Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [504,2,Mod(253,504)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(504, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("504.253");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 504.c (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: | \(4.02446026187\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 253.3 | ||
Root | \(1.22474 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 504.253 |
Dual form | 504.2.c.c.253.4 |
$q$-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 \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).
\(n\) | \(73\) | \(127\) | \(253\) | \(281\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.22474 | − | 0.707107i | 0.866025 | − | 0.500000i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | − | 1.73205i | 0.500000 | − | 0.866025i | ||||
\(5\) | − | 1.41421i | − | 0.632456i | −0.948683 | − | 0.316228i | \(-0.897584\pi\) | ||
0.948683 | − | 0.316228i | \(-0.102416\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | − | 2.82843i | − | 1.00000i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.00000 | − | 1.73205i | −0.316228 | − | 0.547723i | ||||
\(11\) | − | 1.41421i | − | 0.426401i | −0.977008 | − | 0.213201i | \(-0.931611\pi\) | ||
0.977008 | − | 0.213201i | \(-0.0683888\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(14\) | 1.22474 | − | 0.707107i | 0.327327 | − | 0.188982i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.00000 | − | 3.46410i | −0.500000 | − | 0.866025i | ||||
\(17\) | −2.44949 | −0.594089 | −0.297044 | − | 0.954864i | \(-0.596001\pi\) | ||||
−0.297044 | + | 0.954864i | \(0.596001\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.46410i | 0.794719i | 0.917663 | + | 0.397360i | \(0.130073\pi\) | ||||
−0.917663 | + | 0.397360i | \(0.869927\pi\) | |||||||
\(20\) | −2.44949 | − | 1.41421i | −0.547723 | − | 0.316228i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.00000 | − | 1.73205i | −0.213201 | − | 0.369274i | ||||
\(23\) | 2.44949 | 0.510754 | 0.255377 | − | 0.966842i | \(-0.417800\pi\) | ||||
0.255377 | + | 0.966842i | \(0.417800\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.00000 | 0.600000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.00000 | − | 1.73205i | 0.188982 | − | 0.327327i | ||||
\(29\) | − | 5.65685i | − | 1.05045i | −0.850963 | − | 0.525226i | \(-0.823981\pi\) | ||
0.850963 | − | 0.525226i | \(-0.176019\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.00000 | 0.359211 | 0.179605 | − | 0.983739i | \(-0.442518\pi\) | ||||
0.179605 | + | 0.983739i | \(0.442518\pi\) | |||||||
\(32\) | −4.89898 | − | 2.82843i | −0.866025 | − | 0.500000i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −3.00000 | + | 1.73205i | −0.514496 | + | 0.297044i | ||||
\(35\) | − | 1.41421i | − | 0.239046i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.46410i | 0.569495i | 0.958603 | + | 0.284747i | \(0.0919097\pi\) | ||||
−0.958603 | + | 0.284747i | \(0.908090\pi\) | |||||||
\(38\) | 2.44949 | + | 4.24264i | 0.397360 | + | 0.688247i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −4.00000 | −0.632456 | ||||||||
\(41\) | −7.34847 | −1.14764 | −0.573819 | − | 0.818982i | \(-0.694539\pi\) | ||||
−0.573819 | + | 0.818982i | \(0.694539\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.3923i | 1.58481i | 0.609994 | + | 0.792406i | \(0.291172\pi\) | ||||
−0.609994 | + | 0.792406i | \(0.708828\pi\) | |||||||
\(44\) | −2.44949 | − | 1.41421i | −0.369274 | − | 0.213201i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.00000 | − | 1.73205i | 0.442326 | − | 0.255377i | ||||
\(47\) | 9.79796 | 1.42918 | 0.714590 | − | 0.699544i | \(-0.246613\pi\) | ||||
0.714590 | + | 0.699544i | \(0.246613\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 3.67423 | − | 2.12132i | 0.519615 | − | 0.300000i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 5.65685i | − | 0.777029i | −0.921443 | − | 0.388514i | \(-0.872988\pi\) | ||
0.921443 | − | 0.388514i | \(-0.127012\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.00000 | −0.269680 | ||||||||
\(56\) | − | 2.82843i | − | 0.377964i | ||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.00000 | − | 6.92820i | −0.525226 | − | 0.909718i | ||||
\(59\) | 11.3137i | 1.47292i | 0.676481 | + | 0.736460i | \(0.263504\pi\) | ||||
−0.676481 | + | 0.736460i | \(0.736496\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.8564i | 1.77413i | 0.461644 | + | 0.887066i | \(0.347260\pi\) | ||||
−0.461644 | + | 0.887066i | \(0.652740\pi\) | |||||||
\(62\) | 2.44949 | − | 1.41421i | 0.311086 | − | 0.179605i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.00000 | −1.00000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 3.46410i | − | 0.423207i | −0.977356 | − | 0.211604i | \(-0.932131\pi\) | ||
0.977356 | − | 0.211604i | \(-0.0678686\pi\) | |||||||
\(68\) | −2.44949 | + | 4.24264i | −0.297044 | + | 0.514496i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.00000 | − | 1.73205i | −0.119523 | − | 0.207020i | ||||
\(71\) | 7.34847 | 0.872103 | 0.436051 | − | 0.899922i | \(-0.356377\pi\) | ||||
0.436051 | + | 0.899922i | \(0.356377\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.00000 | 0.234082 | 0.117041 | − | 0.993127i | \(-0.462659\pi\) | ||||
0.117041 | + | 0.993127i | \(0.462659\pi\) | |||||||
\(74\) | 2.44949 | + | 4.24264i | 0.284747 | + | 0.493197i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.00000 | + | 3.46410i | 0.688247 | + | 0.397360i | ||||
\(77\) | − | 1.41421i | − | 0.161165i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.00000 | 0.900070 | 0.450035 | − | 0.893011i | \(-0.351411\pi\) | ||||
0.450035 | + | 0.893011i | \(0.351411\pi\) | |||||||
\(80\) | −4.89898 | + | 2.82843i | −0.547723 | + | 0.316228i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −9.00000 | + | 5.19615i | −0.993884 | + | 0.573819i | ||||
\(83\) | 2.82843i | 0.310460i | 0.987878 | + | 0.155230i | \(0.0496119\pi\) | ||||
−0.987878 | + | 0.155230i | \(0.950388\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.46410i | 0.375735i | ||||||||
\(86\) | 7.34847 | + | 12.7279i | 0.792406 | + | 1.37249i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −4.00000 | −0.426401 | ||||||||
\(89\) | −12.2474 | −1.29823 | −0.649113 | − | 0.760692i | \(-0.724860\pi\) | ||||
−0.649113 | + | 0.760692i | \(0.724860\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 2.44949 | − | 4.24264i | 0.255377 | − | 0.442326i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 12.0000 | − | 6.92820i | 1.23771 | − | 0.714590i | ||||
\(95\) | 4.89898 | 0.502625 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.0000 | −1.01535 | −0.507673 | − | 0.861550i | \(-0.669494\pi\) | ||||
−0.507673 | + | 0.861550i | \(0.669494\pi\) | |||||||
\(98\) | 1.22474 | − | 0.707107i | 0.123718 | − | 0.0714286i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.00000 | − | 5.19615i | 0.300000 | − | 0.519615i | ||||
\(101\) | 15.5563i | 1.54791i | 0.633238 | + | 0.773957i | \(0.281726\pi\) | ||||
−0.633238 | + | 0.773957i | \(0.718274\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.00000 | 0.197066 | 0.0985329 | − | 0.995134i | \(-0.468585\pi\) | ||||
0.0985329 | + | 0.995134i | \(0.468585\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.00000 | − | 6.92820i | −0.388514 | − | 0.672927i | ||||
\(107\) | 7.07107i | 0.683586i | 0.939775 | + | 0.341793i | \(0.111034\pi\) | ||||
−0.939775 | + | 0.341793i | \(0.888966\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 13.8564i | − | 1.32720i | −0.748086 | − | 0.663602i | \(-0.769027\pi\) | ||
