826008i | \(-0.309393\pi\) |
−0.997173 | + | 0.0751385i | \(0.976060\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −25.0000 | −1.20142 | −0.600712 | − | 0.799466i | \(-0.705116\pi\) | ||||
−0.600712 | + | 0.799466i | \(0.705116\pi\) | |||||||
\(434\) | 0.500000 | − | 2.59808i | 0.0240008 | − | 0.124712i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.50000 | − | 4.33013i | −0.119728 | − | 0.207375i | ||||
\(437\) | 24.0000 | 1.14808 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.00000 | 0.381819 | 0.190910 | − | 0.981608i | \(-0.438856\pi\) | ||||
0.190910 | + | 0.981608i | \(0.438856\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −30.0000 | −1.42695 | ||||||||
\(443\) | 24.0000 | 1.14027 | 0.570137 | − | 0.821549i | \(-0.306890\pi\) | ||||
0.570137 | + | 0.821549i | \(0.306890\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −4.00000 | − | 6.92820i | −0.189405 | − | 0.328060i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.500000 | + | 2.59808i | −0.0236228 | + | 0.122748i | ||||
\(449\) | 24.0000 | 1.13263 | 0.566315 | − | 0.824189i | \(-0.308369\pi\) | ||||
0.566315 | + | 0.824189i | \(0.308369\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 18.0000 | + | 31.1769i | 0.847587 | + | 1.46806i | ||||
\(452\) | 6.00000 | − | 10.3923i | 0.282216 | − | 0.488813i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −3.00000 | + | 5.19615i | −0.140797 | + | 0.243868i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −19.0000 | −0.888783 | −0.444391 | − | 0.895833i | \(-0.646580\pi\) | ||||
−0.444391 | + | 0.895833i | \(0.646580\pi\) | |||||||
\(458\) | −2.50000 | − | 4.33013i | −0.116817 | − | 0.202334i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9.00000 | + | 15.5885i | 0.419172 | + | 0.726027i | 0.995856 | − | 0.0909401i | \(-0.0289872\pi\) |
−0.576685 | + | 0.816967i | \(0.695654\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.00000 | + | 6.92820i | −0.185896 | + | 0.321981i | −0.943878 | − | 0.330294i | \(-0.892852\pi\) |
0.757982 | + | 0.652275i | \(0.226185\pi\) | |||||||
\(464\) | 3.00000 | + | 5.19615i | 0.139272 | + | 0.241225i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 12.0000 | − | 20.7846i | 0.555889 | − | 0.962828i | ||||
\(467\) | 6.00000 | − | 10.3923i | 0.277647 | − | 0.480899i | −0.693153 | − | 0.720791i | \(-0.743779\pi\) |
0.970799 | + | 0.239892i | \(0.0771121\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.500000 | − | 2.59808i | 0.0230879 | − | 0.119968i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 6.00000 | 0.276172 | ||||||||
\(473\) | 6.00000 | 0.275880 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −10.0000 | − | 17.3205i | −0.458831 | − | 0.794719i | ||||
\(476\) | −15.0000 | + | 5.19615i | −0.687524 | + | 0.238165i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 12.0000 | − | 20.7846i | 0.548867 | − | 0.950666i | ||||
\(479\) | 6.00000 | − | 10.3923i | 0.274147 | − | 0.474837i | −0.695773 | − | 0.718262i | \(-0.744938\pi\) |
0.969920 | + | 0.243426i | \(0.0782712\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.50000 | + | 4.33013i | 0.113990 | + | 0.197437i | ||||
\(482\) | −8.50000 | + | 14.7224i | −0.387164 | + | 0.670588i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −12.5000 | − | 21.6506i | −0.568182 | − | 0.984120i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 20.0000 | + | 34.6410i | 0.906287 | + | 1.56973i | 0.819181 | + | 0.573535i | \(0.194428\pi\) |
0.0871056 | + | 0.996199i | \(0.472238\pi\) | |||||||
\(488\) | −1.00000 | −0.0452679 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15.0000 | + | 25.9808i | −0.676941 | + | 1.17250i | 0.298957 | + | 0.954267i | \(0.403361\pi\) |
−0.975898 | + | 0.218229i | \(0.929972\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −18.0000 | + | 31.1769i | −0.810679 | + | 1.40414i | ||||
\(494\) | 10.0000 | + | 17.3205i | 0.449921 | + | 0.779287i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.00000 | −0.0449013 | ||||||||
\(497\) | 6.00000 | − | 31.1769i | 0.269137 | − | 1.39848i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.5000 | + | 21.6506i | 0.559577 | + | 0.969216i | 0.997532 | + | 0.0702185i | \(0.0223697\pi\) |
