Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [378,2,Mod(377,378)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(378, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("378.377");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 378 = 2 \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 378.d (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: | \(3.01834519640\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 377.3 | ||
Root | \(0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 378.377 |
Dual form | 378.2.d.a.377.1 |
$q$-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 \(\left(\mathbb{Z}/378\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(325\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −1.73205 | −0.774597 | −0.387298 | − | 0.921954i | \(-0.626592\pi\) | ||||
−0.387298 | + | 0.921954i | \(0.626592\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.50000 | − | 0.866025i | −0.944911 | − | 0.327327i | ||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | − | 1.73205i | − | 0.547723i | ||||||
\(11\) | 3.00000i | 0.904534i | 0.891883 | + | 0.452267i | \(0.149385\pi\) | ||||
−0.891883 | + | 0.452267i | \(0.850615\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 6.92820i | − | 1.92154i | −0.277350 | − | 0.960769i | \(-0.589456\pi\) | ||
0.277350 | − | 0.960769i | \(-0.410544\pi\) | |||||||
\(14\) | 0.866025 | − | 2.50000i | 0.231455 | − | 0.668153i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −6.92820 | −1.68034 | −0.840168 | − | 0.542326i | \(-0.817544\pi\) | ||||
−0.840168 | + | 0.542326i | \(0.817544\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 3.46410i | − | 0.794719i | −0.917663 | − | 0.397360i | \(-0.869927\pi\) | ||
0.917663 | − | 0.397360i | \(-0.130073\pi\) | |||||||
\(20\) | 1.73205 | 0.387298 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.00000 | −0.639602 | ||||||||
\(23\) | − | 6.00000i | − | 1.25109i | −0.780189 | − | 0.625543i | \(-0.784877\pi\) | ||
0.780189 | − | 0.625543i | \(-0.215123\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.00000 | −0.400000 | ||||||||
\(26\) | 6.92820 | 1.35873 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.50000 | + | 0.866025i | 0.472456 | + | 0.163663i | ||||
\(29\) | 6.00000i | 1.11417i | 0.830455 | + | 0.557086i | \(0.188081\pi\) | ||||
−0.830455 | + | 0.557086i | \(0.811919\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.19615i | 0.933257i | 0.884454 | + | 0.466628i | \(0.154531\pi\) | ||||
−0.884454 | + | 0.466628i | \(0.845469\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 6.92820i | − | 1.18818i | ||||||
\(35\) | 4.33013 | + | 1.50000i | 0.731925 | + | 0.253546i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.00000 | −0.328798 | −0.164399 | − | 0.986394i | \(-0.552568\pi\) | ||||
−0.164399 | + | 0.986394i | \(0.552568\pi\) | |||||||
\(38\) | 3.46410 | 0.561951 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.73205i | 0.273861i | ||||||||
\(41\) | −3.46410 | −0.541002 | −0.270501 | − | 0.962720i | \(-0.587189\pi\) | ||||
−0.270501 | + | 0.962720i | \(0.587189\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.00000 | −0.304997 | −0.152499 | − | 0.988304i | \(-0.548732\pi\) | ||||
−0.152499 | + | 0.988304i | \(0.548732\pi\) | |||||||
\(44\) | − | 3.00000i | − | 0.452267i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.00000 | 0.884652 | ||||||||
\(47\) | 3.46410 | 0.505291 | 0.252646 | − | 0.967559i | \(-0.418699\pi\) | ||||
0.252646 | + | 0.967559i | \(0.418699\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.50000 | + | 4.33013i | 0.785714 | + | 0.618590i | ||||
\(50\) | − | 2.00000i | − | 0.282843i | ||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 6.92820i | 0.960769i | ||||||||
\(53\) | − | 3.00000i | − | 0.412082i | −0.978543 | − | 0.206041i | \(-0.933942\pi\) | ||
0.978543 | − | 0.206041i | \(-0.0660580\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 5.19615i | − | 0.700649i | ||||||
\(56\) | −0.866025 | + | 2.50000i | −0.115728 | + | 0.334077i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −6.00000 | −0.787839 | ||||||||
\(59\) | −3.46410 | −0.450988 | −0.225494 | − | 0.974245i | \(-0.572400\pi\) | ||||
−0.225494 | + | 0.974245i | \(0.572400\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.92820i | 0.887066i | 0.896258 | + | 0.443533i | \(0.146275\pi\) | ||||
−0.896258 | + | 0.443533i | \(0.853725\pi\) | |||||||
\(62\) | −5.19615 | −0.659912 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 12.0000i | 1.48842i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.00000 | 0.244339 | 0.122169 | − | 0.992509i | \(-0.461015\pi\) | ||||
0.122169 | + | 0.992509i | \(0.461015\pi\) | |||||||
\(68\) | 6.92820 | 0.840168 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.50000 | + | 4.33013i | −0.179284 | + | 0.517549i | ||||
\(71\) | − | 12.0000i | − | 1.42414i | −0.702109 | − | 0.712069i | \(-0.747758\pi\) | ||
0.702109 | − | 0.712069i | \(-0.252242\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.1244i | 1.41905i | 0.704681 | + | 0.709524i | \(0.251090\pi\) | ||||
−0.704681 | + | 0.709524i | \(0.748910\pi\) | |||||||
\(74\) | − | 2.00000i | − | 0.232495i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.46410i | 0.397360i | ||||||||
\(77\) | 2.59808 | − | 7.50000i | 0.296078 | − | 0.854704i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.00000 | 0.900070 | 0.450035 | − | 0.893011i | \(-0.351411\pi\) | ||||
0.450035 | + | 0.893011i | \(0.351411\pi\) | |||||||
\(80\) | −1.73205 | −0.193649 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − | 3.46410i | − | 0.382546i | ||||||
\(83\) | 1.73205 | 0.190117 | 0.0950586 | − | 0.995472i | \(-0.469696\pi\) | ||||
0.0950586 | + | 0.995472i | \(0.469696\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 12.0000 | 1.30158 | ||||||||
\(86\) | − | 2.00000i | − | 0.215666i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.00000 | 0.319801 | ||||||||
\(89\) | −10.3923 | −1.10158 | −0.550791 | − | 0.834643i | \(-0.685674\pi\) | ||||
−0.550791 | + | 0.834643i | \(0.685674\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.00000 | + | 17.3205i | −0.628971 | + | 1.81568i | ||||
\(92\) | 6.00000i | 0.625543i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 3.46410i | 0.357295i | ||||||||
\(95\) | 6.00000i | 0.615587i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 12.1244i | − | 1.23104i | −0.788121 | − | 0.615521i | \(-0.788946\pi\) | ||
0.788121 | − | 0.615521i | \(-0.211054\pi\) | |||||||
\(98\) | −4.33013 | + | 5.50000i | −0.437409 | + | 0.555584i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.00000 | 0.200000 | ||||||||
\(101\) | −15.5885 | −1.55111 | −0.775555 | − | 0.631280i | \(-0.782530\pi\) | ||||
−0.775555 | + | 0.631280i | \(0.782530\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 3.46410i | − | 0.341328i | −0.985329 | − | 0.170664i | \(-0.945409\pi\) | ||
0.985329 | − | 0.170664i | \(-0.0545913\pi\) | |||||||
\(104\) | −6.92820 | −0.679366 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.00000 | 0.291386 | ||||||||
\(107\) | 9.00000i | 0.870063i | 0.900415 | + | 0.435031i | \(0.143263\pi\) | ||||
−0.900415 | + | 0.435031i | \(0.856737\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −14.0000 | −1.34096 | −0.670478 | − | 0.741929i | \(-0.733911\pi\) | ||||
