Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4032,2,Mod(575,4032)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4032, 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("4032.575");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4032 = 2^{6} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4032.h (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: | \(32.1956820950\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | no (minimal twist has level 1008) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 575.4 | ||
Root | \(-0.258819 - 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4032.575 |
Dual form | 4032.2.h.f.575.5 |
$q$-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 \(\left(\mathbb{Z}/4032\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(1793\) | \(3781\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(1\) |
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 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 1.03528i | − 0.462990i | −0.972836 | − | 0.231495i | \(-0.925638\pi\) | ||||
0.972836 | − | 0.231495i | \(-0.0743616\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.378937 | 0.114254 | 0.0571270 | − | 0.998367i | \(-0.481806\pi\) | ||||
0.0571270 | + | 0.998367i | \(0.481806\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.00000 | −0.554700 | −0.277350 | − | 0.960769i | \(-0.589456\pi\) | ||||
−0.277350 | + | 0.960769i | \(0.589456\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.86370i | 0.937086i | 0.883441 | + | 0.468543i | \(0.155221\pi\) | ||||
−0.883441 | + | 0.468543i | \(0.844779\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 1.46410i | − 0.335888i | −0.985797 | − | 0.167944i | \(-0.946287\pi\) | ||||
0.985797 | − | 0.167944i | \(-0.0537128\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.27792 | −1.10052 | −0.550261 | − | 0.834993i | \(-0.685472\pi\) | ||||
−0.550261 | + | 0.834993i | \(0.685472\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.92820 | 0.785641 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 3.48477i | − 0.647105i | −0.946210 | − | 0.323552i | \(-0.895123\pi\) | ||||
0.946210 | − | 0.323552i | \(-0.104877\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.53590i | 0.455461i | 0.973724 | + | 0.227730i | \(0.0731305\pi\) | ||||
−0.973724 | + | 0.227730i | \(0.926870\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.03528 | 0.174994 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.92820 | −0.481394 | −0.240697 | − | 0.970600i | \(-0.577376\pi\) | ||||
−0.240697 | + | 0.970600i | \(0.577376\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.76268i | 1.36850i | 0.729247 | + | 0.684251i | \(0.239871\pi\) | ||||
−0.729247 | + | 0.684251i | \(0.760129\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 4.00000i | − 0.609994i | −0.952353 | − | 0.304997i | \(-0.901344\pi\) | ||||
0.952353 | − | 0.304997i | \(-0.0986555\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.48528 | −1.23771 | −0.618853 | − | 0.785507i | \(-0.712402\pi\) | ||||
−0.618853 | + | 0.785507i | \(0.712402\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 7.07107i | − 0.971286i | −0.874157 | − | 0.485643i | \(-0.838586\pi\) | ||||
0.874157 | − | 0.485643i | \(-0.161414\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 0.392305i | − 0.0528984i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.82843 | −0.368230 | −0.184115 | − | 0.982905i | \(-0.558942\pi\) | ||||
−0.184115 | + | 0.982905i | \(0.558942\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.46410 | −0.443533 | −0.221766 | − | 0.975100i | \(-0.571182\pi\) | ||||
−0.221766 | + | 0.975100i | \(0.571182\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.07055i | 0.256820i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.53590i | 1.04283i | 0.853304 | + | 0.521413i | \(0.174595\pi\) | ||||
−0.853304 | + | 0.521413i | \(0.825405\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.1769 | −1.20778 | −0.603888 | − | 0.797069i | \(-0.706382\pi\) | ||||
−0.603888 | + | 0.797069i | \(0.706382\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.46410 | 0.873607 | 0.436804 | − | 0.899557i | \(-0.356111\pi\) | ||||
0.436804 | + | 0.899557i | \(0.356111\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.378937i | 0.0431839i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.3923i | 1.16923i | 0.811312 | + | 0.584613i | \(0.198754\pi\) | ||||
−0.811312 | + | 0.584613i | \(0.801246\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −17.5254 | −1.92366 | −0.961829 | − | 0.273650i | \(-0.911769\pi\) | ||||
−0.961829 | + | 0.273650i | \(0.911769\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.00000 | 0.433861 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 1.03528i | − 0.109739i | −0.998494 | − | 0.0548695i | \(-0.982526\pi\) | ||||
0.998494 | − | 0.0548695i | \(-0.0174743\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 2.00000i | − 0.209657i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.51575 | −0.155513 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.53590 | 0.460551 | 0.230275 | − | 0.973126i | \(-0.426037\pi\) | ||||
