Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6048,2,Mod(2591,6048)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6048, 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("6048.2591");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6048 = 2^{5} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6048.h (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(48.2935231425\) |
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: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2591.7 | ||
Root | \(-0.258819 + 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6048.2591 |
Dual form | 6048.2.h.f.2591.2 |
$q$-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 \(\left(\mathbb{Z}/6048\mathbb{Z}\right)^\times\).
\(n\) | \(2593\) | \(3781\) | \(3809\) | \(4159\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(5\) | 3.34607i | 1.49641i | 0.663470 | + | 0.748203i | \(0.269083\pi\) | ||||
−0.663470 | + | 0.748203i | \(0.730917\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 1.00000i | − 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.896575 | 0.270328 | 0.135164 | − | 0.990823i | \(-0.456844\pi\) | ||||
0.135164 | + | 0.990823i | \(0.456844\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.00000 | 1.10940 | 0.554700 | − | 0.832050i | \(-0.312833\pi\) | ||||
0.554700 | + | 0.832050i | \(0.312833\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 6.31319i | − 1.53117i | −0.643332 | − | 0.765587i | \(-0.722449\pi\) | ||||
0.643332 | − | 0.765587i | \(-0.277551\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000i | 0.229416i | 0.993399 | + | 0.114708i | \(0.0365932\pi\) | ||||
−0.993399 | + | 0.114708i | \(0.963407\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −7.20977 | −1.50334 | −0.751670 | − | 0.659539i | \(-0.770752\pi\) | ||||
−0.751670 | + | 0.659539i | \(0.770752\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −6.19615 | −1.23923 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 7.72741i | − 1.43494i | −0.696588 | − | 0.717472i | \(-0.745299\pi\) | ||||
0.696588 | − | 0.717472i | \(-0.254701\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.73205i | 0.670296i | 0.942165 | + | 0.335148i | \(0.108786\pi\) | ||||
−0.942165 | + | 0.335148i | \(0.891214\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.34607 | 0.565588 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −11.7321 | −1.92874 | −0.964369 | − | 0.264562i | \(-0.914773\pi\) | ||||
−0.964369 | + | 0.264562i | \(0.914773\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 7.86611i | − 1.22848i | −0.789119 | − | 0.614240i | \(-0.789463\pi\) | ||||
0.789119 | − | 0.614240i | \(-0.210537\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.46410i | 1.13826i | 0.822246 | + | 0.569132i | \(0.192721\pi\) | ||||
−0.822246 | + | 0.569132i | \(0.807279\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.76268 | −1.27817 | −0.639084 | − | 0.769137i | \(-0.720687\pi\) | ||||
−0.639084 | + | 0.769137i | \(0.720687\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 2.82843i | − 0.388514i | −0.980951 | − | 0.194257i | \(-0.937770\pi\) | ||||
0.980951 | − | 0.194257i | \(-0.0622296\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.00000i | 0.404520i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.86370 | 0.503011 | 0.251506 | − | 0.967856i | \(-0.419074\pi\) | ||||
0.251506 | + | 0.967856i | \(0.419074\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.3923 | −1.58667 | −0.793336 | − | 0.608784i | \(-0.791658\pi\) | ||||
−0.793336 | + | 0.608784i | \(0.791658\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 13.3843i | 1.66011i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.9282i | 1.33509i | 0.744568 | + | 0.667546i | \(0.232655\pi\) | ||||
−0.744568 | + | 0.667546i | \(0.767345\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.79555 | −0.687806 | −0.343903 | − | 0.939005i | \(-0.611749\pi\) | ||||
−0.343903 | + | 0.939005i | \(0.611749\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −14.3923 | −1.68449 | −0.842246 | − | 0.539093i | \(-0.818767\pi\) | ||||
−0.842246 | + | 0.539093i | \(0.818767\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 0.896575i | − 0.102174i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 7.46410i | − 0.839777i | −0.907576 | − | 0.419889i | \(-0.862069\pi\) | ||||
0.907576 | − | 0.419889i | \(-0.137931\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.96953 | 0.765006 | 0.382503 | − | 0.923954i | \(-0.375062\pi\) | ||||
0.382503 | + | 0.923954i | \(0.375062\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 21.1244 | 2.29126 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 13.2456i | − 1.40403i | −0.712164 | − | 0.702013i | \(-0.752285\pi\) | ||||
0.712164 | − | 0.702013i | \(-0.247715\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 4.00000i | − 0.419314i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.34607 | −0.343299 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.92820 | 0.297314 | 0.148657 | − | 0.988889i | \(-0.452505\pi\) | ||||