0.748086 | − | 0.663602i | \(-0.230973\pi\) | |||||||
\(110\) | −2.44949 | + | 1.41421i | −0.233550 | + | 0.134840i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.00000 | − | 3.46410i | −0.188982 | − | 0.327327i | ||||
\(113\) | −14.6969 | −1.38257 | −0.691286 | − | 0.722581i | \(-0.742955\pi\) | ||||
−0.691286 | + | 0.722581i | \(0.742955\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 3.46410i | − | 0.323029i | ||||||
\(116\) | −9.79796 | − | 5.65685i | −0.909718 | − | 0.525226i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 8.00000 | + | 13.8564i | 0.736460 | + | 1.27559i | ||||
\(119\) | −2.44949 | −0.224544 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.00000 | 0.818182 | ||||||||
\(122\) | 9.79796 | + | 16.9706i | 0.887066 | + | 1.53644i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.00000 | − | 3.46410i | 0.179605 | − | 0.311086i | ||||
\(125\) | − | 11.3137i | − | 1.01193i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.00000 | −0.354943 | −0.177471 | − | 0.984126i | \(-0.556792\pi\) | ||||
−0.177471 | + | 0.984126i | \(0.556792\pi\) | |||||||
\(128\) | −9.79796 | + | 5.65685i | −0.866025 | + | 0.500000i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 19.7990i | 1.72985i | 0.501905 | + | 0.864923i | \(0.332633\pi\) | ||||
−0.501905 | + | 0.864923i | \(0.667367\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.46410i | 0.300376i | ||||||||
\(134\) | −2.44949 | − | 4.24264i | −0.211604 | − | 0.366508i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.92820i | 0.594089i | ||||||||
\(137\) | 4.89898 | 0.418548 | 0.209274 | − | 0.977857i | \(-0.432890\pi\) | ||||
0.209274 | + | 0.977857i | \(0.432890\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 20.7846i | − | 1.76293i | −0.472252 | − | 0.881464i | \(-0.656559\pi\) | ||
0.472252 | − | 0.881464i | \(-0.343441\pi\) | |||||||
\(140\) | −2.44949 | − | 1.41421i | −0.207020 | − | 0.119523i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 9.00000 | − | 5.19615i | 0.755263 | − | 0.436051i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.00000 | −0.664364 | ||||||||
\(146\) | 2.44949 | − | 1.41421i | 0.202721 | − | 0.117041i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 6.00000 | + | 3.46410i | 0.493197 | + | 0.284747i | ||||
\(149\) | 11.3137i | 0.926855i | 0.886135 | + | 0.463428i | \(0.153381\pi\) | ||||
−0.886135 | + | 0.463428i | \(0.846619\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.00000 | −0.325515 | −0.162758 | − | 0.986666i | \(-0.552039\pi\) | ||||
−0.162758 | + | 0.986666i | \(0.552039\pi\) | |||||||
\(152\) | 9.79796 | 0.794719 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.00000 | − | 1.73205i | −0.0805823 | − | 0.139573i | ||||
\(155\) | − | 2.82843i | − | 0.227185i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 13.8564i | − | 1.10586i | −0.833227 | − | 0.552931i | \(-0.813509\pi\) | ||
0.833227 | − | 0.552931i | \(-0.186491\pi\) | |||||||
\(158\) | 9.79796 | − | 5.65685i | 0.779484 | − | 0.450035i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −4.00000 | + | 6.92820i | −0.316228 | + | 0.547723i | ||||
\(161\) | 2.44949 | 0.193047 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.46410i | 0.271329i | 0.990755 | + | 0.135665i | \(0.0433170\pi\) | ||||
−0.990755 | + | 0.135665i | \(0.956683\pi\) | |||||||
\(164\) | −7.34847 | + | 12.7279i | −0.573819 | + | 0.993884i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.00000 | + | 3.46410i | 0.155230 | + | 0.268866i | ||||
\(167\) | 14.6969 | 1.13728 | 0.568642 | − | 0.822585i | \(-0.307469\pi\) | ||||
0.568642 | + | 0.822585i | \(0.307469\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 13.0000 | 1.00000 | ||||||||
\(170\) | 2.44949 | + | 4.24264i | 0.187867 | + | 0.325396i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 18.0000 | + | 10.3923i | 1.37249 | + | 0.792406i | ||||
\(173\) | − | 9.89949i | − | 0.752645i | −0.926489 | − | 0.376322i | \(-0.877189\pi\) | ||
0.926489 | − | 0.376322i | \(-0.122811\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.00000 | 0.226779 | ||||||||
\(176\) | −4.89898 | + | 2.82843i | −0.369274 | + | 0.213201i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −15.0000 | + | 8.66025i | −1.12430 | + | 0.649113i | ||||
\(179\) | − | 18.3848i | − | 1.37414i | −0.726590 | − | 0.687071i | \(-0.758896\pi\) | ||
0.726590 | − | 0.687071i | \(-0.241104\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 20.7846i | − | 1.54491i | −0.635071 | − | 0.772454i | \(-0.719029\pi\) | ||
0.635071 | − | 0.772454i | \(-0.280971\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | − | 6.92820i | − | 0.510754i | ||||||
\(185\) | 4.89898 | 0.360180 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.46410i | 0.253320i | ||||||||
\(188\) | 9.79796 | − | 16.9706i | 0.714590 | − | 1.23771i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 6.00000 | − | 3.46410i | 0.435286 | − | 0.251312i | ||||
\(191\) | −12.2474 | −0.886194 | −0.443097 | − | 0.896474i | \(-0.646120\pi\) | ||||
−0.443097 | + | 0.896474i | \(0.646120\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −16.0000 | −1.15171 | −0.575853 | − | 0.817554i | \(-0.695330\pi\) | ||||
−0.575853 | + | 0.817554i | \(0.695330\pi\) | |||||||
\(194\) | −12.2474 | + | 7.07107i | −0.879316 | + | 0.507673i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | − | 1.73205i | 0.0714286 | − | 0.123718i | ||||
\(197\) | − | 14.1421i | − | 1.00759i | −0.863825 | − | 0.503793i | \(-0.831938\pi\) | ||
0.863825 | − | 0.503793i | \(-0.168062\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.0000 | −1.13421 | −0.567105 | − | 0.823646i | \(-0.691937\pi\) | ||||
−0.567105 | + | 0.823646i | \(0.691937\pi\) | |||||||
\(200\) | − | 8.48528i | − | 0.600000i | ||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 11.0000 | + | 19.0526i | 0.773957 | + | 1.34053i | ||||
\(203\) | − | 5.65685i | − | 0.397033i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 10.3923i | 0.725830i | ||||||||
\(206\) | 2.44949 | − | 1.41421i | 0.170664 | − | 0.0985329i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.89898 | 0.338869 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.3923i | 0.715436i | 0.933830 | + | 0.357718i | \(0.116445\pi\) | ||||
−0.933830 | + | 0.357718i | \(0.883555\pi\) | |||||||
\(212\) | −9.79796 | − | 5.65685i | −0.672927 | − | 0.388514i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 5.00000 | + | 8.66025i | 0.341793 | + | 0.592003i | ||||
\(215\) | 14.6969 | 1.00232 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.00000 | 0.135769 | ||||||||
\(218\) | −9.79796 | − | 16.9706i | −0.663602 | − | 1.14939i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2.00000 | + | 3.46410i | −0.134840 | + | 0.233550i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −16.0000 | −1.07144 | −0.535720 | − | 0.844396i | \(-0.679960\pi\) | ||||
−0.535720 | + | 0.844396i | \(0.679960\pi\) | |||||||
\(224\) | −4.89898 | − | 2.82843i | −0.327327 | − | 0.188982i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −18.0000 | + | 10.3923i | −1.19734 | + | 0.691286i | ||||
\(227\) | 2.82843i | 0.187729i | 0.995585 | + | 0.0938647i | \(0.0299221\pi\) | ||||
−0.995585 | + | 0.0938647i | \(0.970078\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 6.92820i | − | 0.457829i | −0.973447 | − | 0.228914i | \(-0.926482\pi\) | ||
0.973447 | − | 0.228914i | \(-0.0735176\pi\) | |||||||
\(230\) | −2.44949 | − | 4.24264i | −0.161515 | − | 0.279751i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −16.0000 | −1.05045 | ||||||||
