Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [672,2,Mod(559,672)]
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, 1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("672.559");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 672 = 2^{5} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 672.p (of order \(2\), degree \(1\), 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: | \(5.36594701583\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + x^{14} - 4x^{12} - 4x^{10} + 16x^{8} - 16x^{6} - 64x^{4} + 64x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{17} \) |
Twist minimal: | no (minimal twist has level 168) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 559.4 | ||
Root | \(1.20933 - 0.733159i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 672.559 |
Dual form | 672.2.p.a.559.12 |
$q$-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 | ||||||||
\(3\) | − | 1.00000i | − | 0.577350i | ||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.12786 | −0.504397 | −0.252198 | − | 0.967676i | \(-0.581154\pi\) | ||||
−0.252198 | + | 0.967676i | \(0.581154\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.11337 | − | 1.59175i | 0.798777 | − | 0.601627i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.11151 | −1.54118 | −0.770590 | − | 0.637332i | \(-0.780038\pi\) | ||||
−0.770590 | + | 0.637332i | \(0.780038\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.88054 | 1.63097 | 0.815484 | − | 0.578779i | \(-0.196471\pi\) | ||||
0.815484 | + | 0.578779i | \(0.196471\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.12786i | 0.291213i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 3.31623i | − | 0.804304i | −0.915573 | − | 0.402152i | \(-0.868262\pi\) | ||
0.915573 | − | 0.402152i | \(-0.131738\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 7.49510i | − | 1.71949i | −0.510719 | − | 0.859747i | \(-0.670621\pi\) | ||
0.510719 | − | 0.859747i | \(-0.329379\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.59175 | − | 2.11337i | −0.347349 | − | 0.461174i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.73845i | 0.362492i | 0.983438 | + | 0.181246i | \(0.0580130\pi\) | ||||
−0.983438 | + | 0.181246i | \(0.941987\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.72792 | −0.745584 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 5.88054i | − | 1.09199i | −0.837789 | − | 0.545995i | \(-0.816152\pi\) | ||
0.837789 | − | 0.545995i | \(-0.183848\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.04982 | −1.08658 | −0.543290 | − | 0.839545i | \(-0.682822\pi\) | ||||
−0.543290 | + | 0.839545i | \(0.682822\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.11151i | 0.889800i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.38359 | + | 1.79528i | −0.402901 | + | 0.303458i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.65381i | 0.271885i | 0.990717 | + | 0.135942i | \(0.0434062\pi\) | ||||
−0.990717 | + | 0.135942i | \(0.956594\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 5.88054i | − | 0.941640i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 1.45096i | − | 0.226601i | −0.993561 | − | 0.113301i | \(-0.963858\pi\) | ||
0.993561 | − | 0.113301i | \(-0.0361423\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.79528 | −0.273778 | −0.136889 | − | 0.990586i | \(-0.543710\pi\) | ||||
−0.136889 | + | 0.990586i | \(0.543710\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.12786 | 0.168132 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.56335 | 0.811498 | 0.405749 | − | 0.913985i | \(-0.367011\pi\) | ||||
0.405749 | + | 0.913985i | \(0.367011\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.93264 | − | 6.72792i | 0.276091 | − | 0.961132i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.31623 | −0.464365 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 3.62481i | − | 0.497906i | −0.968516 | − | 0.248953i | \(-0.919913\pi\) | ||
0.968516 | − | 0.248953i | \(-0.0800865\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.76510 | 0.777365 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7.49510 | −0.992751 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.767184i | 0.0998789i | 0.998752 | + | 0.0499394i | \(0.0159028\pi\) | ||||
−0.998752 | + | 0.0499394i | \(0.984097\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.317194 | 0.0406125 | 0.0203063 | − | 0.999794i | \(-0.493536\pi\) | ||||
0.0203063 | + | 0.999794i | \(0.493536\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.11337 | + | 1.59175i | −0.266259 | + | 0.200542i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −6.63246 | −0.822655 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.56247 | 0.801733 | 0.400867 | − | 0.916136i | \(-0.368709\pi\) | ||||
0.400867 | + | 0.916136i | \(0.368709\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.73845 | 0.209285 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 10.1919i | − | 1.20956i | −0.796393 | − | 0.604779i | \(-0.793261\pi\) | ||
0.796393 | − | 0.604779i | \(-0.206739\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 6.63246i | − | 0.776270i | −0.921602 | − | 0.388135i | \(-0.873119\pi\) | ||
0.921602 | − | 0.388135i | \(-0.126881\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.72792i | 0.430463i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −10.8025 | + | 8.13627i | −1.23106 | + | 0.927214i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.01423i | 0.339127i | 0.985519 | + | 0.169564i | \(0.0542358\pi\) | ||||
−0.985519 | + | 0.169564i | \(0.945764\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 16.0883i | 1.76592i | 0.469448 | + | 0.882960i | \(0.344453\pi\) | ||||
−0.469448 | + | 0.882960i | \(0.655547\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.74026i | 0.405688i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −5.88054 | −0.630460 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.08341i | 0.856840i | 0.903580 | + | 0.428420i | \(0.140930\pi\) | ||||
−0.903580 | + | 0.428420i | \(0.859070\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 12.4277 | − | 9.36038i | 1.30278 | − | 0.981234i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.04982i | 0.627337i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 8.45347i | 0.867307i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 0.357752i | − | 0.0363242i | −0.999835 | − | 0.0181621i | \(-0.994219\pi\) | ||
0.999835 | − | 0.0181621i | \(-0.00578150\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.11151 | 0.513726 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.38359 | 0.336680 | 0.168340 | − | 0.985729i | \(-0.446159\pi\) | ||||
0.168340 | + | 0.985729i | \(0.446159\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.5033 | 1.42905 | 0.714526 | − | 0.699609i | \(-0.246643\pi\) | ||||
0.714526 | + | 0.699609i | \(0.246643\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.79528 | + | 2.38359i | 0.175202 | + | 0.232615i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.87870 | 0.181621 | 0.0908103 | − | 0.995868i | \(-0.471054\pi\) | ||||
