Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [672,2,Mod(575,672)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(672, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("672.575");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 672 = 2^{5} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 672.h (of order \(2\), degree \(1\), 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: | \(5.36594701583\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.40960000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 7x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 575.7 | ||
Root | \(0.437016 + 0.437016i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 672.575 |
Dual form | 672.2.h.e.575.6 |
$q$-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 \(\left(\mathbb{Z}/672\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(421\) | \(449\) | \(577\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.707107 | + | 1.58114i | 0.408248 | + | 0.912871i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 1.41421i | − | 0.632456i | −0.948683 | − | 0.316228i | \(-0.897584\pi\) | ||
0.948683 | − | 0.316228i | \(-0.102416\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.00000 | + | 2.23607i | −0.666667 | + | 0.745356i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.47214 | 1.34840 | 0.674200 | − | 0.738549i | \(-0.264489\pi\) | ||||
0.674200 | + | 0.738549i | \(0.264489\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.837722 | −0.232342 | −0.116171 | − | 0.993229i | \(-0.537062\pi\) | ||||
−0.116171 | + | 0.993229i | \(0.537062\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.23607 | − | 1.00000i | 0.577350 | − | 0.258199i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.64371i | 0.398658i | 0.979933 | + | 0.199329i | \(0.0638762\pi\) | ||||
−0.979933 | + | 0.199329i | \(0.936124\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.16228i | 1.64314i | 0.570108 | + | 0.821570i | \(0.306901\pi\) | ||||
−0.570108 | + | 0.821570i | \(0.693099\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.58114 | + | 0.707107i | −0.345033 | + | 0.154303i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.65685 | 1.17954 | 0.589768 | − | 0.807573i | \(-0.299219\pi\) | ||||
0.589768 | + | 0.807573i | \(0.299219\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.00000 | 0.600000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.94975 | − | 1.58114i | −0.952579 | − | 0.304290i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.30056i | 1.35568i | 0.735209 | + | 0.677840i | \(0.237084\pi\) | ||||
−0.735209 | + | 0.677840i | \(0.762916\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 6.32456i | − | 1.13592i | −0.823055 | − | 0.567962i | \(-0.807732\pi\) | ||
0.823055 | − | 0.567962i | \(-0.192268\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.16228 | + | 7.07107i | 0.550482 | + | 1.23091i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.41421 | 0.239046 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.32456 | −1.36855 | −0.684274 | − | 0.729225i | \(-0.739881\pi\) | ||||
−0.684274 | + | 0.729225i | \(0.739881\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.592359 | − | 1.32456i | −0.0948534 | − | 0.212099i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 1.18472i | − | 0.185022i | −0.995712 | − | 0.0925110i | \(-0.970511\pi\) | ||
0.995712 | − | 0.0925110i | \(-0.0294893\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.32456i | 0.659489i | 0.944070 | + | 0.329744i | \(0.106963\pi\) | ||||
−0.944070 | + | 0.329744i | \(0.893037\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.16228 | + | 2.82843i | 0.471405 | + | 0.421637i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.94427 | 1.30466 | 0.652328 | − | 0.757937i | \(-0.273792\pi\) | ||||
0.652328 | + | 0.757937i | \(0.273792\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.59893 | + | 1.16228i | −0.363923 | + | 0.162751i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 10.1290i | − | 1.39132i | −0.718369 | − | 0.695662i | \(-0.755111\pi\) | ||
0.718369 | − | 0.695662i | \(-0.244889\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 6.32456i | − | 0.852803i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −11.3246 | + | 5.06450i | −1.49997 | + | 0.670809i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.41421 | −0.184115 | −0.0920575 | − | 0.995754i | \(-0.529344\pi\) | ||||
−0.0920575 | + | 0.995754i | \(0.529344\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.16228 | −0.404888 | −0.202444 | − | 0.979294i | \(-0.564888\pi\) | ||||
−0.202444 | + | 0.979294i | \(0.564888\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.23607 | − | 2.00000i | −0.281718 | − | 0.251976i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.18472i | 0.146946i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.00000i | 0.244339i | 0.992509 | + | 0.122169i | \(0.0389851\pi\) | ||||
−0.992509 | + | 0.122169i | \(0.961015\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.00000 | + | 8.94427i | 0.481543 | + | 1.07676i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.18472 | 0.140600 | 0.0703001 | − | 0.997526i | \(-0.477604\pi\) | ||||
0.0703001 | + | 0.997526i | \(0.477604\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.32456 | −0.974316 | −0.487158 | − | 0.873314i | \(-0.661966\pi\) | ||||
−0.487158 | + | 0.873314i | \(0.661966\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.12132 | + | 4.74342i | 0.244949 | + | 0.547723i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.47214i | 0.509647i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.00000i | 0.450035i | 0.974355 | + | 0.225018i | \(0.0722440\pi\) | ||||
−0.974355 | + | 0.225018i | \(0.927756\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.00000 | − | 8.94427i | −0.111111 | − | 0.993808i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −10.3585 | −1.13699 | −0.568496 | − | 0.822686i | \(-0.692474\pi\) | ||||
−0.568496 | + | 0.822686i | \(0.692474\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.32456 | 0.252133 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −11.5432 | + | 5.16228i | −1.23756 | + | 0.553454i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 10.1290i | − | 1.07367i | −0.843687 | − | 0.536835i | \(-0.819620\pi\) | ||
0.843687 | − | 0.536835i | \(-0.180380\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 0.837722i | − | 0.0878172i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 10.0000 | − | 4.47214i | 1.03695 | − | 0.463739i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 10.1290 | 1.03921 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.6491 | 1.48739 | 0.743696 | − | 0.668518i | \(-0.233071\pi\) | ||||
0.743696 | + | 0.668518i | \(0.233071\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −8.94427 | + | 10.0000i | −0.898933 | + | 1.00504i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 1.41421i | − | 0.140720i | −0.997522 | − | 0.0703598i | \(-0.977585\pi\) | ||
0.997522 | − | 0.0703598i | \(-0.0224147\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 8.00000i | − | 0.788263i | −0.919054 | − | 0.394132i | \(-0.871045\pi\) | ||
0.919054 | − | 0.394132i | \(-0.128955\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.00000 | + | 2.23607i | 0.0975900 | + | 0.218218i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 18.6143 | 1.79951 | 0.899755 | − | 0.436396i | \(-0.143745\pi\) | ||||