0.230275 | + | 0.973126i | \(0.426037\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 0.277401i | − 0.0276025i | −0.999905 | − | 0.0138012i | \(-0.995607\pi\) | ||||
0.999905 | − | 0.0138012i | \(-0.00439321\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.46410i | 0.144262i | 0.997395 | + | 0.0721311i | \(0.0229800\pi\) | ||||
−0.997395 | + | 0.0721311i | \(0.977020\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.52004 | 0.436969 | 0.218484 | − | 0.975840i | \(-0.429889\pi\) | ||||
0.218484 | + | 0.975840i | \(0.429889\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.00000 | −0.766261 | −0.383131 | − | 0.923694i | \(-0.625154\pi\) | ||||
−0.383131 | + | 0.923694i | \(0.625154\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 9.89949i | − 0.931266i | −0.884978 | − | 0.465633i | \(-0.845827\pi\) | ||||
0.884978 | − | 0.465633i | \(-0.154173\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.46410i | 0.509530i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.86370 | −0.354185 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.8564 | −0.986946 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 9.24316i | − 0.826733i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.3923i | 1.27711i | 0.769576 | + | 0.638555i | \(0.220468\pi\) | ||||
−0.769576 | + | 0.638555i | \(0.779532\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.51575 | −0.132432 | −0.0662158 | − | 0.997805i | \(-0.521093\pi\) | ||||
−0.0662158 | + | 0.997805i | \(0.521093\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.46410 | 0.126954 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 6.31319i | − 0.539372i | −0.962948 | − | 0.269686i | \(-0.913080\pi\) | ||||
0.962948 | − | 0.269686i | \(-0.0869200\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 21.8564i | 1.85384i | 0.375264 | + | 0.926918i | \(0.377552\pi\) | ||||
−0.375264 | + | 0.926918i | \(0.622448\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.757875 | −0.0633767 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.60770 | −0.299603 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 16.8690i | 1.38196i | 0.722872 | + | 0.690982i | \(0.242822\pi\) | ||||
−0.722872 | + | 0.690982i | \(0.757178\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 2.92820i | − 0.238294i | −0.992877 | − | 0.119147i | \(-0.961984\pi\) | ||||
0.992877 | − | 0.119147i | \(-0.0380159\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.62536 | 0.210874 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 17.3205 | 1.38233 | 0.691164 | − | 0.722698i | \(-0.257098\pi\) | ||||
0.691164 | + | 0.722698i | \(0.257098\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − 5.27792i | − 0.415958i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.535898i | 0.0419748i | 0.999780 | + | 0.0209874i | \(0.00668099\pi\) | ||||
−0.999780 | + | 0.0209874i | \(0.993319\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 22.4243 | 1.73525 | 0.867624 | − | 0.497221i | \(-0.165646\pi\) | ||||
0.867624 | + | 0.497221i | \(0.165646\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 11.5911i | 0.881256i | 0.897690 | + | 0.440628i | \(0.145244\pi\) | ||||
−0.897690 | + | 0.440628i | \(0.854756\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.92820i | 0.296944i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −26.3896 | −1.97245 | −0.986225 | − | 0.165409i | \(-0.947106\pi\) | ||||
−0.986225 | + | 0.165409i | \(0.947106\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.9282 | −0.960946 | −0.480473 | − | 0.877010i | \(-0.659535\pi\) | ||||
−0.480473 | + | 0.877010i | \(0.659535\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.03150i | 0.222880i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.46410i | 0.107066i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −20.7327 | −1.50017 | −0.750084 | − | 0.661343i | \(-0.769987\pi\) | ||||
−0.750084 | + | 0.661343i | \(0.769987\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −13.8564 | −0.997406 | −0.498703 | − | 0.866773i | \(-0.666190\pi\) | ||||
−0.498703 | + | 0.866773i | \(0.666190\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 15.3533i | 1.09388i | 0.837173 | + | 0.546938i | \(0.184207\pi\) | ||||
−0.837173 | + | 0.546938i | \(0.815793\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 4.00000i | − 0.283552i | −0.989899 | − | 0.141776i | \(-0.954719\pi\) | ||||
0.989899 | − | 0.141776i | \(-0.0452813\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.48477 | 0.244583 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.07180 | 0.633602 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 0.554803i | − 0.0383765i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.07180i | 0.624528i | 0.949995 | + | 0.312264i | \(0.101087\pi\) | ||||
−0.949995 | + | 0.312264i | \(0.898913\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.14110 | −0.282421 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.53590 | −0.172148 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 7.72741i | − 0.519802i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 17.8564i | − 1.19575i | −0.801588 | − | 0.597877i | \(-0.796011\pi\) | ||||
0.801588 | − | 0.597877i | \(-0.203989\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −23.9401 | −1.58896 | −0.794480 | − | 0.607290i | \(-0.792256\pi\) | ||||