0.0908103 | + | 0.995868i | \(0.471054\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.6166i | 1.30424i | 0.758117 | + | 0.652119i | \(0.226120\pi\) | ||||
−0.758117 | + | 0.652119i | \(0.773880\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.65381 | 0.156973 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.63246 | 0.435785 | 0.217892 | − | 0.975973i | \(-0.430082\pi\) | ||||
0.217892 | + | 0.975973i | \(0.430082\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 1.96074i | − | 0.182840i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.88054 | −0.543656 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.27862 | − | 7.00841i | −0.483890 | − | 0.642460i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 15.1276 | 1.37523 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.45096 | −0.130828 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.84392 | 0.880467 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.38124i | 0.832451i | 0.909261 | + | 0.416225i | \(0.136647\pi\) | ||||
−0.909261 | + | 0.416225i | \(0.863353\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.79528i | 0.158066i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 6.22303i | − | 0.543708i | −0.962338 | − | 0.271854i | \(-0.912363\pi\) | ||
0.962338 | − | 0.271854i | \(-0.0876368\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −11.9304 | − | 15.8399i | −1.03449 | − | 1.37349i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 1.12786i | − | 0.0970712i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 7.45584 | 0.636996 | 0.318498 | − | 0.947924i | \(-0.396822\pi\) | ||||
0.318498 | + | 0.947924i | \(0.396822\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.27471i | 0.192938i | 0.995336 | + | 0.0964690i | \(0.0307549\pi\) | ||||
−0.995336 | + | 0.0964690i | \(0.969245\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 5.56335i | − | 0.468518i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −30.0585 | −2.51362 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.63246i | 0.550796i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.72792 | − | 1.93264i | −0.554910 | − | 0.159401i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 4.19427i | − | 0.343608i | −0.985131 | − | 0.171804i | \(-0.945040\pi\) | ||
0.985131 | − | 0.171804i | \(-0.0549595\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.79874i | 0.797411i | 0.917079 | + | 0.398705i | \(0.130540\pi\) | ||||
−0.917079 | + | 0.398705i | \(0.869460\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.31623i | 0.268101i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.82338 | 0.548067 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.82865 | 0.385369 | 0.192684 | − | 0.981261i | \(-0.438281\pi\) | ||||
0.192684 | + | 0.981261i | \(0.438281\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.62481 | −0.287466 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.76718 | + | 3.67398i | 0.218085 | + | 0.289550i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.43753 | 0.112596 | 0.0562981 | − | 0.998414i | \(-0.482070\pi\) | ||||
0.0562981 | + | 0.998414i | \(0.482070\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − | 5.76510i | − | 0.448812i | ||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 16.0417 | 1.24134 | 0.620670 | − | 0.784072i | \(-0.286861\pi\) | ||||
0.620670 | + | 0.784072i | \(0.286861\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 21.5808 | 1.66006 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.49510i | 0.573165i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.01798 | −0.305482 | −0.152741 | − | 0.988266i | \(-0.548810\pi\) | ||||
−0.152741 | + | 0.988266i | \(0.548810\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −7.87846 | + | 5.93393i | −0.595556 | + | 0.448563i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.767184 | 0.0576651 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.97679 | 0.521469 | 0.260735 | − | 0.965410i | \(-0.416035\pi\) | ||||
0.260735 | + | 0.965410i | \(0.416035\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.4687 | 1.00112 | 0.500561 | − | 0.865701i | \(-0.333127\pi\) | ||||
0.500561 | + | 0.865701i | \(0.333127\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 0.317194i | − | 0.0234477i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 1.86527i | − | 0.137138i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 16.9509i | 1.23958i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.59175 | + | 2.11337i | 0.115783 | + | 0.153725i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 21.0704i | 1.52460i | 0.647224 | + | 0.762300i | \(0.275930\pi\) | ||||
−0.647224 | + | 0.762300i | \(0.724070\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.13735 | −0.369795 | −0.184897 | − | 0.982758i | \(-0.559195\pi\) | ||||
−0.184897 | + | 0.982758i | \(0.559195\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 6.63246i | 0.474960i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 26.4337i | 1.88332i | 0.336566 | + | 0.941660i | \(0.390735\pi\) | ||||
−0.336566 | + | 0.941660i | \(0.609265\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.8420 | −0.768567 | −0.384283 | − | 0.923215i | \(-0.625551\pi\) | ||||
−0.384283 | + | 0.923215i | \(0.625551\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 6.56247i | − | 0.462881i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −9.36038 | − | 12.4277i | −0.656970 | − | 0.872256i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.63648i | 0.114297i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 1.73845i | − | 0.120831i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 38.3113i | 2.65005i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.79528 | −0.674335 | −0.337168 | − | 0.941445i | \(-0.609469\pi\) | ||||
−0.337168 | + | 0.941445i | \(0.609469\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −10.1919 | −0.698339 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.02484 | 0.138093 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −12.7855 | + | 9.62983i | −0.867936 | + | 0.653716i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −6.63246 | −0.448180 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 19.5012i | − | 1.31179i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 15.3534 | 1.02814 | 0.514071 | − | 0.857748i | \(-0.328137\pi\) | ||||
0.514071 | + | 0.857748i | \(0.328137\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.72792 | 0.248528 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 5.86527i | − | 0.389292i | −0.980874 | − | 0.194646i | \(-0.937644\pi\) | ||
0.980874 | − | 0.194646i | \(-0.0623558\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.57292 | −0.170024 | −0.0850118 | − | 0.996380i | \(-0.527093\pi\) | ||||
−0.0850118 | + | 0.996380i | \(0.527093\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 8.13627 | + | 10.8025i | 0.535327 | + | 0.710752i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −19.6227 | −1.28552 | −0.642762 | − | 0.766066i | \(-0.722212\pi\) | ||||