−0.437955 | + | 0.898997i | \(0.644297\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −18.0000 | −0.803379 | ||||||||
\(503\) | −6.00000 | −0.267527 | −0.133763 | − | 0.991013i | \(-0.542706\pi\) | ||||
−0.133763 | + | 0.991013i | \(0.542706\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 36.0000 | 1.60040 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −13.0000 | −0.576782 | ||||||||
\(509\) | 15.0000 | + | 25.9808i | 0.664863 | + | 1.15158i | 0.979322 | + | 0.202306i | \(0.0648436\pi\) |
−0.314459 | + | 0.949271i | \(0.601823\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.00000 | − | 1.73205i | 0.221187 | − | 0.0766214i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −3.00000 | − | 5.19615i | −0.132324 | − | 0.229192i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 18.0000 | − | 31.1769i | 0.791639 | − | 1.37116i | ||||
\(518\) | 2.00000 | + | 1.73205i | 0.0878750 | + | 0.0761019i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 21.0000 | + | 36.3731i | 0.920027 | + | 1.59353i | 0.799370 | + | 0.600839i | \(0.205167\pi\) |
0.120656 | + | 0.992694i | \(0.461500\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11.5000 | + | 19.9186i | −0.502860 | + | 0.870979i | 0.497135 | + | 0.867673i | \(0.334385\pi\) |
−0.999995 | + | 0.00330547i | \(0.998948\pi\) | |||||||
\(524\) | −6.00000 | − | 10.3923i | −0.262111 | − | 0.453990i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.00000 | − | 5.19615i | 0.130806 | − | 0.226563i | ||||
\(527\) | −3.00000 | − | 5.19615i | −0.130682 | − | 0.226348i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.50000 | + | 11.2583i | −0.282609 | + | 0.489493i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 8.00000 | + | 6.92820i | 0.346844 | + | 0.300376i | ||||
\(533\) | −15.0000 | − | 25.9808i | −0.649722 | − | 1.12535i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −1.00000 | −0.0431934 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −33.0000 | + | 25.9808i | −1.42141 | + | 1.11907i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.00000 | − | 8.66025i | 0.214967 | − | 0.372333i | −0.738296 | − | 0.674477i | \(-0.764369\pi\) |
0.953262 | + | 0.302144i | \(0.0977023\pi\) | |||||||
\(542\) | 3.50000 | − | 6.06218i | 0.150338 | − | 0.260393i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 3.00000 | + | 5.19615i | 0.128624 | + | 0.222783i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18.5000 | + | 32.0429i | 0.791003 | + | 1.37006i | 0.925347 | + | 0.379122i | \(0.123774\pi\) |
−0.134344 | + | 0.990935i | \(0.542893\pi\) | |||||||
\(548\) | −3.00000 | + | 5.19615i | −0.128154 | + | 0.221969i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −15.0000 | − | 25.9808i | −0.639602 | − | 1.10782i | ||||
\(551\) | 24.0000 | 1.02243 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.500000 | − | 2.59808i | 0.0212622 | − | 0.110481i | ||||
\(554\) | −8.50000 | + | 14.7224i | −0.361130 | + | 0.625496i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.50000 | − | 6.06218i | 0.148433 | − | 0.257094i | ||||
\(557\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.00000 | −0.211477 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 6.00000 | + | 10.3923i | 0.253095 | + | 0.438373i | ||||
\(563\) | 42.0000 | 1.77009 | 0.885044 | − | 0.465506i | \(-0.154128\pi\) | ||||
0.885044 | + | 0.465506i | \(0.154128\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −13.0000 | −0.546431 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −12.0000 | −0.503509 | ||||||||
\(569\) | 36.0000 | 1.50920 | 0.754599 | − | 0.656186i | \(-0.227831\pi\) | ||||
0.754599 | + | 0.656186i | \(0.227831\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16.0000 | −0.669579 | −0.334790 | − | 0.942293i | \(-0.608665\pi\) | ||||
−0.334790 | + | 0.942293i | \(0.608665\pi\) | |||||||
\(572\) | 15.0000 | + | 25.9808i | 0.627182 | + | 1.08631i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −12.0000 | − | 10.3923i | −0.500870 | − | 0.433766i | ||||
\(575\) | 30.0000 | 1.25109 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11.5000 | − | 19.9186i | −0.478751 | − | 0.829222i | 0.520952 | − | 0.853586i | \(-0.325577\pi\) |
−0.999703 | + | 0.0243645i | \(0.992244\pi\) | |||||||