−0.794480 | + | 0.607290i | \(0.792256\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 25.7128 | 1.69915 | 0.849575 | − | 0.527467i | \(-0.176858\pi\) | ||||
0.849575 | + | 0.527467i | \(0.176858\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 10.6574i | − 0.698188i | −0.937088 | − | 0.349094i | \(-0.886489\pi\) | ||||
0.937088 | − | 0.349094i | \(-0.113511\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.78461i | 0.573045i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −17.3495 | −1.12225 | −0.561123 | − | 0.827732i | \(-0.689631\pi\) | ||||
−0.561123 | + | 0.827732i | \(0.689631\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.3923 | 0.927090 | 0.463545 | − | 0.886073i | \(-0.346577\pi\) | ||||
0.463545 | + | 0.886073i | \(0.346577\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.03528i | 0.0661414i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.92820i | 0.186317i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −24.4949 | −1.54610 | −0.773052 | − | 0.634343i | \(-0.781271\pi\) | ||||
−0.773052 | + | 0.634343i | \(0.781271\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.00000 | −0.125739 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 14.4195i | − 0.899466i | −0.893163 | − | 0.449733i | \(-0.851519\pi\) | ||||
0.893163 | − | 0.449733i | \(-0.148481\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 2.92820i | − 0.181950i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 17.3495 | 1.06982 | 0.534908 | − | 0.844910i | \(-0.320346\pi\) | ||||
0.534908 | + | 0.844910i | \(0.320346\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.32051 | −0.449695 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 18.0058i | 1.09784i | 0.835876 | + | 0.548918i | \(0.184960\pi\) | ||||
−0.835876 | + | 0.548918i | \(0.815040\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 31.3205i | 1.90259i | 0.308289 | + | 0.951293i | \(0.400244\pi\) | ||||
−0.308289 | + | 0.951293i | \(0.599756\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.48854 | 0.0897625 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.143594 | −0.00862770 | −0.00431385 | − | 0.999991i | \(-0.501373\pi\) | ||||
−0.00431385 | + | 0.999991i | \(0.501373\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 10.6574i | − 0.635765i | −0.948130 | − | 0.317883i | \(-0.897028\pi\) | ||||
0.948130 | − | 0.317883i | \(-0.102972\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.5359i | 0.864069i | 0.901857 | + | 0.432035i | \(0.142204\pi\) | ||||
−0.901857 | + | 0.432035i | \(0.857796\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.76268 | −0.517245 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.07180 | 0.121870 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 13.1069i | − 0.765711i | −0.923808 | − | 0.382855i | \(-0.874941\pi\) | ||||
0.923808 | − | 0.382855i | \(-0.125059\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.92820i | 0.170487i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 10.5558 | 0.610460 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.00000 | 0.230556 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.58630i | 0.205351i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 21.4641i | 1.22502i | 0.790462 | + | 0.612510i | \(0.209840\pi\) | ||||
−0.790462 | + | 0.612510i | \(0.790160\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.31268 | 0.0744351 | 0.0372176 | − | 0.999307i | \(-0.488151\pi\) | ||||
0.0372176 | + | 0.999307i | \(0.488151\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.0718 | 0.625815 | 0.312907 | − | 0.949784i | \(-0.398697\pi\) | ||||
0.312907 | + | 0.949784i | \(0.398697\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 23.8386i | 1.33891i | 0.742854 | + | 0.669453i | \(0.233472\pi\) | ||||
−0.742854 | + | 0.669453i | \(0.766528\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 1.32051i | − 0.0739343i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.65685 | 0.314756 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.85641 | −0.435795 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − 8.48528i | − 0.467809i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 28.7846i | − 1.58215i | −0.611722 | − | 0.791073i | \(-0.709523\pi\) | ||||
0.611722 | − | 0.791073i | \(-0.290477\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 8.83701 | 0.482818 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −28.7846 | −1.56800 | −0.783999 | − | 0.620762i | \(-0.786823\pi\) | ||||
−0.783999 | + | 0.620762i | \(0.786823\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.960947i | 0.0520382i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 1.00000i | − 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −10.9348 | −0.587009 | −0.293505 | − | 0.955958i | \(-0.594822\pi\) | ||||
−0.293505 | + | 0.955958i | \(0.594822\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −21.3205 | −1.14126 | −0.570630 | − | 0.821207i | \(-0.693301\pi\) | ||||
−0.570630 | + | 0.821207i | \(0.693301\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 20.8343i | 1.10890i | 0.832218 | + | 0.554448i | \(0.187071\pi\) | ||||