0.148657 | + | 0.988889i | \(0.452505\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 0.656339i | − 0.0653082i | −0.999467 | − | 0.0326541i | \(-0.989604\pi\) | ||||
0.999467 | − | 0.0326541i | \(-0.0103960\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 18.1244i | 1.78585i | 0.450210 | + | 0.892923i | \(0.351349\pi\) | ||||
−0.450210 | + | 0.892923i | \(0.648651\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.52004 | −0.436969 | −0.218484 | − | 0.975840i | \(-0.570111\pi\) | ||||
−0.218484 | + | 0.975840i | \(0.570111\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.53590 | −0.338678 | −0.169339 | − | 0.985558i | \(-0.554163\pi\) | ||||
−0.169339 | + | 0.985558i | \(0.554163\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.52056i | 0.895619i | 0.894129 | + | 0.447809i | \(0.147796\pi\) | ||||
−0.894129 | + | 0.447809i | \(0.852204\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 24.1244i | − 2.24961i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6.31319 | −0.578729 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.1962 | −0.926923 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 4.00240i | − 0.357986i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.3923i | 1.45458i | 0.686329 | + | 0.727291i | \(0.259221\pi\) | ||||
−0.686329 | + | 0.727291i | \(0.740779\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.37945 | 0.470005 | 0.235002 | − | 0.971995i | \(-0.424490\pi\) | ||||
0.235002 | + | 0.971995i | \(0.424490\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.00000 | 0.0867110 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 1.31268i | − 0.112150i | −0.998427 | − | 0.0560748i | \(-0.982141\pi\) | ||||
0.998427 | − | 0.0560748i | \(-0.0178585\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.535898i | 0.0454543i | 0.999742 | + | 0.0227272i | \(0.00723490\pi\) | ||||
−0.999742 | + | 0.0227272i | \(0.992765\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.58630 | 0.299902 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 25.8564 | 2.14726 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 6.69213i | − 0.548241i | −0.961695 | − | 0.274120i | \(-0.911613\pi\) | ||||
0.961695 | − | 0.274120i | \(-0.0883867\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.3205i | 1.40952i | 0.709444 | + | 0.704761i | \(0.248946\pi\) | ||||
−0.709444 | + | 0.704761i | \(0.751054\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −12.4877 | −1.00304 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.46410 | −0.116848 | −0.0584240 | − | 0.998292i | \(-0.518608\pi\) | ||||
−0.0584240 | + | 0.998292i | \(0.518608\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.20977i | 0.568209i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 19.3205i | − 1.51330i | −0.653821 | − | 0.756649i | \(-0.726835\pi\) | ||||
0.653821 | − | 0.756649i | \(-0.273165\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −10.8332 | −0.838301 | −0.419150 | − | 0.907917i | \(-0.637672\pi\) | ||||
−0.419150 | + | 0.907917i | \(0.637672\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.00000 | 0.230769 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 1.17398i | − 0.0892558i | −0.999004 | − | 0.0446279i | \(-0.985790\pi\) | ||||
0.999004 | − | 0.0446279i | \(-0.0142102\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.19615i | 0.468385i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −8.10634 | −0.605897 | −0.302948 | − | 0.953007i | \(-0.597971\pi\) | ||||
−0.302948 | + | 0.953007i | \(0.597971\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.46410 | 0.257485 | 0.128742 | − | 0.991678i | \(-0.458906\pi\) | ||||
0.128742 | + | 0.991678i | \(0.458906\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − 39.2562i | − 2.88617i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 5.66025i | − 0.413919i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −25.7704 | −1.86468 | −0.932341 | − | 0.361581i | \(-0.882237\pi\) | ||||
−0.932341 | + | 0.361581i | \(0.882237\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.9282 | 1.07456 | 0.537278 | − | 0.843405i | \(-0.319453\pi\) | ||||
0.537278 | + | 0.843405i | \(0.319453\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 8.76268i | − 0.624315i | −0.950030 | − | 0.312158i | \(-0.898948\pi\) | ||||
0.950030 | − | 0.312158i | \(-0.101052\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 26.4641i | − 1.87599i | −0.346648 | − | 0.937995i | \(-0.612680\pi\) | ||||
0.346648 | − | 0.937995i | \(-0.387320\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −7.72741 | −0.542358 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 26.3205 | 1.83830 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.896575i | 0.0620174i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 13.3205i | − 0.917022i | −0.888689 | − | 0.458511i | \(-0.848383\pi\) | ||||
0.888689 | − | 0.458511i | \(-0.151617\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −24.9754 | −1.70331 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.73205 | 0.253348 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 25.2528i | − 1.69869i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 7.53590i | − 0.504641i | −0.967644 | − | 0.252321i | \(-0.918806\pi\) | ||||
