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 | 575.1 | ||
Root | \(0.965926 - 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4032.575 |
Dual form | 4032.2.h.f.575.8 |
$q$-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 | ||||||||
\(5\) | − 3.86370i | − 1.72790i | −0.503577 | − | 0.863950i | \(-0.667983\pi\) | ||||
0.503577 | − | 0.863950i | \(-0.332017\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 1.00000i | − 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.27792 | 1.59135 | 0.795676 | − | 0.605723i | \(-0.207116\pi\) | ||||
0.795676 | + | 0.605723i | \(0.207116\pi\) | |||||||
\(12\) | 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 | ||||||||
\(17\) | 1.03528i | 0.251091i | 0.992088 | + | 0.125546i | \(0.0400682\pi\) | ||||
−0.992088 | + | 0.125546i | \(0.959932\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 5.46410i | − 1.25355i | −0.779200 | − | 0.626775i | \(-0.784374\pi\) | ||||
0.779200 | − | 0.626775i | \(-0.215626\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.378937 | −0.0790139 | −0.0395070 | − | 0.999219i | \(-0.512579\pi\) | ||||
−0.0395070 | + | 0.999219i | \(0.512579\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −9.92820 | −1.98564 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 6.31319i | − 1.17233i | −0.810192 | − | 0.586165i | \(-0.800637\pi\) | ||||
0.810192 | − | 0.586165i | \(-0.199363\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 9.46410i | − 1.69980i | −0.526942 | − | 0.849901i | \(-0.676661\pi\) | ||||
0.526942 | − | 0.849901i | \(-0.323339\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.86370 | −0.653085 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.9282 | 1.79659 | 0.898293 | − | 0.439397i | \(-0.144808\pi\) | ||||
0.898293 | + | 0.439397i | \(0.144808\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.93426i | 0.926775i | 0.886156 | + | 0.463388i | \(0.153366\pi\) | ||||
−0.886156 | + | 0.463388i | \(0.846634\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.00000i | 0.609994i | 0.952353 | + | 0.304997i | \(0.0986555\pi\) | ||||
−0.952353 | + | 0.304997i | \(0.901344\pi\) | |||||||
\(44\) | 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 | \(0.161414\pi\) | ||||
−0.874157 | + | 0.485643i | \(0.838586\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 20.3923i | − 2.74970i | ||||||||
\(56\) | 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 | \(-0.428818\pi\) | ||||
0.221766 | + | 0.975100i | \(0.428818\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 7.72741i | 0.958467i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 15.4641i | − 1.88924i | −0.328165 | − | 0.944620i | \(-0.606430\pi\) | ||||
0.328165 | − | 0.944620i | \(-0.393570\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.52004 | 0.536430 | 0.268215 | − | 0.963359i | \(-0.413566\pi\) | ||||
0.268215 | + | 0.963359i | \(0.413566\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.535898 | 0.0627222 | 0.0313611 | − | 0.999508i | \(-0.490016\pi\) | ||||
0.0313611 | + | 0.999508i | \(0.490016\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 5.27792i | − 0.601474i | ||||||||
\(78\) | 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 | ||||||||
\(83\) | 11.8685 | 1.30274 | 0.651369 | − | 0.758761i | \(-0.274195\pi\) | ||||
0.651369 | + | 0.758761i | \(0.274195\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.00000 | 0.433861 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 3.86370i | − 0.409552i | −0.978809 | − | 0.204776i | \(-0.934353\pi\) | ||||
0.978809 | − | 0.204776i | \(-0.0656465\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.00000i | 0.209657i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −21.1117 | −2.16601 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.4641 | 1.16400 | 0.582002 | − | 0.813188i | \(-0.302270\pi\) | ||||
0.582002 | + | 0.813188i | \(0.302270\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 14.4195i | − 1.43480i | −0.696663 | − | 0.717399i | \(-0.745333\pi\) | ||||
0.696663 | − | 0.717399i | \(-0.254667\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.46410i | 0.538394i | 0.963085 | + | 0.269197i | \(0.0867583\pi\) | ||||
−0.963085 | + | 0.269197i | \(0.913242\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −10.1769 | −0.983838 | −0.491919 | − | 0.870641i | \(-0.663704\pi\) | ||||
−0.491919 | + | 0.870641i | \(0.663704\pi\) | |||||||
\(108\) | 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 | \(0.154173\pi\) | ||||
−0.884978 | + | 0.465633i | \(0.845827\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.46410i | 0.136528i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.03528 | 0.0949036 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 16.8564 | 1.53240 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 19.0411i | 1.70309i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.39230i | 0.567225i | 0.958939 | + | 0.283613i | \(0.0915330\pi\) | ||||