−0.832218 | + | 0.554448i | \(0.812929\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 10.5359i | 0.559187i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −9.41902 | −0.497117 | −0.248558 | − | 0.968617i | \(-0.579957\pi\) | ||||
−0.248558 | + | 0.968617i | \(0.579957\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 16.8564 | 0.887179 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 7.72741i | − 0.404471i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 2.92820i | − 0.152851i | −0.997075 | − | 0.0764255i | \(-0.975649\pi\) | ||||
0.997075 | − | 0.0764255i | \(-0.0243507\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.07107 | 0.367112 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 22.0000 | 1.13912 | 0.569558 | − | 0.821951i | \(-0.307114\pi\) | ||||
0.569558 | + | 0.821951i | \(0.307114\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.96953i | 0.358949i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 20.7846i | − 1.06763i | −0.845600 | − | 0.533817i | \(-0.820757\pi\) | ||||
0.845600 | − | 0.533817i | \(-0.179243\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −13.9391 | −0.712253 | −0.356126 | − | 0.934438i | \(-0.615903\pi\) | ||||
−0.356126 | + | 0.934438i | \(0.615903\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.392305 | 0.0199937 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 23.2838i | − 1.18053i | −0.807208 | − | 0.590267i | \(-0.799023\pi\) | ||||
0.807208 | − | 0.590267i | \(-0.200977\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 20.3923i | − 1.03128i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 10.7589 | 0.541339 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.53590 | 0.227650 | 0.113825 | − | 0.993501i | \(-0.463690\pi\) | ||||
0.113825 | + | 0.993501i | \(0.463690\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 24.5964i | 1.22829i | 0.789194 | + | 0.614144i | \(0.210498\pi\) | ||||
−0.789194 | + | 0.614144i | \(0.789502\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 5.07180i | − 0.252644i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.10961 | −0.0550011 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.46410 | 0.171289 | 0.0856444 | − | 0.996326i | \(-0.472705\pi\) | ||||
0.0856444 | + | 0.996326i | \(0.472705\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 2.82843i | − 0.139178i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 18.1436i | 0.890634i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −26.0106 | −1.27070 | −0.635352 | − | 0.772223i | \(-0.719145\pi\) | ||||
−0.635352 | + | 0.772223i | \(0.719145\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −29.7128 | −1.44811 | −0.724057 | − | 0.689740i | \(-0.757725\pi\) | ||||
−0.724057 | + | 0.689740i | \(0.757725\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 15.1774i | 0.736213i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 3.46410i | − 0.167640i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.79367 | −0.327239 | −0.163620 | − | 0.986523i | \(-0.552317\pi\) | ||||
−0.163620 | + | 0.986523i | \(0.552317\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 18.7846 | 0.902731 | 0.451365 | − | 0.892339i | \(-0.350937\pi\) | ||||
0.451365 | + | 0.892339i | \(0.350937\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.72741i | 0.369652i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 13.8564i | − 0.661330i | −0.943748 | − | 0.330665i | \(-0.892727\pi\) | ||||
0.943748 | − | 0.330665i | \(-0.107273\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 23.0064 | 1.09306 | 0.546532 | − | 0.837438i | \(-0.315948\pi\) | ||||
0.546532 | + | 0.837438i | \(0.315948\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.07180 | −0.0508080 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 11.4152i | − 0.538719i | −0.963040 | − | 0.269359i | \(-0.913188\pi\) | ||||
0.963040 | − | 0.269359i | \(-0.0868119\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.32051i | 0.156357i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.07055 | −0.0970690 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 37.8048i | − 1.76075i | −0.474282 | − | 0.880373i | \(-0.657292\pi\) | ||||
0.474282 | − | 0.880373i | \(-0.342708\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.46410i | 0.346886i | 0.984844 | + | 0.173443i | \(0.0554893\pi\) | ||||
−0.984844 | + | 0.173443i | \(0.944511\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −0.757875 | −0.0350703 | −0.0175351 | − | 0.999846i | \(-0.505582\pi\) | ||||
−0.0175351 | + | 0.999846i | \(0.505582\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.53590 | −0.394151 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 1.51575i | − 0.0696942i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 5.75129i | − 0.263887i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9.04008 | −0.413052 | −0.206526 | − | 0.978441i | \(-0.566216\pi\) | ||||
−0.206526 | + | 0.978441i | \(0.566216\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.85641 | 0.267029 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 4.69591i | − 0.213230i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 10.9282i | − 0.495204i | −0.968862 | − | 0.247602i | \(-0.920357\pi\) | ||||