\(578\) | −9.50000 | + | 16.4545i | −0.395148 | + | 0.684416i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −15.0000 | + | 5.19615i | −0.622305 | + | 0.215573i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −36.0000 | −1.49097 | ||||||||
\(584\) | −1.00000 | − | 1.73205i | −0.0413803 | − | 0.0716728i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 9.00000 | − | 15.5885i | 0.371787 | − | 0.643953i | ||||
\(587\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.00000 | + | 3.46410i | −0.0824086 | + | 0.142736i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0.500000 | − | 0.866025i | 0.0205499 | − | 0.0355934i | ||||
\(593\) | 18.0000 | − | 31.1769i | 0.739171 | − | 1.28028i | −0.213697 | − | 0.976900i | \(-0.568551\pi\) |
0.952869 | − | 0.303383i | \(-0.0981160\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −6.00000 | − | 10.3923i | −0.245770 | − | 0.425685i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −30.0000 | −1.22679 | ||||||||
\(599\) | −36.0000 | −1.47092 | −0.735460 | − | 0.677568i | \(-0.763034\pi\) | ||||
−0.735460 | + | 0.677568i | \(0.763034\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −23.5000 | − | 40.7032i | −0.958585 | − | 1.66032i | −0.725942 | − | 0.687756i | \(-0.758596\pi\) |
−0.232643 | − | 0.972562i | \(-0.574737\pi\) | |||||||
\(602\) | −2.50000 | + | 0.866025i | −0.101892 | + | 0.0352966i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −8.50000 | + | 14.7224i | −0.345860 | + | 0.599047i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.00000 | + | 13.8564i | 0.324710 | + | 0.562414i | 0.981454 | − | 0.191700i | \(-0.0614000\pi\) |
−0.656744 | + | 0.754114i | \(0.728067\pi\) | |||||||
\(608\) | 2.00000 | − | 3.46410i | 0.0811107 | − | 0.140488i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −15.0000 | + | 25.9808i | −0.606835 | + | 1.05107i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.50000 | − | 9.52628i | −0.222143 | − | 0.384763i | 0.733316 | − | 0.679888i | \(-0.237972\pi\) |
−0.955458 | + | 0.295126i | \(0.904638\pi\) | |||||||
\(614\) | 17.0000 | 0.686064 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 12.0000 | + | 10.3923i | 0.483494 | + | 0.418718i | ||||
\(617\) | −15.0000 | + | 25.9808i | −0.603877 | + | 1.04595i | 0.388351 | + | 0.921512i | \(0.373045\pi\) |
−0.992228 | + | 0.124434i | \(0.960288\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12.5000 | − | 21.6506i | 0.502417 | − | 0.870212i | −0.497579 | − | 0.867419i | \(-0.665777\pi\) |
0.999996 | − | 0.00279365i | \(-0.000889247\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 12.0000 | 0.481156 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12.5000 | − | 21.6506i | −0.500000 | − | 0.866025i | ||||
\(626\) | −22.0000 | −0.879297 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −22.0000 | −0.877896 | ||||||||
\(629\) | 6.00000 | 0.239236 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.00000 | −0.278666 | −0.139333 | − | 0.990246i | \(-0.544496\pi\) | ||||
−0.139333 | + | 0.990246i | \(0.544496\pi\) | |||||||
\(632\) | −1.00000 | −0.0397779 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −18.0000 | −0.714871 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 27.5000 | − | 21.6506i | 1.08959 | − | 0.857829i | ||||
\(638\) | 36.0000 | 1.42525 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9.00000 | − | 15.5885i | 0.355479 | − | 0.615707i | −0.631721 | − | 0.775196i | \(-0.717651\pi\) |
0.987200 | + | 0.159489i | \(0.0509845\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12.5000 | − | 21.6506i | 0.492952 | − | 0.853818i | −0.507015 | − | 0.861937i | \(-0.669251\pi\) |
0.999967 | + | 0.00811944i | \(0.00258453\pi\) | |||||||
\(644\) | −15.0000 | + | 5.19615i | −0.591083 | + | 0.204757i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 24.0000 | 0.944267 | ||||||||
\(647\) | −6.00000 | − | 10.3923i | −0.235884 | − | 0.408564i | 0.723645 | − | 0.690172i | \(-0.242465\pi\) |
−0.959529 | + | 0.281609i | \(0.909132\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 18.0000 | − | 31.1769i | 0.706562 | − | 1.22380i | ||||
\(650\) | 12.5000 | + | 21.6506i | 0.490290 | + | 0.849208i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −5.50000 | + | 9.52628i | −0.215397 | + | 0.373078i | ||||