−0.958939 | + | 0.283613i | \(0.908467\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −21.1117 | −1.84453 | −0.922267 | − | 0.386552i | \(-0.873666\pi\) | ||||
−0.922267 | + | 0.386552i | \(0.873666\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.46410 | −0.473798 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 3.48477i | − 0.297724i | −0.988858 | − | 0.148862i | \(-0.952439\pi\) | ||||
0.988858 | − | 0.148862i | \(-0.0475610\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.85641i | 0.496734i | 0.968666 | + | 0.248367i | \(0.0798939\pi\) | ||||
−0.968666 | + | 0.248367i | \(0.920106\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −10.5558 | −0.882723 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −24.3923 | −2.02567 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.72689i | 0.223396i | 0.993742 | + | 0.111698i | \(0.0356289\pi\) | ||||
−0.993742 | + | 0.111698i | \(0.964371\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 10.9282i | − 0.889325i | −0.895698 | − | 0.444662i | \(-0.853324\pi\) | ||||
0.895698 | − | 0.444662i | \(-0.146676\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −36.5665 | −2.93709 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −17.3205 | −1.38233 | −0.691164 | − | 0.722698i | \(-0.742902\pi\) | ||||
−0.691164 | + | 0.722698i | \(0.742902\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.378937i | 0.0298644i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 7.46410i | − 0.584634i | −0.956322 | − | 0.292317i | \(-0.905574\pi\) | ||||
0.956322 | − | 0.292317i | \(-0.0944262\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −16.7675 | −1.29751 | −0.648754 | − | 0.760998i | \(-0.724709\pi\) | ||||
−0.648754 | + | 0.760998i | \(0.724709\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.10583i | 0.236132i | 0.993006 | + | 0.118066i | \(0.0376694\pi\) | ||||
−0.993006 | + | 0.118066i | \(0.962331\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 9.92820i | 0.750502i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.89469 | −0.141616 | −0.0708078 | − | 0.997490i | \(-0.522558\pi\) | ||||
−0.0708078 | + | 0.997490i | \(0.522558\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.928203 | 0.0689928 | 0.0344964 | − | 0.999405i | \(-0.489017\pi\) | ||||
0.0344964 | + | 0.999405i | \(0.489017\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − 42.2233i | − 3.10432i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.46410i | 0.399575i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.76217 | 0.272221 | 0.136110 | − | 0.990694i | \(-0.456540\pi\) | ||||
0.136110 | + | 0.990694i | \(0.456540\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.8564 | 0.997406 | 0.498703 | − | 0.866773i | \(-0.333810\pi\) | ||||
0.498703 | + | 0.866773i | \(0.333810\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 23.8386i | 1.69843i | 0.528050 | + | 0.849213i | \(0.322923\pi\) | ||||
−0.528050 | + | 0.849213i | \(0.677077\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.00000i | 0.283552i | 0.989899 | + | 0.141776i | \(0.0452813\pi\) | ||||
−0.989899 | + | 0.141776i | \(0.954719\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −6.31319 | −0.443099 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 22.9282 | 1.60138 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 28.8391i | − 1.99484i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 22.9282i | − 1.57844i | −0.614109 | − | 0.789221i | \(-0.710484\pi\) | ||||
0.614109 | − | 0.789221i | \(-0.289516\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 15.4548 | 1.05401 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −9.46410 | −0.642465 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 2.07055i | − 0.139280i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 9.85641i | − 0.660034i | −0.943975 | − | 0.330017i | \(-0.892946\pi\) | ||||
0.943975 | − | 0.330017i | \(-0.107054\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.34418 | −0.288333 | −0.144167 | − | 0.989553i | \(-0.546050\pi\) | ||||
−0.144167 | + | 0.989553i | \(0.546050\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −29.7128 | −1.96348 | −0.981739 | − | 0.190233i | \(-0.939076\pi\) | ||||
−0.981739 | + | 0.190233i | \(0.939076\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 20.4553i | 1.34007i | 0.742328 | + | 0.670037i | \(0.233722\pi\) | ||||
−0.742328 | + | 0.670037i | \(0.766278\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 32.7846i | 2.13863i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −22.2485 | −1.43913 | −0.719567 | − | 0.694423i | \(-0.755660\pi\) | ||||
−0.719567 | + | 0.694423i | \(0.755660\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.39230 | −0.411765 | −0.205882 | − | 0.978577i | \(-0.566006\pi\) | ||||