−0.642762 | + | 0.766066i | \(0.722212\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.27471 | −0.409317 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.01423 | 0.195795 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.348000i | 0.0225102i | 0.999937 | + | 0.0112551i | \(0.00358269\pi\) | ||||
−0.999937 | + | 0.0112551i | \(0.996417\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 20.0883i | − | 1.29400i | −0.762490 | − | 0.647001i | \(-0.776023\pi\) | ||
0.762490 | − | 0.647001i | \(-0.223977\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.17975 | + | 7.58819i | −0.139259 | + | 0.484791i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 44.0753i | − | 2.80444i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 16.0883 | 1.01955 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 9.12494i | − | 0.575961i | −0.957636 | − | 0.287980i | \(-0.907016\pi\) | ||
0.957636 | − | 0.287980i | \(-0.0929838\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 8.88611i | − | 0.558665i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 3.74026 | 0.234224 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 21.8970i | − | 1.36590i | −0.730466 | − | 0.682949i | \(-0.760697\pi\) | ||
0.730466 | − | 0.682949i | \(-0.239303\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.63246 | + | 3.49510i | 0.163573 | + | 0.217175i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.88054i | 0.363996i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 28.1507i | − | 1.73585i | −0.496696 | − | 0.867924i | \(-0.665454\pi\) | ||
0.496696 | − | 0.867924i | \(-0.334546\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.08830i | 0.251142i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.08341 | 0.494697 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −25.6230 | −1.56226 | −0.781130 | − | 0.624368i | \(-0.785357\pi\) | ||||
−0.781130 | + | 0.624368i | \(0.785357\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −19.0147 | −1.15506 | −0.577532 | − | 0.816368i | \(-0.695984\pi\) | ||||
−0.577532 | + | 0.816368i | \(0.695984\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −9.36038 | − | 12.4277i | −0.566516 | − | 0.752161i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 19.0553 | 1.14908 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 18.2649i | 1.09743i | 0.836009 | + | 0.548716i | \(0.184883\pi\) | ||||
−0.836009 | + | 0.548716i | \(0.815117\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6.04982 | 0.362193 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −19.8136 | −1.18198 | −0.590990 | − | 0.806679i | \(-0.701263\pi\) | ||||
−0.590990 | + | 0.806679i | \(0.701263\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 13.7698i | − | 0.818530i | −0.912416 | − | 0.409265i | \(-0.865785\pi\) | ||
0.912416 | − | 0.409265i | \(-0.134215\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 8.45347 | 0.500740 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.30956 | − | 3.06640i | −0.136329 | − | 0.181004i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.00263 | 0.353096 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.357752 | −0.0209718 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 25.2844 | 1.47713 | 0.738566 | − | 0.674181i | \(-0.235503\pi\) | ||||
0.738566 | + | 0.674181i | \(0.235503\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 0.865280i | − | 0.0503786i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 5.11151i | − | 0.296600i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 10.2230i | 0.591213i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.79409 | + | 2.85765i | −0.218688 | + | 0.164712i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 3.38359i | − | 0.194382i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.357752 | −0.0204848 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.96074i | 0.340197i | 0.985427 | + | 0.170099i | \(0.0544086\pi\) | ||||
−0.985427 | + | 0.170099i | \(0.945591\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 14.5033i | − | 0.825063i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 26.4123 | 1.49770 | 0.748852 | − | 0.662738i | \(-0.230606\pi\) | ||||
0.748852 | + | 0.662738i | \(0.230606\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 9.53437i | − | 0.538914i | −0.963012 | − | 0.269457i | \(-0.913156\pi\) | ||
0.963012 | − | 0.269457i | \(-0.0868443\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.38359 | − | 1.79528i | 0.134300 | − | 0.101153i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 24.8123i | − | 1.39360i | −0.717266 | − | 0.696799i | \(-0.754607\pi\) | ||
0.717266 | − | 0.696799i | \(-0.245393\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 30.0585i | 1.68295i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 1.87870i | − | 0.104859i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −24.8555 | −1.38300 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −21.9222 | −1.21602 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 13.6166 | 0.753002 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 11.7574 | − | 8.85548i | 0.648206 | − | 0.488219i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.46438 | −0.520209 | −0.260105 | − | 0.965580i | \(-0.583757\pi\) | ||||
−0.260105 | + | 0.965580i | \(0.583757\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 1.65381i | − | 0.0906282i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −7.40158 | −0.404391 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −35.7110 | −1.94530 | −0.972650 | − | 0.232275i | \(-0.925383\pi\) | ||||
−0.972650 | + | 0.232275i | \(0.925383\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 4.63246i | − | 0.251601i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 30.9237 | 1.67461 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6.62483 | − | 17.2948i | −0.357707 | − | 0.933834i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.96074 | −0.105562 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 26.3764 | 1.41596 | 0.707980 | − | 0.706232i | \(-0.249606\pi\) | ||||
0.707980 | + | 0.706232i | \(0.249606\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.90538 | 0.423165 | 0.211583 | − | 0.977360i | \(-0.432138\pi\) | ||||
0.211583 | + | 0.977360i | \(0.432138\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.88054i | 0.313880i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 14.5490i | − | 0.774368i | −0.922003 | − | 0.387184i | \(-0.873448\pi\) | ||
0.922003 | − | 0.387184i | \(-0.126552\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 11.4951i | 0.610097i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −7.00841 | + | 5.27862i | −0.370924 | + | 0.279374i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 21.3186i | 1.12515i | 0.826745 | + | 0.562577i | \(0.190190\pi\) | ||||
−0.826745 | + | 0.562577i | \(0.809810\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −37.1766 | −1.95666 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 15.1276i | − | 0.793991i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.48052i | 0.391548i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.89996 | 0.360175 | 0.180088 | − | 0.983651i | \(-0.442362\pi\) | ||||