\(233\) | 9.79796 | 0.641886 | 0.320943 | − | 0.947099i | \(-0.396000\pi\) | ||||
0.320943 | + | 0.947099i | \(0.396000\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 13.8564i | − | 0.903892i | ||||||
\(236\) | 19.5959 | + | 11.3137i | 1.27559 | + | 0.736460i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −3.00000 | + | 1.73205i | −0.194461 | + | 0.112272i | ||||
\(239\) | 7.34847 | 0.475333 | 0.237666 | − | 0.971347i | \(-0.423617\pi\) | ||||
0.237666 | + | 0.971347i | \(0.423617\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.0000 | −0.644157 | −0.322078 | − | 0.946713i | \(-0.604381\pi\) | ||||
−0.322078 | + | 0.946713i | \(0.604381\pi\) | |||||||
\(242\) | 11.0227 | − | 6.36396i | 0.708566 | − | 0.409091i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 24.0000 | + | 13.8564i | 1.53644 | + | 0.887066i | ||||
\(245\) | − | 1.41421i | − | 0.0903508i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | − | 5.65685i | − | 0.359211i | ||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −8.00000 | − | 13.8564i | −0.505964 | − | 0.876356i | ||||
\(251\) | − | 14.1421i | − | 0.892644i | −0.894873 | − | 0.446322i | \(-0.852734\pi\) | ||
0.894873 | − | 0.446322i | \(-0.147266\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 3.46410i | − | 0.217786i | ||||||
\(254\) | −4.89898 | + | 2.82843i | −0.307389 | + | 0.177471i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | + | 13.8564i | −0.500000 | + | 0.866025i | ||||
\(257\) | −26.9444 | −1.68074 | −0.840372 | − | 0.542010i | \(-0.817664\pi\) | ||||
−0.840372 | + | 0.542010i | \(0.817664\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.46410i | 0.215249i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 14.0000 | + | 24.2487i | 0.864923 | + | 1.49809i | ||||
\(263\) | −31.8434 | −1.96355 | −0.981773 | − | 0.190057i | \(-0.939133\pi\) | ||||
−0.981773 | + | 0.190057i | \(0.939133\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.00000 | −0.491436 | ||||||||
\(266\) | 2.44949 | + | 4.24264i | 0.150188 | + | 0.260133i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −6.00000 | − | 3.46410i | −0.366508 | − | 0.211604i | ||||
\(269\) | 7.07107i | 0.431131i | 0.976489 | + | 0.215565i | \(0.0691594\pi\) | ||||
−0.976489 | + | 0.215565i | \(0.930841\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.00000 | 0.121491 | 0.0607457 | − | 0.998153i | \(-0.480652\pi\) | ||||
0.0607457 | + | 0.998153i | \(0.480652\pi\) | |||||||
\(272\) | 4.89898 | + | 8.48528i | 0.297044 | + | 0.514496i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6.00000 | − | 3.46410i | 0.362473 | − | 0.209274i | ||||
\(275\) | − | 4.24264i | − | 0.255841i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 3.46410i | − | 0.208138i | −0.994570 | − | 0.104069i | \(-0.966814\pi\) | ||
0.994570 | − | 0.104069i | \(-0.0331862\pi\) | |||||||
\(278\) | −14.6969 | − | 25.4558i | −0.881464 | − | 1.52674i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −4.00000 | −0.239046 | ||||||||
\(281\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 3.46410i | − | 0.205919i | −0.994686 | − | 0.102960i | \(-0.967169\pi\) | ||
0.994686 | − | 0.102960i | \(-0.0328313\pi\) | |||||||
\(284\) | 7.34847 | − | 12.7279i | 0.436051 | − | 0.755263i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.34847 | −0.433766 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11.0000 | −0.647059 | ||||||||
\(290\) | −9.79796 | + | 5.65685i | −0.575356 | + | 0.332182i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2.00000 | − | 3.46410i | 0.117041 | − | 0.202721i | ||||
\(293\) | − | 9.89949i | − | 0.578335i | −0.957279 | − | 0.289167i | \(-0.906622\pi\) | ||
0.957279 | − | 0.289167i | \(-0.0933784\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 16.0000 | 0.931556 | ||||||||
\(296\) | 9.79796 | 0.569495 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 8.00000 | + | 13.8564i | 0.463428 | + | 0.802680i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.3923i | 0.599002i | ||||||||
\(302\) | −4.89898 | + | 2.82843i | −0.281905 | + | 0.162758i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 12.0000 | − | 6.92820i | 0.688247 | − | 0.397360i | ||||
\(305\) | 19.5959 | 1.12206 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 31.1769i | − | 1.77936i | −0.456584 | − | 0.889680i | \(-0.650927\pi\) | ||
0.456584 | − | 0.889680i | \(-0.349073\pi\) | |||||||
\(308\) | −2.44949 | − | 1.41421i | −0.139573 | − | 0.0805823i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −2.00000 | − | 3.46410i | −0.113592 | − | 0.196748i | ||||
\(311\) | −9.79796 | −0.555591 | −0.277796 | − | 0.960640i | \(-0.589604\pi\) | ||||
−0.277796 | + | 0.960640i | \(0.589604\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 26.0000 | 1.46961 | 0.734803 | − | 0.678280i | \(-0.237274\pi\) | ||||
0.734803 | + | 0.678280i | \(0.237274\pi\) | |||||||
\(314\) | −9.79796 | − | 16.9706i | −0.552931 | − | 0.957704i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8.00000 | − | 13.8564i | 0.450035 | − | 0.779484i | ||||
\(317\) | 11.3137i | 0.635441i | 0.948184 | + | 0.317721i | \(0.102917\pi\) | ||||
−0.948184 | + | 0.317721i | \(0.897083\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.00000 | −0.447914 | ||||||||
\(320\) | 11.3137i | 0.632456i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 3.00000 | − | 1.73205i | 0.167183 | − | 0.0965234i | ||||
\(323\) | − | 8.48528i | − | 0.472134i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2.44949 | + | 4.24264i | 0.135665 | + | 0.234978i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 20.7846i | 1.14764i | ||||||||
\(329\) | 9.79796 | 0.540179 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 24.2487i | 1.33283i | 0.745581 | + | 0.666415i | \(0.232172\pi\) | ||||
−0.745581 | + | 0.666415i | \(0.767828\pi\) | |||||||
\(332\) | 4.89898 | + | 2.82843i | 0.268866 | + | 0.155230i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 18.0000 | − | 10.3923i | 0.984916 | − | 0.568642i | ||||
\(335\) | −4.89898 | −0.267660 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10.0000 | −0.544735 | −0.272367 | − | 0.962193i | \(-0.587807\pi\) | ||||
−0.272367 | + | 0.962193i | \(0.587807\pi\) | |||||||
\(338\) | 15.9217 | − | 9.19239i | 0.866025 | − | 0.500000i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 6.00000 | + | 3.46410i | 0.325396 | + | 0.187867i | ||||
\(341\) | − | 2.82843i | − | 0.153168i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 29.3939 | 1.58481 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −7.00000 | − | 12.1244i | −0.376322 | − | 0.651809i | ||||
\(347\) | − | 1.41421i | − | 0.0759190i | −0.999279 | − | 0.0379595i | \(-0.987914\pi\) | ||
0.999279 | − | 0.0379595i | \(-0.0120858\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 20.7846i | − | 1.11257i | −0.830990 | − | 0.556287i | \(-0.812225\pi\) | ||
0.830990 | − | 0.556287i | \(-0.187775\pi\) | |||||||
\(350\) | 3.67423 | − | 2.12132i | 0.196396 | − | 0.113389i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −4.00000 | + | 6.92820i | −0.213201 | + | 0.369274i | ||||
\(353\) | 26.9444 | 1.43411 | 0.717053 | − | 0.697019i | \(-0.245491\pi\) | ||||
0.717053 | + | 0.697019i | \(0.245491\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 10.3923i | − | 0.551566i | ||||||
\(356\) | −12.2474 | + | 21.2132i | −0.649113 | + | 1.12430i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −13.0000 | − | 22.5167i | −0.687071 | − | 1.19004i | ||||
\(359\) | −26.9444 | −1.42207 | −0.711035 | − | 0.703156i | \(-0.751773\pi\) | ||||