−0.205882 | + | 0.978577i | \(0.566006\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.86370i | 0.246843i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 10.9282i | 0.695345i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 24.4949 | 1.54610 | 0.773052 | − | 0.634343i | \(-0.218729\pi\) | ||||
0.773052 | + | 0.634343i | \(0.218729\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.00000 | −0.125739 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 0.277401i | − 0.0173038i | −0.999963 | − | 0.00865191i | \(-0.997246\pi\) | ||||
0.999963 | − | 0.00865191i | \(-0.00275402\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 10.9282i | − 0.679046i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 22.2485 | 1.37190 | 0.685950 | − | 0.727649i | \(-0.259387\pi\) | ||||
0.685950 | + | 0.727649i | \(0.259387\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 27.3205 | 1.67829 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 13.1069i | − 0.799139i | −0.916703 | − | 0.399570i | \(-0.869160\pi\) | ||||
0.916703 | − | 0.399570i | \(-0.130840\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.32051i | 0.201707i | 0.994901 | + | 0.100853i | \(0.0321573\pi\) | ||||
−0.994901 | + | 0.100853i | \(0.967843\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −52.4002 | −3.15985 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −27.8564 | −1.67373 | −0.836865 | − | 0.547410i | \(-0.815614\pi\) | ||||
−0.836865 | + | 0.547410i | \(0.815614\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 20.4553i | 1.22026i | 0.792300 | + | 0.610131i | \(0.208883\pi\) | ||||
−0.792300 | + | 0.610131i | \(0.791117\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 21.4641i | − 1.27591i | −0.770074 | − | 0.637954i | \(-0.779781\pi\) | ||||
0.770074 | − | 0.637954i | \(-0.220219\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.93426 | 0.350288 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15.9282 | 0.936953 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 18.0058i | 1.05191i | 0.850512 | + | 0.525956i | \(0.176292\pi\) | ||||
−0.850512 | + | 0.525956i | \(0.823708\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10.9282i | 0.636265i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.757875 | 0.0438290 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.00000 | 0.230556 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − 13.3843i | − 0.766381i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 14.5359i | − 0.829608i | −0.909911 | − | 0.414804i | \(-0.863850\pi\) | ||||
0.909911 | − | 0.414804i | \(-0.136150\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −18.2832 | −1.03675 | −0.518374 | − | 0.855154i | \(-0.673462\pi\) | ||||
−0.518374 | + | 0.855154i | \(0.673462\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 24.9282 | 1.40903 | 0.704513 | − | 0.709691i | \(-0.251166\pi\) | ||||
0.704513 | + | 0.709691i | \(0.251166\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 15.3533i | 0.862326i | 0.902274 | + | 0.431163i | \(0.141897\pi\) | ||||
−0.902274 | + | 0.431163i | \(0.858103\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 33.3205i | − 1.86559i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.65685 | 0.314756 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 19.8564 | 1.10144 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8.48528i | 0.467809i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 12.7846i | − 0.702706i | −0.936243 | − | 0.351353i | \(-0.885722\pi\) | ||||
0.936243 | − | 0.351353i | \(-0.114278\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −59.7487 | −3.26442 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.7846 | 0.696422 | 0.348211 | − | 0.937416i | \(-0.386789\pi\) | ||||
0.348211 | + | 0.937416i | \(0.386789\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 49.9507i | − 2.70498i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −6.03579 | −0.324018 | −0.162009 | − | 0.986789i | \(-0.551797\pi\) | ||||
−0.162009 | + | 0.986789i | \(0.551797\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.3205 | 0.713030 | 0.356515 | − | 0.934290i | \(-0.383965\pi\) | ||||
0.356515 | + | 0.934290i | \(0.383965\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 15.9353i | − 0.848150i | −0.905627 | − | 0.424075i | \(-0.860599\pi\) | ||||
0.905627 | − | 0.424075i | \(-0.139401\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 17.4641i | − 0.926898i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 15.0759 | 0.795674 | 0.397837 | − | 0.917456i | \(-0.369761\pi\) | ||||
0.397837 | + | 0.917456i | \(0.369761\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −10.8564 | −0.571390 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 2.07055i | − 0.108378i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 10.9282i | − 0.570448i | −0.958461 | − | 0.285224i | \(-0.907932\pi\) | ||||