\(653\) | −9.00000 | − | 15.5885i | −0.352197 | − | 0.610023i | 0.634437 | − | 0.772975i | \(-0.281232\pi\) |
−0.986634 | + | 0.162951i | \(0.947899\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −3.00000 | + | 5.19615i | −0.117130 | + | 0.202876i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −3.00000 | + | 15.5885i | −0.116952 | + | 0.607701i | ||||
\(659\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 50.0000 | 1.94477 | 0.972387 | − | 0.233373i | \(-0.0749763\pi\) | ||||
0.972387 | + | 0.233373i | \(0.0749763\pi\) | |||||||
\(662\) | 20.0000 | 0.777322 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3.00000 | + | 5.19615i | 0.116423 | + | 0.201650i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −18.0000 | + | 31.1769i | −0.696963 | + | 1.20717i | ||||
\(668\) | −9.00000 | + | 15.5885i | −0.348220 | + | 0.603136i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.00000 | + | 5.19615i | −0.115814 | + | 0.200595i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 17.0000 | + | 29.4449i | 0.655302 | + | 1.13502i | 0.981818 | + | 0.189824i | \(0.0607919\pi\) |
−0.326516 | + | 0.945192i | \(0.605875\pi\) | |||||||
\(674\) | −1.00000 | + | 1.73205i | −0.0385186 | + | 0.0667161i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −6.00000 | − | 10.3923i | −0.230769 | − | 0.399704i | ||||
\(677\) | −12.0000 | −0.461197 | −0.230599 | − | 0.973049i | \(-0.574068\pi\) | ||||
−0.230599 | + | 0.973049i | \(0.574068\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 42.5000 | − | 14.7224i | 1.63100 | − | 0.564995i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −3.00000 | + | 5.19615i | −0.114876 | + | 0.198971i | ||||
\(683\) | 6.00000 | + | 10.3923i | 0.229584 | + | 0.397650i | 0.957685 | − | 0.287819i | \(-0.0929302\pi\) |
−0.728101 | + | 0.685470i | \(0.759597\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 10.0000 | − | 15.5885i | 0.381802 | − | 0.595170i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0.500000 | + | 0.866025i | 0.0190623 | + | 0.0330169i | ||||
\(689\) | 30.0000 | 1.14291 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17.0000 | 0.646710 | 0.323355 | − | 0.946278i | \(-0.395189\pi\) | ||||
0.323355 | + | 0.946278i | \(0.395189\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 24.0000 | 0.911028 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −36.0000 | −1.36360 | ||||||||
\(698\) | 0.500000 | + | 0.866025i | 0.0189253 | + | 0.0327795i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 10.0000 | + | 8.66025i | 0.377964 | + | 0.327327i | ||||
\(701\) | −48.0000 | −1.81293 | −0.906467 | − | 0.422276i | \(-0.861231\pi\) | ||||
−0.906467 | + | 0.422276i | \(0.861231\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.00000 | − | 3.46410i | −0.0754314 | − | 0.130651i | ||||
\(704\) | 3.00000 | − | 5.19615i | 0.113067 | − | 0.195837i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −18.0000 | + | 31.1769i | −0.677439 | + | 1.17336i | ||||
\(707\) | 24.0000 | + | 20.7846i | 0.902613 | + | 0.781686i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 17.0000 | 0.638448 | 0.319224 | − | 0.947679i | \(-0.396578\pi\) | ||||
0.319224 | + | 0.947679i | \(0.396578\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.00000 | − | 5.19615i | −0.112351 | − | 0.194597i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 3.00000 | − | 5.19615i | 0.111959 | − | 0.193919i | ||||
\(719\) | 6.00000 | − | 10.3923i | 0.223762 | − | 0.387568i | −0.732185 | − | 0.681106i | \(-0.761499\pi\) |
0.955947 | + | 0.293538i | \(0.0948328\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −47.5000 | + | 16.4545i | −1.76899 | + | 0.612797i | ||||
\(722\) | 1.50000 | + | 2.59808i | 0.0558242 | + | 0.0966904i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −10.0000 | −0.371647 | ||||||||
\(725\) | 30.0000 | 1.11417 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.50000 | − | 4.33013i | −0.0927199 | − | 0.160596i | 0.815935 | − | 0.578144i | \(-0.196223\pi\) |
−0.908655 | + | 0.417548i | \(0.862889\pi\) | |||||||