0.180088 | + | 0.983651i | \(0.442362\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.45096i | 0.0755337i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.76981 | − | 7.66056i | −0.299554 | − | 0.397716i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 26.5816i | − | 1.37634i | −0.725549 | − | 0.688171i | \(-0.758414\pi\) | ||
0.725549 | − | 0.688171i | \(-0.241586\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 9.84392i | − | 0.508338i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 34.5808i | − | 1.78100i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.52583 | −0.283843 | −0.141921 | − | 0.989878i | \(-0.545328\pi\) | ||||
−0.141921 | + | 0.989878i | \(0.545328\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.38124 | 0.480616 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 10.3706 | 0.529915 | 0.264957 | − | 0.964260i | \(-0.414642\pi\) | ||||
0.264957 | + | 0.964260i | \(0.414642\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 12.1838 | − | 9.17662i | 0.620942 | − | 0.467684i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.79528 | 0.0912594 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 12.2302i | 0.620097i | 0.950721 | + | 0.310049i | \(0.100345\pi\) | ||||
−0.950721 | + | 0.310049i | \(0.899655\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.76510 | 0.291553 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6.22303 | −0.313910 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 3.39964i | − | 0.171055i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.50188 | 0.376509 | 0.188254 | − | 0.982120i | \(-0.439717\pi\) | ||||
0.188254 | + | 0.982120i | \(0.439717\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −15.8399 | + | 11.9304i | −0.792987 | + | 0.597265i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.4558 | 0.572077 | 0.286039 | − | 0.958218i | \(-0.407661\pi\) | ||||
0.286039 | + | 0.958218i | \(0.407661\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −35.5762 | −1.77218 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.12786 | −0.0560441 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 8.45347i | − | 0.419023i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 29.6227i | 1.46475i | 0.680903 | + | 0.732373i | \(0.261587\pi\) | ||||
−0.680903 | + | 0.732373i | \(0.738413\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 7.45584i | − | 0.367770i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.22117 | + | 1.62134i | 0.0600898 | + | 0.0797810i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 18.1454i | − | 0.890724i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.27471 | 0.111393 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 17.8136i | − | 0.870251i | −0.900370 | − | 0.435125i | \(-0.856704\pi\) | ||
0.900370 | − | 0.435125i | \(-0.143296\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 13.4149i | − | 0.653802i | −0.945059 | − | 0.326901i | \(-0.893996\pi\) | ||
0.945059 | − | 0.326901i | \(-0.106004\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −5.56335 | −0.270499 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 12.3626i | 0.599676i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.670347 | − | 0.504895i | 0.0324404 | − | 0.0244336i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 30.0585i | 1.45124i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 17.6108i | − | 0.848283i | −0.905596 | − | 0.424142i | \(-0.860576\pi\) | ||
0.905596 | − | 0.424142i | \(-0.139424\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 36.4461i | 1.75149i | 0.482778 | + | 0.875743i | \(0.339628\pi\) | ||||
−0.482778 | + | 0.875743i | \(0.660372\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.63246 | 0.318002 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 13.0299 | 0.623303 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.79619 | 0.228909 | 0.114455 | − | 0.993428i | \(-0.463488\pi\) | ||||
0.114455 | + | 0.993428i | \(0.463488\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.93264 | + | 6.72792i | −0.0920303 | + | 0.320377i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −32.7021 | −1.55372 | −0.776861 | − | 0.629672i | \(-0.783189\pi\) | ||||
−0.776861 | + | 0.629672i | \(0.783189\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 9.11700i | − | 0.432187i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4.19427 | −0.198382 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 25.3480 | 1.19624 | 0.598122 | − | 0.801405i | \(-0.295914\pi\) | ||||
0.598122 | + | 0.801405i | \(0.295914\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.41658i | 0.349233i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 9.79874 | 0.460385 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −14.0168 | + | 10.5572i | −0.657118 | + | 0.494931i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.66910 | −0.0780770 | −0.0390385 | − | 0.999238i | \(-0.512429\pi\) | ||||
−0.0390385 | + | 0.999238i | \(0.512429\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.31623 | 0.154788 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −33.0246 | −1.53811 | −0.769054 | − | 0.639184i | \(-0.779272\pi\) | ||||
−0.769054 | + | 0.639184i | \(0.779272\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15.6833i | 0.728866i | 0.931230 | + | 0.364433i | \(0.118737\pi\) | ||||
−0.931230 | + | 0.364433i | \(0.881263\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 6.82338i | − | 0.316427i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4.85548i | 0.224685i | 0.993670 | + | 0.112342i | \(0.0358354\pi\) | ||||
−0.993670 | + | 0.112342i | \(0.964165\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13.8689 | − | 10.4458i | 0.640406 | − | 0.482344i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 4.82865i | − | 0.222493i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9.17662 | 0.421941 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 27.9412i | 1.28203i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.62481i | 0.165969i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.10575 | 0.324670 | 0.162335 | − | 0.986736i | \(-0.448097\pi\) | ||||
0.162335 | + | 0.986736i | \(0.448097\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.72529i | 0.443435i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.67398 | − | 2.76718i | 0.167172 | − | 0.125911i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.403496i | 0.0183218i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 4.29701i | − | 0.194716i | −0.995249 | − | 0.0973580i | \(-0.968961\pi\) | ||
0.995249 | − | 0.0973580i | \(-0.0310392\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 1.43753i | − | 0.0650074i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 19.3862 | 0.874888 | 0.437444 | − | 0.899246i | \(-0.355884\pi\) | ||||