0.958461 | − | 0.285224i | \(-0.0920679\pi\) | |||||||
\(368\) | 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 | ||||||||
\(377\) | 12.6264i | 0.650292i | ||||||||
\(378\) | 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 | ||||||||
\(383\) | 25.2528 | 1.29036 | 0.645178 | − | 0.764032i | \(-0.276783\pi\) | ||||
0.645178 | + | 0.764032i | \(0.276783\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −20.3923 | −1.03929 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 13.4858i | 0.683757i | 0.939744 | + | 0.341879i | \(0.111063\pi\) | ||||
−0.939744 | + | 0.341879i | \(0.888937\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 0.392305i | − 0.0198397i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 40.1528 | 2.02031 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11.4641 | 0.575367 | 0.287683 | − | 0.957726i | \(-0.407115\pi\) | ||||
0.287683 | + | 0.957726i | \(0.407115\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.79744i | 0.239573i | 0.992800 | + | 0.119786i | \(0.0382210\pi\) | ||||
−0.992800 | + | 0.119786i | \(0.961779\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 18.9282i | 0.942881i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 57.6781 | 2.85900 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.46410 | −0.171289 | −0.0856444 | − | 0.996326i | \(-0.527295\pi\) | ||||
−0.0856444 | + | 0.996326i | \(0.527295\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.82843i | 0.139178i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 45.8564i | − 2.25100i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.38323 | 0.165282 | 0.0826408 | − | 0.996579i | \(-0.473665\pi\) | ||||
0.0826408 | + | 0.996579i | \(0.473665\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 25.7128 | 1.25317 | 0.626583 | − | 0.779355i | \(-0.284453\pi\) | ||||
0.626583 | + | 0.779355i | \(0.284453\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − 10.2784i | − 0.498577i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 3.46410i | − 0.167640i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −21.4906 | −1.03517 | −0.517583 | − | 0.855633i | \(-0.673168\pi\) | ||||
−0.517583 | + | 0.855633i | \(0.673168\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −22.7846 | −1.09496 | −0.547479 | − | 0.836819i | \(-0.684412\pi\) | ||||
−0.547479 | + | 0.836819i | \(0.684412\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.07055i | 0.0990480i | ||||||||
\(438\) | 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 | ||||||||
\(443\) | 27.9053 | 1.32582 | 0.662911 | − | 0.748698i | \(-0.269321\pi\) | ||||
0.662911 | + | 0.748698i | \(0.269321\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −14.9282 | −0.707665 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 31.0112i | 1.46351i | 0.681569 | + | 0.731754i | \(0.261298\pi\) | ||||
−0.681569 | + | 0.731754i | \(0.738702\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 31.3205i | 1.47483i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 7.72741 | 0.362266 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 32.9058i | 1.53258i | 0.642496 | + | 0.766289i | \(0.277899\pi\) | ||||
−0.642496 | + | 0.766289i | \(0.722101\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 0.535898i | − 0.0249053i | −0.999922 | − | 0.0124527i | \(-0.996036\pi\) | ||||
0.999922 | − | 0.0124527i | \(-0.00396391\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −10.5558 | −0.488466 | −0.244233 | − | 0.969717i | \(-0.578536\pi\) | ||||
−0.244233 | + | 0.969717i | \(0.578536\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −15.4641 | −0.714066 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 21.1117i | 0.970716i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 54.2487i | 2.48910i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 20.3538 | 0.929989 | 0.464994 | − | 0.885314i | \(-0.346056\pi\) | ||||
0.464994 | + | 0.885314i | \(0.346056\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −21.8564 | −0.996566 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 44.2939i | − 2.01128i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 2.92820i | − 0.132690i | −0.997797 | − | 0.0663448i | \(-0.978866\pi\) | ||||
0.997797 | − | 0.0663448i | \(-0.0211337\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 34.3201 | 1.54884 | 0.774421 | − | 0.632670i | \(-0.218041\pi\) | ||||
0.774421 | + | 0.632670i | \(0.218041\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.53590 | 0.294362 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 4.52004i | − 0.202752i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 33.8564i | − 1.51562i | −0.652475 | − | 0.757810i | \(-0.726269\pi\) | ||||
0.652475 | − | 0.757810i | \(-0.273731\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6.21166 | −0.276964 | −0.138482 | − | 0.990365i | \(-0.544222\pi\) | ||||