0.899755 | + | 0.436396i | \(0.143745\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.32456 | 0.797348 | 0.398674 | − | 0.917093i | \(-0.369471\pi\) | ||||
0.398674 | + | 0.917093i | \(0.369471\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.88635 | − | 13.1623i | −0.558708 | − | 1.24931i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 15.7858i | − | 1.48501i | −0.669842 | − | 0.742504i | \(-0.733638\pi\) | ||
0.669842 | − | 0.742504i | \(-0.266362\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 8.00000i | − | 0.746004i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.67544 | − | 1.87320i | 0.154895 | − | 0.173178i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.64371 | −0.150679 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.00000 | 0.818182 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.87320 | − | 0.837722i | 0.168901 | − | 0.0755349i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 11.3137i | − | 1.01193i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 6.00000i | − | 0.532414i | −0.963916 | − | 0.266207i | \(-0.914230\pi\) | ||
0.963916 | − | 0.266207i | \(-0.0857705\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −6.83772 | + | 3.05792i | −0.602028 | + | 0.269235i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −13.1869 | −1.15215 | −0.576073 | − | 0.817398i | \(-0.695416\pi\) | ||||
−0.576073 | + | 0.817398i | \(0.695416\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.16228 | −0.621048 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.23607 | + | 7.00000i | −0.192450 | + | 0.602464i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 17.8885i | − | 1.52832i | −0.645026 | − | 0.764161i | \(-0.723153\pi\) | ||
0.645026 | − | 0.764161i | \(-0.276847\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 0.837722i | − | 0.0710547i | −0.999369 | − | 0.0355273i | \(-0.988689\pi\) | ||
0.999369 | − | 0.0355273i | \(-0.0113111\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.32456 | + | 14.1421i | 0.532624 | + | 1.19098i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.74641 | −0.313290 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 10.3246 | 0.857408 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.707107 | − | 1.58114i | −0.0583212 | − | 0.130410i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 4.47214i | − | 0.366372i | −0.983078 | − | 0.183186i | \(-0.941359\pi\) | ||
0.983078 | − | 0.183186i | \(-0.0586410\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.0000i | 0.813788i | 0.913475 | + | 0.406894i | \(0.133388\pi\) | ||||
−0.913475 | + | 0.406894i | \(0.866612\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.67544 | − | 3.28742i | −0.297142 | − | 0.265772i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.94427 | −0.718421 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.48683 | 0.437897 | 0.218948 | − | 0.975736i | \(-0.429737\pi\) | ||||
0.218948 | + | 0.975736i | \(0.429737\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 16.0153 | − | 7.16228i | 1.27010 | − | 0.568006i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.65685i | 0.445823i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.32456i | 0.652029i | 0.945365 | + | 0.326015i | \(0.105706\pi\) | ||||
−0.945365 | + | 0.326015i | \(0.894294\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 10.0000 | − | 4.47214i | 0.778499 | − | 0.348155i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −17.4296 | −1.34874 | −0.674370 | − | 0.738394i | \(-0.735585\pi\) | ||||
−0.674370 | + | 0.738394i | \(0.735585\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.2982 | −0.946017 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −16.0153 | − | 14.3246i | −1.22472 | − | 1.09543i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 21.6722i | − | 1.64771i | −0.566803 | − | 0.823853i | \(-0.691820\pi\) | ||
0.566803 | − | 0.823853i | \(-0.308180\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.00000i | 0.226779i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.00000 | − | 2.23607i | −0.0751646 | − | 0.168073i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 25.1891 | 1.88272 | 0.941361 | − | 0.337401i | \(-0.109548\pi\) | ||||
0.941361 | + | 0.337401i | \(0.109548\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −26.1359 | −1.94267 | −0.971335 | − | 0.237716i | \(-0.923601\pi\) | ||||
−0.971335 | + | 0.237716i | \(0.923601\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.23607 | − | 5.00000i | −0.165295 | − | 0.369611i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 11.7727i | 0.865546i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.35089i | 0.537550i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.58114 | − | 4.94975i | 0.115011 | − | 0.360041i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −21.4427 | −1.55154 | −0.775770 | − | 0.631016i | \(-0.782638\pi\) | ||||
−0.775770 | + | 0.631016i | \(0.782638\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 16.0000 | 1.15171 | 0.575853 | − | 0.817554i | \(-0.304670\pi\) | ||||
0.575853 | + | 0.817554i | \(0.304670\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.87320 | + | 0.837722i | −0.134143 | + | 0.0599905i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 1.18472i | − | 0.0844077i | −0.999109 | − | 0.0422038i | \(-0.986562\pi\) | ||
0.999109 | − | 0.0422038i | \(-0.0134379\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.649111i | 0.0460142i | 0.999735 | + | 0.0230071i | \(0.00732404\pi\) | ||||
−0.999735 | + | 0.0230071i | \(0.992676\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.16228 | + | 1.41421i | −0.223050 | + | 0.0997509i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −7.30056 | −0.512399 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.67544 | −0.117018 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −11.3137 | + | 12.6491i | −0.786357 | + | 0.879174i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 32.0307i | 2.21561i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 26.6491i | − | 1.83460i | −0.398196 | − | 0.917300i | \(-0.630364\pi\) | ||
0.398196 | − | 0.917300i | \(-0.369636\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.837722 | + | 1.87320i | 0.0573998 | + | 0.128350i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.11584 | 0.417097 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.32456 | 0.429339 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −5.88635 | − | 13.1623i | −0.397763 | − | 0.889424i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 1.37697i | − | 0.0926251i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.3246i | 0.691383i | 0.938348 | + | 0.345692i | \(0.112356\pi\) | ||||
−0.938348 | + | 0.345692i | \(0.887644\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −6.00000 | + | 6.70820i | −0.400000 | + | 0.447214i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.70163 | −0.312058 | −0.156029 | − | 0.987752i | \(-0.549869\pi\) | ||||
−0.156029 | + | 0.987752i | \(0.549869\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −27.8114 | −1.83783 | −0.918914 | − | 0.394458i | \(-0.870932\pi\) | ||||