0.437444 | + | 0.899246i | \(0.355884\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −19.5012 | −0.878291 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5.76510 | −0.259122 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −16.2230 | − | 21.5393i | −0.727702 | − | 0.966168i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 30.5722 | 1.36860 | 0.684301 | − | 0.729200i | \(-0.260108\pi\) | ||||
0.684301 | + | 0.729200i | \(0.260108\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 16.0417i | − | 0.716688i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 26.9817 | 1.20306 | 0.601528 | − | 0.798852i | \(-0.294559\pi\) | ||||
0.601528 | + | 0.798852i | \(0.294559\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.81624 | −0.169820 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 21.5808i | − | 0.958436i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −14.1717 | −0.628151 | −0.314075 | − | 0.949398i | \(-0.601694\pi\) | ||||
−0.314075 | + | 0.949398i | \(0.601694\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10.5572 | − | 14.0168i | −0.467025 | − | 0.620067i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 7.49510 | 0.330917 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −16.3578 | −0.720809 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −28.4371 | −1.25066 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4.01798i | 0.176370i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 25.9487i | 1.13683i | 0.822741 | + | 0.568416i | \(0.192444\pi\) | ||||
−0.822741 | + | 0.568416i | \(0.807556\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 24.6370i | − | 1.07730i | −0.842530 | − | 0.538650i | \(-0.818935\pi\) | ||
0.842530 | − | 0.538650i | \(-0.181065\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 5.93393 | + | 7.87846i | 0.258978 | + | 0.343844i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 20.0626i | 0.873940i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19.9778 | 0.868600 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 0.767184i | − | 0.0332930i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 8.53241i | − | 0.369579i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.11892 | −0.0916088 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 6.97679i | − | 0.301071i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −9.87870 | + | 34.3899i | −0.425506 | + | 1.48128i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 5.59582i | − | 0.240583i | −0.992739 | − | 0.120291i | \(-0.961617\pi\) | ||
0.992739 | − | 0.120291i | \(-0.0383829\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 13.4687i | − | 0.577998i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 15.3577i | − | 0.657853i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.15304 | 0.0920572 | 0.0460286 | − | 0.998940i | \(-0.485343\pi\) | ||||
0.0460286 | + | 0.998940i | \(0.485343\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.317194 | −0.0135375 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −44.0753 | −1.87767 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.79791 | + | 6.37017i | 0.204028 | + | 0.270887i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.86527 | −0.0791764 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 31.1317i | − | 1.31909i | −0.751664 | − | 0.659547i | \(-0.770748\pi\) | ||
0.751664 | − | 0.659547i | \(-0.229252\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −10.5572 | −0.446524 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 16.9509 | 0.715670 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 17.6227i | − | 0.742707i | −0.928492 | − | 0.371353i | \(-0.878894\pi\) | ||
0.928492 | − | 0.371353i | \(-0.121106\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.22479 | −0.219808 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.11337 | − | 1.59175i | 0.0887531 | − | 0.0668474i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 13.5389 | 0.567580 | 0.283790 | − | 0.958887i | \(-0.408408\pi\) | ||||
0.283790 | + | 0.958887i | \(0.408408\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −30.2145 | −1.26444 | −0.632218 | − | 0.774790i | \(-0.717855\pi\) | ||||
−0.632218 | + | 0.774790i | \(0.717855\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 21.0704 | 0.880228 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 6.48080i | − | 0.270268i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 38.1570i | 1.58850i | 0.607593 | + | 0.794249i | \(0.292135\pi\) | ||||
−0.607593 | + | 0.794249i | \(0.707865\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5.13735i | 0.213501i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 25.6086 | + | 34.0005i | 1.06242 | + | 1.41058i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 18.5283i | 0.767363i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 6.63246 | 0.274218 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 35.7057i | 1.47373i | 0.676039 | + | 0.736866i | \(0.263695\pi\) | ||||
−0.676039 | + | 0.736866i | \(0.736305\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 45.3441i | 1.86837i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 26.4337 | 1.08734 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 16.9630i | 0.696587i | 0.937386 | + | 0.348293i | \(0.113239\pi\) | ||||
−0.937386 | + | 0.348293i | \(0.886761\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.95357 | + | 7.90454i | 0.244073 | + | 0.324054i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 10.8420i | 0.443732i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 30.2372i | 1.23546i | 0.786391 | + | 0.617729i | \(0.211947\pi\) | ||||
−0.786391 | + | 0.617729i | \(0.788053\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 29.4558i | − | 1.20153i | −0.799426 | − | 0.600764i | \(-0.794863\pi\) | ||
0.799426 | − | 0.600764i | \(-0.205137\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6.56247 | −0.267244 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −17.0618 | −0.693663 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −21.7031 | −0.880902 | −0.440451 | − | 0.897777i | \(-0.645182\pi\) | ||||
−0.440451 | + | 0.897777i | \(0.645182\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −12.4277 | + | 9.36038i | −0.503598 | + | 0.379302i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 32.7155 | 1.32353 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 41.0159i | 1.65662i | 0.560273 | + | 0.828308i | \(0.310696\pi\) | ||||
−0.560273 | + | 0.828308i | \(0.689304\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.63648 | 0.0659893 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 42.2551 | 1.70113 | 0.850564 | − | 0.525872i | \(-0.176261\pi\) | ||||
0.850564 | + | 0.525872i | \(0.176261\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 14.5442i | 0.584579i | 0.956330 | + | 0.292290i | \(0.0944171\pi\) | ||||
−0.956330 | + | 0.292290i | \(0.905583\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.73845 | −0.0697616 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 12.8668 | + | 17.0832i | 0.515498 | + | 0.684425i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7.53699 | 0.301480 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 38.3113 | 1.53001 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.48441 | 0.218678 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11.6986i | 0.465713i | 0.972511 | + | 0.232857i | \(0.0748073\pi\) | ||||