0.968862 | − | 0.247602i | \(-0.0796426\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 39.2190 | 1.76993 | 0.884965 | − | 0.465657i | \(-0.154182\pi\) | ||||
0.884965 | + | 0.465657i | \(0.154182\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 13.4641 | 0.606393 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 10.1769i | − 0.456496i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.14359i | 0.275025i | 0.990500 | + | 0.137513i | \(0.0439107\pi\) | ||||
−0.990500 | + | 0.137513i | \(0.956089\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 23.1822 | 1.03364 | 0.516822 | − | 0.856093i | \(-0.327115\pi\) | ||||
0.516822 | + | 0.856093i | \(0.327115\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.287187 | −0.0127797 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 8.76268i | − 0.388399i | −0.980962 | − | 0.194200i | \(-0.937789\pi\) | ||||
0.980962 | − | 0.194200i | \(-0.0622109\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.46410i | 0.330192i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.51575 | 0.0667919 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.21539 | −0.141413 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 40.4302i | 1.77128i | 0.464374 | + | 0.885639i | \(0.346279\pi\) | ||||
−0.464374 | + | 0.885639i | \(0.653721\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 43.7128i | − 1.91143i | −0.294297 | − | 0.955714i | \(-0.595086\pi\) | ||||
0.294297 | − | 0.955714i | \(-0.404914\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −9.79796 | −0.426806 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.85641 | 0.211148 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 17.5254i | − 0.759108i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 4.67949i | − 0.202312i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.378937 | −0.0163220 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −25.7128 | −1.10548 | −0.552740 | − | 0.833354i | \(-0.686418\pi\) | ||||
−0.552740 | + | 0.833354i | \(0.686418\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8.28221i | 0.354771i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 11.4641i | − 0.490170i | −0.969502 | − | 0.245085i | \(-0.921184\pi\) | ||||
0.969502 | − | 0.245085i | \(-0.0788158\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.10205 | −0.217355 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −10.3923 | −0.441926 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 2.72689i | − 0.115542i | −0.998330 | − | 0.0577710i | \(-0.981601\pi\) | ||||
0.998330 | − | 0.0577710i | \(-0.0183993\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.00000i | 0.338364i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.31268 | 0.0553228 | 0.0276614 | − | 0.999617i | \(-0.491194\pi\) | ||||
0.0276614 | + | 0.999617i | \(0.491194\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10.2487 | −0.431167 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0.656339i | 0.0275152i | 0.999905 | + | 0.0137576i | \(0.00437931\pi\) | ||||
−0.999905 | + | 0.0137576i | \(0.995621\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 2.39230i | − 0.100115i | −0.998746 | − | 0.0500574i | \(-0.984060\pi\) | ||||
0.998746 | − | 0.0500574i | \(-0.0159404\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −20.7327 | −0.864615 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 31.0718 | 1.29354 | 0.646768 | − | 0.762687i | \(-0.276120\pi\) | ||||
0.646768 | + | 0.762687i | \(0.276120\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 17.5254i | − 0.727075i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 2.67949i | − 0.110973i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 19.7990 | 0.817192 | 0.408596 | − | 0.912715i | \(-0.366019\pi\) | ||||
0.408596 | + | 0.912715i | \(0.366019\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.71281 | 0.152984 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 0.277401i | − 0.0113915i | −0.999984 | − | 0.00569576i | \(-0.998187\pi\) | ||||
0.999984 | − | 0.00569576i | \(-0.00181303\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.00000i | 0.163984i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 18.4591 | 0.754219 | 0.377109 | − | 0.926169i | \(-0.376918\pi\) | ||||
0.377109 | + | 0.926169i | \(0.376918\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.92820 | 0.364189 | 0.182095 | − | 0.983281i | \(-0.441712\pi\) | ||||
0.182095 | + | 0.983281i | \(0.441712\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 11.2394i | 0.456946i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 16.7846i | − 0.681266i | −0.940196 | − | 0.340633i | \(-0.889359\pi\) | ||||
0.940196 | − | 0.340633i | \(-0.110641\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 16.9706 | 0.686555 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −30.7846 | −1.24338 | −0.621689 | − | 0.783264i | \(-0.713553\pi\) | ||||
−0.621689 | + | 0.783264i | \(0.713553\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 23.0807i | − 0.929193i | −0.885522 | − | 0.464597i | \(-0.846199\pi\) | ||||
0.885522 | − | 0.464597i | \(-0.153801\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 41.8564i | − 1.68235i | −0.540762 | − | 0.841176i | \(-0.681864\pi\) | ||||