0.967644 | − | 0.252321i | \(-0.0811937\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −20.0764 | −1.33252 | −0.666258 | − | 0.745721i | \(-0.732105\pi\) | ||||
−0.666258 | + | 0.745721i | \(0.732105\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.3205 | −0.748080 | −0.374040 | − | 0.927413i | \(-0.622028\pi\) | ||||
−0.374040 | + | 0.927413i | \(0.622028\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 9.52056i | − 0.623712i | −0.950129 | − | 0.311856i | \(-0.899049\pi\) | ||||
0.950129 | − | 0.311856i | \(-0.100951\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 29.3205i | − 1.91266i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 22.2485 | 1.43913 | 0.719567 | − | 0.694423i | \(-0.244340\pi\) | ||||
0.719567 | + | 0.694423i | \(0.244340\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.9282 | −0.832779 | −0.416389 | − | 0.909186i | \(-0.636705\pi\) | ||||
−0.416389 | + | 0.909186i | \(0.636705\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 3.34607i | − 0.213772i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.00000i | 0.254514i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.04008 | −0.570605 | −0.285303 | − | 0.958438i | \(-0.592094\pi\) | ||||
−0.285303 | + | 0.958438i | \(0.592094\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.46410 | −0.406395 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 12.8666i | 0.802598i | 0.915947 | + | 0.401299i | \(0.131441\pi\) | ||||
−0.915947 | + | 0.401299i | \(0.868559\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 11.7321i | 0.728994i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 24.7351 | 1.52523 | 0.762617 | − | 0.646850i | \(-0.223914\pi\) | ||||
0.762617 | + | 0.646850i | \(0.223914\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.46410 | 0.581375 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 27.3877i | 1.66986i | 0.550358 | + | 0.834929i | \(0.314491\pi\) | ||||
−0.550358 | + | 0.834929i | \(0.685509\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 7.46410i | − 0.453412i | −0.973963 | − | 0.226706i | \(-0.927204\pi\) | ||||
0.973963 | − | 0.226706i | \(-0.0727956\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.55532 | −0.334998 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.803848 | −0.0482985 | −0.0241493 | − | 0.999708i | \(-0.507688\pi\) | ||||
−0.0241493 | + | 0.999708i | \(0.507688\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 5.17638i | − 0.308797i | −0.988009 | − | 0.154398i | \(-0.950656\pi\) | ||||
0.988009 | − | 0.154398i | \(-0.0493440\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 17.8564i | − 1.06145i | −0.847543 | − | 0.530727i | \(-0.821919\pi\) | ||||
0.847543 | − | 0.530727i | \(-0.178081\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.86611 | −0.464322 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −22.8564 | −1.34449 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 2.17209i | − 0.126895i | −0.997985 | − | 0.0634474i | \(-0.979790\pi\) | ||||
0.997985 | − | 0.0634474i | \(-0.0202095\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.9282i | 0.752709i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −28.8391 | −1.66781 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.46410 | 0.430224 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − 41.4655i | − 2.37431i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.00000i | 0.285365i | 0.989769 | + | 0.142683i | \(0.0455728\pi\) | ||||
−0.989769 | + | 0.142683i | \(0.954427\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −15.4548 | −0.876362 | −0.438181 | − | 0.898887i | \(-0.644377\pi\) | ||||
−0.438181 | + | 0.898887i | \(0.644377\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.3923 | 0.700454 | 0.350227 | − | 0.936665i | \(-0.386104\pi\) | ||||
0.350227 | + | 0.936665i | \(0.386104\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 23.4596i | − 1.31762i | −0.752308 | − | 0.658812i | \(-0.771059\pi\) | ||||
0.752308 | − | 0.658812i | \(-0.228941\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 6.92820i | − 0.387905i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.31319 | 0.351275 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −24.7846 | −1.37480 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8.76268i | 0.483102i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 22.2487i | − 1.22290i | −0.791283 | − | 0.611450i | \(-0.790587\pi\) | ||||
0.791283 | − | 0.611450i | \(-0.209413\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −36.5665 | −1.99784 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 22.7128 | 1.23725 | 0.618623 | − | 0.785688i | \(-0.287691\pi\) | ||||
0.618623 | + | 0.785688i | \(0.287691\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.34607i | 0.181200i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 16.1755 | 0.868348 | 0.434174 | − | 0.900829i | \(-0.357040\pi\) | ||||
0.434174 | + | 0.900829i | \(0.357040\pi\) | |||||||
\(348\) | 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 | ||||||||