−0.972511 | + | 0.232857i | \(0.925193\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 9.79528i | 0.389328i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 10.5808i | − | 0.419885i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 11.3650 | − | 39.5638i | 0.450296 | − | 1.56758i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 10.1919i | 0.403186i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −11.5344 | −0.455580 | −0.227790 | − | 0.973710i | \(-0.573150\pi\) | ||||
−0.227790 | + | 0.973710i | \(0.573150\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 13.7698i | − | 0.543028i | −0.962434 | − | 0.271514i | \(-0.912476\pi\) | ||
0.962434 | − | 0.271514i | \(-0.0875244\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 2.02484i | − | 0.0797279i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 18.7149 | 0.735758 | 0.367879 | − | 0.929874i | \(-0.380084\pi\) | ||||
0.367879 | + | 0.929874i | \(0.380084\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 3.92147i | − | 0.153931i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 9.62983 | + | 12.7855i | 0.377423 | + | 0.501103i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 19.5588i | 0.765395i | 0.923874 | + | 0.382697i | \(0.125005\pi\) | ||||
−0.923874 | + | 0.382697i | \(0.874995\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.01873i | 0.274245i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6.63246i | 0.258757i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.56735 | 0.100010 | 0.0500050 | − | 0.998749i | \(-0.484076\pi\) | ||||
0.0500050 | + | 0.998749i | \(0.484076\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.00155 | −0.350120 | −0.175060 | − | 0.984558i | \(-0.556012\pi\) | ||||
−0.175060 | + | 0.984558i | \(0.556012\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −19.5012 | −0.757365 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 13.4558 | + | 17.8653i | 0.521795 | + | 0.692786i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10.2230 | 0.395837 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 15.3534i | − | 0.593598i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.62134 | −0.0625912 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −28.7645 | −1.10879 | −0.554396 | − | 0.832253i | \(-0.687051\pi\) | ||||
−0.554396 | + | 0.832253i | \(0.687051\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − | 3.72792i | − | 0.143488i | ||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −17.2485 | −0.662912 | −0.331456 | − | 0.943471i | \(-0.607540\pi\) | ||||
−0.331456 | + | 0.943471i | \(0.607540\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.569453 | − | 0.756061i | −0.0218536 | − | 0.0290150i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.86527 | −0.224758 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 26.2096 | 1.00288 | 0.501441 | − | 0.865192i | \(-0.332803\pi\) | ||||
0.501441 | + | 0.865192i | \(0.332803\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.40918 | −0.321298 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.57292i | 0.0981632i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 21.3159i | − | 0.812070i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.99021i | 0.113753i | 0.998381 | + | 0.0568765i | \(0.0181141\pi\) | ||||
−0.998381 | + | 0.0568765i | \(0.981886\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 10.8025 | − | 8.13627i | 0.410353 | − | 0.309071i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 2.56556i | − | 0.0973173i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.81170 | −0.182256 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 19.6227i | 0.742197i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 18.1971i | − | 0.687294i | −0.939099 | − | 0.343647i | \(-0.888338\pi\) | ||
0.939099 | − | 0.343647i | \(-0.111662\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12.3955 | 0.467504 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 6.27471i | 0.236319i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 7.15078 | − | 5.38585i | 0.268933 | − | 0.202556i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 4.86735i | − | 0.182797i | −0.995814 | − | 0.0913986i | \(-0.970866\pi\) | ||
0.995814 | − | 0.0913986i | \(-0.0291337\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 3.01423i | − | 0.113042i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 10.5173i | − | 0.393876i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 33.9019 | 1.26786 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0.348000 | 0.0129963 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 7.10575 | 0.265000 | 0.132500 | − | 0.991183i | \(-0.457700\pi\) | ||||
0.132500 | + | 0.991183i | \(0.457700\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 30.6508 | − | 23.0857i | 1.14149 | − | 0.859755i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −20.0883 | −0.747092 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 21.9222i | 0.814170i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −42.5369 | −1.57761 | −0.788803 | − | 0.614645i | \(-0.789299\pi\) | ||||
−0.788803 | + | 0.614645i | \(0.789299\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.95357i | 0.220201i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 38.8291 | 1.43419 | 0.717093 | − | 0.696977i | \(-0.245472\pi\) | ||||
0.717093 | + | 0.696977i | \(0.245472\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 7.58819 | + | 2.17975i | 0.279894 | + | 0.0804014i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −33.5441 | −1.23561 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 27.0085 | 0.993524 | 0.496762 | − | 0.867887i | \(-0.334522\pi\) | ||||
0.496762 | + | 0.867887i | \(0.334522\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −44.0753 | −1.61915 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 28.0242i | − | 1.02811i | −0.857758 | − | 0.514054i | \(-0.828143\pi\) | ||
0.857758 | − | 0.514054i | \(-0.171857\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.73057i | 0.173315i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 16.0883i | − | 0.588640i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.97038 | − | 2.99042i | 0.145074 | − | 0.109268i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 46.6071i | − | 1.70072i | −0.526204 | − | 0.850358i | \(-0.676385\pi\) | ||
0.526204 | − | 0.850358i | \(-0.323615\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −9.12494 | −0.332531 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 11.0517i | − | 0.402211i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 18.9934i | − | 0.690326i | −0.938543 | − | 0.345163i | \(-0.887824\pi\) | ||
0.938543 | − | 0.345163i | \(-0.112176\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −8.88611 | −0.322545 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 25.9487i | − | 0.940639i | −0.882496 | − | 0.470320i | \(-0.844139\pi\) | ||