\(728\) | −10.0000 | − | 8.66025i | −0.370625 | − | 0.320970i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.00000 | + | 5.19615i | −0.110959 | + | 0.192187i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −8.50000 | − | 14.7224i | −0.313955 | − | 0.543785i | 0.665260 | − | 0.746612i | \(-0.268321\pi\) |
−0.979215 | + | 0.202826i | \(0.934987\pi\) | |||||||
\(734\) | 14.0000 | − | 24.2487i | 0.516749 | − | 0.895036i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.00000 | + | 5.19615i | 0.110581 | + | 0.191533i | ||||
\(737\) | −3.00000 | + | 5.19615i | −0.110506 | + | 0.191403i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 24.5000 | + | 42.4352i | 0.901247 | + | 1.56101i | 0.825877 | + | 0.563850i | \(0.190680\pi\) |
0.0753699 | + | 0.997156i | \(0.475986\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 15.0000 | − | 5.19615i | 0.550667 | − | 0.190757i | ||||
\(743\) | 9.00000 | − | 15.5885i | 0.330178 | − | 0.571885i | −0.652369 | − | 0.757902i | \(-0.726225\pi\) |
0.982547 | + | 0.186017i | \(0.0595579\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −13.0000 | − | 22.5167i | −0.475964 | − | 0.824394i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 36.0000 | 1.31629 | ||||||||
\(749\) | 36.0000 | + | 31.1769i | 1.31541 | + | 1.13918i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.00000 | + | 13.8564i | 0.291924 | + | 0.505627i | 0.974265 | − | 0.225407i | \(-0.0723712\pi\) |
−0.682341 | + | 0.731034i | \(0.739038\pi\) | |||||||
\(752\) | 6.00000 | 0.218797 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −30.0000 | −1.09254 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 29.0000 | 1.05402 | 0.527011 | − | 0.849858i | \(-0.323312\pi\) | ||||
0.527011 | + | 0.849858i | \(0.323312\pi\) | |||||||
\(758\) | −1.00000 | −0.0363216 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 12.5000 | − | 4.33013i | 0.452530 | − | 0.156761i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 3.00000 | + | 5.19615i | 0.108394 | + | 0.187745i | ||||
\(767\) | −15.0000 | + | 25.9808i | −0.541619 | + | 0.938111i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5.00000 | − | 8.66025i | 0.180305 | − | 0.312297i | −0.761680 | − | 0.647954i | \(-0.775625\pi\) |
0.941984 | + | 0.335657i | \(0.108958\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.00000 | −0.0359908 | ||||||||
\(773\) | −12.0000 | − | 20.7846i | −0.431610 | − | 0.747570i | 0.565402 | − | 0.824815i | \(-0.308721\pi\) |
−0.997012 | + | 0.0772449i | \(0.975388\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.50000 | + | 4.33013i | −0.0898027 | + | 0.155543i | ||||
\(776\) | −8.50000 | − | 14.7224i | −0.305132 | − | 0.528505i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −6.00000 | + | 10.3923i | −0.215110 | + | 0.372582i | ||||
\(779\) | 12.0000 | + | 20.7846i | 0.429945 | + | 0.744686i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −36.0000 | + | 62.3538i | −1.28818 | + | 2.23120i | ||||
\(782\) | −18.0000 | + | 31.1769i | −0.643679 | + | 1.11488i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −6.50000 | − | 2.59808i | −0.232143 | − | 0.0927884i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −31.0000 | −1.10503 | −0.552515 | − | 0.833503i | \(-0.686332\pi\) | ||||
−0.552515 | + | 0.833503i | \(0.686332\pi\) | |||||||
\(788\) | 12.0000 | 0.427482 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 24.0000 | + | 20.7846i | 0.853342 | + | 0.739016i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.50000 | − | 4.33013i | 0.0887776 | − | 0.153767i | ||||
\(794\) | 6.50000 | − | 11.2583i | 0.230676 | − | 0.399543i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5.50000 | − | 9.52628i | −0.194942 | − | 0.337650i | ||||
\(797\) | −15.0000 | + | 25.9808i | −0.531327 | + | 0.920286i | 0.468004 | + | 0.883726i | \(0.344973\pi\) |
−0.999331 | + | 0.0365596i | \(0.988360\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 18.0000 | + | 31.1769i | 0.636794 | + | 1.10296i | ||||
\(800\) | 2.50000 | − | 4.33013i | 0.0883883 | − | 0.153093i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −3.00000 | − | 5.19615i | −0.105934 | − | 0.183483i | ||||
\(803\) | −12.0000 | −0.423471 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 2.50000 | − | 4.33013i | 0.0880587 | − | 0.152522i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 6.00000 | − | 10.3923i | 0.211079 | − | 0.365600i | ||||