\(353\) | 11.1750i | 0.594786i | 0.954755 | + | 0.297393i | \(0.0961171\pi\) | ||||
−0.954755 | + | 0.297393i | \(0.903883\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 19.3923i | − 1.02924i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 18.6622 | 0.984952 | 0.492476 | − | 0.870326i | \(-0.336092\pi\) | ||||
0.492476 | + | 0.870326i | \(0.336092\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.0000 | 0.947368 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 48.1576i | − 2.52068i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 18.4641i | 0.963818i | 0.876221 | + | 0.481909i | \(0.160056\pi\) | ||||
−0.876221 | + | 0.481909i | \(0.839944\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.82843 | −0.146845 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 15.3923 | 0.796983 | 0.398492 | − | 0.917172i | \(-0.369534\pi\) | ||||
0.398492 | + | 0.917172i | \(0.369534\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 30.9096i | − 1.59193i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 17.3205i | 0.889695i | 0.895606 | + | 0.444847i | \(0.146742\pi\) | ||||
−0.895606 | + | 0.444847i | \(0.853258\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 15.1774 | 0.775530 | 0.387765 | − | 0.921758i | \(-0.373247\pi\) | ||||
0.387765 | + | 0.921758i | \(0.373247\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.00000 | 0.152894 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 35.2538i | 1.78744i | 0.448626 | + | 0.893719i | \(0.351913\pi\) | ||||
−0.448626 | + | 0.893719i | \(0.648087\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 45.5167i | 2.30188i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 24.9754 | 1.25665 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.00000 | 0.100377 | 0.0501886 | − | 0.998740i | \(-0.484018\pi\) | ||||
0.0501886 | + | 0.998740i | \(0.484018\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − 2.27362i | − 0.113539i | −0.998387 | − | 0.0567697i | \(-0.981920\pi\) | ||||
0.998387 | − | 0.0567697i | \(-0.0180801\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 14.9282i | 0.743627i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −10.5187 | −0.521391 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −26.3923 | −1.30502 | −0.652508 | − | 0.757782i | \(-0.726283\pi\) | ||||
−0.652508 | + | 0.757782i | \(0.726283\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 3.86370i | − 0.190120i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 23.3205i | 1.14476i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7.45001 | 0.363957 | 0.181978 | − | 0.983303i | \(-0.441750\pi\) | ||||
0.181978 | + | 0.983303i | \(0.441750\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17.5885 | −0.857209 | −0.428604 | − | 0.903492i | \(-0.640995\pi\) | ||||
−0.428604 | + | 0.903492i | \(0.640995\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 39.1175i | 1.89748i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12.3923i | 0.599706i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −36.5293 | −1.75956 | −0.879778 | − | 0.475385i | \(-0.842309\pi\) | ||||
−0.879778 | + | 0.475385i | \(0.842309\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.00000 | 0.192228 | 0.0961139 | − | 0.995370i | \(-0.469359\pi\) | ||||
0.0961139 | + | 0.995370i | \(0.469359\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 7.20977i | − 0.344890i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 26.9282i | − 1.28521i | −0.766196 | − | 0.642607i | \(-0.777853\pi\) | ||||
0.766196 | − | 0.642607i | \(-0.222147\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.76028 | −0.226168 | −0.113084 | − | 0.993585i | \(-0.536073\pi\) | ||||
−0.113084 | + | 0.993585i | \(0.536073\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 44.3205 | 2.10099 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 5.93426i | − 0.280055i | −0.990148 | − | 0.140027i | \(-0.955281\pi\) | ||||
0.990148 | − | 0.140027i | \(-0.0447191\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 7.05256i | − 0.332092i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 13.3843 | 0.627464 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.78461 | −0.177037 | −0.0885183 | − | 0.996075i | \(-0.528213\pi\) | ||||
−0.0885183 | + | 0.996075i | \(0.528213\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 37.7405i | 1.75775i | 0.477054 | + | 0.878874i | \(0.341705\pi\) | ||||
−0.477054 | + | 0.878874i | \(0.658295\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 12.1436i | − 0.564361i | −0.959361 | − | 0.282180i | \(-0.908942\pi\) | ||||
0.959361 | − | 0.282180i | \(-0.0910576\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.55103 | 0.118047 | 0.0590237 | − | 0.998257i | \(-0.481201\pi\) | ||||
0.0590237 | + | 0.998257i | \(0.481201\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10.9282 | 0.504618 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.69213i | 0.307704i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 6.19615i | − 0.284299i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.62536 | 0.119956 | 0.0599778 | − | 0.998200i | \(-0.480897\pi\) | ||||