−0.918914 | + | 0.394458i | \(0.870932\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −7.07107 | + | 3.16228i | −0.465242 | + | 0.208063i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 5.65685i | − | 0.370593i | −0.982683 | − | 0.185296i | \(-0.940675\pi\) | ||
0.982683 | − | 0.185296i | \(-0.0593245\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 12.6491i | − | 0.825137i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −6.32456 | + | 2.82843i | −0.410824 | + | 0.183726i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.02629 | −0.519178 | −0.259589 | − | 0.965719i | \(-0.583587\pi\) | ||||
−0.259589 | + | 0.965719i | \(0.583587\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.0000 | 0.901819 | 0.450910 | − | 0.892570i | \(-0.351100\pi\) | ||||
0.450910 | + | 0.892570i | \(0.351100\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 13.4350 | − | 7.90569i | 0.861858 | − | 0.507151i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.41421i | 0.0903508i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 6.00000i | − | 0.381771i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −7.32456 | − | 16.3782i | −0.464175 | − | 1.03793i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0.955223 | 0.0602931 | 0.0301466 | − | 0.999545i | \(-0.490403\pi\) | ||||
0.0301466 | + | 0.999545i | \(0.490403\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 25.2982 | 1.59049 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.64371 | + | 3.67544i | 0.102933 | + | 0.230165i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 10.5880i | − | 0.660460i | −0.943900 | − | 0.330230i | \(-0.892874\pi\) | ||
0.943900 | − | 0.330230i | \(-0.107126\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 8.32456i | − | 0.517263i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −16.3246 | − | 14.6011i | −1.01046 | − | 0.903787i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 24.7301 | 1.52492 | 0.762462 | − | 0.647033i | \(-0.223990\pi\) | ||||
0.762462 | + | 0.647033i | \(0.223990\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −14.3246 | −0.879950 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 16.0153 | − | 7.16228i | 0.980123 | − | 0.438324i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 24.5006i | 1.49383i | 0.664920 | + | 0.746915i | \(0.268466\pi\) | ||||
−0.664920 | + | 0.746915i | \(0.731534\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.3246i | 0.870155i | 0.900393 | + | 0.435077i | \(0.143279\pi\) | ||||
−0.900393 | + | 0.435077i | \(0.856721\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.32456 | − | 0.592359i | 0.0801657 | − | 0.0358512i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 13.4164 | 0.809040 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.00000 | 0.120168 | 0.0600842 | − | 0.998193i | \(-0.480863\pi\) | ||||
0.0600842 | + | 0.998193i | \(0.480863\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 14.1421 | + | 12.6491i | 0.846668 | + | 0.757282i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.2317i | 0.729681i | 0.931070 | + | 0.364841i | \(0.118877\pi\) | ||||
−0.931070 | + | 0.364841i | \(0.881123\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 25.4868i | 1.51503i | 0.652815 | + | 0.757517i | \(0.273588\pi\) | ||||
−0.652815 | + | 0.757517i | \(0.726412\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 7.16228 | + | 16.0153i | 0.424257 | + | 0.948667i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.18472 | 0.0699317 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 14.2982 | 0.841072 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 10.3585 | + | 23.1623i | 0.607225 | + | 1.35780i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 13.6459i | 0.797202i | 0.917124 | + | 0.398601i | \(0.130504\pi\) | ||||
−0.917124 | + | 0.398601i | \(0.869496\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.00000i | 0.116445i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −22.1359 | − | 7.07107i | −1.28446 | − | 0.410305i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.73887 | −0.274056 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.32456 | −0.249263 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.23607 | − | 1.00000i | 0.128459 | − | 0.0574485i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.47214i | 0.256074i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 21.4868i | − | 1.22632i | −0.789959 | − | 0.613159i | \(-0.789898\pi\) | ||
0.789959 | − | 0.613159i | \(-0.210102\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 12.6491 | − | 5.65685i | 0.719583 | − | 0.321807i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0.458991 | 0.0260270 | 0.0130135 | − | 0.999915i | \(-0.495858\pi\) | ||||
0.0130135 | + | 0.999915i | \(0.495858\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 32.9737 | 1.86378 | 0.931891 | − | 0.362739i | \(-0.118158\pi\) | ||||
0.931891 | + | 0.362739i | \(0.118158\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.82843 | + | 3.16228i | −0.159364 | + | 0.178174i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 19.0733i | 1.07126i | 0.844452 | + | 0.535631i | \(0.179926\pi\) | ||||
−0.844452 | + | 0.535631i | \(0.820074\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 32.6491i | 1.82800i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 13.1623 | + | 29.4317i | 0.734647 | + | 1.64272i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −11.7727 | −0.655050 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.51317 | −0.139405 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5.88635 | + | 13.1623i | 0.325516 | + | 0.727876i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8.94427i | 0.493114i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 8.97367i | − | 0.493237i | −0.969113 | − | 0.246619i | \(-0.920680\pi\) | ||
0.969113 | − | 0.246619i | \(-0.0793195\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 16.6491 | − | 18.6143i | 0.912366 | − | 1.02006i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.82843 | 0.154533 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −32.6491 | −1.77851 | −0.889255 | − | 0.457411i | \(-0.848777\pi\) | ||||
−0.889255 | + | 0.457411i | \(0.848777\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 24.9596 | − | 11.1623i | 1.35562 | − | 0.606252i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 28.2843i | − | 1.53168i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 12.6491 | − | 5.65685i | 0.681005 | − | 0.304555i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 12.4984 | 0.670951 | 0.335475 | − | 0.942049i | \(-0.391103\pi\) | ||||
0.335475 | + | 0.942049i | \(0.391103\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −23.1623 | −1.23985 | −0.619924 | − | 0.784662i | \(-0.712837\pi\) | ||||
−0.619924 | + | 0.784662i | \(0.712837\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.14651 | + | 1.32456i | 0.221325 | + | 0.0706995i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.01315i | 0.213598i | 0.994281 | + | 0.106799i | \(0.0340602\pi\) | ||||
−0.994281 | + | 0.106799i | \(0.965940\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 1.67544i | − | 0.0889234i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.16228 | − | 2.59893i | −0.0615143 | − | 0.137550i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 23.5454 | 1.24268 | 0.621339 | − | 0.783542i | \(-0.286589\pi\) | ||||