−0.670478 | + | 0.741929i | \(0.733911\pi\) | |||||||
\(110\) | 5.19615 | 0.495434 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.50000 | − | 0.866025i | −0.236228 | − | 0.0818317i | ||||
\(113\) | 6.00000i | 0.564433i | 0.959351 | + | 0.282216i | \(0.0910696\pi\) | ||||
−0.959351 | + | 0.282216i | \(0.908930\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 10.3923i | 0.969087i | ||||||||
\(116\) | − | 6.00000i | − | 0.557086i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 3.46410i | − | 0.318896i | ||||||
\(119\) | 17.3205 | + | 6.00000i | 1.58777 | + | 0.550019i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.00000 | 0.181818 | ||||||||
\(122\) | −6.92820 | −0.627250 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 5.19615i | − | 0.466628i | ||||||
\(125\) | 12.1244 | 1.08444 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.00000 | 0.443678 | 0.221839 | − | 0.975083i | \(-0.428794\pi\) | ||||
0.221839 | + | 0.975083i | \(0.428794\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −12.0000 | −1.05247 | ||||||||
\(131\) | −5.19615 | −0.453990 | −0.226995 | − | 0.973896i | \(-0.572890\pi\) | ||||
−0.226995 | + | 0.973896i | \(0.572890\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.00000 | + | 8.66025i | −0.260133 | + | 0.750939i | ||||
\(134\) | 2.00000i | 0.172774i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.92820i | 0.594089i | ||||||||
\(137\) | − | 18.0000i | − | 1.53784i | −0.639343 | − | 0.768922i | \(-0.720793\pi\) | ||
0.639343 | − | 0.768922i | \(-0.279207\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 13.8564i | − | 1.17529i | −0.809121 | − | 0.587643i | \(-0.800056\pi\) | ||
0.809121 | − | 0.587643i | \(-0.199944\pi\) | |||||||
\(140\) | −4.33013 | − | 1.50000i | −0.365963 | − | 0.126773i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 12.0000 | 1.00702 | ||||||||
\(143\) | 20.7846 | 1.73810 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 10.3923i | − | 0.863034i | ||||||
\(146\) | −12.1244 | −1.00342 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.00000 | 0.164399 | ||||||||
\(149\) | − | 15.0000i | − | 1.22885i | −0.788976 | − | 0.614424i | \(-0.789388\pi\) | ||
0.788976 | − | 0.614424i | \(-0.210612\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 19.0000 | 1.54620 | 0.773099 | − | 0.634285i | \(-0.218706\pi\) | ||||
0.773099 | + | 0.634285i | \(0.218706\pi\) | |||||||
\(152\) | −3.46410 | −0.280976 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 7.50000 | + | 2.59808i | 0.604367 | + | 0.209359i | ||||
\(155\) | − | 9.00000i | − | 0.722897i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(158\) | 8.00000i | 0.636446i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − | 1.73205i | − | 0.136931i | ||||||
\(161\) | −5.19615 | + | 15.0000i | −0.409514 | + | 1.18217i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −16.0000 | −1.25322 | −0.626608 | − | 0.779334i | \(-0.715557\pi\) | ||||
−0.626608 | + | 0.779334i | \(0.715557\pi\) | |||||||
\(164\) | 3.46410 | 0.270501 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.73205i | 0.134433i | ||||||||
\(167\) | 24.2487 | 1.87642 | 0.938211 | − | 0.346064i | \(-0.112482\pi\) | ||||
0.938211 | + | 0.346064i | \(0.112482\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −35.0000 | −2.69231 | ||||||||
\(170\) | 12.0000i | 0.920358i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.00000 | 0.152499 | ||||||||
\(173\) | −5.19615 | −0.395056 | −0.197528 | − | 0.980297i | \(-0.563291\pi\) | ||||
−0.197528 | + | 0.980297i | \(0.563291\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.00000 | + | 1.73205i | 0.377964 | + | 0.130931i | ||||
\(176\) | 3.00000i | 0.226134i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − | 10.3923i | − | 0.778936i | ||||||
\(179\) | − | 15.0000i | − | 1.12115i | −0.828103 | − | 0.560576i | \(-0.810580\pi\) | ||
0.828103 | − | 0.560576i | \(-0.189420\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 6.92820i | − | 0.514969i | −0.966282 | − | 0.257485i | \(-0.917106\pi\) | ||
0.966282 | − | 0.257485i | \(-0.0828937\pi\) | |||||||
\(182\) | −17.3205 | − | 6.00000i | −1.28388 | − | 0.444750i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −6.00000 | −0.442326 | ||||||||
\(185\) | 3.46410 | 0.254686 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 20.7846i | − | 1.51992i | ||||||
\(188\) | −3.46410 | −0.252646 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −6.00000 | −0.435286 | ||||||||
\(191\) | − | 12.0000i | − | 0.868290i | −0.900843 | − | 0.434145i | \(-0.857051\pi\) | ||
0.900843 | − | 0.434145i | \(-0.142949\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.0000 | 0.935760 | 0.467880 | − | 0.883792i | \(-0.345018\pi\) | ||||
0.467880 | + | 0.883792i | \(0.345018\pi\) | |||||||
\(194\) | 12.1244 | 0.870478 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.50000 | − | 4.33013i | −0.392857 | − | 0.309295i | ||||
\(197\) | 3.00000i | 0.213741i | 0.994273 | + | 0.106871i | \(0.0340831\pi\) | ||||
−0.994273 | + | 0.106871i | \(0.965917\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 12.1244i | − | 0.859473i | −0.902954 | − | 0.429736i | \(-0.858606\pi\) | ||
0.902954 | − | 0.429736i | \(-0.141394\pi\) | |||||||
\(200\) | 2.00000i | 0.141421i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 15.5885i | − | 1.09680i | ||||||
\(203\) | 5.19615 | − | 15.0000i | 0.364698 | − | 1.05279i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.00000 | 0.419058 | ||||||||
\(206\) | 3.46410 | 0.241355 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 6.92820i | − | 0.480384i | ||||||
\(209\) | 10.3923 | 0.718851 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.00000 | −0.137686 | −0.0688428 | − | 0.997628i | \(-0.521931\pi\) | ||||
−0.0688428 | + | 0.997628i | \(0.521931\pi\) | |||||||
\(212\) | 3.00000i | 0.206041i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −9.00000 | −0.615227 | ||||||||
\(215\) | 3.46410 | 0.236250 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.50000 | − | 12.9904i | 0.305480 | − | 0.881845i | ||||
\(218\) | − | 14.0000i | − | 0.948200i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 5.19615i | 0.350325i | ||||||||
\(221\) | 48.0000i | 3.22883i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 10.3923i | − | 0.695920i | −0.937509 | − | 0.347960i | \(-0.886874\pi\) | ||
0.937509 | − | 0.347960i | \(-0.113126\pi\) | |||||||
\(224\) | 0.866025 | − | 2.50000i | 0.0578638 | − | 0.167038i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.00000 | −0.399114 | ||||||||
\(227\) | 10.3923 | 0.689761 | 0.344881 | − | 0.938647i | \(-0.387919\pi\) | ||||
0.344881 | + | 0.938647i | \(0.387919\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 10.3923i | − | 0.686743i | −0.939200 | − | 0.343371i | \(-0.888431\pi\) | ||
0.939200 | − | 0.343371i | \(-0.111569\pi\) | |||||||
\(230\) | −10.3923 | −0.685248 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6.00000 | 0.393919 | ||||||||
\(233\) | 6.00000i | 0.393073i | 0.980497 | + | 0.196537i | \(0.0629694\pi\) | ||||
−0.980497 | + | 0.196537i | \(0.937031\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.00000 | −0.391397 | ||||||||