0.0599778 | + | 0.998200i | \(0.480897\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −46.9282 | −2.13974 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 9.79796i | 0.444902i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 29.7128i | 1.34642i | 0.739453 | + | 0.673208i | \(0.235084\pi\) | ||||
−0.739453 | + | 0.673208i | \(0.764916\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.52245 | 0.384613 | 0.192306 | − | 0.981335i | \(-0.438403\pi\) | ||||
0.192306 | + | 0.981335i | \(0.438403\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −48.7846 | −2.19715 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.79555i | 0.259966i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 18.0000i | − 0.805791i | −0.915246 | − | 0.402895i | \(-0.868004\pi\) | ||||
0.915246 | − | 0.402895i | \(-0.131996\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 38.8401 | 1.73179 | 0.865897 | − | 0.500222i | \(-0.166748\pi\) | ||||
0.865897 | + | 0.500222i | \(0.166748\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.19615 | 0.0977275 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 41.0122i | − 1.81783i | −0.416978 | − | 0.908917i | \(-0.636911\pi\) | ||||
0.416978 | − | 0.908917i | \(-0.363089\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 14.3923i | 0.636678i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −60.6453 | −2.67235 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7.85641 | −0.345524 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 25.7704i | − 1.12902i | −0.825425 | − | 0.564511i | \(-0.809065\pi\) | ||||
0.825425 | − | 0.564511i | \(-0.190935\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 28.6603i | − 1.25323i | −0.779331 | − | 0.626613i | \(-0.784441\pi\) | ||||
0.779331 | − | 0.626613i | \(-0.215559\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 23.5612 | 1.02634 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 28.9808 | 1.26003 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 31.4644i | − 1.36288i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 15.1244i | − 0.653883i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.896575 | −0.0386182 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.3397 | −0.745494 | −0.372747 | − | 0.927933i | \(-0.621584\pi\) | ||||
−0.372747 | + | 0.927933i | \(0.621584\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − 11.8313i | − 0.506799i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 29.8564i | − 1.27657i | −0.769801 | − | 0.638284i | \(-0.779645\pi\) | ||||
0.769801 | − | 0.638284i | \(-0.220355\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.72741 | 0.329199 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.46410 | −0.317406 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 11.7942i | − 0.499736i | −0.968280 | − | 0.249868i | \(-0.919613\pi\) | ||||
0.968280 | − | 0.249868i | \(-0.0803872\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 29.8564i | 1.26279i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −27.5264 | −1.16010 | −0.580050 | − | 0.814581i | \(-0.696967\pi\) | ||||
−0.580050 | + | 0.814581i | \(0.696967\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −31.8564 | −1.34021 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 15.9353i | 0.668042i | 0.942566 | + | 0.334021i | \(0.108406\pi\) | ||||
−0.942566 | + | 0.334021i | \(0.891594\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.60770i | 0.234675i | 0.993092 | + | 0.117337i | \(0.0374359\pi\) | ||||
−0.993092 | + | 0.117337i | \(0.962564\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 44.6728 | 1.86299 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 37.3205 | 1.55367 | 0.776837 | − | 0.629702i | \(-0.216823\pi\) | ||||
0.776837 | + | 0.629702i | \(0.216823\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 6.96953i | − 0.289145i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 2.53590i | − 0.105026i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −35.5312 | −1.46653 | −0.733265 | − | 0.679943i | \(-0.762004\pi\) | ||||
−0.733265 | + | 0.679943i | \(0.762004\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.73205 | −0.153776 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 10.3156i | 0.423611i | 0.977312 | + | 0.211805i | \(0.0679343\pi\) | ||||
−0.977312 | + | 0.211805i | \(0.932066\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 21.1244i | − 0.866014i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 7.69024 | 0.314215 | 0.157107 | − | 0.987582i | \(-0.449783\pi\) | ||||
0.157107 | + | 0.987582i | \(0.449783\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −16.7846 | −0.684659 | −0.342329 | − | 0.939580i | \(-0.611216\pi\) | ||||
−0.342329 | + | 0.939580i | \(0.611216\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 34.1170i | − 1.38705i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 20.7846i | 0.843621i | 0.906684 | + | 0.421811i | \(0.138605\pi\) | ||||
−0.906684 | + | 0.421811i | \(0.861395\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −35.0507 | −1.41800 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 25.5359 | 1.03139 | 0.515693 | − | 0.856774i | \(-0.327535\pi\) | ||||