0.540762 | − | 0.841176i | \(-0.318136\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.03528 | 0.0414775 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 10.0718 | 0.402872 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 11.3137i | − 0.451107i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.53590i | 0.339809i | 0.985461 | + | 0.169904i | \(0.0543459\pi\) | ||||
−0.985461 | + | 0.169904i | \(0.945654\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 14.9000 | 0.591289 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.00000 | 0.0792429 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 14.5954i | 0.576484i | 0.957558 | + | 0.288242i | \(0.0930707\pi\) | ||||
−0.957558 | + | 0.288242i | \(0.906929\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10.2487i | 0.404170i | 0.979368 | + | 0.202085i | \(0.0647717\pi\) | ||||
−0.979368 | + | 0.202085i | \(0.935228\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 39.3949 | 1.54877 | 0.774387 | − | 0.632712i | \(-0.218058\pi\) | ||||
0.774387 | + | 0.632712i | \(0.218058\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.07180 | −0.0420717 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 19.1427i | 0.749110i | 0.927205 | + | 0.374555i | \(0.122204\pi\) | ||||
−0.927205 | + | 0.374555i | \(0.877796\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.56922i | 0.0613145i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −18.8652 | −0.734886 | −0.367443 | − | 0.930046i | \(-0.619767\pi\) | ||||
−0.367443 | + | 0.930046i | \(0.619767\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15.4641 | 0.601484 | 0.300742 | − | 0.953706i | \(-0.402766\pi\) | ||||
0.300742 | + | 0.953706i | \(0.402766\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − 1.51575i | − 0.0587782i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 18.3923i | 0.712153i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.31268 | −0.0506754 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9.85641 | −0.379937 | −0.189968 | − | 0.981790i | \(-0.560839\pi\) | ||||
−0.189968 | + | 0.981790i | \(0.560839\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 31.1870i | 1.19861i | 0.800519 | + | 0.599307i | \(0.204557\pi\) | ||||
−0.800519 | + | 0.599307i | \(0.795443\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.53590i | 0.174072i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 33.5622 | 1.28422 | 0.642111 | − | 0.766612i | \(-0.278059\pi\) | ||||
0.642111 | + | 0.766612i | \(0.278059\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.53590 | −0.249724 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 14.1421i | 0.538772i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.85641i | 0.0706210i | 0.999376 | + | 0.0353105i | \(0.0112420\pi\) | ||||
−0.999376 | + | 0.0353105i | \(0.988758\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 22.6274 | 0.858307 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −33.8564 | −1.28240 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 41.5670i | − 1.56996i | −0.619519 | − | 0.784982i | \(-0.712672\pi\) | ||||
0.619519 | − | 0.784982i | \(-0.287328\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.28719i | 0.161694i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.277401 | 0.0104328 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13.8564 | 0.520388 | 0.260194 | − | 0.965556i | \(-0.416213\pi\) | ||||
0.260194 | + | 0.965556i | \(0.416213\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 13.3843i | − 0.501245i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.784610i | 0.0293427i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.51575 | 0.0565279 | 0.0282640 | − | 0.999600i | \(-0.491002\pi\) | ||||
0.0282640 | + | 0.999600i | \(0.491002\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.46410 | −0.0545260 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 13.6889i | − 0.508392i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 22.5359i | − 0.835810i | −0.908491 | − | 0.417905i | \(-0.862764\pi\) | ||||
0.908491 | − | 0.417905i | \(-0.137236\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 15.4548 | 0.571617 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.92820 | −0.182027 | −0.0910137 | − | 0.995850i | \(-0.529011\pi\) | ||||
−0.0910137 | + | 0.995850i | \(0.529011\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.23457i | 0.119147i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 37.3205i | 1.37286i | 0.727197 | + | 0.686429i | \(0.240823\pi\) | ||||
−0.727197 | + | 0.686429i | \(0.759177\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 31.2886 | 1.14787 | 0.573933 | − | 0.818902i | \(-0.305417\pi\) | ||||
0.573933 | + | 0.818902i | \(0.305417\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 17.4641 | 0.639835 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.52004i | 0.165159i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.85641i | 0.213703i | 0.994275 | + | 0.106852i | \(0.0340770\pi\) | ||||
−0.994275 | + | 0.106852i | \(0.965923\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.03150 | −0.110328 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10.1436 | 0.368675 | 0.184338 | − | 0.982863i | \(-0.440986\pi\) | ||||