\(236\) | 3.46410 | 0.225494 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −6.00000 | + | 17.3205i | −0.388922 | + | 1.12272i | ||||
\(239\) | 18.0000i | 1.16432i | 0.813073 | + | 0.582162i | \(0.197793\pi\) | ||||
−0.813073 | + | 0.582162i | \(0.802207\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.92820i | 0.446285i | 0.974786 | + | 0.223142i | \(0.0716315\pi\) | ||||
−0.974786 | + | 0.223142i | \(0.928369\pi\) | |||||||
\(242\) | 2.00000i | 0.128565i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 6.92820i | − | 0.443533i | ||||||
\(245\) | −9.52628 | − | 7.50000i | −0.608612 | − | 0.479157i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −24.0000 | −1.52708 | ||||||||
\(248\) | 5.19615 | 0.329956 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 12.1244i | 0.766812i | ||||||||
\(251\) | −17.3205 | −1.09326 | −0.546630 | − | 0.837374i | \(-0.684090\pi\) | ||||
−0.546630 | + | 0.837374i | \(0.684090\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 18.0000 | 1.13165 | ||||||||
\(254\) | 5.00000i | 0.313728i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −20.7846 | −1.29651 | −0.648254 | − | 0.761424i | \(-0.724501\pi\) | ||||
−0.648254 | + | 0.761424i | \(0.724501\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.00000 | + | 1.73205i | 0.310685 | + | 0.107624i | ||||
\(260\) | − | 12.0000i | − | 0.744208i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − | 5.19615i | − | 0.321019i | ||||||
\(263\) | − | 18.0000i | − | 1.10993i | −0.831875 | − | 0.554964i | \(-0.812732\pi\) | ||
0.831875 | − | 0.554964i | \(-0.187268\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.19615i | 0.319197i | ||||||||
\(266\) | −8.66025 | − | 3.00000i | −0.530994 | − | 0.183942i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2.00000 | −0.122169 | ||||||||
\(269\) | −13.8564 | −0.844840 | −0.422420 | − | 0.906400i | \(-0.638819\pi\) | ||||
−0.422420 | + | 0.906400i | \(0.638819\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 29.4449i | 1.78865i | 0.447420 | + | 0.894324i | \(0.352343\pi\) | ||||
−0.447420 | + | 0.894324i | \(0.647657\pi\) | |||||||
\(272\) | −6.92820 | −0.420084 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 18.0000 | 1.08742 | ||||||||
\(275\) | − | 6.00000i | − | 0.361814i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −16.0000 | −0.961347 | −0.480673 | − | 0.876900i | \(-0.659608\pi\) | ||||
−0.480673 | + | 0.876900i | \(0.659608\pi\) | |||||||
\(278\) | 13.8564 | 0.831052 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.50000 | − | 4.33013i | 0.0896421 | − | 0.258775i | ||||
\(281\) | − | 12.0000i | − | 0.715860i | −0.933748 | − | 0.357930i | \(-0.883483\pi\) | ||
0.933748 | − | 0.357930i | \(-0.116517\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.3923i | 0.617758i | 0.951101 | + | 0.308879i | \(0.0999539\pi\) | ||||
−0.951101 | + | 0.308879i | \(0.900046\pi\) | |||||||
\(284\) | 12.0000i | 0.712069i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 20.7846i | 1.22902i | ||||||||
\(287\) | 8.66025 | + | 3.00000i | 0.511199 | + | 0.177084i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 31.0000 | 1.82353 | ||||||||
\(290\) | 10.3923 | 0.610257 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − | 12.1244i | − | 0.709524i | ||||||
\(293\) | 6.92820 | 0.404750 | 0.202375 | − | 0.979308i | \(-0.435134\pi\) | ||||
0.202375 | + | 0.979308i | \(0.435134\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.00000 | 0.349334 | ||||||||
\(296\) | 2.00000i | 0.116248i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 15.0000 | 0.868927 | ||||||||
\(299\) | −41.5692 | −2.40401 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.00000 | + | 1.73205i | 0.288195 | + | 0.0998337i | ||||
\(302\) | 19.0000i | 1.09333i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 3.46410i | − | 0.198680i | ||||||
\(305\) | − | 12.0000i | − | 0.687118i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(308\) | −2.59808 | + | 7.50000i | −0.148039 | + | 0.427352i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 9.00000 | 0.511166 | ||||||||
\(311\) | 24.2487 | 1.37502 | 0.687509 | − | 0.726176i | \(-0.258704\pi\) | ||||
0.687509 | + | 0.726176i | \(0.258704\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.66025i | 0.489506i | 0.969585 | + | 0.244753i | \(0.0787070\pi\) | ||||
−0.969585 | + | 0.244753i | \(0.921293\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.00000 | −0.450035 | ||||||||
\(317\) | − | 9.00000i | − | 0.505490i | −0.967533 | − | 0.252745i | \(-0.918667\pi\) | ||
0.967533 | − | 0.252745i | \(-0.0813334\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −18.0000 | −1.00781 | ||||||||
\(320\) | 1.73205 | 0.0968246 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −15.0000 | − | 5.19615i | −0.835917 | − | 0.289570i | ||||
\(323\) | 24.0000i | 1.33540i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 13.8564i | 0.768615i | ||||||||
\(326\) | − | 16.0000i | − | 0.886158i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3.46410i | 0.191273i | ||||||||
\(329\) | −8.66025 | − | 3.00000i | −0.477455 | − | 0.165395i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.0000 | 0.549650 | 0.274825 | − | 0.961494i | \(-0.411380\pi\) | ||||
0.274825 | + | 0.961494i | \(0.411380\pi\) | |||||||
\(332\) | −1.73205 | −0.0950586 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 24.2487i | 1.32683i | ||||||||
\(335\) | −3.46410 | −0.189264 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −14.0000 | −0.762629 | −0.381314 | − | 0.924445i | \(-0.624528\pi\) | ||||
−0.381314 | + | 0.924445i | \(0.624528\pi\) | |||||||
\(338\) | − | 35.0000i | − | 1.90375i | ||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −12.0000 | −0.650791 | ||||||||
\(341\) | −15.5885 | −0.844162 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10.0000 | − | 15.5885i | −0.539949 | − | 0.841698i | ||||
\(344\) | 2.00000i | 0.107833i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 5.19615i | − | 0.279347i | ||||||
\(347\) | 27.0000i | 1.44944i | 0.689046 | + | 0.724718i | \(0.258030\pi\) | ||||
−0.689046 | + | 0.724718i | \(0.741970\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 17.3205i | 0.927146i | 0.886059 | + | 0.463573i | \(0.153433\pi\) | ||||
−0.886059 | + | 0.463573i | \(0.846567\pi\) | |||||||
\(350\) | −1.73205 | + | 5.00000i | −0.0925820 | + | 0.267261i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.00000 | −0.159901 | ||||||||
\(353\) | 3.46410 | 0.184376 | 0.0921878 | − | 0.995742i | \(-0.470614\pi\) | ||||
0.0921878 | + | 0.995742i | \(0.470614\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 20.7846i | 1.10313i | ||||||||
\(356\) | 10.3923 | 0.550791 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 15.0000 | 0.792775 | ||||||||
\(359\) | 18.0000i | 0.950004i | 0.879985 | + | 0.475002i | \(0.157553\pi\) | ||||
−0.879985 | + | 0.475002i | \(0.842447\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.00000 | 0.368421 | ||||||||
\(362\) | 6.92820 | 0.364138 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 6.00000 | − | 17.3205i | 0.314485 | − | 0.907841i | ||||
\(365\) | − | 21.0000i | − | 1.09919i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 1.73205i | − | 0.0904123i | −0.998978 | − | 0.0452062i | \(-0.985606\pi\) | ||