−0.711035 | + | 0.703156i | \(0.751773\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.00000 | 0.368421 | ||||||||
\(362\) | −14.6969 | − | 25.4558i | −0.772454 | − | 1.33793i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 2.82843i | − | 0.148047i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.00000 | 0.417597 | 0.208798 | − | 0.977959i | \(-0.433045\pi\) | ||||
0.208798 | + | 0.977959i | \(0.433045\pi\) | |||||||
\(368\) | −4.89898 | − | 8.48528i | −0.255377 | − | 0.442326i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 6.00000 | − | 3.46410i | 0.311925 | − | 0.180090i | ||||
\(371\) | − | 5.65685i | − | 0.293689i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13.8564i | 0.717458i | 0.933442 | + | 0.358729i | \(0.116790\pi\) | ||||
−0.933442 | + | 0.358729i | \(0.883210\pi\) | |||||||
\(374\) | 2.44949 | + | 4.24264i | 0.126660 | + | 0.219382i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 27.7128i | − | 1.42918i | ||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 10.3923i | − | 0.533817i | −0.963722 | − | 0.266908i | \(-0.913998\pi\) | ||
0.963722 | − | 0.266908i | \(-0.0860021\pi\) | |||||||
\(380\) | 4.89898 | − | 8.48528i | 0.251312 | − | 0.435286i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −15.0000 | + | 8.66025i | −0.767467 | + | 0.443097i | ||||
\(383\) | 24.4949 | 1.25163 | 0.625815 | − | 0.779971i | \(-0.284766\pi\) | ||||
0.625815 | + | 0.779971i | \(0.284766\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.00000 | −0.101929 | ||||||||
\(386\) | −19.5959 | + | 11.3137i | −0.997406 | + | 0.575853i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −10.0000 | + | 17.3205i | −0.507673 | + | 0.879316i | ||||
\(389\) | 28.2843i | 1.43407i | 0.697037 | + | 0.717035i | \(0.254501\pi\) | ||||
−0.697037 | + | 0.717035i | \(0.745499\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.00000 | −0.303433 | ||||||||
\(392\) | − | 2.82843i | − | 0.142857i | ||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −10.0000 | − | 17.3205i | −0.503793 | − | 0.872595i | ||||
\(395\) | − | 11.3137i | − | 0.569254i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 6.92820i | − | 0.347717i | −0.984771 | − | 0.173858i | \(-0.944377\pi\) | ||
0.984771 | − | 0.173858i | \(-0.0556235\pi\) | |||||||
\(398\) | −19.5959 | + | 11.3137i | −0.982255 | + | 0.567105i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −6.00000 | − | 10.3923i | −0.300000 | − | 0.519615i | ||||
\(401\) | 24.4949 | 1.22322 | 0.611608 | − | 0.791161i | \(-0.290523\pi\) | ||||
0.611608 | + | 0.791161i | \(0.290523\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 26.9444 | + | 15.5563i | 1.34053 | + | 0.773957i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4.00000 | − | 6.92820i | −0.198517 | − | 0.343841i | ||||
\(407\) | 4.89898 | 0.242833 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.0000 | 0.692255 | 0.346128 | − | 0.938187i | \(-0.387496\pi\) | ||||
0.346128 | + | 0.938187i | \(0.387496\pi\) | |||||||
\(410\) | 7.34847 | + | 12.7279i | 0.362915 | + | 0.628587i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2.00000 | − | 3.46410i | 0.0985329 | − | 0.170664i | ||||
\(413\) | 11.3137i | 0.556711i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.00000 | 0.196352 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 6.00000 | − | 3.46410i | 0.293470 | − | 0.169435i | ||||
\(419\) | 11.3137i | 0.552711i | 0.961056 | + | 0.276355i | \(0.0891267\pi\) | ||||
−0.961056 | + | 0.276355i | \(0.910873\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 31.1769i | 1.51947i | 0.650233 | + | 0.759735i | \(0.274671\pi\) | ||||
−0.650233 | + | 0.759735i | \(0.725329\pi\) | |||||||
\(422\) | 7.34847 | + | 12.7279i | 0.357718 | + | 0.619586i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −16.0000 | −0.777029 | ||||||||
\(425\) | −7.34847 | −0.356453 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 13.8564i | 0.670559i | ||||||||
\(428\) | 12.2474 | + | 7.07107i | 0.592003 | + | 0.341793i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 18.0000 | − | 10.3923i | 0.868037 | − | 0.501161i | ||||
\(431\) | −31.8434 | −1.53384 | −0.766921 | − | 0.641742i | \(-0.778212\pi\) | ||||
−0.766921 | + | 0.641742i | \(0.778212\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −22.0000 | −1.05725 | −0.528626 | − | 0.848855i | \(-0.677293\pi\) | ||||
−0.528626 | + | 0.848855i | \(0.677293\pi\) | |||||||
\(434\) | 2.44949 | − | 1.41421i | 0.117579 | − | 0.0678844i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −24.0000 | − | 13.8564i | −1.14939 | − | 0.663602i | ||||
\(437\) | 8.48528i | 0.405906i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 32.0000 | 1.52728 | 0.763638 | − | 0.645644i | \(-0.223411\pi\) | ||||
0.763638 | + | 0.645644i | \(0.223411\pi\) | |||||||
\(440\) | 5.65685i | 0.269680i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 35.3553i | − | 1.67978i | −0.542754 | − | 0.839891i | \(-0.682619\pi\) | ||
0.542754 | − | 0.839891i | \(-0.317381\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 17.3205i | 0.821071i | ||||||||
\(446\) | −19.5959 | + | 11.3137i | −0.927894 | + | 0.535720i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −8.00000 | −0.377964 | ||||||||
\(449\) | 14.6969 | 0.693591 | 0.346796 | − | 0.937941i | \(-0.387270\pi\) | ||||
0.346796 | + | 0.937941i | \(0.387270\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.3923i | 0.489355i | ||||||||
\(452\) | −14.6969 | + | 25.4558i | −0.691286 | + | 1.19734i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 2.00000 | + | 3.46410i | 0.0938647 | + | 0.162578i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 26.0000 | 1.21623 | 0.608114 | − | 0.793849i | \(-0.291926\pi\) | ||||
0.608114 | + | 0.793849i | \(0.291926\pi\) | |||||||
\(458\) | −4.89898 | − | 8.48528i | −0.228914 | − | 0.396491i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −6.00000 | − | 3.46410i | −0.279751 | − | 0.161515i | ||||
\(461\) | 32.5269i | 1.51493i | 0.652876 | + | 0.757465i | \(0.273562\pi\) | ||||
−0.652876 | + | 0.757465i | \(0.726438\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.00000 | 0.371792 | 0.185896 | − | 0.982569i | \(-0.440481\pi\) | ||||
0.185896 | + | 0.982569i | \(0.440481\pi\) | |||||||
\(464\) | −19.5959 | + | 11.3137i | −0.909718 | + | 0.525226i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 12.0000 | − | 6.92820i | 0.555889 | − | 0.320943i | ||||
\(467\) | 19.7990i | 0.916188i | 0.888904 | + | 0.458094i | \(0.151468\pi\) | ||||
−0.888904 | + | 0.458094i | \(0.848532\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 3.46410i | − | 0.159957i | ||||||
\(470\) | −9.79796 | − | 16.9706i | −0.451946 | − | 0.782794i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 32.0000 | 1.47292 | ||||||||
\(473\) | 14.6969 | 0.675766 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 10.3923i | 0.476832i | ||||||||
\(476\) | −2.44949 | + | 4.24264i | −0.112272 | + | 0.194461i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 9.00000 | − | 5.19615i | 0.411650 | − | 0.237666i | ||||
\(479\) | −39.1918 | −1.79072 | −0.895360 | − | 0.445342i | \(-0.853082\pi\) | ||||
−0.895360 | + | 0.445342i | \(0.853082\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −12.2474 | + | 7.07107i | −0.557856 | + | 0.322078i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 9.00000 | − | 15.5885i | 0.409091 | − | 0.708566i | ||||
\(485\) | 14.1421i | 0.642161i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −16.0000 | −0.725029 | −0.362515 | − | 0.931978i | \(-0.618082\pi\) | ||||