0.621339 | + | 0.783542i | \(0.286589\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −32.2982 | −1.69991 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 6.36396 | + | 14.2302i | 0.334021 | + | 0.746894i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 11.7727i | 0.616211i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 5.67544i | − | 0.296256i | −0.988968 | − | 0.148128i | \(-0.952675\pi\) | ||
0.988968 | − | 0.148128i | \(-0.0473247\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.64911 | + | 2.36944i | 0.137907 | + | 0.123348i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 10.1290 | 0.525871 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.35089 | 0.277059 | 0.138529 | − | 0.990358i | \(-0.455762\pi\) | ||||
0.138529 | + | 0.990358i | \(0.455762\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 17.8885 | − | 8.00000i | 0.923760 | − | 0.413118i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 6.11584i | − | 0.314982i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.6754i | 0.599727i | 0.953982 | + | 0.299864i | \(0.0969412\pi\) | ||||
−0.953982 | + | 0.299864i | \(0.903059\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.48683 | − | 4.24264i | 0.486025 | − | 0.217357i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −22.6274 | −1.15621 | −0.578103 | − | 0.815963i | \(-0.696207\pi\) | ||||
−0.578103 | + | 0.815963i | \(0.696207\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.32456 | 0.322329 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −9.67000 | − | 8.64911i | −0.491554 | − | 0.439659i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 33.2154i | 1.68409i | 0.539409 | + | 0.842044i | \(0.318648\pi\) | ||||
−0.539409 | + | 0.842044i | \(0.681352\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.29822i | 0.470231i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −9.32456 | − | 20.8503i | −0.470362 | − | 1.05176i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.65685 | 0.284627 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 16.8377 | 0.845061 | 0.422531 | − | 0.906349i | \(-0.361142\pi\) | ||||
0.422531 | + | 0.906349i | \(0.361142\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −5.06450 | − | 11.3246i | −0.253542 | − | 0.566937i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12.4984i | 0.624142i | 0.950059 | + | 0.312071i | \(0.101023\pi\) | ||||
−0.950059 | + | 0.312071i | \(0.898977\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.29822i | 0.263923i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −12.6491 | + | 1.41421i | −0.628539 | + | 0.0702728i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −37.2285 | −1.84535 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −24.3246 | −1.20277 | −0.601386 | − | 0.798959i | \(-0.705385\pi\) | ||||
−0.601386 | + | 0.798959i | \(0.705385\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 28.2843 | − | 12.6491i | 1.39516 | − | 0.623935i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 1.41421i | − | 0.0695889i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 14.6491i | 0.719097i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.32456 | − | 0.592359i | 0.0648638 | − | 0.0290080i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7.98905 | 0.390291 | 0.195145 | − | 0.980774i | \(-0.437482\pi\) | ||||
0.195145 | + | 0.980774i | \(0.437482\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.64911 | 0.129110 | 0.0645549 | − | 0.997914i | \(-0.479437\pi\) | ||||
0.0645549 | + | 0.997914i | \(0.479437\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −17.8885 | + | 20.0000i | −0.869771 | + | 0.972433i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.93113i | 0.239195i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 3.16228i | − | 0.153033i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.64911 | − | 5.92359i | −0.127900 | − | 0.285994i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.28742 | 0.158349 | 0.0791747 | − | 0.996861i | \(-0.474772\pi\) | ||||
0.0791747 | + | 0.996861i | \(0.474772\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.00000 | 0.288342 | 0.144171 | − | 0.989553i | \(-0.453949\pi\) | ||||
0.144171 | + | 0.989553i | \(0.453949\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 7.30056 | + | 16.3246i | 0.350035 | + | 0.782703i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 40.5160i | 1.93814i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 24.6491i | − | 1.17644i | −0.808702 | − | 0.588219i | \(-0.799829\pi\) | ||
0.808702 | − | 0.588219i | \(-0.200171\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.00000 | − | 2.23607i | 0.0952381 | − | 0.106479i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −12.9574 | −0.615625 | −0.307813 | − | 0.951447i | \(-0.599597\pi\) | ||||
−0.307813 | + | 0.951447i | \(0.599597\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −14.3246 | −0.679049 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 7.07107 | − | 3.16228i | 0.334450 | − | 0.149571i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 16.9706i | − | 0.800890i | −0.916321 | − | 0.400445i | \(-0.868855\pi\) | ||
0.916321 | − | 0.400445i | \(-0.131145\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 5.29822i | − | 0.249483i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −15.8114 | + | 7.07107i | −0.742884 | + | 0.332228i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.18472 | −0.0555405 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −0.649111 | −0.0303641 | −0.0151821 | − | 0.999885i | \(-0.504833\pi\) | ||||
−0.0151821 | + | 0.999885i | \(0.504833\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.59893 | − | 8.13594i | 0.121308 | − | 0.379753i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 15.0974i | 0.703154i | 0.936159 | + | 0.351577i | \(0.114354\pi\) | ||||
−0.936159 | + | 0.351577i | \(0.885646\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15.3509i | 0.713416i | 0.934216 | + | 0.356708i | \(0.116101\pi\) | ||||
−0.934216 | + | 0.356708i | \(0.883899\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −6.32456 | − | 14.1421i | −0.293294 | − | 0.655826i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −9.44050 | −0.436854 | −0.218427 | − | 0.975853i | \(-0.570093\pi\) | ||||
−0.218427 | + | 0.975853i | \(0.570093\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.00000 | −0.0923514 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.87978 | + | 8.67544i | 0.178771 | + | 0.399743i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 19.3400i | 0.889254i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 21.4868i | 0.985884i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 22.6491 | + | 20.2580i | 1.03703 | + | 0.927549i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5.65685 | −0.258468 | −0.129234 | − | 0.991614i | \(-0.541252\pi\) | ||||
−0.129234 | + | 0.991614i | \(0.541252\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.97367 | 0.317972 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −8.94427 | + | 4.00000i | −0.406978 | + | 0.182006i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 20.7170i | − | 0.940709i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 27.2982i | − | 1.23700i | −0.785785 | − | 0.618500i | \(-0.787741\pi\) | ||