−0.138482 | + | 0.990365i | \(0.544222\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −55.7128 | −2.47919 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 5.93426i | − 0.263031i | −0.991314 | − | 0.131516i | \(-0.958016\pi\) | ||||
0.991314 | − | 0.131516i | \(-0.0419844\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 0.535898i | − 0.0237067i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 21.1117 | 0.930291 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −44.7846 | −1.96962 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.66063i | 0.160375i | 0.996780 | + | 0.0801876i | \(0.0255519\pi\) | ||||
−0.996780 | + | 0.0801876i | \(0.974448\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 11.7128i | − 0.512166i | −0.966655 | − | 0.256083i | \(-0.917568\pi\) | ||||
0.966655 | − | 0.256083i | \(-0.0824320\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 9.79796 | 0.426806 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.8564 | −0.993757 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 11.8685i | − 0.514082i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 39.3205i | 1.69997i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.27792 | −0.227336 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 29.7128 | 1.27745 | 0.638727 | − | 0.769434i | \(-0.279461\pi\) | ||||
0.638727 | + | 0.769434i | \(0.279461\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 30.9096i | 1.32402i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.53590i | 0.193941i | 0.995287 | + | 0.0969705i | \(0.0309153\pi\) | ||||
−0.995287 | + | 0.0969705i | \(0.969085\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −34.4959 | −1.46958 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10.3923 | 0.441926 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 16.8690i | − 0.714764i | −0.933958 | − | 0.357382i | \(-0.883669\pi\) | ||||
0.933958 | − | 0.357382i | \(-0.116331\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 8.00000i | − 0.338364i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −18.2832 | −0.770547 | −0.385273 | − | 0.922802i | \(-0.625893\pi\) | ||||
−0.385273 | + | 0.922802i | \(0.625893\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 38.2487 | 1.60914 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 9.14162i | 0.383237i | 0.981470 | + | 0.191618i | \(0.0613736\pi\) | ||||
−0.981470 | + | 0.191618i | \(0.938626\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 18.3923i | − 0.769694i | −0.922980 | − | 0.384847i | \(-0.874254\pi\) | ||||
0.922980 | − | 0.384847i | \(-0.125746\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.76217 | 0.156893 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 44.9282 | 1.87039 | 0.935193 | − | 0.354139i | \(-0.115226\pi\) | ||||
0.935193 | + | 0.354139i | \(0.115226\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 11.8685i | − 0.492389i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 37.3205i | 1.54566i | ||||||||
\(584\) | 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 | ||||||||
\(589\) | −51.7128 | −2.13079 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 14.4195i | − 0.592139i | −0.955166 | − | 0.296070i | \(-0.904324\pi\) | ||||
0.955166 | − | 0.296070i | \(-0.0956761\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 4.00000i | − 0.163984i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −35.4297 | −1.44762 | −0.723809 | − | 0.690001i | \(-0.757610\pi\) | ||||
−0.723809 | + | 0.690001i | \(0.757610\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.92820 | −0.201026 | −0.100513 | − | 0.994936i | \(-0.532048\pi\) | ||||
−0.100513 | + | 0.994936i | \(0.532048\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 65.1282i | − 2.64784i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 24.7846i | − 1.00598i | −0.864293 | − | 0.502988i | \(-0.832234\pi\) | ||||
0.864293 | − | 0.502988i | \(-0.167766\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 16.9706 | 0.686555 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 10.7846 | 0.435586 | 0.217793 | − | 0.975995i | \(-0.430114\pi\) | ||||
0.217793 | + | 0.975995i | \(0.430114\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 25.9091i | − 1.04306i | −0.853232 | − | 0.521531i | \(-0.825361\pi\) | ||||
0.853232 | − | 0.521531i | \(-0.174639\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 14.1436i | 0.568479i | 0.958753 | + | 0.284240i | \(0.0917411\pi\) | ||||
−0.958753 | + | 0.284240i | \(0.908259\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.86370 | −0.154796 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.9282 | 0.957128 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 11.3137i | 0.451107i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 15.4641i | − 0.615616i | −0.951448 | − | 0.307808i | \(-0.900405\pi\) | ||||