−0.362515 | + | 0.931978i | \(0.618082\pi\) | |||||||
\(488\) | 39.1918 | 1.77413 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.00000 | − | 1.73205i | −0.0451754 | − | 0.0782461i | ||||
\(491\) | 41.0122i | 1.85085i | 0.378925 | + | 0.925427i | \(0.376294\pi\) | ||||
−0.378925 | + | 0.925427i | \(0.623706\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 13.8564i | 0.624061i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.00000 | − | 6.92820i | −0.179605 | − | 0.311086i | ||||
\(497\) | 7.34847 | 0.329624 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 24.2487i | 1.08552i | 0.839887 | + | 0.542761i | \(0.182621\pi\) | ||||
−0.839887 | + | 0.542761i | \(0.817379\pi\) | |||||||
\(500\) | −19.5959 | − | 11.3137i | −0.876356 | − | 0.505964i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −10.0000 | − | 17.3205i | −0.446322 | − | 0.773052i | ||||
\(503\) | −14.6969 | −0.655304 | −0.327652 | − | 0.944798i | \(-0.606257\pi\) | ||||
−0.327652 | + | 0.944798i | \(0.606257\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 22.0000 | 0.978987 | ||||||||
\(506\) | −2.44949 | − | 4.24264i | −0.108893 | − | 0.188608i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −4.00000 | + | 6.92820i | −0.177471 | + | 0.307389i | ||||
\(509\) | − | 18.3848i | − | 0.814891i | −0.913230 | − | 0.407445i | \(-0.866420\pi\) | ||
0.913230 | − | 0.407445i | \(-0.133580\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.00000 | 0.0884748 | ||||||||
\(512\) | 22.6274i | 1.00000i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −33.0000 | + | 19.0526i | −1.45557 | + | 0.840372i | ||||
\(515\) | − | 2.82843i | − | 0.124635i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 13.8564i | − | 0.609404i | ||||||
\(518\) | 2.44949 | + | 4.24264i | 0.107624 | + | 0.186411i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.2474 | 0.536570 | 0.268285 | − | 0.963340i | \(-0.413543\pi\) | ||||
0.268285 | + | 0.963340i | \(0.413543\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13.8564i | 0.605898i | 0.953007 | + | 0.302949i | \(0.0979712\pi\) | ||||
−0.953007 | + | 0.302949i | \(0.902029\pi\) | |||||||
\(524\) | 34.2929 | + | 19.7990i | 1.49809 | + | 0.864923i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −39.0000 | + | 22.5167i | −1.70048 | + | 0.981773i | ||||
\(527\) | −4.89898 | −0.213403 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.0000 | −0.739130 | ||||||||
\(530\) | −9.79796 | + | 5.65685i | −0.425596 | + | 0.245718i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 6.00000 | + | 3.46410i | 0.260133 | + | 0.150188i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 10.0000 | 0.432338 | ||||||||
\(536\) | −9.79796 | −0.423207 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 5.00000 | + | 8.66025i | 0.215565 | + | 0.373370i | ||||
\(539\) | − | 1.41421i | − | 0.0609145i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 24.2487i | 1.04253i | 0.853394 | + | 0.521267i | \(0.174540\pi\) | ||||
−0.853394 | + | 0.521267i | \(0.825460\pi\) | |||||||
\(542\) | 2.44949 | − | 1.41421i | 0.105215 | − | 0.0607457i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 12.0000 | + | 6.92820i | 0.514496 | + | 0.297044i | ||||
\(545\) | −19.5959 | −0.839397 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.3923i | 0.444343i | 0.975008 | + | 0.222171i | \(0.0713145\pi\) | ||||
−0.975008 | + | 0.222171i | \(0.928686\pi\) | |||||||
\(548\) | 4.89898 | − | 8.48528i | 0.209274 | − | 0.362473i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −3.00000 | − | 5.19615i | −0.127920 | − | 0.221565i | ||||
\(551\) | 19.5959 | 0.834814 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.00000 | 0.340195 | ||||||||
\(554\) | −2.44949 | − | 4.24264i | −0.104069 | − | 0.180253i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −36.0000 | − | 20.7846i | −1.52674 | − | 0.881464i | ||||
\(557\) | 28.2843i | 1.19844i | 0.800583 | + | 0.599222i | \(0.204523\pi\) | ||||
−0.800583 | + | 0.599222i | \(0.795477\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −4.89898 | + | 2.82843i | −0.207020 | + | 0.119523i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 39.5980i | − | 1.66886i | −0.551117 | − | 0.834428i | \(-0.685798\pi\) | ||
0.551117 | − | 0.834428i | \(-0.314202\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 20.7846i | 0.874415i | ||||||||
\(566\) | −2.44949 | − | 4.24264i | −0.102960 | − | 0.178331i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 20.7846i | − | 0.872103i | ||||||
\(569\) | 39.1918 | 1.64301 | 0.821504 | − | 0.570203i | \(-0.193136\pi\) | ||||
0.821504 | + | 0.570203i | \(0.193136\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17.3205i | 0.724841i | 0.932015 | + | 0.362420i | \(0.118050\pi\) | ||||
−0.932015 | + | 0.362420i | \(0.881950\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −9.00000 | + | 5.19615i | −0.375653 | + | 0.216883i | ||||
\(575\) | 7.34847 | 0.306452 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −34.0000 | −1.41544 | −0.707719 | − | 0.706494i | \(-0.750276\pi\) | ||||
−0.707719 | + | 0.706494i | \(0.750276\pi\) | |||||||
\(578\) | −13.4722 | + | 7.77817i | −0.560369 | + | 0.323529i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −8.00000 | + | 13.8564i | −0.332182 | + | 0.575356i | ||||
\(581\) | 2.82843i | 0.117343i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8.00000 | −0.331326 | ||||||||
\(584\) | − | 5.65685i | − | 0.234082i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −7.00000 | − | 12.1244i | −0.289167 | − | 0.500853i | ||||
\(587\) | 19.7990i | 0.817192i | 0.912715 | + | 0.408596i | \(0.133981\pi\) | ||||
−0.912715 | + | 0.408596i | \(0.866019\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.92820i | 0.285472i | ||||||||
\(590\) | 19.5959 | − | 11.3137i | 0.806751 | − | 0.465778i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 12.0000 | − | 6.92820i | 0.493197 | − | 0.284747i | ||||
\(593\) | −26.9444 | −1.10647 | −0.553237 | − | 0.833024i | \(-0.686607\pi\) | ||||
−0.553237 | + | 0.833024i | \(0.686607\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.46410i | 0.142014i | ||||||||
\(596\) | 19.5959 | + | 11.3137i | 0.802680 | + | 0.463428i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2.44949 | −0.100083 | −0.0500417 | − | 0.998747i | \(-0.515935\pi\) | ||||
−0.0500417 | + | 0.998747i | \(0.515935\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 38.0000 | 1.55005 | 0.775026 | − | 0.631929i | \(-0.217737\pi\) | ||||
0.775026 | + | 0.631929i | \(0.217737\pi\) | |||||||
\(602\) | 7.34847 | + | 12.7279i | 0.299501 | + | 0.518751i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −4.00000 | + | 6.92820i | −0.162758 | + | 0.281905i | ||||
\(605\) | − | 12.7279i | − | 0.517464i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −40.0000 | −1.62355 | −0.811775 | − | 0.583970i | \(-0.801498\pi\) | ||||
−0.811775 | + | 0.583970i | \(0.801498\pi\) | |||||||
\(608\) | 9.79796 | − | 16.9706i | 0.397360 | − | 0.688247i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 24.0000 | − | 13.8564i | 0.971732 | − | 0.561029i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 13.8564i | − | 0.559655i | −0.960050 | − | 0.279827i | \(-0.909723\pi\) | ||
0.960050 | − | 0.279827i | \(-0.0902773\pi\) | |||||||
\(614\) | −22.0454 | − | 38.1838i | −0.889680 | − | 1.54097i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4.00000 | −0.161165 | ||||||||
\(617\) | −44.0908 | −1.77503 | −0.887515 | − | 0.460779i | \(-0.847570\pi\) | ||||