\(809\) | −15.0000 | − | 25.9808i | −0.527372 | − | 0.913435i | −0.999491 | − | 0.0319002i | \(-0.989844\pi\) |
0.472119 | − | 0.881535i | \(-0.343489\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −16.0000 | −0.561836 | −0.280918 | − | 0.959732i | \(-0.590639\pi\) | ||||
−0.280918 | + | 0.959732i | \(0.590639\pi\) | |||||||
\(812\) | −15.0000 | + | 5.19615i | −0.526397 | + | 0.182349i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −3.00000 | − | 5.19615i | −0.105150 | − | 0.182125i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.00000 | 0.139942 | ||||||||
\(818\) | 29.0000 | 1.01396 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6.00000 | −0.209401 | −0.104701 | − | 0.994504i | \(-0.533388\pi\) | ||||
−0.104701 | + | 0.994504i | \(0.533388\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −31.0000 | −1.08059 | −0.540296 | − | 0.841475i | \(-0.681688\pi\) | ||||
−0.540296 | + | 0.841475i | \(0.681688\pi\) | |||||||
\(824\) | 9.50000 | + | 16.4545i | 0.330948 | + | 0.573219i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.00000 | + | 15.5885i | −0.104383 | + | 0.542392i | ||||
\(827\) | 12.0000 | 0.417281 | 0.208640 | − | 0.977992i | \(-0.433096\pi\) | ||||
0.208640 | + | 0.977992i | \(0.433096\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7.00000 | − | 12.1244i | −0.243120 | − | 0.421096i | 0.718481 | − | 0.695546i | \(-0.244838\pi\) |
−0.961601 | + | 0.274450i | \(0.911504\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −2.50000 | + | 4.33013i | −0.0866719 | + | 0.150120i | ||||
\(833\) | −6.00000 | − | 41.5692i | −0.207888 | − | 1.44029i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −12.0000 | − | 20.7846i | −0.415029 | − | 0.718851i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −12.0000 | + | 20.7846i | −0.414533 | + | 0.717992i | ||||
\(839\) | 9.00000 | + | 15.5885i | 0.310715 | + | 0.538173i | 0.978517 | − | 0.206165i | \(-0.0660984\pi\) |
−0.667803 | + | 0.744338i | \(0.732765\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.50000 | + | 6.06218i | −0.120690 | + | 0.209041i | ||||
\(842\) | −7.00000 | − | 12.1244i | −0.241236 | − | 0.417833i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 6.50000 | − | 11.2583i | 0.223739 | − | 0.387528i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 62.5000 | − | 21.6506i | 2.14753 | − | 0.743925i | ||||
\(848\) | −3.00000 | − | 5.19615i | −0.103020 | − | 0.178437i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 30.0000 | 1.02899 | ||||||||
\(851\) | 6.00000 | 0.205677 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 23.0000 | + | 39.8372i | 0.787505 | + | 1.36400i | 0.927491 | + | 0.373845i | \(0.121961\pi\) |
−0.139986 | + | 0.990153i | \(0.544706\pi\) | |||||||
\(854\) | 0.500000 | − | 2.59808i | 0.0171096 | − | 0.0889043i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 9.00000 | − | 15.5885i | 0.307614 | − | 0.532803i | ||||
\(857\) | −6.00000 | + | 10.3923i | −0.204956 | + | 0.354994i | −0.950119 | − | 0.311888i | \(-0.899038\pi\) |
0.745163 | + | 0.666883i | \(0.232372\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11.5000 | − | 19.9186i | −0.392375 | − | 0.679613i | 0.600387 | − | 0.799709i | \(-0.295013\pi\) |
−0.992762 | + | 0.120096i | \(0.961680\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −9.00000 | − | 15.5885i | −0.306541 | − | 0.530945i | ||||
\(863\) | 18.0000 | − | 31.1769i | 0.612727 | − | 1.06127i | −0.378052 | − | 0.925785i | \(-0.623406\pi\) |
0.990779 | − | 0.135490i | \(-0.0432609\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −25.0000 | −0.849535 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0.500000 | − | 2.59808i | 0.0169711 | − | 0.0881845i | ||||
\(869\) | −3.00000 | + | 5.19615i | −0.101768 | + | 0.176267i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.50000 | − | 4.33013i | 0.0847093 | − | 0.146721i | ||||
\(872\) | −2.50000 | − | 4.33013i | −0.0846607 | − | 0.146637i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 24.0000 | 0.811812 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.50000 | + | 11.2583i | 0.219489 | + | 0.380167i | 0.954652 | − | 0.297724i | \(-0.0962275\pi\) |