0.785785 | − | 0.618500i | \(-0.212259\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −13.1623 | + | 5.88635i | −0.595219 | + | 0.266190i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −20.9837 | −0.946981 | −0.473491 | − | 0.880799i | \(-0.657006\pi\) | ||||
−0.473491 | + | 0.880799i | \(0.657006\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −12.0000 | −0.540453 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 14.1421 | + | 12.6491i | 0.635642 | + | 0.568535i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.18472i | 0.0531419i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 2.00000i | − | 0.0895323i | −0.998997 | − | 0.0447661i | \(-0.985746\pi\) | ||
0.998997 | − | 0.0447661i | \(-0.0142543\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −12.3246 | − | 27.5585i | −0.550621 | − | 1.23122i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6.11584 | −0.272692 | −0.136346 | − | 0.990661i | \(-0.543536\pi\) | ||||
−0.136346 | + | 0.990661i | \(0.543536\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.00000 | −0.0889988 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −8.69616 | − | 19.4452i | −0.386210 | − | 0.863591i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 13.1869i | 0.584500i | 0.956342 | + | 0.292250i | \(0.0944039\pi\) | ||||
−0.956342 | + | 0.292250i | \(0.905596\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 8.32456i | − | 0.368257i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 11.3246 | − | 35.4515i | 0.499991 | − | 1.56522i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −11.3137 | −0.498542 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 40.0000 | 1.75920 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 34.2667 | − | 15.3246i | 1.50414 | − | 0.672673i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 24.7301i | − | 1.08345i | −0.840557 | − | 0.541723i | \(-0.817772\pi\) | ||
0.840557 | − | 0.541723i | \(-0.182228\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 8.18861i | − | 0.358063i | −0.983843 | − | 0.179031i | \(-0.942704\pi\) | ||
0.983843 | − | 0.179031i | \(-0.0572964\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4.74342 | + | 2.12132i | −0.207020 | + | 0.0925820i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 10.3957 | 0.452845 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.00000 | 0.391304 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.82843 | − | 3.16228i | 0.122743 | − | 0.137231i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.992465i | 0.0429884i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 26.3246i | − | 1.13811i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 17.8114 | + | 39.8275i | 0.768618 | + | 1.71868i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.47214 | −0.192629 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.00000 | −0.0859867 | −0.0429934 | − | 0.999075i | \(-0.513689\pi\) | ||||
−0.0429934 | + | 0.999075i | \(0.513689\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −18.4809 | − | 41.3246i | −0.793091 | − | 1.77341i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 11.7727i | − | 0.504287i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 23.6754i | − | 1.01229i | −0.862449 | − | 0.506144i | \(-0.831070\pi\) | ||
0.862449 | − | 0.506144i | \(-0.168930\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6.32456 | − | 7.07107i | 0.269925 | − | 0.301786i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −52.2887 | −2.22757 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.00000 | −0.170097 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −18.6143 | + | 8.32456i | −0.790132 | + | 0.353358i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 23.8121i | − | 1.00895i | −0.863426 | − | 0.504476i | \(-0.831686\pi\) | ||
0.863426 | − | 0.504476i | \(-0.168314\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 3.62278i | − | 0.153227i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −11.6228 | + | 5.19786i | −0.490714 | + | 0.219454i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −13.6459 | −0.575106 | −0.287553 | − | 0.957765i | \(-0.592842\pi\) | ||||
−0.287553 | + | 0.957765i | \(0.592842\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −22.3246 | −0.939201 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 8.94427 | − | 1.00000i | 0.375624 | − | 0.0419961i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 38.4133i | 1.61037i | 0.593025 | + | 0.805184i | \(0.297933\pi\) | ||||
−0.593025 | + | 0.805184i | \(0.702067\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 0.324555i | − | 0.0135822i | −0.999977 | − | 0.00679111i | \(-0.997838\pi\) | ||
0.999977 | − | 0.00679111i | \(-0.00216169\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −15.1623 | − | 33.9039i | −0.633413 | − | 1.41636i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 16.9706 | 0.707721 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −15.2982 | −0.636873 | −0.318437 | − | 0.947944i | \(-0.603158\pi\) | ||||
−0.318437 | + | 0.947944i | \(0.603158\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 11.3137 | + | 25.2982i | 0.470182 | + | 1.05136i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 10.3585i | − | 0.429742i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 45.2982i | − | 1.87606i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.64911 | − | 2.36944i | −0.109527 | − | 0.0979641i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −27.3290 | −1.12799 | −0.563995 | − | 0.825778i | \(-0.690736\pi\) | ||||
−0.563995 | + | 0.825778i | \(0.690736\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 45.2982 | 1.86648 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.87320 | − | 0.837722i | 0.0770533 | − | 0.0344593i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 15.3269i | − | 0.629398i | −0.949191 | − | 0.314699i | \(-0.898096\pi\) | ||
0.949191 | − | 0.314699i | \(-0.101904\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.32456i | 0.0952975i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.02633 | + | 0.458991i | −0.0420051 | + | 0.0187852i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2.10270 | −0.0859140 | −0.0429570 | − | 0.999077i | \(-0.513678\pi\) | ||||
−0.0429570 | + | 0.999077i | \(0.513678\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 33.6228 | 1.37150 | 0.685751 | − | 0.727836i | \(-0.259474\pi\) | ||||
0.685751 | + | 0.727836i | \(0.259474\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.47214 | − | 4.00000i | −0.182119 | − | 0.162893i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 12.7279i | − | 0.517464i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 30.3246i | 1.23084i | 0.788201 | + | 0.615418i | \(0.211013\pi\) | ||||
−0.788201 | + | 0.615418i | \(0.788987\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5.16228 | − | 11.5432i | −0.209186 | − | 0.467754i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.49282 | −0.303127 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 32.3246 | 1.30558 | 0.652788 | − | 0.757540i | \(-0.273599\pi\) | ||||
0.652788 | + | 0.757540i | \(0.273599\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.18472 | − | 2.64911i | −0.0477725 | − | 0.106822i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 18.1553i | − | 0.730904i | −0.930830 | − | 0.365452i | \(-0.880914\pi\) | ||