0.998978 | − | 0.0452062i | \(-0.0143945\pi\) | |||||||
\(368\) | − | 6.00000i | − | 0.312772i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 3.46410i | 0.180090i | ||||||||
\(371\) | −2.59808 | + | 7.50000i | −0.134885 | + | 0.389381i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.00000 | −0.207112 | −0.103556 | − | 0.994624i | \(-0.533022\pi\) | ||||
−0.103556 | + | 0.994624i | \(0.533022\pi\) | |||||||
\(374\) | 20.7846 | 1.07475 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 3.46410i | − | 0.178647i | ||||||
\(377\) | 41.5692 | 2.14092 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 16.0000 | 0.821865 | 0.410932 | − | 0.911666i | \(-0.365203\pi\) | ||||
0.410932 | + | 0.911666i | \(0.365203\pi\) | |||||||
\(380\) | − | 6.00000i | − | 0.307794i | ||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 12.0000 | 0.613973 | ||||||||
\(383\) | −13.8564 | −0.708029 | −0.354015 | − | 0.935240i | \(-0.615184\pi\) | ||||
−0.354015 | + | 0.935240i | \(0.615184\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.50000 | + | 12.9904i | −0.229341 | + | 0.662051i | ||||
\(386\) | 13.0000i | 0.661683i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 12.1244i | 0.615521i | ||||||||
\(389\) | 15.0000i | 0.760530i | 0.924878 | + | 0.380265i | \(0.124167\pi\) | ||||
−0.924878 | + | 0.380265i | \(0.875833\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 41.5692i | 2.10225i | ||||||||
\(392\) | 4.33013 | − | 5.50000i | 0.218704 | − | 0.277792i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −3.00000 | −0.151138 | ||||||||
\(395\) | −13.8564 | −0.697191 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(398\) | 12.1244 | 0.607739 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.00000 | −0.100000 | ||||||||
\(401\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 36.0000 | 1.79329 | ||||||||
\(404\) | 15.5885 | 0.775555 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 15.0000 | + | 5.19615i | 0.744438 | + | 0.257881i | ||||
\(407\) | − | 6.00000i | − | 0.297409i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 29.4449i | − | 1.45595i | −0.685601 | − | 0.727977i | \(-0.740461\pi\) | ||
0.685601 | − | 0.727977i | \(-0.259539\pi\) | |||||||
\(410\) | 6.00000i | 0.296319i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 3.46410i | 0.170664i | ||||||||
\(413\) | 8.66025 | + | 3.00000i | 0.426143 | + | 0.147620i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.00000 | −0.147264 | ||||||||
\(416\) | 6.92820 | 0.339683 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 10.3923i | 0.508304i | ||||||||
\(419\) | −38.1051 | −1.86156 | −0.930778 | − | 0.365584i | \(-0.880869\pi\) | ||||
−0.930778 | + | 0.365584i | \(0.880869\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.00000 | −0.194948 | −0.0974740 | − | 0.995238i | \(-0.531076\pi\) | ||||
−0.0974740 | + | 0.995238i | \(0.531076\pi\) | |||||||
\(422\) | − | 2.00000i | − | 0.0973585i | ||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3.00000 | −0.145693 | ||||||||
\(425\) | 13.8564 | 0.672134 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.00000 | − | 17.3205i | 0.290360 | − | 0.838198i | ||||
\(428\) | − | 9.00000i | − | 0.435031i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3.46410i | 0.167054i | ||||||||
\(431\) | − | 30.0000i | − | 1.44505i | −0.691345 | − | 0.722525i | \(-0.742982\pi\) | ||
0.691345 | − | 0.722525i | \(-0.257018\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.19615i | 0.249711i | 0.992175 | + | 0.124856i | \(0.0398468\pi\) | ||||
−0.992175 | + | 0.124856i | \(0.960153\pi\) | |||||||
\(434\) | 12.9904 | + | 4.50000i | 0.623558 | + | 0.216007i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 14.0000 | 0.670478 | ||||||||
\(437\) | −20.7846 | −0.994263 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.19615i | 0.247999i | 0.992282 | + | 0.123999i | \(0.0395721\pi\) | ||||
−0.992282 | + | 0.123999i | \(0.960428\pi\) | |||||||
\(440\) | −5.19615 | −0.247717 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −48.0000 | −2.28313 | ||||||||
\(443\) | 36.0000i | 1.71041i | 0.518289 | + | 0.855206i | \(0.326569\pi\) | ||||
−0.518289 | + | 0.855206i | \(0.673431\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 18.0000 | 0.853282 | ||||||||
\(446\) | 10.3923 | 0.492090 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.50000 | + | 0.866025i | 0.118114 | + | 0.0409159i | ||||
\(449\) | − | 30.0000i | − | 1.41579i | −0.706319 | − | 0.707894i | \(-0.749646\pi\) | ||
0.706319 | − | 0.707894i | \(-0.250354\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 10.3923i | − | 0.489355i | ||||||
\(452\) | − | 6.00000i | − | 0.282216i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 10.3923i | 0.487735i | ||||||||
\(455\) | 10.3923 | − | 30.0000i | 0.487199 | − | 1.40642i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17.0000 | −0.795226 | −0.397613 | − | 0.917553i | \(-0.630161\pi\) | ||||
−0.397613 | + | 0.917553i | \(0.630161\pi\) | |||||||
\(458\) | 10.3923 | 0.485601 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | − | 10.3923i | − | 0.484544i | ||||||
\(461\) | 12.1244 | 0.564688 | 0.282344 | − | 0.959313i | \(-0.408888\pi\) | ||||
0.282344 | + | 0.959313i | \(0.408888\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −31.0000 | −1.44069 | −0.720346 | − | 0.693615i | \(-0.756017\pi\) | ||||
−0.720346 | + | 0.693615i | \(0.756017\pi\) | |||||||
\(464\) | 6.00000i | 0.278543i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −6.00000 | −0.277945 | ||||||||
\(467\) | −15.5885 | −0.721348 | −0.360674 | − | 0.932692i | \(-0.617453\pi\) | ||||
−0.360674 | + | 0.932692i | \(0.617453\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.00000 | − | 1.73205i | −0.230879 | − | 0.0799787i | ||||
\(470\) | − | 6.00000i | − | 0.276759i | ||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3.46410i | 0.159448i | ||||||||
\(473\) | − | 6.00000i | − | 0.275880i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.92820i | 0.317888i | ||||||||
\(476\) | −17.3205 | − | 6.00000i | −0.793884 | − | 0.275010i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −18.0000 | −0.823301 | ||||||||
\(479\) | −3.46410 | −0.158279 | −0.0791394 | − | 0.996864i | \(-0.525217\pi\) | ||||
−0.0791394 | + | 0.996864i | \(0.525217\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 13.8564i | 0.631798i | ||||||||
\(482\) | −6.92820 | −0.315571 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.00000 | −0.0909091 | ||||||||
\(485\) | 21.0000i | 0.953561i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.00000 | −0.362515 | −0.181257 | − | 0.983436i | \(-0.558017\pi\) | ||||
−0.181257 | + | 0.983436i | \(0.558017\pi\) | |||||||
\(488\) | 6.92820 | 0.313625 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 7.50000 | − | 9.52628i | 0.338815 | − | 0.430353i | ||||
\(491\) | 9.00000i | 0.406164i | 0.979162 | + | 0.203082i | \(0.0650959\pi\) | ||||
−0.979162 | + | 0.203082i | \(0.934904\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 41.5692i | − | 1.87218i | ||||||
\(494\) | − | 24.0000i | − | 1.07981i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 5.19615i | 0.233314i | ||||||||