−0.735163 | + | 0.677891i | \(0.762894\pi\) | |||||||
\(878\) | 8.00000 | 0.269987 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −30.0000 | −1.01073 | −0.505363 | − | 0.862907i | \(-0.668641\pi\) | ||||
−0.505363 | + | 0.862907i | \(0.668641\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −40.0000 | −1.34611 | −0.673054 | − | 0.739594i | \(-0.735018\pi\) | ||||
−0.673054 | + | 0.739594i | \(0.735018\pi\) | |||||||
\(884\) | −30.0000 | −1.00901 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 24.0000 | 0.806296 | ||||||||
\(887\) | −9.00000 | − | 15.5885i | −0.302190 | − | 0.523409i | 0.674441 | − | 0.738328i | \(-0.264385\pi\) |
−0.976632 | + | 0.214919i | \(0.931051\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.50000 | − | 33.7750i | 0.218003 | − | 1.13278i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −4.00000 | − | 6.92820i | −0.133930 | − | 0.231973i | ||||
\(893\) | 12.0000 | − | 20.7846i | 0.401565 | − | 0.695530i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −0.500000 | + | 2.59808i | −0.0167038 | + | 0.0867956i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 24.0000 | 0.800890 | ||||||||
\(899\) | −3.00000 | − | 5.19615i | −0.100056 | − | 0.173301i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 18.0000 | − | 31.1769i | 0.599667 | − | 1.03865i | ||||
\(902\) | 18.0000 | + | 31.1769i | 0.599334 | + | 1.03808i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 6.00000 | − | 10.3923i | 0.199557 | − | 0.345643i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 18.5000 | − | 32.0429i | 0.614282 | − | 1.06397i | −0.376228 | − | 0.926527i | \(-0.622779\pi\) |
0.990510 | − | 0.137441i | \(-0.0438878\pi\) | |||||||
\(908\) | −3.00000 | + | 5.19615i | −0.0995585 | + | 0.172440i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.00000 | − | 5.19615i | −0.0993944 | − | 0.172156i | 0.812040 | − | 0.583602i | \(-0.198357\pi\) |
−0.911434 | + | 0.411446i | \(0.865024\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 36.0000 | 1.19143 | ||||||||
\(914\) | −19.0000 | −0.628464 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2.50000 | − | 4.33013i | −0.0826023 | − | 0.143071i | ||||
\(917\) | 30.0000 | − | 10.3923i | 0.990687 | − | 0.343184i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 27.5000 | − | 47.6314i | 0.907141 | − | 1.57121i | 0.0891245 | − | 0.996020i | \(-0.471593\pi\) |
0.818017 | − | 0.575194i | \(-0.195074\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 9.00000 | + | 15.5885i | 0.296399 | + | 0.513378i | ||||
\(923\) | 30.0000 | − | 51.9615i | 0.987462 | − | 1.71033i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.50000 | − | 4.33013i | −0.0821995 | − | 0.142374i | ||||
\(926\) | −4.00000 | + | 6.92820i | −0.131448 | + | 0.227675i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3.00000 | + | 5.19615i | 0.0984798 | + | 0.170572i | ||||
\(929\) | −48.0000 | −1.57483 | −0.787414 | − | 0.616424i | \(-0.788581\pi\) | ||||
−0.787414 | + | 0.616424i | \(0.788581\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −22.0000 | + | 17.3205i | −0.721021 | + | 0.567657i | ||||
\(932\) | 12.0000 | − | 20.7846i | 0.393073 | − | 0.680823i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 6.00000 | − | 10.3923i | 0.196326 | − | 0.340047i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −37.0000 | −1.20874 | −0.604369 | − | 0.796705i | \(-0.706575\pi\) | ||||
−0.604369 | + | 0.796705i | \(0.706575\pi\) | |||||||
\(938\) | 0.500000 | − | 2.59808i | 0.0163256 | − | 0.0848302i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −18.0000 | −0.586783 | −0.293392 | − | 0.955992i | \(-0.594784\pi\) | ||||
−0.293392 | + | 0.955992i | \(0.594784\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −36.0000 | −1.17232 | ||||||||
\(944\) | 6.00000 | 0.195283 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 6.00000 | 0.195077 | ||||||||
\(947\) | −18.0000 | −0.584921 | −0.292461 | − | 0.956278i | \(-0.594474\pi\) | ||||
−0.292461 | + | 0.956278i | \(0.594474\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10.0000 | 0.324614 | ||||||||
\(950\) | −10.0000 | − | 17.3205i | −0.324443 | − | 0.561951i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −15.0000 | + | 5.19615i | −0.486153 | + | 0.168408i | ||||