0.930830 | − | 0.365452i | \(-0.119086\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 39.8114i | 1.60015i | 0.599897 | + | 0.800077i | \(0.295208\pi\) | ||||
−0.599897 | + | 0.800077i | \(0.704792\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −28.0000 | − | 8.94427i | −1.12360 | − | 0.358921i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 10.1290 | 0.405809 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.00000 | −0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −50.6450 | + | 22.6491i | −2.02256 | + | 0.904518i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 13.6831i | − | 0.545583i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 37.9473i | 1.51066i | 0.655345 | + | 0.755330i | \(0.272523\pi\) | ||||
−0.655345 | + | 0.755330i | \(0.727477\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 42.1359 | − | 18.8438i | 1.67475 | − | 0.748972i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −8.48528 | −0.336728 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.837722 | 0.0331918 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.36944 | + | 2.64911i | −0.0937335 | + | 0.104797i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 21.4427i | 0.846936i | 0.905911 | + | 0.423468i | \(0.139187\pi\) | ||||
−0.905911 | + | 0.423468i | \(0.860813\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 11.1623i | − | 0.440197i | −0.975478 | − | 0.220099i | \(-0.929362\pi\) | ||
0.975478 | − | 0.220099i | \(-0.0706379\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.32456 | + | 9.67000i | 0.170279 | + | 0.380756i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 49.0012 | 1.92644 | 0.963219 | − | 0.268718i | \(-0.0866001\pi\) | ||||
0.963219 | + | 0.268718i | \(0.0866001\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.32456 | −0.248261 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.47214 | + | 10.0000i | 0.175277 | + | 0.391931i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3.09516i | 0.121123i | 0.998164 | + | 0.0605616i | \(0.0192891\pi\) | ||||
−0.998164 | + | 0.0605616i | \(0.980711\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 18.6491i | 0.728681i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 16.6491 | − | 18.6143i | 0.649544 | − | 0.726212i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 28.0175 | 1.09141 | 0.545704 | − | 0.837978i | \(-0.316262\pi\) | ||||
0.545704 | + | 0.837978i | \(0.316262\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 41.4868 | 1.61365 | 0.806825 | − | 0.590790i | \(-0.201184\pi\) | ||||
0.806825 | + | 0.590790i | \(0.201184\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.17718 | − | 0.973666i | 0.0845548 | − | 0.0378141i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 10.1290i | 0.392785i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 41.2982i | 1.59907i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −16.3246 | + | 7.30056i | −0.631144 | + | 0.282256i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −14.1421 | −0.545951 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −23.2982 | −0.898080 | −0.449040 | − | 0.893512i | \(-0.648234\pi\) | ||||
−0.449040 | + | 0.893512i | \(0.648234\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −14.8492 | − | 4.74342i | −0.571548 | − | 0.182574i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 45.2176i | − | 1.73785i | −0.494941 | − | 0.868927i | \(-0.664810\pi\) | ||
0.494941 | − | 0.868927i | \(-0.335190\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 14.6491i | 0.562181i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.32456 | − | 7.43393i | −0.127397 | − | 0.284869i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −11.5060 | −0.440263 | −0.220132 | − | 0.975470i | \(-0.570649\pi\) | ||||
−0.220132 | + | 0.975470i | \(0.570649\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −25.2982 | −0.966595 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −19.6656 | − | 43.9737i | −0.750290 | − | 1.67770i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 8.48528i | 0.323263i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 8.83772i | − | 0.336203i | −0.985770 | − | 0.168101i | \(-0.946236\pi\) | ||
0.985770 | − | 0.168101i | \(-0.0537636\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −10.0000 | − | 8.94427i | −0.379869 | − | 0.339765i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.18472 | −0.0449389 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.94733 | 0.0737605 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 8.94427 | − | 4.00000i | 0.338303 | − | 0.151294i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 35.5848i | − | 1.34402i | −0.740542 | − | 0.672010i | \(-0.765431\pi\) | ||
0.740542 | − | 0.672010i | \(-0.234569\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 59.6228i | − | 2.24872i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 20.0000 | − | 8.94427i | 0.753244 | − | 0.336861i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.41421 | 0.0531870 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −40.9737 | −1.53880 | −0.769399 | − | 0.638768i | \(-0.779444\pi\) | ||||
−0.769399 | + | 0.638768i | \(0.779444\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.94427 | − | 8.00000i | −0.335436 | − | 0.300023i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 35.7771i | − | 1.33986i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.29822i | 0.198142i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −5.67544 | − | 12.6907i | −0.211953 | − | 0.473942i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −23.5454 | −0.878095 | −0.439048 | − | 0.898464i | \(-0.644684\pi\) | ||||
−0.439048 | + | 0.898464i | \(0.644684\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.00000 | 0.297936 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 9.89949 | + | 22.1359i | 0.368166 | + | 0.823245i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 21.9017i | 0.813408i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.64911i | 0.320778i | 0.987054 | + | 0.160389i | \(0.0512748\pi\) | ||||
−0.987054 | + | 0.160389i | \(0.948725\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 22.0000 | + | 15.6525i | 0.814815 | + | 0.579721i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −7.10831 | −0.262910 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.86406 | 0.0688505 | 0.0344252 | − | 0.999407i | \(-0.489040\pi\) | ||||
0.0344252 | + | 0.999407i | \(0.489040\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.23607 | + | 1.00000i | −0.0824786 | + | 0.0368856i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 8.94427i | 0.329466i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.97367i | 0.182959i | 0.995807 | + | 0.0914796i | \(0.0291596\pi\) | ||||
−0.995807 | + | 0.0914796i | \(0.970840\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 9.48683 | − | 4.24264i | 0.348508 | − | 0.155857i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −12.2317 | −0.448737 | −0.224369 | − | 0.974504i | \(-0.572032\pi\) | ||||
−0.224369 | + | 0.974504i | \(0.572032\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.32456 | −0.231714 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 20.7170 | − | 23.1623i | 0.757994 | − | 0.847463i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 18.6143i | 0.680151i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 42.6491i | − | 1.55629i | −0.628086 | − | 0.778144i | \(-0.716161\pi\) | ||