−0.887515 | + | 0.460779i | \(0.847570\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 13.8564i | − | 0.556936i | −0.960446 | − | 0.278468i | \(-0.910173\pi\) | ||
0.960446 | − | 0.278468i | \(-0.0898266\pi\) | |||||||
\(620\) | −4.89898 | − | 2.82843i | −0.196748 | − | 0.113592i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −12.0000 | + | 6.92820i | −0.481156 | + | 0.277796i | ||||
\(623\) | −12.2474 | −0.490684 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.00000 | −0.0400000 | ||||||||
\(626\) | 31.8434 | − | 18.3848i | 1.27272 | − | 0.734803i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −24.0000 | − | 13.8564i | −0.957704 | − | 0.552931i | ||||
\(629\) | − | 8.48528i | − | 0.338330i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20.0000 | 0.796187 | 0.398094 | − | 0.917345i | \(-0.369672\pi\) | ||||
0.398094 | + | 0.917345i | \(0.369672\pi\) | |||||||
\(632\) | − | 22.6274i | − | 0.900070i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 8.00000 | + | 13.8564i | 0.317721 | + | 0.550308i | ||||
\(635\) | 5.65685i | 0.224485i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −9.79796 | + | 5.65685i | −0.387905 | + | 0.223957i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 8.00000 | + | 13.8564i | 0.316228 | + | 0.547723i | ||||
\(641\) | 34.2929 | 1.35449 | 0.677243 | − | 0.735759i | \(-0.263174\pi\) | ||||
0.677243 | + | 0.735759i | \(0.263174\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10.3923i | 0.409832i | 0.978780 | + | 0.204916i | \(0.0656922\pi\) | ||||
−0.978780 | + | 0.204916i | \(0.934308\pi\) | |||||||
\(644\) | 2.44949 | − | 4.24264i | 0.0965234 | − | 0.167183i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −6.00000 | − | 10.3923i | −0.236067 | − | 0.408880i | ||||
\(647\) | 4.89898 | 0.192599 | 0.0962994 | − | 0.995352i | \(-0.469299\pi\) | ||||
0.0962994 | + | 0.995352i | \(0.469299\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 16.0000 | 0.628055 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 6.00000 | + | 3.46410i | 0.234978 | + | 0.135665i | ||||
\(653\) | − | 14.1421i | − | 0.553425i | −0.960953 | − | 0.276712i | \(-0.910755\pi\) | ||
0.960953 | − | 0.276712i | \(-0.0892449\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 28.0000 | 1.09405 | ||||||||
\(656\) | 14.6969 | + | 25.4558i | 0.573819 | + | 0.993884i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 12.0000 | − | 6.92820i | 0.467809 | − | 0.270089i | ||||
\(659\) | − | 18.3848i | − | 0.716169i | −0.933689 | − | 0.358085i | \(-0.883430\pi\) | ||
0.933689 | − | 0.358085i | \(-0.116570\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.92820i | 0.269476i | 0.990881 | + | 0.134738i | \(0.0430193\pi\) | ||||
−0.990881 | + | 0.134738i | \(0.956981\pi\) | |||||||
\(662\) | 17.1464 | + | 29.6985i | 0.666415 | + | 1.15426i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 8.00000 | 0.310460 | ||||||||
\(665\) | 4.89898 | 0.189974 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 13.8564i | − | 0.536522i | ||||||
\(668\) | 14.6969 | − | 25.4558i | 0.568642 | − | 0.984916i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −6.00000 | + | 3.46410i | −0.231800 | + | 0.133830i | ||||
\(671\) | 19.5959 | 0.756492 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16.0000 | −0.616755 | −0.308377 | − | 0.951264i | \(-0.599786\pi\) | ||||
−0.308377 | + | 0.951264i | \(0.599786\pi\) | |||||||
\(674\) | −12.2474 | + | 7.07107i | −0.471754 | + | 0.272367i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 13.0000 | − | 22.5167i | 0.500000 | − | 0.866025i | ||||
\(677\) | − | 35.3553i | − | 1.35882i | −0.733761 | − | 0.679408i | \(-0.762237\pi\) | ||
0.733761 | − | 0.679408i | \(-0.237763\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.0000 | −0.383765 | ||||||||
\(680\) | 9.79796 | 0.375735 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −2.00000 | − | 3.46410i | −0.0765840 | − | 0.132647i | ||||
\(683\) | − | 18.3848i | − | 0.703474i | −0.936099 | − | 0.351737i | \(-0.885591\pi\) | ||
0.936099 | − | 0.351737i | \(-0.114409\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 6.92820i | − | 0.264713i | ||||||
\(686\) | 1.22474 | − | 0.707107i | 0.0467610 | − | 0.0269975i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 36.0000 | − | 20.7846i | 1.37249 | − | 0.792406i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 34.6410i | 1.31781i | 0.752228 | + | 0.658903i | \(0.228979\pi\) | ||||
−0.752228 | + | 0.658903i | \(0.771021\pi\) | |||||||
\(692\) | −17.1464 | − | 9.89949i | −0.651809 | − | 0.376322i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.00000 | − | 1.73205i | −0.0379595 | − | 0.0657477i | ||||
\(695\) | −29.3939 | −1.11497 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 18.0000 | 0.681799 | ||||||||
\(698\) | −14.6969 | − | 25.4558i | −0.556287 | − | 0.963518i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 3.00000 | − | 5.19615i | 0.113389 | − | 0.196396i | ||||
\(701\) | 36.7696i | 1.38877i | 0.719605 | + | 0.694383i | \(0.244323\pi\) | ||||
−0.719605 | + | 0.694383i | \(0.755677\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −12.0000 | −0.452589 | ||||||||
\(704\) | 11.3137i | 0.426401i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 33.0000 | − | 19.0526i | 1.24197 | − | 0.717053i | ||||
\(707\) | 15.5563i | 0.585057i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 27.7128i | − | 1.04078i | −0.853930 | − | 0.520388i | \(-0.825787\pi\) | ||
0.853930 | − | 0.520388i | \(-0.174213\pi\) | |||||||
\(710\) | −7.34847 | − | 12.7279i | −0.275783 | − | 0.477670i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 34.6410i | 1.29823i | ||||||||
\(713\) | 4.89898 | 0.183468 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −31.8434 | − | 18.3848i | −1.19004 | − | 0.687071i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −33.0000 | + | 19.0526i | −1.23155 | + | 0.711035i | ||||
\(719\) | 24.4949 | 0.913506 | 0.456753 | − | 0.889594i | \(-0.349012\pi\) | ||||
0.456753 | + | 0.889594i | \(0.349012\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.00000 | 0.0744839 | ||||||||
\(722\) | 8.57321 | − | 4.94975i | 0.319062 | − | 0.184211i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −36.0000 | − | 20.7846i | −1.33793 | − | 0.772454i | ||||
\(725\) | − | 16.9706i | − | 0.630271i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.00000 | 0.0741759 | 0.0370879 | − | 0.999312i | \(-0.488192\pi\) | ||||
0.0370879 | + | 0.999312i | \(0.488192\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −2.00000 | − | 3.46410i | −0.0740233 | − | 0.128212i | ||||
\(731\) | − | 25.4558i | − | 0.941518i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 27.7128i | − | 1.02360i | −0.859106 | − | 0.511798i | \(-0.828980\pi\) | ||
0.859106 | − | 0.511798i | \(-0.171020\pi\) | |||||||
\(734\) | 9.79796 | − | 5.65685i | 0.361649 | − | 0.208798i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −12.0000 | − | 6.92820i | −0.442326 | − | 0.255377i | ||||
\(737\) | −4.89898 | −0.180456 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 24.2487i | − | 0.892003i | −0.895032 | − | 0.446002i | \(-0.852848\pi\) | ||
0.895032 | − | 0.446002i | \(-0.147152\pi\) | |||||||
\(740\) | 4.89898 | − | 8.48528i | 0.180090 | − | 0.311925i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −4.00000 | − | 6.92820i | −0.146845 | − | 0.254342i | ||||
\(743\) | 22.0454 | 0.808768 | 0.404384 | − | 0.914589i | \(-0.367486\pi\) | ||||
0.404384 | + | 0.914589i | \(0.367486\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 16.0000 | 0.586195 | ||||||||