0.951448 | − | 0.307808i | \(-0.0995955\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 24.6980 | 0.980109 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.00000 | 0.0792429 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 34.3944i | 1.35850i | 0.733908 | + | 0.679248i | \(0.237694\pi\) | ||||
−0.733908 | + | 0.679248i | \(0.762306\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 38.2487i | 1.50838i | 0.656655 | + | 0.754191i | \(0.271971\pi\) | ||||
−0.656655 | + | 0.754191i | \(0.728029\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0.203072 | 0.00798358 | 0.00399179 | − | 0.999992i | \(-0.498729\pi\) | ||||
0.00399179 | + | 0.999992i | \(0.498729\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −14.9282 | −0.585983 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 28.9406i | − 1.13253i | −0.824222 | − | 0.566267i | \(-0.808387\pi\) | ||||
0.824222 | − | 0.566267i | \(-0.191613\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 81.5692i | 3.18717i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −43.3601 | −1.68907 | −0.844536 | − | 0.535499i | \(-0.820124\pi\) | ||||
−0.844536 | + | 0.535499i | \(0.820124\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.53590 | 0.332008 | 0.166004 | − | 0.986125i | \(-0.446914\pi\) | ||||
0.166004 | + | 0.986125i | \(0.446914\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 21.1117i | 0.818675i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.39230i | 0.0926304i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 18.2832 | 0.705817 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 17.8564 | 0.688314 | 0.344157 | − | 0.938912i | \(-0.388165\pi\) | ||||
0.344157 | + | 0.938912i | \(0.388165\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 22.7017i | 0.872499i | 0.899826 | + | 0.436249i | \(0.143693\pi\) | ||||
−0.899826 | + | 0.436249i | \(0.856307\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 11.4641i | − 0.439952i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 28.6632 | 1.09677 | 0.548384 | − | 0.836227i | \(-0.315243\pi\) | ||||
0.548384 | + | 0.836227i | \(0.315243\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −13.4641 | −0.514437 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 14.1421i | − 0.538772i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 25.8564i | 0.983624i | 0.870701 | + | 0.491812i | \(0.163665\pi\) | ||||
−0.870701 | + | 0.491812i | \(0.836335\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 22.6274 | 0.858307 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.14359 | −0.232705 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 12.1731i | 0.459772i | 0.973218 | + | 0.229886i | \(0.0738354\pi\) | ||||
−0.973218 | + | 0.229886i | \(0.926165\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 59.7128i | − 2.25211i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −14.4195 | −0.542303 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −13.8564 | −0.520388 | −0.260194 | − | 0.965556i | \(-0.583787\pi\) | ||||
−0.260194 | + | 0.965556i | \(0.583787\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.58630i | 0.134308i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 40.7846i | 1.52526i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 21.1117 | 0.787332 | 0.393666 | − | 0.919253i | \(-0.371207\pi\) | ||||
0.393666 | + | 0.919253i | \(0.371207\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.46410 | 0.203494 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 62.6787i | 2.32783i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 29.4641i | 1.09276i | 0.837536 | + | 0.546382i | \(0.183995\pi\) | ||||
−0.837536 | + | 0.546382i | \(0.816005\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.14110 | −0.153164 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 8.92820 | 0.329771 | 0.164885 | − | 0.986313i | \(-0.447275\pi\) | ||||
0.164885 | + | 0.986313i | \(0.447275\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 81.6182i | − 3.00645i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 2.67949i | − 0.0985667i | −0.998785 | − | 0.0492834i | \(-0.984306\pi\) | ||||
0.998785 | − | 0.0492834i | \(-0.0156937\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −3.00429 | −0.110217 | −0.0551084 | − | 0.998480i | \(-0.517550\pi\) | ||||
−0.0551084 | + | 0.998480i | \(0.517550\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 10.5359 | 0.386005 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 10.1769i | 0.371856i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21.8564i | 0.797552i | 0.917048 | + | 0.398776i | \(0.130565\pi\) | ||||
−0.917048 | + | 0.398776i | \(0.869435\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −42.2233 | −1.53666 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 37.8564 | 1.37591 | 0.687957 | − | 0.725751i | \(-0.258508\pi\) | ||||