0.628086 | − | 0.778144i | \(-0.283839\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0.675445 | + | 1.51034i | 0.0246146 | + | 0.0550399i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 14.1421 | 0.514685 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −7.67544 | −0.278969 | −0.139484 | − | 0.990224i | \(-0.544545\pi\) | ||||
−0.139484 | + | 0.990224i | \(0.544545\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 17.8885 | + | 40.0000i | 0.649313 | + | 1.45191i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 4.47214i | − | 0.162115i | −0.996709 | − | 0.0810574i | \(-0.974170\pi\) | ||
0.996709 | − | 0.0810574i | \(-0.0258297\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.32456i | 0.301369i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.64911 | + | 5.19786i | −0.168089 | + | 0.187929i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.18472 | 0.0427777 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 23.2982 | 0.840155 | 0.420078 | − | 0.907488i | \(-0.362003\pi\) | ||||
0.420078 | + | 0.907488i | \(0.362003\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 16.7411 | − | 7.48683i | 0.602915 | − | 0.269632i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 25.8776i | − | 0.930752i | −0.885113 | − | 0.465376i | \(-0.845919\pi\) | ||
0.885113 | − | 0.465376i | \(-0.154081\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 18.9737i | − | 0.681554i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 13.1623 | − | 5.88635i | 0.472194 | − | 0.211172i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 8.48528 | 0.304017 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.29822 | 0.189585 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 11.5432 | − | 36.1359i | 0.412520 | − | 1.29139i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 7.75955i | − | 0.276950i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 32.8377i | 1.17054i | 0.810839 | + | 0.585269i | \(0.199011\pi\) | ||||
−0.810839 | + | 0.585269i | \(0.800989\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 17.4868 | + | 39.1017i | 0.622548 | + | 1.39206i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 15.7858 | 0.561280 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.64911 | 0.0940727 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −10.1290 | − | 22.6491i | −0.359238 | − | 0.803281i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 35.8143i | − | 1.26861i | −0.773083 | − | 0.634304i | \(-0.781287\pi\) | ||
0.773083 | − | 0.634304i | \(-0.218713\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 14.7018i | 0.520112i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 22.6491 | + | 20.2580i | 0.800267 | + | 0.715781i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −37.2285 | −1.31377 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.00000 | 0.281963 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −38.7389 | + | 17.3246i | −1.36367 | + | 0.609853i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 0.266737i | − | 0.00937798i | −0.999989 | − | 0.00468899i | \(-0.998507\pi\) | ||
0.999989 | − | 0.00468899i | \(-0.00149256\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 14.5132i | − | 0.509626i | −0.966990 | − | 0.254813i | \(-0.917986\pi\) | ||
0.966990 | − | 0.254813i | \(-0.0820140\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −22.6491 | + | 10.1290i | −0.794339 | + | 0.355239i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 11.7727 | 0.412380 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −30.9737 | −1.08363 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.87320 | + | 1.67544i | 0.0654550 | + | 0.0585448i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 22.3607i | 0.780393i | 0.920732 | + | 0.390197i | \(0.127593\pi\) | ||||
−0.920732 | + | 0.390197i | \(0.872407\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 53.9473i | − | 1.88049i | −0.340504 | − | 0.940243i | \(-0.610598\pi\) | ||
0.340504 | − | 0.940243i | \(-0.389402\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 9.48683 | + | 21.2132i | 0.330289 | + | 0.738549i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 21.9017 | 0.761596 | 0.380798 | − | 0.924658i | \(-0.375649\pi\) | ||||
0.380798 | + | 0.924658i | \(0.375649\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 28.8377 | 1.00158 | 0.500788 | − | 0.865570i | \(-0.333044\pi\) | ||||
0.500788 | + | 0.865570i | \(0.333044\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.41421 | + | 3.16228i | 0.0490585 | + | 0.109698i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 1.64371i | − | 0.0569511i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 24.6491i | 0.853018i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −10.0000 | + | 31.3050i | −0.345651 | + | 1.08206i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −13.2242 | −0.456549 | −0.228274 | − | 0.973597i | \(-0.573308\pi\) | ||||
−0.228274 | + | 0.973597i | \(0.573308\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.2982 | −0.837870 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −19.3400 | + | 8.64911i | −0.666105 | + | 0.297891i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 17.3923i | 0.598314i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.00000i | 0.309244i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −40.2982 | + | 18.0219i | −1.38303 | + | 0.618510i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −47.0908 | −1.61425 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 18.1359 | 0.620963 | 0.310481 | − | 0.950579i | \(-0.399510\pi\) | ||||
0.310481 | + | 0.950579i | \(0.399510\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −20.2580 | + | 22.6491i | −0.692808 | + | 0.774583i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 7.75955i | − | 0.265061i | −0.991179 | − | 0.132531i | \(-0.957690\pi\) | ||
0.991179 | − | 0.132531i | \(-0.0423103\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 8.46050i | − | 0.288668i | −0.989529 | − | 0.144334i | \(-0.953896\pi\) | ||
0.989529 | − | 0.144334i | \(-0.0461040\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.837722 | + | 1.87320i | 0.0285495 | + | 0.0638386i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 33.6744 | 1.14629 | 0.573145 | − | 0.819454i | \(-0.305723\pi\) | ||||
0.573145 | + | 0.819454i | \(0.305723\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −30.6491 | −1.04210 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 10.1104 | + | 22.6075i | 0.343366 | + | 0.767790i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 17.8885i | 0.606827i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 1.67544i | − | 0.0567703i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −29.2982 | + | 32.7564i | −0.991595 | + | 1.10864i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 11.3137 | 0.382473 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.02633 | 0.102192 | 0.0510960 | − | 0.998694i | \(-0.483729\pi\) | ||||
0.0510960 | + | 0.998694i | \(0.483729\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −21.5761 | + | 9.64911i | −0.727743 | + | 0.325456i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 15.3269i | − | 0.516375i | −0.966095 | − | 0.258187i | \(-0.916875\pi\) | ||