\(746\) | 9.79796 | + | 16.9706i | 0.358729 | + | 0.621336i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 6.00000 | + | 3.46410i | 0.219382 | + | 0.126660i | ||||
\(749\) | 7.07107i | 0.258371i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 32.0000 | 1.16770 | 0.583848 | − | 0.811863i | \(-0.301546\pi\) | ||||
0.583848 | + | 0.811863i | \(0.301546\pi\) | |||||||
\(752\) | −19.5959 | − | 33.9411i | −0.714590 | − | 1.23771i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.65685i | 0.205874i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(758\) | −7.34847 | − | 12.7279i | −0.266908 | − | 0.462299i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | − | 13.8564i | − | 0.502625i | ||||||
\(761\) | −41.6413 | −1.50950 | −0.754748 | − | 0.656014i | \(-0.772241\pi\) | ||||
−0.754748 | + | 0.656014i | \(0.772241\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 13.8564i | − | 0.501636i | ||||||
\(764\) | −12.2474 | + | 21.2132i | −0.443097 | + | 0.767467i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 30.0000 | − | 17.3205i | 1.08394 | − | 0.625815i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −22.0000 | −0.793340 | −0.396670 | − | 0.917961i | \(-0.629834\pi\) | ||||
−0.396670 | + | 0.917961i | \(0.629834\pi\) | |||||||
\(770\) | −2.44949 | + | 1.41421i | −0.0882735 | + | 0.0509647i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −16.0000 | + | 27.7128i | −0.575853 | + | 0.997406i | ||||
\(773\) | − | 35.3553i | − | 1.27164i | −0.771836 | − | 0.635822i | \(-0.780661\pi\) | ||
0.771836 | − | 0.635822i | \(-0.219339\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.00000 | 0.215526 | ||||||||
\(776\) | 28.2843i | 1.01535i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 20.0000 | + | 34.6410i | 0.717035 | + | 1.24194i | ||||
\(779\) | − | 25.4558i | − | 0.912050i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 10.3923i | − | 0.371866i | ||||||
\(782\) | −7.34847 | + | 4.24264i | −0.262781 | + | 0.151717i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2.00000 | − | 3.46410i | −0.0714286 | − | 0.123718i | ||||
\(785\) | −19.5959 | −0.699408 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 34.6410i | − | 1.23482i | −0.786642 | − | 0.617409i | \(-0.788182\pi\) | ||
0.786642 | − | 0.617409i | \(-0.211818\pi\) | |||||||
\(788\) | −24.4949 | − | 14.1421i | −0.872595 | − | 0.503793i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −8.00000 | − | 13.8564i | −0.284627 | − | 0.492989i | ||||
\(791\) | −14.6969 | −0.522563 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −4.89898 | − | 8.48528i | −0.173858 | − | 0.301131i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −16.0000 | + | 27.7128i | −0.567105 | + | 0.982255i | ||||
\(797\) | − | 26.8701i | − | 0.951786i | −0.879503 | − | 0.475893i | \(-0.842125\pi\) | ||
0.879503 | − | 0.475893i | \(-0.157875\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −24.0000 | −0.849059 | ||||||||
\(800\) | −14.6969 | − | 8.48528i | −0.519615 | − | 0.300000i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 30.0000 | − | 17.3205i | 1.05934 | − | 0.611608i | ||||
\(803\) | − | 2.82843i | − | 0.0998130i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 3.46410i | − | 0.122094i | ||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 44.0000 | 1.54791 | ||||||||
\(809\) | 34.2929 | 1.20567 | 0.602836 | − | 0.797865i | \(-0.294037\pi\) | ||||
0.602836 | + | 0.797865i | \(0.294037\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(812\) | −9.79796 | − | 5.65685i | −0.343841 | − | 0.198517i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 6.00000 | − | 3.46410i | 0.210300 | − | 0.121417i | ||||
\(815\) | 4.89898 | 0.171604 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −36.0000 | −1.25948 | ||||||||
\(818\) | 17.1464 | − | 9.89949i | 0.599511 | − | 0.346128i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 18.0000 | + | 10.3923i | 0.628587 | + | 0.362915i | ||||
\(821\) | − | 22.6274i | − | 0.789702i | −0.918745 | − | 0.394851i | \(-0.870796\pi\) | ||
0.918745 | − | 0.394851i | \(-0.129204\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.00000 | −0.139431 | −0.0697156 | − | 0.997567i | \(-0.522209\pi\) | ||||
−0.0697156 | + | 0.997567i | \(0.522209\pi\) | |||||||
\(824\) | − | 5.65685i | − | 0.197066i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 8.00000 | + | 13.8564i | 0.278356 | + | 0.482126i | ||||
\(827\) | 49.4975i | 1.72120i | 0.509285 | + | 0.860598i | \(0.329910\pi\) | ||||
−0.509285 | + | 0.860598i | \(0.670090\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.92820i | 0.240626i | 0.992736 | + | 0.120313i | \(0.0383899\pi\) | ||||
−0.992736 | + | 0.120313i | \(0.961610\pi\) | |||||||
\(830\) | 4.89898 | − | 2.82843i | 0.170046 | − | 0.0981761i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.44949 | −0.0848698 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 20.7846i | − | 0.719281i | ||||||
\(836\) | 4.89898 | − | 8.48528i | 0.169435 | − | 0.293470i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 8.00000 | + | 13.8564i | 0.276355 | + | 0.478662i | ||||
\(839\) | 14.6969 | 0.507395 | 0.253697 | − | 0.967284i | \(-0.418353\pi\) | ||||
0.253697 | + | 0.967284i | \(0.418353\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.00000 | −0.103448 | ||||||||
\(842\) | 22.0454 | + | 38.1838i | 0.759735 | + | 1.31590i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 18.0000 | + | 10.3923i | 0.619586 | + | 0.357718i | ||||
\(845\) | − | 18.3848i | − | 0.632456i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.00000 | 0.309244 | ||||||||
\(848\) | −19.5959 | + | 11.3137i | −0.672927 | + | 0.388514i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −9.00000 | + | 5.19615i | −0.308697 | + | 0.178227i | ||||
\(851\) | 8.48528i | 0.290872i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 20.7846i | 0.711651i | 0.934552 | + | 0.355826i | \(0.115800\pi\) | ||||
−0.934552 | + | 0.355826i | \(0.884200\pi\) | |||||||
\(854\) | 9.79796 | + | 16.9706i | 0.335279 | + | 0.580721i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 20.0000 | 0.683586 | ||||||||
\(857\) | −2.44949 | −0.0836730 | −0.0418365 | − | 0.999124i | \(-0.513321\pi\) | ||||
−0.0418365 | + | 0.999124i | \(0.513321\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 17.3205i | − | 0.590968i | −0.955348 | − | 0.295484i | \(-0.904519\pi\) | ||
0.955348 | − | 0.295484i | \(-0.0954809\pi\) | |||||||
\(860\) | 14.6969 | − | 25.4558i | 0.501161 | − | 0.868037i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −39.0000 | + | 22.5167i | −1.32835 | + | 0.766921i | ||||
\(863\) | 2.44949 | 0.0833816 | 0.0416908 | − | 0.999131i | \(-0.486726\pi\) | ||||
0.0416908 | + | 0.999131i | \(0.486726\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −14.0000 | −0.476014 | ||||||||
\(866\) | −26.9444 | + | 15.5563i | −0.915608 | + | 0.528626i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 2.00000 | − | 3.46410i | 0.0678844 | − | 0.117579i | ||||
\(869\) | − | 11.3137i | − | 0.383791i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −39.1918 | −1.32720 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 6.00000 | + | 10.3923i | 0.202953 | + | 0.351525i | ||||
\(875\) | − | 11.3137i | − | 0.382473i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 27.7128i | − | 0.935795i | −0.883783 | − | 0.467898i | \(-0.845012\pi\) | ||
0.883783 | − | 0.467898i | \(-0.154988\pi\) | |||||||
\(878\) | 39.1918 | − | 22.6274i | 1.32266 | − | 0.763638i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 4.00000 | + | 6.92820i | 0.134840 | + | 0.233550i | ||||