\(497\) | −10.3923 | + | 30.0000i | −0.466159 | + | 1.34568i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 10.0000 | 0.447661 | 0.223831 | − | 0.974628i | \(-0.428144\pi\) | ||||
0.223831 | + | 0.974628i | \(0.428144\pi\) | |||||||
\(500\) | −12.1244 | −0.542218 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 17.3205i | − | 0.773052i | ||||||
\(503\) | −24.2487 | −1.08120 | −0.540598 | − | 0.841281i | \(-0.681802\pi\) | ||||
−0.540598 | + | 0.841281i | \(0.681802\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 27.0000 | 1.20148 | ||||||||
\(506\) | 18.0000i | 0.800198i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −5.00000 | −0.221839 | ||||||||
\(509\) | 32.9090 | 1.45866 | 0.729332 | − | 0.684160i | \(-0.239831\pi\) | ||||
0.729332 | + | 0.684160i | \(0.239831\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10.5000 | − | 30.3109i | 0.464493 | − | 1.34087i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 20.7846i | − | 0.916770i | ||||||
\(515\) | 6.00000i | 0.264392i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10.3923i | 0.457053i | ||||||||
\(518\) | −1.73205 | + | 5.00000i | −0.0761019 | + | 0.219687i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 12.0000 | 0.526235 | ||||||||
\(521\) | 6.92820 | 0.303530 | 0.151765 | − | 0.988417i | \(-0.451504\pi\) | ||||
0.151765 | + | 0.988417i | \(0.451504\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 6.92820i | − | 0.302949i | −0.988461 | − | 0.151475i | \(-0.951598\pi\) | ||
0.988461 | − | 0.151475i | \(-0.0484022\pi\) | |||||||
\(524\) | 5.19615 | 0.226995 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 18.0000 | 0.784837 | ||||||||
\(527\) | − | 36.0000i | − | 1.56818i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −13.0000 | −0.565217 | ||||||||
\(530\) | −5.19615 | −0.225706 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 3.00000 | − | 8.66025i | 0.130066 | − | 0.375470i | ||||
\(533\) | 24.0000i | 1.03956i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 15.5885i | − | 0.673948i | ||||||
\(536\) | − | 2.00000i | − | 0.0863868i | ||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 13.8564i | − | 0.597392i | ||||||
\(539\) | −12.9904 | + | 16.5000i | −0.559535 | + | 0.710705i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −16.0000 | −0.687894 | −0.343947 | − | 0.938989i | \(-0.611764\pi\) | ||||
−0.343947 | + | 0.938989i | \(0.611764\pi\) | |||||||
\(542\) | −29.4449 | −1.26477 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 6.92820i | − | 0.297044i | ||||||
\(545\) | 24.2487 | 1.03870 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.00000 | 0.342055 | 0.171028 | − | 0.985266i | \(-0.445291\pi\) | ||||
0.171028 | + | 0.985266i | \(0.445291\pi\) | |||||||
\(548\) | 18.0000i | 0.768922i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 6.00000 | 0.255841 | ||||||||
\(551\) | 20.7846 | 0.885454 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −20.0000 | − | 6.92820i | −0.850487 | − | 0.294617i | ||||
\(554\) | − | 16.0000i | − | 0.679775i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 13.8564i | 0.587643i | ||||||||
\(557\) | − | 33.0000i | − | 1.39825i | −0.714997 | − | 0.699127i | \(-0.753572\pi\) | ||
0.714997 | − | 0.699127i | \(-0.246428\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 13.8564i | 0.586064i | ||||||||
\(560\) | 4.33013 | + | 1.50000i | 0.182981 | + | 0.0633866i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 12.0000 | 0.506189 | ||||||||
\(563\) | −25.9808 | −1.09496 | −0.547479 | − | 0.836819i | \(-0.684413\pi\) | ||||
−0.547479 | + | 0.836819i | \(0.684413\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 10.3923i | − | 0.437208i | ||||||
\(566\) | −10.3923 | −0.436821 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −12.0000 | −0.503509 | ||||||||
\(569\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −40.0000 | −1.67395 | −0.836974 | − | 0.547243i | \(-0.815677\pi\) | ||||
−0.836974 | + | 0.547243i | \(0.815677\pi\) | |||||||
\(572\) | −20.7846 | −0.869048 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −3.00000 | + | 8.66025i | −0.125218 | + | 0.361472i | ||||
\(575\) | 12.0000i | 0.500435i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 34.6410i | − | 1.44212i | −0.692870 | − | 0.721062i | \(-0.743654\pi\) | ||
0.692870 | − | 0.721062i | \(-0.256346\pi\) | |||||||
\(578\) | 31.0000i | 1.28943i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 10.3923i | 0.431517i | ||||||||
\(581\) | −4.33013 | − | 1.50000i | −0.179644 | − | 0.0622305i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.00000 | 0.372742 | ||||||||
\(584\) | 12.1244 | 0.501709 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6.92820i | 0.286201i | ||||||||
\(587\) | −25.9808 | −1.07234 | −0.536170 | − | 0.844110i | \(-0.680130\pi\) | ||||
−0.536170 | + | 0.844110i | \(0.680130\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 18.0000 | 0.741677 | ||||||||
\(590\) | 6.00000i | 0.247016i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2.00000 | −0.0821995 | ||||||||
\(593\) | −3.46410 | −0.142254 | −0.0711268 | − | 0.997467i | \(-0.522659\pi\) | ||||
−0.0711268 | + | 0.997467i | \(0.522659\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −30.0000 | − | 10.3923i | −1.22988 | − | 0.426043i | ||||
\(596\) | 15.0000i | 0.614424i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − | 41.5692i | − | 1.69989i | ||||||
\(599\) | 18.0000i | 0.735460i | 0.929933 | + | 0.367730i | \(0.119865\pi\) | ||||
−0.929933 | + | 0.367730i | \(0.880135\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 46.7654i | 1.90760i | 0.300443 | + | 0.953800i | \(0.402865\pi\) | ||||
−0.300443 | + | 0.953800i | \(0.597135\pi\) | |||||||
\(602\) | −1.73205 | + | 5.00000i | −0.0705931 | + | 0.203785i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −19.0000 | −0.773099 | ||||||||
\(605\) | −3.46410 | −0.140836 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 38.1051i | − | 1.54664i | −0.634017 | − | 0.773320i | \(-0.718595\pi\) | ||
0.634017 | − | 0.773320i | \(-0.281405\pi\) | |||||||
\(608\) | 3.46410 | 0.140488 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 12.0000 | 0.485866 | ||||||||
\(611\) | − | 24.0000i | − | 0.970936i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −46.0000 | −1.85792 | −0.928961 | − | 0.370177i | \(-0.879297\pi\) | ||||
−0.928961 | + | 0.370177i | \(0.879297\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −7.50000 | − | 2.59808i | −0.302184 | − | 0.104679i | ||||
\(617\) | 18.0000i | 0.724653i | 0.932051 | + | 0.362326i | \(0.118017\pi\) | ||||
−0.932051 | + | 0.362326i | \(0.881983\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 27.7128i | − | 1.11387i | −0.830555 | − | 0.556936i | \(-0.811977\pi\) | ||
0.830555 | − | 0.556936i | \(-0.188023\pi\) | |||||||
\(620\) | 9.00000i | 0.361449i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 24.2487i | 0.972285i | ||||||||
\(623\) | 25.9808 | + | 9.00000i | 1.04090 | + | 0.360577i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11.0000 | −0.440000 | ||||||||
\(626\) | −8.66025 | −0.346133 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 13.8564 | 0.552491 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 29.0000 | 1.15447 | 0.577236 | − | 0.816577i | \(-0.304131\pi\) | ||||