0.515693 | + | 0.856774i | \(0.327535\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 17.0449i | − 0.686202i | −0.939299 | − | 0.343101i | \(-0.888523\pi\) | ||||
0.939299 | − | 0.343101i | \(-0.111477\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12.1244i | 0.487319i | 0.969861 | + | 0.243659i | \(0.0783479\pi\) | ||||
−0.969861 | + | 0.243659i | \(0.921652\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −13.2456 | −0.530672 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −17.5885 | −0.703538 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 74.0667i | 2.95323i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 38.7846i | 1.54399i | 0.635628 | + | 0.771995i | \(0.280741\pi\) | ||||
−0.635628 | + | 0.771995i | \(0.719259\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −54.8497 | −2.17664 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.00000 | −0.158486 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 10.2784i | 0.405974i | 0.979181 | + | 0.202987i | \(0.0650649\pi\) | ||||
−0.979181 | + | 0.202987i | \(0.934935\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 23.9282i | − 0.943636i | −0.881696 | − | 0.471818i | \(-0.843598\pi\) | ||||
0.881696 | − | 0.471818i | \(-0.156402\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 16.6932 | 0.656276 | 0.328138 | − | 0.944630i | \(-0.393579\pi\) | ||||
0.328138 | + | 0.944630i | \(0.393579\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.46410 | 0.135978 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.55103i | 0.0998294i | 0.998753 | + | 0.0499147i | \(0.0158949\pi\) | ||||
−0.998753 | + | 0.0499147i | \(0.984105\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 18.0000i | 0.703318i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 30.5679 | 1.19075 | 0.595377 | − | 0.803446i | \(-0.297003\pi\) | ||||
0.595377 | + | 0.803446i | \(0.297003\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16.7846 | −0.652846 | −0.326423 | − | 0.945224i | \(-0.605843\pi\) | ||||
−0.326423 | + | 0.945224i | \(0.605843\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.34607i | 0.129755i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 55.7128i | 2.15721i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −11.1106 | −0.428921 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20.0000 | 0.770943 | 0.385472 | − | 0.922720i | \(-0.374039\pi\) | ||||
0.385472 | + | 0.922720i | \(0.374039\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 15.6950i | 0.603210i | 0.953433 | + | 0.301605i | \(0.0975223\pi\) | ||||
−0.953433 | + | 0.301605i | \(0.902478\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 2.92820i | − 0.112374i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8.62398 | 0.329988 | 0.164994 | − | 0.986295i | \(-0.447240\pi\) | ||||
0.164994 | + | 0.986295i | \(0.447240\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.39230 | 0.167821 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 11.3137i | − 0.431018i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 24.5359i | 0.933390i | 0.884418 | + | 0.466695i | \(0.154555\pi\) | ||||
−0.884418 | + | 0.466695i | \(0.845445\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.79315 | −0.0680181 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −49.6603 | −1.88102 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 44.0908i | − 1.66529i | −0.553809 | − | 0.832644i | \(-0.686826\pi\) | ||||
0.553809 | − | 0.832644i | \(-0.313174\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 11.7321i | − 0.442483i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.656339 | −0.0246842 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0.607695 | 0.0228225 | 0.0114112 | − | 0.999935i | \(-0.496368\pi\) | ||||
0.0114112 | + | 0.999935i | \(0.496368\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 26.9072i | − 1.00768i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 12.0000i | 0.448775i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 3.30890 | 0.123401 | 0.0617006 | − | 0.998095i | \(-0.480348\pi\) | ||||
0.0617006 | + | 0.998095i | \(0.480348\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 18.1244 | 0.674986 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 47.8802i | 1.77823i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 14.6795i | − 0.544432i | −0.962236 | − | 0.272216i | \(-0.912243\pi\) | ||||
0.962236 | − | 0.272216i | \(-0.0877566\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 47.1223 | 1.74288 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14.0000 | −0.517102 | −0.258551 | − | 0.965998i | \(-0.583245\pi\) | ||||
−0.258551 | + | 0.965998i | \(0.583245\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 9.79796i | 0.360912i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 35.8564i | 1.31900i | 0.751705 | + | 0.659500i | \(0.229232\pi\) | ||||
−0.751705 | + | 0.659500i | \(0.770768\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 14.0778 | 0.516463 | 0.258232 | − | 0.966083i | \(-0.416860\pi\) | ||||