\(953\) | 6.00000 | 0.194359 | 0.0971795 | − | 0.995267i | \(-0.469018\pi\) | ||||
0.0971795 | + | 0.995267i | \(0.469018\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 12.0000 | − | 20.7846i | 0.388108 | − | 0.672222i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 6.00000 | − | 10.3923i | 0.193851 | − | 0.335760i | ||||
\(959\) | −12.0000 | − | 10.3923i | −0.387500 | − | 0.335585i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.0000 | −0.967742 | ||||||||
\(962\) | 2.50000 | + | 4.33013i | 0.0806032 | + | 0.139609i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −8.50000 | + | 14.7224i | −0.273767 | + | 0.474178i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −17.5000 | + | 30.3109i | −0.562762 | + | 0.974732i | 0.434492 | + | 0.900676i | \(0.356928\pi\) |
−0.997254 | + | 0.0740568i | \(0.976405\pi\) | |||||||
\(968\) | −12.5000 | − | 21.6506i | −0.401765 | − | 0.695878i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −18.0000 | + | 31.1769i | −0.577647 | + | 1.00051i | 0.418101 | + | 0.908401i | \(0.362696\pi\) |
−0.995748 | + | 0.0921142i | \(0.970638\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 14.0000 | + | 12.1244i | 0.448819 | + | 0.388689i | ||||
\(974\) | 20.0000 | + | 34.6410i | 0.640841 | + | 1.10997i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.00000 | −0.0320092 | ||||||||
\(977\) | −6.00000 | −0.191957 | −0.0959785 | − | 0.995383i | \(-0.530598\pi\) | ||||
−0.0959785 | + | 0.995383i | \(0.530598\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −15.0000 | + | 25.9808i | −0.478669 | + | 0.829079i | ||||
\(983\) | −12.0000 | + | 20.7846i | −0.382741 | + | 0.662926i | −0.991453 | − | 0.130465i | \(-0.958353\pi\) |
0.608712 | + | 0.793391i | \(0.291686\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −18.0000 | + | 31.1769i | −0.573237 | + | 0.992875i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 10.0000 | + | 17.3205i | 0.318142 | + | 0.551039i | ||||
\(989\) | −3.00000 | + | 5.19615i | −0.0953945 | + | 0.165228i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.50000 | − | 4.33013i | −0.0794151 | − | 0.137551i | 0.823583 | − | 0.567196i | \(-0.191972\pi\) |
−0.902998 | + | 0.429645i | \(0.858639\pi\) | |||||||
\(992\) | −1.00000 | −0.0317500 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 6.00000 | − | 31.1769i | 0.190308 | − | 0.988872i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −11.5000 | + | 19.9186i | −0.364209 | + | 0.630828i | −0.988649 | − | 0.150245i | \(-0.951994\pi\) |
0.624440 | + | 0.781073i | \(0.285327\pi\) | |||||||
\(998\) | 12.5000 | + | 21.6506i | 0.395681 | + | 0.685339i | ||||
\(999\) | 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 | 1134.2.e.m.919.1 | 2 | ||
3.2 | odd | 2 | 1134.2.e.c.919.1 | 2 | |||
7.4 | even | 3 | 1134.2.h.d.109.1 | 2 | |||
9.2 | odd | 6 | 1134.2.h.n.541.1 | 2 | |||
9.4 | even | 3 | 378.2.g.b.163.1 | yes | 2 | ||
9.5 | odd | 6 | 378.2.g.e.163.1 | yes | 2 | ||
9.7 | even | 3 | 1134.2.h.d.541.1 | 2 | |||
21.11 | odd | 6 | 1134.2.h.n.109.1 | 2 | |||
63.4 | even | 3 | 378.2.g.b.109.1 | ✓ | 2 | ||
63.5 | even | 6 | 2646.2.a.g.1.1 | 1 | |||
63.11 | odd | 6 | 1134.2.e.c.865.1 | 2 | |||
63.23 | odd | 6 | 2646.2.a.h.1.1 | 1 | |||
63.25 | even | 3 | inner | 1134.2.e.m.865.1 | 2 | ||
63.32 | odd | 6 | 378.2.g.e.109.1 | yes | 2 | ||
63.40 | odd | 6 | 2646.2.a.w.1.1 | 1 | |||
63.58 | even | 3 | 2646.2.a.x.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
378.2.g.b.109.1 | ✓ | 2 | 63.4 | even | 3 | ||
378.2.g.b.163.1 | yes | 2 | 9.4 | even | 3 | ||
378.2.g.e.109.1 | yes | 2 | 63.32 | odd | 6 | ||
378.2.g.e.163.1 | yes | 2 | 9.5 | odd | 6 | ||
1134.2.e.c.865.1 | 2 | 63.11 | odd | 6 | |||
1134.2.e.c.919.1 | 2 | 3.2 | odd | 2 | |||
1134.2.e.m.865.1 | 2 | 63.25 | even | 3 | inner | ||
1134.2.e.m.919.1 | 2 | 1.1 | even | 1 | trivial | ||
1134.2.h.d.109.1 | 2 | 7.4 | even | 3 | |||
1134.2.h.d.541.1 | 2 | 9.7 | even | 3 | |||
1134.2.h.n.109.1 | 2 | 21.11 | odd | 6 | |||
1134.2.h.n.541.1 | 2 | 9.2 | odd | 6 | |||
2646.2.a.g.1.1 | 1 | 63.5 | even | 6 | |||
2646.2.a.h.1.1 | 1 | 63.23 | odd | 6 | |||
2646.2.a.w.1.1 | 1 | 63.40 | odd | 6 | |||
2646.2.a.x.1.1 | 1 | 63.58 | even | 3 |