0.577236 | + | 0.816577i | \(0.304131\pi\) | |||||||
\(632\) | − | 8.00000i | − | 0.318223i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 9.00000 | 0.357436 | ||||||||
\(635\) | −8.66025 | −0.343672 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 30.0000 | − | 38.1051i | 1.18864 | − | 1.50978i | ||||
\(638\) | − | 18.0000i | − | 0.712627i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.73205i | 0.0684653i | ||||||||
\(641\) | − | 18.0000i | − | 0.710957i | −0.934684 | − | 0.355479i | \(-0.884318\pi\) | ||
0.934684 | − | 0.355479i | \(-0.115682\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 20.7846i | − | 0.819665i | −0.912161 | − | 0.409832i | \(-0.865587\pi\) | ||
0.912161 | − | 0.409832i | \(-0.134413\pi\) | |||||||
\(644\) | 5.19615 | − | 15.0000i | 0.204757 | − | 0.591083i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −24.0000 | −0.944267 | ||||||||
\(647\) | 20.7846 | 0.817127 | 0.408564 | − | 0.912730i | \(-0.366030\pi\) | ||||
0.408564 | + | 0.912730i | \(0.366030\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 10.3923i | − | 0.407934i | ||||||
\(650\) | −13.8564 | −0.543493 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 16.0000 | 0.626608 | ||||||||
\(653\) | − | 45.0000i | − | 1.76099i | −0.474059 | − | 0.880493i | \(-0.657212\pi\) | ||
0.474059 | − | 0.880493i | \(-0.342788\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9.00000 | 0.351659 | ||||||||
\(656\) | −3.46410 | −0.135250 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 3.00000 | − | 8.66025i | 0.116952 | − | 0.337612i | ||||
\(659\) | − | 3.00000i | − | 0.116863i | −0.998291 | − | 0.0584317i | \(-0.981390\pi\) | ||
0.998291 | − | 0.0584317i | \(-0.0186100\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 24.2487i | 0.943166i | 0.881822 | + | 0.471583i | \(0.156317\pi\) | ||||
−0.881822 | + | 0.471583i | \(0.843683\pi\) | |||||||
\(662\) | 10.0000i | 0.388661i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 1.73205i | − | 0.0672166i | ||||||
\(665\) | 5.19615 | − | 15.0000i | 0.201498 | − | 0.581675i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 36.0000 | 1.39393 | ||||||||
\(668\) | −24.2487 | −0.938211 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | − | 3.46410i | − | 0.133830i | ||||||
\(671\) | −20.7846 | −0.802381 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.00000 | −0.192736 | −0.0963679 | − | 0.995346i | \(-0.530723\pi\) | ||||
−0.0963679 | + | 0.995346i | \(0.530723\pi\) | |||||||
\(674\) | − | 14.0000i | − | 0.539260i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 35.0000 | 1.34615 | ||||||||
\(677\) | 41.5692 | 1.59763 | 0.798817 | − | 0.601574i | \(-0.205459\pi\) | ||||
0.798817 | + | 0.601574i | \(0.205459\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.5000 | + | 30.3109i | −0.402953 | + | 1.16323i | ||||
\(680\) | − | 12.0000i | − | 0.460179i | ||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − | 15.5885i | − | 0.596913i | ||||||
\(683\) | 12.0000i | 0.459167i | 0.973289 | + | 0.229584i | \(0.0737364\pi\) | ||||
−0.973289 | + | 0.229584i | \(0.926264\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 31.1769i | 1.19121i | ||||||||
\(686\) | 15.5885 | − | 10.0000i | 0.595170 | − | 0.381802i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −2.00000 | −0.0762493 | ||||||||
\(689\) | −20.7846 | −0.791831 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.7846i | 0.790684i | 0.918534 | + | 0.395342i | \(0.129374\pi\) | ||||
−0.918534 | + | 0.395342i | \(0.870626\pi\) | |||||||
\(692\) | 5.19615 | 0.197528 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −27.0000 | −1.02491 | ||||||||
\(695\) | 24.0000i | 0.910372i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 24.0000 | 0.909065 | ||||||||
\(698\) | −17.3205 | −0.655591 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −5.00000 | − | 1.73205i | −0.188982 | − | 0.0654654i | ||||
\(701\) | 3.00000i | 0.113308i | 0.998394 | + | 0.0566542i | \(0.0180433\pi\) | ||||
−0.998394 | + | 0.0566542i | \(0.981957\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.92820i | 0.261302i | ||||||||
\(704\) | − | 3.00000i | − | 0.113067i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 3.46410i | 0.130373i | ||||||||
\(707\) | 38.9711 | + | 13.5000i | 1.46566 | + | 0.507720i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −44.0000 | −1.65245 | −0.826227 | − | 0.563337i | \(-0.809517\pi\) | ||||
−0.826227 | + | 0.563337i | \(0.809517\pi\) | |||||||
\(710\) | −20.7846 | −0.780033 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 10.3923i | 0.389468i | ||||||||
\(713\) | 31.1769 | 1.16758 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −36.0000 | −1.34632 | ||||||||
\(716\) | 15.0000i | 0.560576i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −18.0000 | −0.671754 | ||||||||
\(719\) | 27.7128 | 1.03351 | 0.516757 | − | 0.856132i | \(-0.327139\pi\) | ||||
0.516757 | + | 0.856132i | \(0.327139\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.00000 | + | 8.66025i | −0.111726 | + | 0.322525i | ||||
\(722\) | 7.00000i | 0.260513i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 6.92820i | 0.257485i | ||||||||
\(725\) | − | 12.0000i | − | 0.445669i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 25.9808i | 0.963573i | 0.876289 | + | 0.481787i | \(0.160012\pi\) | ||||
−0.876289 | + | 0.481787i | \(0.839988\pi\) | |||||||
\(728\) | 17.3205 | + | 6.00000i | 0.641941 | + | 0.222375i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 21.0000 | 0.777245 | ||||||||
\(731\) | 13.8564 | 0.512498 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10.3923i | 0.383849i | 0.981410 | + | 0.191924i | \(0.0614728\pi\) | ||||
−0.981410 | + | 0.191924i | \(0.938527\pi\) | |||||||
\(734\) | 1.73205 | 0.0639312 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6.00000 | 0.221163 | ||||||||
\(737\) | 6.00000i | 0.221013i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 20.0000 | 0.735712 | 0.367856 | − | 0.929883i | \(-0.380092\pi\) | ||||
0.367856 | + | 0.929883i | \(0.380092\pi\) | |||||||
\(740\) | −3.46410 | −0.127343 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −7.50000 | − | 2.59808i | −0.275334 | − | 0.0953784i | ||||
\(743\) | − | 36.0000i | − | 1.32071i | −0.750953 | − | 0.660356i | \(-0.770405\pi\) | ||
0.750953 | − | 0.660356i | \(-0.229595\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 25.9808i | 0.951861i | ||||||||
\(746\) | − | 4.00000i | − | 0.146450i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 20.7846i | 0.759961i | ||||||||
\(749\) | 7.79423 | − | 22.5000i | 0.284795 | − | 0.822132i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 43.0000 | 1.56909 | 0.784546 | − | 0.620070i | \(-0.212896\pi\) | ||||
0.784546 | + | 0.620070i | \(0.212896\pi\) | |||||||
\(752\) | 3.46410 | 0.126323 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 41.5692i | 1.51386i | ||||||||
\(755\) | −32.9090 | −1.19768 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.00000 | −0.0726912 | −0.0363456 | − | 0.999339i | \(-0.511572\pi\) | ||||
−0.0363456 | + | 0.999339i | \(0.511572\pi\) | |||||||
\(758\) | 16.0000i | 0.581146i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 6.00000 | 0.217643 | ||||||||