0.882496 | − | 0.470320i | \(-0.155861\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 21.6743 | + | 28.7770i | 0.784664 | + | 1.04180i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − | 3.74026i | − | 0.135229i | ||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.51146i | 0.162899i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5.27924i | 0.190374i | 0.995459 | + | 0.0951872i | \(0.0303450\pi\) | ||||
−0.995459 | + | 0.0951872i | \(0.969655\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −21.8970 | −0.788601 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 5.30076 | 0.190655 | 0.0953276 | − | 0.995446i | \(-0.469610\pi\) | ||||
0.0953276 | + | 0.995446i | \(0.469610\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 22.5533 | 0.810137 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.49510 | − | 2.63246i | 0.125386 | − | 0.0944389i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −10.8751 | −0.389640 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 52.0961i | 1.86415i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.88054 | 0.210153 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5.44607 | −0.194379 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15.7305i | 0.560733i | 0.959893 | + | 0.280367i | \(0.0904561\pi\) | ||||
−0.959893 | + | 0.280367i | \(0.909544\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −28.1507 | −1.00219 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.79008 | − | 7.37373i | 0.348095 | − | 0.262180i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.86527 | 0.0662378 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4.08830 | 0.144997 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −8.71605 | −0.308738 | −0.154369 | − | 0.988013i | \(-0.549335\pi\) | ||||
−0.154369 | + | 0.988013i | \(0.549335\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 18.4493i | − | 0.652691i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 8.08341i | − | 0.285613i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 33.9019i | 1.19637i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.12101 | − | 4.14375i | −0.110001 | − | 0.146048i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 25.6230i | 0.901972i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 4.28448 | 0.150634 | 0.0753171 | − | 0.997160i | \(-0.476003\pi\) | ||||
0.0753171 | + | 0.997160i | \(0.476003\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 30.7208i | − | 1.07875i | −0.842065 | − | 0.539376i | \(-0.818660\pi\) | ||
0.842065 | − | 0.539376i | \(-0.181340\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 19.0147i | 0.666876i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.62134 | −0.0567931 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 13.4558i | 0.470760i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −12.4277 | + | 9.36038i | −0.434260 | + | 0.327078i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 27.1897i | 0.948928i | 0.880275 | + | 0.474464i | \(0.157358\pi\) | ||||
−0.880275 | + | 0.474464i | \(0.842642\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 49.5318i | 1.72657i | 0.504715 | + | 0.863286i | \(0.331597\pi\) | ||||
−0.504715 | + | 0.863286i | \(0.668403\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 19.0553i | − | 0.663421i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −27.4228 | −0.953585 | −0.476793 | − | 0.879016i | \(-0.658201\pi\) | ||||
−0.476793 | + | 0.879016i | \(0.658201\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 44.3135 | 1.53907 | 0.769536 | − | 0.638603i | \(-0.220487\pi\) | ||||
0.769536 | + | 0.638603i | \(0.220487\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 18.2649 | 0.633603 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −22.3113 | − | 6.40907i | −0.773042 | − | 0.222061i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −18.0928 | −0.626128 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 6.04982i | − | 0.209112i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −52.9322 | −1.82742 | −0.913712 | − | 0.406362i | \(-0.866797\pi\) | ||||
−0.913712 | + | 0.406362i | \(0.866797\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.58078 | −0.192441 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 19.8136i | 0.682416i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −24.3402 | −0.837328 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 31.9701 | − | 24.0794i | 1.09851 | − | 0.827377i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −13.7698 | −0.472579 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.87506 | −0.0985559 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −23.8821 | −0.817707 | −0.408854 | − | 0.912600i | \(-0.634071\pi\) | ||||
−0.408854 | + | 0.912600i | \(0.634071\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 8.45347i | − | 0.289102i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 46.2279i | 1.57912i | 0.613676 | + | 0.789558i | \(0.289690\pi\) | ||||
−0.613676 | + | 0.789558i | \(0.710310\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 18.2159i | − | 0.621517i | −0.950489 | − | 0.310759i | \(-0.899417\pi\) | ||
0.950489 | − | 0.310759i | \(-0.100583\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.06640 | + | 2.30956i | −0.104503 | + | 0.0787098i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 3.72055i | − | 0.126649i | −0.997993 | − | 0.0633245i | \(-0.979830\pi\) | ||
0.997993 | − | 0.0633245i | \(-0.0201703\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.53174 | 0.154084 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 6.00263i | − | 0.203860i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 15.4073i | − | 0.522656i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 38.5909 | 1.30760 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.357752i | 0.0121081i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 20.8038 | − | 15.6691i | 0.703297 | − | 0.529712i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 19.1011i | 0.644997i | 0.946570 | + | 0.322498i | \(0.104523\pi\) | ||||
−0.946570 | + | 0.322498i | \(0.895477\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 25.2844i | − | 0.852822i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 29.3993i | 0.990487i | 0.868754 | + | 0.495243i | \(0.164921\pi\) | ||||
−0.868754 | + | 0.495243i | \(0.835079\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.33944 | 0.146034 | 0.0730169 | − | 0.997331i | \(-0.476737\pi\) | ||||
0.0730169 | + | 0.997331i | \(0.476737\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.865280 | −0.0290861 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 8.74929 | 0.293773 | 0.146886 | − | 0.989153i | \(-0.453075\pi\) | ||||