0.184338 | + | 0.982863i | \(0.440986\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 31.9449i | 1.15800i | 0.815327 | + | 0.579001i | \(0.196557\pi\) | ||||
−0.815327 | + | 0.579001i | \(0.803443\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 8.00000i | − 0.289619i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5.65685 | 0.204257 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −34.0000 | −1.22607 | −0.613036 | − | 0.790055i | \(-0.710052\pi\) | ||||
−0.613036 | + | 0.790055i | \(0.710052\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 36.8439i | 1.32518i | 0.748981 | + | 0.662591i | \(0.230543\pi\) | ||||
−0.748981 | + | 0.662591i | \(0.769457\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9.96152i | 0.357829i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 12.8295 | 0.459663 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.85641 | −0.137993 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 17.9315i | − 0.640003i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 20.7846i | 0.740891i | 0.928854 | + | 0.370446i | \(0.120795\pi\) | ||||
−0.928854 | + | 0.370446i | \(0.879205\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.89949 | 0.351986 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.92820 | 0.246028 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 22.9048i | 0.811330i | 0.914022 | + | 0.405665i | \(0.132960\pi\) | ||||
−0.914022 | + | 0.405665i | \(0.867040\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 32.7846i | − 1.15984i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.82843 | 0.0998130 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.46410 | −0.192584 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − 50.4040i | − 1.77211i | −0.463580 | − | 0.886055i | \(-0.653435\pi\) | ||||
0.463580 | − | 0.886055i | \(-0.346565\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 49.8564i | − 1.75070i | −0.483494 | − | 0.875348i | \(-0.660633\pi\) | ||||
0.483494 | − | 0.875348i | \(-0.339367\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.554803 | 0.0194339 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.85641 | −0.204890 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.41421i | 0.0493564i | 0.999695 | + | 0.0246782i | \(0.00785611\pi\) | ||||
−0.999695 | + | 0.0246782i | \(0.992144\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 13.6077i | − 0.474334i | −0.971469 | − | 0.237167i | \(-0.923781\pi\) | ||||
0.971469 | − | 0.237167i | \(-0.0762189\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −8.66115 | −0.301178 | −0.150589 | − | 0.988596i | \(-0.548117\pi\) | ||||
−0.150589 | + | 0.988596i | \(0.548117\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 40.9282 | 1.42150 | 0.710748 | − | 0.703447i | \(-0.248357\pi\) | ||||
0.710748 | + | 0.703447i | \(0.248357\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 3.86370i | − 0.133869i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 23.2154i | − 0.803402i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 7.93048 | 0.273791 | 0.136895 | − | 0.990586i | \(-0.456288\pi\) | ||||
0.136895 | + | 0.990586i | \(0.456288\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 16.8564 | 0.581255 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 9.31749i | 0.320531i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 10.8564i | − 0.373031i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 15.4548 | 0.529784 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 13.3205 | 0.456086 | 0.228043 | − | 0.973651i | \(-0.426767\pi\) | ||||
0.228043 | + | 0.973651i | \(0.426767\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 9.72363i | 0.332153i | 0.986113 | + | 0.166076i | \(0.0531098\pi\) | ||||
−0.986113 | + | 0.166076i | \(0.946890\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 29.4641i | 1.00530i | 0.864489 | + | 0.502651i | \(0.167642\pi\) | ||||
−0.864489 | + | 0.502651i | \(0.832358\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 11.6926 | 0.398022 | 0.199011 | − | 0.979997i | \(-0.436227\pi\) | ||||
0.199011 | + | 0.979997i | \(0.436227\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 12.0000 | 0.408012 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.93803i | 0.133589i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 17.0718i | − 0.578456i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 9.24316 | 0.312476 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 46.7846 | 1.57980 | 0.789902 | − | 0.613233i | \(-0.210131\pi\) | ||||
0.789902 | + | 0.613233i | \(0.210131\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 18.7637i | − 0.632166i | −0.948732 | − | 0.316083i | \(-0.897632\pi\) | ||||
0.948732 | − | 0.316083i | \(-0.102368\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 1.85641i | − 0.0624731i | −0.999512 | − | 0.0312365i | \(-0.990055\pi\) | ||||
0.999512 | − | 0.0312365i | \(-0.00994451\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 48.0833 | 1.61448 | 0.807239 | − | 0.590225i | \(-0.200961\pi\) | ||||