0.258232 | + | 0.966083i | \(0.416860\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 22.3923 | 0.820391 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.52004i | 0.165159i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 23.0718i | − 0.841902i | −0.907083 | − | 0.420951i | \(-0.861696\pi\) | ||||
0.907083 | − | 0.420951i | \(-0.138304\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −57.9555 | −2.10922 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −18.0000 | −0.654221 | −0.327111 | − | 0.944986i | \(-0.606075\pi\) | ||||
−0.327111 | + | 0.944986i | \(0.606075\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 2.92996i | − 0.106211i | −0.998589 | − | 0.0531055i | \(-0.983088\pi\) | ||||
0.998589 | − | 0.0531055i | \(-0.0169120\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.53590i | 0.128008i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 15.4548 | 0.558041 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −38.2487 | −1.37928 | −0.689642 | − | 0.724151i | \(-0.742232\pi\) | ||||
−0.689642 | + | 0.724151i | \(0.742232\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 22.3872i | − 0.805211i | −0.915374 | − | 0.402605i | \(-0.868105\pi\) | ||||
0.915374 | − | 0.402605i | \(-0.131895\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 23.1244i | − 0.830651i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7.86611 | 0.281833 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.19615 | −0.185933 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 4.89898i | − 0.174852i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.60770i | 0.199893i | 0.994993 | + | 0.0999464i | \(0.0318671\pi\) | ||||
−0.994993 | + | 0.0999464i | \(0.968133\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.52056 | 0.338512 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −49.5692 | −1.76025 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 47.1595i | 1.67047i | 0.549890 | + | 0.835237i | \(0.314670\pi\) | ||||
−0.549890 | + | 0.835237i | \(0.685330\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 55.3205i | 1.95710i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −12.9038 | −0.455365 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −24.1244 | −0.850272 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − 3.03150i | − 0.106582i | −0.998579 | − | 0.0532909i | \(-0.983029\pi\) | ||||
0.998579 | − | 0.0532909i | \(-0.0169711\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.48334i | 0.0520871i | 0.999661 | + | 0.0260435i | \(0.00829086\pi\) | ||||
−0.999661 | + | 0.0260435i | \(0.991709\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 64.6477 | 2.26451 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.46410 | −0.261136 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 36.8439i | 1.28586i | 0.765925 | + | 0.642930i | \(0.222281\pi\) | ||||
−0.765925 | + | 0.642930i | \(0.777719\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 37.7128i | 1.31459i | 0.753635 | + | 0.657293i | \(0.228299\pi\) | ||||
−0.753635 | + | 0.657293i | \(0.771701\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 39.4321 | 1.37119 | 0.685594 | − | 0.727984i | \(-0.259543\pi\) | ||||
0.685594 | + | 0.727984i | \(0.259543\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 47.1769 | 1.63852 | 0.819261 | − | 0.573421i | \(-0.194384\pi\) | ||||
0.819261 | + | 0.573421i | \(0.194384\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.31319i | 0.218739i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 36.2487i | − 1.25444i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −45.8096 | −1.58152 | −0.790762 | − | 0.612124i | \(-0.790316\pi\) | ||||
−0.790762 | + | 0.612124i | \(0.790316\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −30.7128 | −1.05906 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 10.0382i | 0.345324i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.1962i | 0.350344i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 84.5854 | 2.89955 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9.85641 | 0.337477 | 0.168738 | − | 0.985661i | \(-0.446031\pi\) | ||||
0.168738 | + | 0.985661i | \(0.446031\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 47.7415i | 1.63082i | 0.578885 | + | 0.815409i | \(0.303488\pi\) | ||||
−0.578885 | + | 0.815409i | \(0.696512\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 42.7128i | − 1.45734i | −0.684864 | − | 0.728671i | \(-0.740138\pi\) | ||||
0.684864 | − | 0.728671i | \(-0.259862\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.89469 | −0.0644959 | −0.0322479 | − | 0.999480i | \(-0.510267\pi\) | ||||
−0.0322479 | + | 0.999480i | \(0.510267\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.92820 | 0.133563 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 6.69213i | − 0.227015i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 43.7128i | 1.48115i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.00240 | −0.135306 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 50.7846 | 1.71487 | 0.857437 | − | 0.514589i | \(-0.172055\pi\) | ||||