0.966095 | − | 0.258187i | \(-0.0831252\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 18.0000i | 0.605748i | 0.953031 | + | 0.302874i | \(0.0979462\pi\) | ||||
−0.953031 | + | 0.302874i | \(0.902054\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.16228 | + | 1.41421i | −0.106299 | + | 0.0475383i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 34.4001 | 1.15504 | 0.577521 | − | 0.816376i | \(-0.304020\pi\) | ||||
0.577521 | + | 0.816376i | \(0.304020\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.00000 | 0.201234 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.47214 | − | 40.0000i | −0.149822 | − | 1.34005i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 64.0614i | 2.14373i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 35.6228i | − | 1.19074i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.35089 | − | 7.49282i | −0.111883 | − | 0.250178i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 46.1728 | 1.53995 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 16.6491 | 0.554662 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3.05792 | − | 6.83772i | −0.101761 | − | 0.227545i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 36.9618i | 1.22865i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 47.9473i | − | 1.59207i | −0.605254 | − | 0.796033i | \(-0.706928\pi\) | ||
0.605254 | − | 0.796033i | \(-0.293072\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.16228 | + | 2.82843i | 0.104886 | + | 0.0938130i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 31.5717 | 1.04602 | 0.523008 | − | 0.852328i | \(-0.324810\pi\) | ||||
0.523008 | + | 0.852328i | \(0.324810\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −46.3246 | −1.53312 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −7.07107 | + | 3.16228i | −0.233762 | + | 0.104542i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 13.1869i | − | 0.435470i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.64911i | 0.153360i | 0.997056 | + | 0.0766800i | \(0.0244320\pi\) | ||||
−0.997056 | + | 0.0766800i | \(0.975568\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 33.9737 | − | 15.1935i | 1.11947 | − | 0.500642i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −0.992465 | −0.0326674 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −24.9737 | −0.821129 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 17.8885 | + | 16.0000i | 0.587537 | + | 0.525509i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 37.4208i | 1.22774i | 0.789408 | + | 0.613868i | \(0.210387\pi\) | ||||
−0.789408 | + | 0.613868i | \(0.789613\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 7.16228i | − | 0.234734i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0.324555 | + | 0.725728i | 0.0106255 | + | 0.0237593i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 10.3957 | 0.339977 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −20.3246 | −0.663974 | −0.331987 | − | 0.943284i | \(-0.607719\pi\) | ||||
−0.331987 | + | 0.943284i | \(0.607719\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 23.3159 | + | 52.1359i | 0.760886 | + | 1.70139i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 48.5050i | − | 1.58122i | −0.612321 | − | 0.790609i | \(-0.709764\pi\) | ||
0.612321 | − | 0.790609i | \(-0.290236\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 6.70178i | − | 0.218240i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −7.00000 | − | 2.23607i | −0.227710 | − | 0.0727393i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4.47214 | 0.145325 | 0.0726624 | − | 0.997357i | \(-0.476850\pi\) | ||||
0.0726624 | + | 0.997357i | \(0.476850\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.97367 | 0.226375 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −30.1575 | + | 13.4868i | −0.977923 | + | 0.437341i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 26.8328i | − | 0.869200i | −0.900624 | − | 0.434600i | \(-0.856890\pi\) | ||
0.900624 | − | 0.434600i | \(-0.143110\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 30.3246i | 0.981280i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −51.6228 | + | 23.0864i | −1.66873 | + | 0.746278i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 17.8885 | 0.577651 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.00000 | −0.290323 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −37.2285 | + | 41.6228i | −1.19967 | + | 1.34128i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 22.6274i | − | 0.728402i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 9.35089i | 0.300704i | 0.988633 | + | 0.150352i | \(0.0480408\pi\) | ||||
−0.988633 | + | 0.150352i | \(0.951959\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −8.32456 | − | 18.6143i | −0.267423 | − | 0.597977i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 43.8406 | 1.40691 | 0.703456 | − | 0.710739i | \(-0.251639\pi\) | ||||
0.703456 | + | 0.710739i | \(0.251639\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.837722 | 0.0268561 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.77708 | − | 3.97367i | −0.0569120 | − | 0.127259i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4.20540i | 0.134543i | 0.997735 | + | 0.0672713i | \(0.0214293\pi\) | ||||
−0.997735 | + | 0.0672713i | \(0.978571\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 45.2982i | − | 1.44774i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −16.6491 | + | 18.6143i | −0.531565 | + | 0.594308i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −34.4001 | −1.09719 | −0.548597 | − | 0.836087i | \(-0.684838\pi\) | ||||
−0.548597 | + | 0.836087i | \(0.684838\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.67544 | −0.0533841 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −14.1421 | + | 6.32456i | −0.450149 | + | 0.201313i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 24.4634i | 0.777890i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 54.5964i | 1.73431i | 0.498036 | + | 0.867157i | \(0.334055\pi\) | ||||
−0.498036 | + | 0.867157i | \(0.665945\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 14.1886 | − | 6.34534i | 0.450262 | − | 0.201363i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0.917981 | 0.0291020 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −6.51317 | −0.206274 | −0.103137 | − | 0.994667i | \(-0.532888\pi\) | ||||
−0.103137 | + | 0.994667i | \(0.532888\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 41.2044 | + | 13.1623i | 1.30365 | + | 0.416436i |
(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 | 672.2.h.e.575.7 | yes | 8 | |
3.2 | odd | 2 | inner | 672.2.h.e.575.4 | yes | 8 | |
4.3 | odd | 2 | inner | 672.2.h.e.575.1 | ✓ | 8 | |
8.3 | odd | 2 | 1344.2.h.f.575.8 | 8 | |||
8.5 | even | 2 | 1344.2.h.f.575.2 | 8 | |||
12.11 | even | 2 | inner | 672.2.h.e.575.6 | yes | 8 | |
24.5 | odd | 2 | 1344.2.h.f.575.5 | 8 | |||
24.11 | even | 2 | 1344.2.h.f.575.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
672.2.h.e.575.1 | ✓ | 8 | 4.3 | odd | 2 | inner | |
672.2.h.e.575.4 | yes | 8 | 3.2 | odd | 2 | inner | |
672.2.h.e.575.6 | yes | 8 | 12.11 | even | 2 | inner | |
672.2.h.e.575.7 | yes | 8 | 1.1 | even | 1 | trivial | |
1344.2.h.f.575.2 | 8 | 8.5 | even | 2 | |||
1344.2.h.f.575.3 | 8 | 24.11 | even | 2 | |||
1344.2.h.f.575.5 | 8 | 24.5 | odd | 2 | |||
1344.2.h.f.575.8 | 8 | 8.3 | odd | 2 |