0.807239 | + | 0.590225i | \(0.200961\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −14.3923 | −0.482702 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 12.4233i | 0.415730i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 27.3205i | 0.913224i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 8.83701 | 0.294731 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 27.3205 | 0.910178 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 13.3843i | 0.444908i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 47.7128i | − 1.58428i | −0.610341 | − | 0.792139i | \(-0.708967\pi\) | ||||
0.610341 | − | 0.792139i | \(-0.291033\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 26.3896 | 0.874326 | 0.437163 | − | 0.899382i | \(-0.355983\pi\) | ||||
0.437163 | + | 0.899382i | \(0.355983\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.64102 | −0.219786 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 1.51575i | − 0.0500545i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 34.9282i | − 1.15218i | −0.817388 | − | 0.576088i | \(-0.804579\pi\) | ||||
0.817388 | − | 0.576088i | \(-0.195421\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 20.3538 | 0.669953 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −11.5026 | −0.378202 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 25.7332i | − 0.844280i | −0.906531 | − | 0.422140i | \(-0.861279\pi\) | ||||
0.906531 | − | 0.422140i | \(-0.138721\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.46410i | 0.0479840i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.51575 | 0.0495703 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −39.5692 | −1.29267 | −0.646335 | − | 0.763054i | \(-0.723699\pi\) | ||||
−0.646335 | + | 0.763054i | \(0.723699\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 34.4216i | 1.12211i | 0.827778 | + | 0.561056i | \(0.189605\pi\) | ||||
−0.827778 | + | 0.561056i | \(0.810395\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 46.2487i | − 1.50607i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −40.3286 | −1.31050 | −0.655252 | − | 0.755410i | \(-0.727438\pi\) | ||||
−0.655252 | + | 0.755410i | \(0.727438\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −14.9282 | −0.484590 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 25.1512i | − 0.814728i | −0.913266 | − | 0.407364i | \(-0.866448\pi\) | ||||
0.913266 | − | 0.407364i | \(-0.133552\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 21.4641i | 0.694562i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 6.31319 | 0.203864 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 24.5692 | 0.792555 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 14.3452i | 0.461789i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 16.5359i | − 0.531759i | −0.964006 | − | 0.265879i | \(-0.914338\pi\) | ||||
0.964006 | − | 0.265879i | \(-0.0856623\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 26.2137 | 0.841238 | 0.420619 | − | 0.907237i | \(-0.361813\pi\) | ||||
0.420619 | + | 0.907237i | \(0.361813\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −21.8564 | −0.700684 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 47.2239i | − 1.51082i | −0.655250 | − | 0.755412i | \(-0.727437\pi\) | ||||
0.655250 | − | 0.755412i | \(-0.272563\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 0.392305i | − 0.0125381i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 12.2747 | 0.391501 | 0.195750 | − | 0.980654i | \(-0.437286\pi\) | ||||
0.195750 | + | 0.980654i | \(0.437286\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 15.8949 | 0.506453 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 21.1117i | 0.671312i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 14.6410i | − 0.465087i | −0.972586 | − | 0.232544i | \(-0.925295\pi\) | ||||
0.972586 | − | 0.232544i | \(-0.0747048\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.14110 | −0.131282 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 35.4641 | 1.12316 | 0.561580 | − | 0.827423i | \(-0.310194\pi\) | ||||
0.561580 | + | 0.827423i | \(0.310194\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 4032.2.h.f.575.4 | 8 | ||
3.2 | odd | 2 | inner | 4032.2.h.f.575.6 | 8 | ||
4.3 | odd | 2 | inner | 4032.2.h.f.575.3 | 8 | ||
8.3 | odd | 2 | 1008.2.h.b.575.5 | yes | 8 | ||
8.5 | even | 2 | 1008.2.h.b.575.6 | yes | 8 | ||
12.11 | even | 2 | inner | 4032.2.h.f.575.5 | 8 | ||
24.5 | odd | 2 | 1008.2.h.b.575.4 | yes | 8 | ||
24.11 | even | 2 | 1008.2.h.b.575.3 | ✓ | 8 | ||
56.13 | odd | 2 | 7056.2.h.k.4607.3 | 8 | |||
56.27 | even | 2 | 7056.2.h.k.4607.4 | 8 | |||
168.83 | odd | 2 | 7056.2.h.k.4607.5 | 8 | |||
168.125 | even | 2 | 7056.2.h.k.4607.6 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1008.2.h.b.575.3 | ✓ | 8 | 24.11 | even | 2 | ||
1008.2.h.b.575.4 | yes | 8 | 24.5 | odd | 2 | ||
1008.2.h.b.575.5 | yes | 8 | 8.3 | odd | 2 | ||
1008.2.h.b.575.6 | yes | 8 | 8.5 | even | 2 | ||
4032.2.h.f.575.3 | 8 | 4.3 | odd | 2 | inner | ||
4032.2.h.f.575.4 | 8 | 1.1 | even | 1 | trivial | ||
4032.2.h.f.575.5 | 8 | 12.11 | even | 2 | inner | ||
4032.2.h.f.575.6 | 8 | 3.2 | odd | 2 | inner | ||
7056.2.h.k.4607.3 | 8 | 56.13 | odd | 2 | |||
7056.2.h.k.4607.4 | 8 | 56.27 | even | 2 | |||
7056.2.h.k.4607.5 | 8 | 168.83 | odd | 2 | |||
7056.2.h.k.4607.6 | 8 | 168.125 | even | 2 |