0.687957 | + | 0.725751i | \(0.258508\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 12.1459i | 0.440289i | 0.975467 | + | 0.220144i | \(0.0706529\pi\) | ||||
−0.975467 | + | 0.220144i | \(0.929347\pi\) | |||||||
\(762\) | 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 | ||||||||
\(773\) | 17.0449i | 0.613062i | 0.951861 | + | 0.306531i | \(0.0991683\pi\) | ||||
−0.951861 | + | 0.306531i | \(0.900832\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 93.9615i | 3.37520i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 32.4254 | 1.16176 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 23.8564 | 0.853649 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 66.9213i | 2.38852i | ||||||||
\(786\) | 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 | ||||||||
\(797\) | − 8.20788i | − 0.290738i | −0.989378 | − | 0.145369i | \(-0.953563\pi\) | ||||
0.989378 | − | 0.145369i | \(-0.0464369\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 8.78461i | − 0.310777i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.82843 | 0.0998130 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.46410 | 0.0516028 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − 47.5756i | − 1.67267i | −0.548220 | − | 0.836334i | \(-0.684694\pi\) | ||||
0.548220 | − | 0.836334i | \(-0.315306\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 22.1436i | 0.777567i | 0.921329 | + | 0.388783i | \(0.127105\pi\) | ||||
−0.921329 | + | 0.388783i | \(0.872895\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −28.8391 | −1.01019 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 21.8564 | 0.764659 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 1.41421i | − 0.0493564i | −0.999695 | − | 0.0246782i | \(-0.992144\pi\) | ||||
0.999695 | − | 0.0246782i | \(-0.00785611\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 34.3923i | 1.19884i | 0.800435 | + | 0.599420i | \(0.204602\pi\) | ||||
−0.800435 | + | 0.599420i | \(0.795398\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 25.6317 | 0.891302 | 0.445651 | − | 0.895207i | \(-0.352972\pi\) | ||||
0.445651 | + | 0.895207i | \(0.352972\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 27.0718 | 0.940242 | 0.470121 | − | 0.882602i | \(-0.344210\pi\) | ||||
0.470121 | + | 0.882602i | \(0.344210\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 1.03528i | − 0.0358702i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 64.7846i | 2.24196i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 37.3244 | 1.28858 | 0.644290 | − | 0.764781i | \(-0.277153\pi\) | ||||
0.644290 | + | 0.764781i | \(0.277153\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.8564 | −0.374359 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 34.7733i | 1.19624i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 16.8564i | − 0.579193i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.14110 | −0.141955 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −21.3205 | −0.730000 | −0.365000 | − | 0.931007i | \(-0.618931\pi\) | ||||
−0.365000 | + | 0.931007i | \(0.618931\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 44.0165i | − 1.50357i | −0.659406 | − | 0.751787i | \(-0.729192\pi\) | ||||
0.659406 | − | 0.751787i | \(-0.270808\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 22.5359i | − 0.768915i | −0.923143 | − | 0.384457i | \(-0.874389\pi\) | ||||
0.923143 | − | 0.384457i | \(-0.125611\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 16.5916 | 0.564785 | 0.282393 | − | 0.959299i | \(-0.408872\pi\) | ||||
0.282393 | + | 0.959299i | \(0.408872\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 12.0000 | 0.408012 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 54.8497i | 1.86065i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 30.9282i | 1.04796i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 19.0411 | 0.643707 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.21539 | 0.176111 | 0.0880556 | − | 0.996116i | \(-0.471935\pi\) | ||||
0.0880556 | + | 0.996116i | \(0.471935\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 23.6627i | 0.797216i | 0.917121 | + | 0.398608i | \(0.130507\pi\) | ||||
−0.917121 | + | 0.398608i | \(0.869493\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 25.8564i | − 0.870137i | −0.900397 | − | 0.435069i | \(-0.856724\pi\) | ||||
0.900397 | − | 0.435069i | \(-0.143276\pi\) | |||||||
\(884\) | 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 | ||||||||
\(889\) | 6.39230 | 0.214391 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 46.3644i | 1.55153i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.32051i | 0.244698i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −59.7487 | −1.99273 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.32051 | −0.243881 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − 3.58630i | − 0.119213i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 7.71281i | − 0.256100i | −0.991768 | − | 0.128050i | \(-0.959128\pi\) | ||||