\(881\) | −7.34847 | −0.247576 | −0.123788 | − | 0.992309i | \(-0.539504\pi\) | ||||
−0.123788 | + | 0.992309i | \(0.539504\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 31.1769i | − | 1.04919i | −0.851353 | − | 0.524593i | \(-0.824217\pi\) | ||
0.851353 | − | 0.524593i | \(-0.175783\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −25.0000 | − | 43.3013i | −0.839891 | − | 1.45473i | ||||
\(887\) | 53.8888 | 1.80941 | 0.904704 | − | 0.426041i | \(-0.140092\pi\) | ||||
0.904704 | + | 0.426041i | \(0.140092\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.00000 | −0.134156 | ||||||||
\(890\) | 12.2474 | + | 21.2132i | 0.410535 | + | 0.711068i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −16.0000 | + | 27.7128i | −0.535720 | + | 0.927894i | ||||
\(893\) | 33.9411i | 1.13580i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −26.0000 | −0.869084 | ||||||||
\(896\) | −9.79796 | + | 5.65685i | −0.327327 | + | 0.188982i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 18.0000 | − | 10.3923i | 0.600668 | − | 0.346796i | ||||
\(899\) | − | 11.3137i | − | 0.377333i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 13.8564i | 0.461624i | ||||||||
\(902\) | 7.34847 | + | 12.7279i | 0.244677 | + | 0.423793i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 41.5692i | 1.38257i | ||||||||
\(905\) | −29.3939 | −0.977086 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 24.2487i | − | 0.805165i | −0.915384 | − | 0.402583i | \(-0.868113\pi\) | ||
0.915384 | − | 0.402583i | \(-0.131887\pi\) | |||||||
\(908\) | 4.89898 | + | 2.82843i | 0.162578 | + | 0.0938647i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7.34847 | 0.243466 | 0.121733 | − | 0.992563i | \(-0.461155\pi\) | ||||
0.121733 | + | 0.992563i | \(0.461155\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.00000 | 0.132381 | ||||||||
\(914\) | 31.8434 | − | 18.3848i | 1.05328 | − | 0.608114i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −12.0000 | − | 6.92820i | −0.396491 | − | 0.228914i | ||||
\(917\) | 19.7990i | 0.653820i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −16.0000 | −0.527791 | −0.263896 | − | 0.964551i | \(-0.585007\pi\) | ||||
−0.263896 | + | 0.964551i | \(0.585007\pi\) | |||||||
\(920\) | −9.79796 | −0.323029 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 23.0000 | + | 39.8372i | 0.757465 | + | 1.31197i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10.3923i | 0.341697i | ||||||||
\(926\) | 9.79796 | − | 5.65685i | 0.321981 | − | 0.185896i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −16.0000 | + | 27.7128i | −0.525226 | + | 0.909718i | ||||
\(929\) | −12.2474 | −0.401826 | −0.200913 | − | 0.979609i | \(-0.564391\pi\) | ||||
−0.200913 | + | 0.979609i | \(0.564391\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.46410i | 0.113531i | ||||||||
\(932\) | 9.79796 | − | 16.9706i | 0.320943 | − | 0.555889i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 14.0000 | + | 24.2487i | 0.458094 | + | 0.793442i | ||||
\(935\) | 4.89898 | 0.160214 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 14.0000 | 0.457360 | 0.228680 | − | 0.973502i | \(-0.426559\pi\) | ||||
0.228680 | + | 0.973502i | \(0.426559\pi\) | |||||||
\(938\) | −2.44949 | − | 4.24264i | −0.0799787 | − | 0.138527i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −24.0000 | − | 13.8564i | −0.782794 | − | 0.451946i | ||||
\(941\) | − | 18.3848i | − | 0.599327i | −0.954045 | − | 0.299663i | \(-0.903126\pi\) | ||
0.954045 | − | 0.299663i | \(-0.0968743\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −18.0000 | −0.586161 | ||||||||
\(944\) | 39.1918 | − | 22.6274i | 1.27559 | − | 0.736460i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 18.0000 | − | 10.3923i | 0.585230 | − | 0.337883i | ||||
\(947\) | − | 9.89949i | − | 0.321690i | −0.986980 | − | 0.160845i | \(-0.948578\pi\) | ||
0.986980 | − | 0.160845i | \(-0.0514220\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 7.34847 | + | 12.7279i | 0.238416 | + | 0.412948i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 6.92820i | 0.224544i | ||||||||
\(953\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 17.3205i | 0.560478i | ||||||||
\(956\) | 7.34847 | − | 12.7279i | 0.237666 | − | 0.411650i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −48.0000 | + | 27.7128i | −1.55081 | + | 0.895360i | ||||
\(959\) | 4.89898 | 0.158196 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.0000 | −0.870968 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −10.0000 | + | 17.3205i | −0.322078 | + | 0.557856i | ||||
\(965\) | 22.6274i | 0.728402i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −28.0000 | −0.900419 | −0.450210 | − | 0.892923i | \(-0.648651\pi\) | ||||
−0.450210 | + | 0.892923i | \(0.648651\pi\) | |||||||
\(968\) | − | 25.4558i | − | 0.818182i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 10.0000 | + | 17.3205i | 0.321081 | + | 0.556128i | ||||
\(971\) | 45.2548i | 1.45230i | 0.687538 | + | 0.726148i | \(0.258691\pi\) | ||||
−0.687538 | + | 0.726148i | \(0.741309\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 20.7846i | − | 0.666324i | ||||||
\(974\) | −19.5959 | + | 11.3137i | −0.627894 | + | 0.362515i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 48.0000 | − | 27.7128i | 1.53644 | − | 0.887066i | ||||
\(977\) | −39.1918 | −1.25386 | −0.626929 | − | 0.779076i | \(-0.715688\pi\) | ||||
−0.626929 | + | 0.779076i | \(0.715688\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 17.3205i | 0.553566i | ||||||||
\(980\) | −2.44949 | − | 1.41421i | −0.0782461 | − | 0.0451754i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 29.0000 | + | 50.2295i | 0.925427 | + | 1.60289i | ||||
\(983\) | −9.79796 | −0.312506 | −0.156253 | − | 0.987717i | \(-0.549942\pi\) | ||||
−0.156253 | + | 0.987717i | \(0.549942\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −20.0000 | −0.637253 | ||||||||
\(986\) | 9.79796 | + | 16.9706i | 0.312031 | + | 0.540453i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 25.4558i | 0.809449i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 20.0000 | 0.635321 | 0.317660 | − | 0.948205i | \(-0.397103\pi\) | ||||
0.317660 | + | 0.948205i | \(0.397103\pi\) | |||||||
\(992\) | −9.79796 | − | 5.65685i | −0.311086 | − | 0.179605i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 9.00000 | − | 5.19615i | 0.285463 | − | 0.164812i | ||||
\(995\) | 22.6274i | 0.717337i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 34.6410i | − | 1.09709i | −0.836120 | − | 0.548546i | \(-0.815182\pi\) | ||
0.836120 | − | 0.548546i | \(-0.184818\pi\) | |||||||
\(998\) | 17.1464 | + | 29.6985i | 0.542761 | + | 0.940089i | ||||
\(999\) | 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 | 504.2.c.c.253.3 | yes | 4 | |
3.2 | odd | 2 | inner | 504.2.c.c.253.2 | yes | 4 | |
4.3 | odd | 2 | 2016.2.c.b.1009.1 | 4 | |||
8.3 | odd | 2 | 2016.2.c.b.1009.3 | 4 | |||
8.5 | even | 2 | inner | 504.2.c.c.253.4 | yes | 4 | |
12.11 | even | 2 | 2016.2.c.b.1009.4 | 4 | |||
24.5 | odd | 2 | inner | 504.2.c.c.253.1 | ✓ | 4 | |
24.11 | even | 2 | 2016.2.c.b.1009.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.c.c.253.1 | ✓ | 4 | 24.5 | odd | 2 | inner | |
504.2.c.c.253.2 | yes | 4 | 3.2 | odd | 2 | inner | |
504.2.c.c.253.3 | yes | 4 | 1.1 | even | 1 | trivial | |
504.2.c.c.253.4 | yes | 4 | 8.5 | even | 2 | inner | |
2016.2.c.b.1009.1 | 4 | 4.3 | odd | 2 | |||
2016.2.c.b.1009.2 | 4 | 24.11 | even | 2 | |||
2016.2.c.b.1009.3 | 4 | 8.3 | odd | 2 | |||
2016.2.c.b.1009.4 | 4 | 12.11 | even | 2 |