0.857437 | + | 0.514589i | \(0.172055\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 20.0120i | 0.674222i | 0.941465 | + | 0.337111i | \(0.109450\pi\) | ||||
−0.941465 | + | 0.337111i | \(0.890550\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0.679492i | 0.0228667i | 0.999935 | + | 0.0114334i | \(0.00363943\pi\) | ||||
−0.999935 | + | 0.0114334i | \(0.996361\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −42.9812 | −1.44317 | −0.721584 | − | 0.692327i | \(-0.756586\pi\) | ||||
−0.721584 | + | 0.692327i | \(0.756586\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 16.3923 | 0.549780 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 8.76268i | − 0.293232i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 27.1244i | − 0.906667i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 28.8391 | 0.961837 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −17.8564 | −0.594883 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 11.5911i | 0.385302i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 38.7846i | − 1.28782i | −0.765100 | − | 0.643911i | \(-0.777311\pi\) | ||||
0.765100 | − | 0.643911i | \(-0.222689\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −45.6338 | −1.51191 | −0.755957 | − | 0.654621i | \(-0.772828\pi\) | ||||
−0.755957 | + | 0.654621i | \(0.772828\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.24871 | 0.206802 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 5.37945i | − 0.177645i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 50.9282i | 1.67997i | 0.542612 | + | 0.839983i | \(0.317435\pi\) | ||||
−0.542612 | + | 0.839983i | \(0.682565\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −23.1822 | −0.763052 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 72.6936 | 2.39015 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 25.9091i | 0.850050i | 0.905182 | + | 0.425025i | \(0.139735\pi\) | ||||
−0.905182 | + | 0.425025i | \(0.860265\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 1.00000i | − 0.0327737i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 18.9396 | 0.619390 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −23.3205 | −0.761848 | −0.380924 | − | 0.924606i | \(-0.624394\pi\) | ||||
−0.380924 | + | 0.924606i | \(0.624394\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 13.0697i | − 0.426060i | −0.977046 | − | 0.213030i | \(-0.931667\pi\) | ||||
0.977046 | − | 0.213030i | \(-0.0683332\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 56.7128i | 1.84682i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.34984 | 0.0438640 | 0.0219320 | − | 0.999759i | \(-0.493018\pi\) | ||||
0.0219320 | + | 0.999759i | \(0.493018\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −57.5692 | −1.86878 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 35.2538i | − 1.14198i | −0.820956 | − | 0.570991i | \(-0.806559\pi\) | ||||
0.820956 | − | 0.570991i | \(-0.193441\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 86.2295i | − 2.79032i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.31268 | −0.0423886 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 17.0718 | 0.550703 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 49.9507i | 1.60797i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 12.5359i | − 0.403127i | −0.979475 | − | 0.201564i | \(-0.935398\pi\) | ||||
0.979475 | − | 0.201564i | \(-0.0646023\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 33.7381 | 1.08271 | 0.541353 | − | 0.840796i | \(-0.317912\pi\) | ||||
0.541353 | + | 0.840796i | \(0.317912\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.535898 | 0.0171801 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 34.4959i | − 1.10362i | −0.833969 | − | 0.551811i | \(-0.813937\pi\) | ||||
0.833969 | − | 0.551811i | \(-0.186063\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 11.8756i | − 0.379547i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −54.5723 | −1.74059 | −0.870293 | − | 0.492534i | \(-0.836071\pi\) | ||||
−0.870293 | + | 0.492534i | \(0.836071\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 29.3205 | 0.934229 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 53.8144i | − 1.71120i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 24.3923i | − 0.774847i | −0.921902 | − | 0.387424i | \(-0.873365\pi\) | ||||
0.921902 | − | 0.387424i | \(-0.126635\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 88.5506 | 2.80724 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −36.2487 | −1.14801 | −0.574004 | − | 0.818852i | \(-0.694611\pi\) | ||||
−0.574004 | + | 0.818852i | \(0.694611\pi\) | |||||||
\(998\) | 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 | 6048.2.h.f.2591.7 | yes | 8 | |
3.2 | odd | 2 | inner | 6048.2.h.f.2591.1 | ✓ | 8 | |
4.3 | odd | 2 | inner | 6048.2.h.f.2591.8 | yes | 8 | |
12.11 | even | 2 | inner | 6048.2.h.f.2591.2 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6048.2.h.f.2591.1 | ✓ | 8 | 3.2 | odd | 2 | inner | |
6048.2.h.f.2591.2 | yes | 8 | 12.11 | even | 2 | inner | |
6048.2.h.f.2591.7 | yes | 8 | 1.1 | even | 1 | trivial | |
6048.2.h.f.2591.8 | yes | 8 | 4.3 | odd | 2 | inner |