0.146886 | + | 0.989153i | \(0.453075\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 14.9326 | + | 19.8260i | 0.500825 | + | 0.664943i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.11151 | −0.171242 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 41.6979i | − | 1.39537i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.86887 | −0.263027 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 10.2230 | 0.341337 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 35.5762i | 1.18653i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −12.0207 | −0.400468 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.85765 | + | 3.79409i | 0.0950967 | + | 0.126260i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −15.1909 | −0.504963 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −40.5946 | −1.34792 | −0.673960 | − | 0.738768i | \(-0.735408\pi\) | ||||
−0.673960 | + | 0.738768i | \(0.735408\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.38359 | −0.112227 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 30.4887i | − | 1.01014i | −0.863079 | − | 0.505068i | \(-0.831467\pi\) | ||
0.863079 | − | 0.505068i | \(-0.168533\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 82.2355i | − | 2.72160i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0.357752i | 0.0118269i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −9.90553 | − | 13.1515i | −0.327109 | − | 0.434302i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 16.6925i | 0.550634i | 0.961353 | + | 0.275317i | \(0.0887828\pi\) | ||||
−0.961353 | + | 0.275317i | \(0.911217\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5.96074 | 0.196413 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 59.9340i | − | 1.97275i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 6.16527i | − | 0.202713i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −14.5033 | −0.476351 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 44.6963i | 1.46644i | 0.679993 | + | 0.733219i | \(0.261983\pi\) | ||||
−0.679993 | + | 0.733219i | \(0.738017\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −50.4265 | − | 14.4853i | −1.65266 | − | 0.474737i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 26.4123i | − | 0.864699i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 19.1184i | − | 0.625238i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 58.7208i | − | 1.91832i | −0.282858 | − | 0.959162i | \(-0.591283\pi\) | ||
0.282858 | − | 0.959162i | \(-0.408717\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −9.53437 | −0.311142 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 28.7137 | 0.936040 | 0.468020 | − | 0.883718i | \(-0.344967\pi\) | ||||
0.468020 | + | 0.883718i | \(0.344967\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.52241 | 0.0821411 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.79528 | − | 2.38359i | −0.0584006 | − | 0.0775383i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −40.7146 | −1.32305 | −0.661523 | − | 0.749925i | \(-0.730090\pi\) | ||||
−0.661523 | + | 0.749925i | \(0.730090\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 39.0024i | − | 1.26607i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −24.8123 | −0.804594 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −25.5396 | −0.827309 | −0.413655 | − | 0.910434i | \(-0.635748\pi\) | ||||
−0.413655 | + | 0.910434i | \(0.635748\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 23.7646i | − | 0.769003i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 30.0585 | 0.971652 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 15.7569 | − | 11.8679i | 0.508818 | − | 0.383233i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.60036 | 0.180657 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.87870 | −0.0605402 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5.79424 | 0.186523 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 20.8465i | 0.670378i | 0.942151 | + | 0.335189i | \(0.108800\pi\) | ||||
−0.942151 | + | 0.335189i | \(0.891200\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 24.8555i | 0.798473i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 35.1302i | − | 1.12738i | −0.825986 | − | 0.563691i | \(-0.809381\pi\) | ||
0.825986 | − | 0.563691i | \(-0.190619\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.62077 | + | 4.80729i | 0.116077 | + | 0.154115i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 21.9222i | 0.702072i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 8.63246 | 0.276177 | 0.138088 | − | 0.990420i | \(-0.455904\pi\) | ||||
0.138088 | + | 0.990420i | \(0.455904\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 41.3185i | − | 1.32054i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 13.6166i | − | 0.434746i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −25.0646 | −0.799436 | −0.399718 | − | 0.916638i | \(-0.630892\pi\) | ||||
−0.399718 | + | 0.916638i | \(0.630892\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 29.8136i | − | 0.949940i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −8.85548 | − | 11.7574i | −0.281873 | − | 0.374242i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 3.12101i | − | 0.0992424i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10.3855i | 0.329907i | 0.986301 | + | 0.164954i | \(0.0527474\pi\) | ||||
−0.986301 | + | 0.164954i | \(0.947253\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 9.46438i | 0.300343i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 12.2283 | 0.387662 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 50.1424 | 1.58803 | 0.794013 | − | 0.607900i | \(-0.207988\pi\) | ||||
0.794013 | + | 0.607900i | \(0.207988\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.65381 | −0.0523242 |
(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.p.a.559.4 | 16 | ||
3.2 | odd | 2 | 2016.2.p.g.559.9 | 16 | |||
4.3 | odd | 2 | 168.2.p.a.139.12 | yes | 16 | ||
7.6 | odd | 2 | inner | 672.2.p.a.559.13 | 16 | ||
8.3 | odd | 2 | inner | 672.2.p.a.559.5 | 16 | ||
8.5 | even | 2 | 168.2.p.a.139.10 | yes | 16 | ||
12.11 | even | 2 | 504.2.p.g.307.6 | 16 | |||
21.20 | even | 2 | 2016.2.p.g.559.7 | 16 | |||
24.5 | odd | 2 | 504.2.p.g.307.7 | 16 | |||
24.11 | even | 2 | 2016.2.p.g.559.8 | 16 | |||
28.27 | even | 2 | 168.2.p.a.139.11 | yes | 16 | ||
56.13 | odd | 2 | 168.2.p.a.139.9 | ✓ | 16 | ||
56.27 | even | 2 | inner | 672.2.p.a.559.12 | 16 | ||
84.83 | odd | 2 | 504.2.p.g.307.5 | 16 | |||
168.83 | odd | 2 | 2016.2.p.g.559.10 | 16 | |||
168.125 | even | 2 | 504.2.p.g.307.8 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
168.2.p.a.139.9 | ✓ | 16 | 56.13 | odd | 2 | ||
168.2.p.a.139.10 | yes | 16 | 8.5 | even | 2 | ||
168.2.p.a.139.11 | yes | 16 | 28.27 | even | 2 | ||
168.2.p.a.139.12 | yes | 16 | 4.3 | odd | 2 | ||
504.2.p.g.307.5 | 16 | 84.83 | odd | 2 | |||
504.2.p.g.307.6 | 16 | 12.11 | even | 2 | |||
504.2.p.g.307.7 | 16 | 24.5 | odd | 2 | |||
504.2.p.g.307.8 | 16 | 168.125 | even | 2 | |||
672.2.p.a.559.4 | 16 | 1.1 | even | 1 | trivial | ||
672.2.p.a.559.5 | 16 | 8.3 | odd | 2 | inner | ||
672.2.p.a.559.12 | 16 | 56.27 | even | 2 | inner | ||
672.2.p.a.559.13 | 16 | 7.6 | odd | 2 | inner | ||
2016.2.p.g.559.7 | 16 | 21.20 | even | 2 | |||
2016.2.p.g.559.8 | 16 | 24.11 | even | 2 | |||
2016.2.p.g.559.9 | 16 | 3.2 | odd | 2 | |||
2016.2.p.g.559.10 | 16 | 168.83 | odd | 2 |