0.991768 | − | 0.128050i | \(-0.0408718\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.89469 | 0.0627738 | 0.0313869 | − | 0.999507i | \(-0.490008\pi\) | ||||
0.0313869 | + | 0.999507i | \(0.490008\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 62.6410 | 2.07312 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 21.1117i | 0.697169i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 21.0718i | 0.695094i | 0.937662 | + | 0.347547i | \(0.112985\pi\) | ||||
−0.937662 | + | 0.347547i | \(0.887015\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −9.04008 | −0.297558 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −108.497 | −3.56737 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 11.0363i | 0.362089i | 0.983475 | + | 0.181045i | \(0.0579479\pi\) | ||||
−0.983475 | + | 0.181045i | \(0.942052\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.46410i | 0.179079i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 21.1117 | 0.690425 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 43.5692 | 1.42334 | 0.711672 | − | 0.702512i | \(-0.247938\pi\) | ||||
0.711672 | + | 0.702512i | \(0.247938\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 58.9165i | − 1.92062i | −0.278930 | − | 0.960311i | \(-0.589980\pi\) | ||||
0.278930 | − | 0.960311i | \(-0.410020\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 2.24871i | − 0.0732281i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 23.3581 | 0.759036 | 0.379518 | − | 0.925184i | \(-0.376090\pi\) | ||||
0.379518 | + | 0.925184i | \(0.376090\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.07180 | −0.0347920 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 33.6365i | − 1.08959i | −0.838568 | − | 0.544797i | \(-0.816607\pi\) | ||||
0.838568 | − | 0.544797i | \(-0.183393\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 14.5359i | − 0.470371i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.48477 | −0.112529 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −58.5692 | −1.88933 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 53.5370i | − 1.72342i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 23.4641i | 0.754555i | 0.926100 | + | 0.377277i | \(0.123140\pi\) | ||||
−0.926100 | + | 0.377277i | \(0.876860\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 36.0117 | 1.15567 | 0.577835 | − | 0.816154i | \(-0.303898\pi\) | ||||
0.577835 | + | 0.816154i | \(0.303898\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.85641 | 0.187748 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 17.8300i | 0.570431i | 0.958463 | + | 0.285216i | \(0.0920652\pi\) | ||||
−0.958463 | + | 0.285216i | \(0.907935\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 20.3923i | − 0.651741i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 61.2645 | 1.95403 | 0.977016 | − | 0.213165i | \(-0.0683771\pi\) | ||||
0.977016 | + | 0.213165i | \(0.0683771\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 92.1051 | 2.93471 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 1.51575i | − 0.0481980i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 54.6410i | − 1.73573i | −0.496801 | − | 0.867865i | \(-0.665492\pi\) | ||||
0.496801 | − | 0.867865i | \(-0.334508\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 15.4548 | 0.489951 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 28.5359 | 0.903741 | 0.451870 | − | 0.892084i | \(-0.350757\pi\) | ||||
0.451870 | + | 0.892084i | \(0.350757\pi\) | |||||||
\(998\) | 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.575.1 | 8 | ||
3.2 | odd | 2 | inner | 4032.2.h.f.575.7 | 8 | ||
4.3 | odd | 2 | inner | 4032.2.h.f.575.2 | 8 | ||
8.3 | odd | 2 | 1008.2.h.b.575.8 | yes | 8 | ||
8.5 | even | 2 | 1008.2.h.b.575.7 | yes | 8 | ||
12.11 | even | 2 | inner | 4032.2.h.f.575.8 | 8 | ||
24.5 | odd | 2 | 1008.2.h.b.575.1 | ✓ | 8 | ||
24.11 | even | 2 | 1008.2.h.b.575.2 | yes | 8 | ||
56.13 | odd | 2 | 7056.2.h.k.4607.1 | 8 | |||
56.27 | even | 2 | 7056.2.h.k.4607.2 | 8 | |||
168.83 | odd | 2 | 7056.2.h.k.4607.7 | 8 | |||
168.125 | even | 2 | 7056.2.h.k.4607.8 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1008.2.h.b.575.1 | ✓ | 8 | 24.5 | odd | 2 | ||
1008.2.h.b.575.2 | yes | 8 | 24.11 | even | 2 | ||
1008.2.h.b.575.7 | yes | 8 | 8.5 | even | 2 | ||
1008.2.h.b.575.8 | yes | 8 | 8.3 | odd | 2 | ||
4032.2.h.f.575.1 | 8 | 1.1 | even | 1 | trivial | ||
4032.2.h.f.575.2 | 8 | 4.3 | odd | 2 | inner | ||
4032.2.h.f.575.7 | 8 | 3.2 | odd | 2 | inner | ||
4032.2.h.f.575.8 | 8 | 12.11 | even | 2 | inner | ||
7056.2.h.k.4607.1 | 8 | 56.13 | odd | 2 | |||
7056.2.h.k.4607.2 | 8 | 56.27 | even | 2 | |||
7056.2.h.k.4607.7 | 8 | 168.83 | odd | 2 | |||
7056.2.h.k.4607.8 | 8 | 168.125 | even | 2 |