\(761\) | 48.4974 | 1.75803 | 0.879015 | − | 0.476794i | \(-0.158201\pi\) | ||||
0.879015 | + | 0.476794i | \(0.158201\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 35.0000 | + | 12.1244i | 1.26709 | + | 0.438931i | ||||
\(764\) | 12.0000i | 0.434145i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 13.8564i | − | 0.500652i | ||||||
\(767\) | 24.0000i | 0.866590i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.73205i | 0.0624593i | 0.999512 | + | 0.0312297i | \(0.00994233\pi\) | ||||
−0.999512 | + | 0.0312297i | \(0.990058\pi\) | |||||||
\(770\) | −12.9904 | − | 4.50000i | −0.468141 | − | 0.162169i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −13.0000 | −0.467880 | ||||||||
\(773\) | −27.7128 | −0.996761 | −0.498380 | − | 0.866959i | \(-0.666072\pi\) | ||||
−0.498380 | + | 0.866959i | \(0.666072\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 10.3923i | − | 0.373303i | ||||||
\(776\) | −12.1244 | −0.435239 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −15.0000 | −0.537776 | ||||||||
\(779\) | 12.0000i | 0.429945i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 36.0000 | 1.28818 | ||||||||
\(782\) | −41.5692 | −1.48651 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 5.50000 | + | 4.33013i | 0.196429 | + | 0.154647i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13.8564i | 0.493928i | 0.969025 | + | 0.246964i | \(0.0794329\pi\) | ||||
−0.969025 | + | 0.246964i | \(0.920567\pi\) | |||||||
\(788\) | − | 3.00000i | − | 0.106871i | ||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | − | 13.8564i | − | 0.492989i | ||||||
\(791\) | 5.19615 | − | 15.0000i | 0.184754 | − | 0.533339i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 48.0000 | 1.70453 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 12.1244i | 0.429736i | ||||||||
\(797\) | 46.7654 | 1.65651 | 0.828257 | − | 0.560348i | \(-0.189333\pi\) | ||||
0.828257 | + | 0.560348i | \(0.189333\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −24.0000 | −0.849059 | ||||||||
\(800\) | − | 2.00000i | − | 0.0707107i | ||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −36.3731 | −1.28358 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9.00000 | − | 25.9808i | 0.317208 | − | 0.915702i | ||||
\(806\) | 36.0000i | 1.26805i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 15.5885i | 0.548400i | ||||||||
\(809\) | 30.0000i | 1.05474i | 0.849635 | + | 0.527372i | \(0.176823\pi\) | ||||
−0.849635 | + | 0.527372i | \(0.823177\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 31.1769i | 1.09477i | 0.836881 | + | 0.547385i | \(0.184377\pi\) | ||||
−0.836881 | + | 0.547385i | \(0.815623\pi\) | |||||||
\(812\) | −5.19615 | + | 15.0000i | −0.182349 | + | 0.526397i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 6.00000 | 0.210300 | ||||||||
\(815\) | 27.7128 | 0.970737 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.92820i | 0.242387i | ||||||||
\(818\) | 29.4449 | 1.02952 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −6.00000 | −0.209529 | ||||||||
\(821\) | 6.00000i | 0.209401i | 0.994504 | + | 0.104701i | \(0.0333885\pi\) | ||||
−0.994504 | + | 0.104701i | \(0.966612\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −13.0000 | −0.453152 | −0.226576 | − | 0.973994i | \(-0.572753\pi\) | ||||
−0.226576 | + | 0.973994i | \(0.572753\pi\) | |||||||
\(824\) | −3.46410 | −0.120678 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.00000 | + | 8.66025i | −0.104383 | + | 0.301329i | ||||
\(827\) | − | 48.0000i | − | 1.66912i | −0.550914 | − | 0.834562i | \(-0.685721\pi\) | ||
0.550914 | − | 0.834562i | \(-0.314279\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 17.3205i | − | 0.601566i | −0.953693 | − | 0.300783i | \(-0.902752\pi\) | ||
0.953693 | − | 0.300783i | \(-0.0972480\pi\) | |||||||
\(830\) | − | 3.00000i | − | 0.104132i | ||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 6.92820i | 0.240192i | ||||||||
\(833\) | −38.1051 | − | 30.0000i | −1.32026 | − | 1.03944i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −42.0000 | −1.45347 | ||||||||
\(836\) | −10.3923 | −0.359425 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − | 38.1051i | − | 1.31632i | ||||||
\(839\) | −6.92820 | −0.239188 | −0.119594 | − | 0.992823i | \(-0.538159\pi\) | ||||
−0.119594 | + | 0.992823i | \(0.538159\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.00000 | −0.241379 | ||||||||
\(842\) | − | 4.00000i | − | 0.137849i | ||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 2.00000 | 0.0688428 | ||||||||
\(845\) | 60.6218 | 2.08545 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.00000 | − | 1.73205i | −0.171802 | − | 0.0595140i | ||||
\(848\) | − | 3.00000i | − | 0.103020i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 13.8564i | 0.475271i | ||||||||
\(851\) | 12.0000i | 0.411355i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 17.3205i | − | 0.593043i | −0.955026 | − | 0.296521i | \(-0.904173\pi\) | ||
0.955026 | − | 0.296521i | \(-0.0958266\pi\) | |||||||
\(854\) | 17.3205 | + | 6.00000i | 0.592696 | + | 0.205316i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 9.00000 | 0.307614 | ||||||||
\(857\) | 34.6410 | 1.18331 | 0.591657 | − | 0.806190i | \(-0.298474\pi\) | ||||
0.591657 | + | 0.806190i | \(0.298474\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 55.4256i | 1.89110i | 0.325480 | + | 0.945549i | \(0.394474\pi\) | ||||
−0.325480 | + | 0.945549i | \(0.605526\pi\) | |||||||
\(860\) | −3.46410 | −0.118125 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 30.0000 | 1.02180 | ||||||||
\(863\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.00000 | 0.306009 | ||||||||
\(866\) | −5.19615 | −0.176572 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −4.50000 | + | 12.9904i | −0.152740 | + | 0.440922i | ||||
\(869\) | 24.0000i | 0.814144i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 13.8564i | − | 0.469506i | ||||||
\(872\) | 14.0000i | 0.474100i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 20.7846i | − | 0.703050i | ||||||
\(875\) | −30.3109 | − | 10.5000i | −1.02470 | − | 0.354965i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −22.0000 | −0.742887 | −0.371444 | − | 0.928456i | \(-0.621137\pi\) | ||||
−0.371444 | + | 0.928456i | \(0.621137\pi\) | |||||||
\(878\) | −5.19615 | −0.175362 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | − | 5.19615i | − | 0.175162i | ||||||
\(881\) | −20.7846 | −0.700251 | −0.350126 | − | 0.936703i | \(-0.613861\pi\) | ||||
−0.350126 | + | 0.936703i | \(0.613861\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.00000 | −0.0673054 | −0.0336527 | − | 0.999434i | \(-0.510714\pi\) | ||||
−0.0336527 | + | 0.999434i | \(0.510714\pi\) | |||||||
\(884\) | − | 48.0000i | − | 1.61441i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −36.0000 | −1.20944 | ||||||||
\(887\) | −6.92820 | −0.232626 | −0.116313 | − | 0.993213i | \(-0.537108\pi\) | ||||
−0.116313 | + | 0.993213i | \(0.537108\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −12.5000 | − | 4.33013i | −0.419237 | − | 0.145228i | ||||
\(890\) | 18.0000i | 0.603361i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 10.3923i | 0.347960i | ||||||||
\(893\) | − | 12.0000i | − | 0.401565i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 25.9808i | 0.868441i | ||||||||
\(896\) | −0.866025 | + | 2.50000i | −0.0289319 | + | 0.0835191i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 30.0000 | 1.00111 | ||||||||
\(899\) | −31.1769 | −1.03981 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 20.7846i | 0.692436i | ||||||||
\(902\) | 10.3923 | 0.346026 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 6.00000 | 0.199557 | ||||||||
\(905\) | 12.0000i | 0.398893i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −26.0000 | −0.863316 | −0.431658 | − | 0.902037i | \(-0.642071\pi\) | ||||
−0.431658 | + | 0.902037i | \(0.642071\pi\) | |||||||
\(908\) | −10.3923 | −0.344881 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 30.0000 | + | 10.3923i | 0.994490 | + | 0.344502i | ||||
\(911\) | 6.00000i | 0.198789i | 0.995048 | + | 0.0993944i | \(0.0316906\pi\) | ||||
−0.995048 | + | 0.0993944i | \(0.968309\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.19615i | 0.171968i | ||||||||
\(914\) | − | 17.0000i | − | 0.562310i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 10.3923i | 0.343371i | ||||||||
\(917\) | 12.9904 | + | 4.50000i | 0.428980 | + | 0.148603i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −23.0000 | −0.758700 | −0.379350 | − | 0.925253i | \(-0.623852\pi\) | ||||
−0.379350 | + | 0.925253i | \(0.623852\pi\) | |||||||
\(920\) | 10.3923 | 0.342624 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 12.1244i | 0.399294i | ||||||||
\(923\) | −83.1384 | −2.73654 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.00000 | 0.131519 | ||||||||
\(926\) | − | 31.0000i | − | 1.01872i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −6.00000 | −0.196960 | ||||||||
\(929\) | −27.7128 | −0.909228 | −0.454614 | − | 0.890689i | \(-0.650223\pi\) | ||||
−0.454614 | + | 0.890689i | \(0.650223\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 15.0000 | − | 19.0526i | 0.491605 | − | 0.624422i | ||||
\(932\) | − | 6.00000i | − | 0.196537i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − | 15.5885i | − | 0.510070i | ||||||
\(935\) | 36.0000i | 1.17733i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 19.0526i | − | 0.622420i | −0.950341 | − | 0.311210i | \(-0.899266\pi\) | ||
0.950341 | − | 0.311210i | \(-0.100734\pi\) | |||||||
\(938\) | 1.73205 | − | 5.00000i | 0.0565535 | − | 0.163256i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 6.00000 | 0.195698 | ||||||||
\(941\) | −19.0526 | −0.621096 | −0.310548 | − | 0.950558i | \(-0.600512\pi\) | ||||
−0.310548 | + | 0.950558i | \(0.600512\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 20.7846i | 0.676840i | ||||||||
\(944\) | −3.46410 | −0.112747 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 6.00000 | 0.195077 | ||||||||
\(947\) | − | 51.0000i | − | 1.65728i | −0.559784 | − | 0.828639i | \(-0.689116\pi\) | ||
0.559784 | − | 0.828639i | \(-0.310884\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 84.0000 | 2.72676 | ||||||||
\(950\) | −6.92820 | −0.224781 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 6.00000 | − | 17.3205i | 0.194461 | − | 0.561361i | ||||
\(953\) | 36.0000i | 1.16615i | 0.812417 | + | 0.583077i | \(0.198151\pi\) | ||||
−0.812417 | + | 0.583077i | \(0.801849\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 20.7846i | 0.672574i | ||||||||
\(956\) | − | 18.0000i | − | 0.582162i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 3.46410i | − | 0.111920i | ||||||
\(959\) | −15.5885 | + | 45.0000i | −0.503378 | + | 1.45313i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.00000 | 0.129032 | ||||||||
\(962\) | −13.8564 | −0.446748 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 6.92820i | − | 0.223142i | ||||||
\(965\) | −22.5167 | −0.724837 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 11.0000 | 0.353736 | 0.176868 | − | 0.984235i | \(-0.443403\pi\) | ||||
0.176868 | + | 0.984235i | \(0.443403\pi\) | |||||||
\(968\) | − | 2.00000i | − | 0.0642824i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −21.0000 | −0.674269 | ||||||||
\(971\) | 43.3013 | 1.38960 | 0.694802 | − | 0.719201i | \(-0.255492\pi\) | ||||
0.694802 | + | 0.719201i | \(0.255492\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −12.0000 | + | 34.6410i | −0.384702 | + | 1.11054i | ||||
\(974\) | − | 8.00000i | − | 0.256337i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 6.92820i | 0.221766i | ||||||||
\(977\) | − | 6.00000i | − | 0.191957i | −0.995383 | − | 0.0959785i | \(-0.969402\pi\) | ||
0.995383 | − | 0.0959785i | \(-0.0305980\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 31.1769i | − | 0.996419i | ||||||
\(980\) | 9.52628 | + | 7.50000i | 0.304306 | + | 0.239579i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −9.00000 | −0.287202 | ||||||||
\(983\) | −3.46410 | −0.110488 | −0.0552438 | − | 0.998473i | \(-0.517594\pi\) | ||||
−0.0552438 | + | 0.998473i | \(0.517594\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 5.19615i | − | 0.165563i | ||||||
\(986\) | 41.5692 | 1.32383 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 24.0000 | 0.763542 | ||||||||
\(989\) | 12.0000i | 0.381578i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −29.0000 | −0.921215 | −0.460608 | − | 0.887604i | \(-0.652368\pi\) | ||||
−0.460608 | + | 0.887604i | \(0.652368\pi\) | |||||||
\(992\) | −5.19615 | −0.164978 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −30.0000 | − | 10.3923i | −0.951542 | − | 0.329624i | ||||
\(995\) | 21.0000i | 0.665745i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 62.3538i | 1.97477i | 0.158352 | + | 0.987383i | \(0.449382\pi\) | ||||
−0.158352 | + | 0.987383i | \(0.550618\pi\) | |||||||
\(998\) | 10.0000i | 0.316544i | ||||||||
\(999\) | 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 | 378.2.d.a.377.3 | yes | 4 | |
3.2 | odd | 2 | inner | 378.2.d.a.377.2 | yes | 4 | |
4.3 | odd | 2 | 3024.2.k.j.1889.2 | 4 | |||
7.6 | odd | 2 | inner | 378.2.d.a.377.4 | yes | 4 | |
9.2 | odd | 6 | 1134.2.m.e.377.1 | 4 | |||
9.4 | even | 3 | 1134.2.m.f.755.1 | 4 | |||
9.5 | odd | 6 | 1134.2.m.f.755.2 | 4 | |||
9.7 | even | 3 | 1134.2.m.e.377.2 | 4 | |||
12.11 | even | 2 | 3024.2.k.j.1889.4 | 4 | |||
21.20 | even | 2 | inner | 378.2.d.a.377.1 | ✓ | 4 | |
28.27 | even | 2 | 3024.2.k.j.1889.3 | 4 | |||
63.13 | odd | 6 | 1134.2.m.e.755.1 | 4 | |||
63.20 | even | 6 | 1134.2.m.f.377.1 | 4 | |||
63.34 | odd | 6 | 1134.2.m.f.377.2 | 4 | |||
63.41 | even | 6 | 1134.2.m.e.755.2 | 4 | |||
84.83 | odd | 2 | 3024.2.k.j.1889.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
378.2.d.a.377.1 | ✓ | 4 | 21.20 | even | 2 | inner | |
378.2.d.a.377.2 | yes | 4 | 3.2 | odd | 2 | inner | |
378.2.d.a.377.3 | yes | 4 | 1.1 | even | 1 | trivial | |
378.2.d.a.377.4 | yes | 4 | 7.6 | odd | 2 | inner | |
1134.2.m.e.377.1 | 4 | 9.2 | odd | 6 | |||
1134.2.m.e.377.2 | 4 | 9.7 | even | 3 | |||
1134.2.m.e.755.1 | 4 | 63.13 | odd | 6 | |||
1134.2.m.e.755.2 | 4 | 63.41 | even | 6 | |||
1134.2.m.f.377.1 | 4 | 63.20 | even | 6 | |||
1134.2.m.f.377.2 | 4 | 63.34 | odd | 6 | |||
1134.2.m.f.755.1 | 4 | 9.4 | even | 3 | |||
1134.2.m.f.755.2 | 4 | 9.5 | odd | 6 | |||
3024.2.k.j.1889.1 | 4 | 84.83 | odd | 2 | |||
3024.2.k.j.1889.2 | 4 | 4.3 | odd | 2 | |||
3024.2.k.j.1889.3 | 4 | 28.27 | even | 2 | |||
3024.2.k.j.1889.4 | 4 | 12.11 | even | 2 |