Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2940,2,Mod(589,2940)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2940, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2940.589");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2940 = 2^{2} \cdot 3 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2940.k (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: | \(23.4760181943\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 420) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 589.2 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2940.589 |
Dual form | 2940.2.k.d.589.1 |
$q$-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 \(\left(\mathbb{Z}/2940\mathbb{Z}\right)^\times\).
\(n\) | \(1081\) | \(1177\) | \(1471\) | \(1961\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.00000 | − | 1.00000i | 0.894427 | − | 0.447214i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.00000 | −1.20605 | −0.603023 | − | 0.797724i | \(-0.706037\pi\) | ||||
−0.603023 | + | 0.797724i | \(0.706037\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.00000i | 1.66410i | 0.554700 | + | 0.832050i | \(0.312833\pi\) | ||||
−0.554700 | + | 0.832050i | \(0.687167\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.00000 | + | 2.00000i | 0.258199 | + | 0.516398i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.00000i | 0.485071i | 0.970143 | + | 0.242536i | \(0.0779791\pi\) | ||||
−0.970143 | + | 0.242536i | \(0.922021\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.00000 | 1.37649 | 0.688247 | − | 0.725476i | \(-0.258380\pi\) | ||||
0.688247 | + | 0.725476i | \(0.258380\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.00000i | 0.417029i | 0.978019 | + | 0.208514i | \(0.0668628\pi\) | ||||
−0.978019 | + | 0.208514i | \(0.933137\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.00000 | − | 4.00000i | 0.600000 | − | 0.800000i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.00000 | −1.11417 | −0.557086 | − | 0.830455i | \(-0.688081\pi\) | ||||
−0.557086 | + | 0.830455i | \(0.688081\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.00000 | 0.359211 | 0.179605 | − | 0.983739i | \(-0.442518\pi\) | ||||
0.179605 | + | 0.983739i | \(0.442518\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 4.00000i | − | 0.696311i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.00000i | 0.657596i | 0.944400 | + | 0.328798i | \(0.106644\pi\) | ||||
−0.944400 | + | 0.328798i | \(0.893356\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −6.00000 | −0.960769 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.00000 | −1.24939 | −0.624695 | − | 0.780869i | \(-0.714777\pi\) | ||||
−0.624695 | + | 0.780869i | \(0.714777\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 4.00000i | − | 0.609994i | −0.952353 | − | 0.304997i | \(-0.901344\pi\) | ||
0.952353 | − | 0.304997i | \(-0.0986555\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.00000 | + | 1.00000i | −0.298142 | + | 0.149071i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.00000i | 0.583460i | 0.956501 | + | 0.291730i | \(0.0942309\pi\) | ||||
−0.956501 | + | 0.291730i | \(0.905769\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.00000 | −0.280056 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.00000i | 0.824163i | 0.911147 | + | 0.412082i | \(0.135198\pi\) | ||||
−0.911147 | + | 0.412082i | \(0.864802\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −8.00000 | + | 4.00000i | −1.07872 | + | 0.539360i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.00000i | 0.794719i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.00000 | 0.520756 | 0.260378 | − | 0.965507i | \(-0.416153\pi\) | ||||
0.260378 | + | 0.965507i | \(0.416153\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −14.0000 | −1.79252 | −0.896258 | − | 0.443533i | \(-0.853725\pi\) | ||||
−0.896258 | + | 0.443533i | \(0.853725\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.00000 | + | 12.0000i | 0.744208 | + | 1.48842i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 4.00000i | − | 0.488678i | −0.969690 | − | 0.244339i | \(-0.921429\pi\) | ||
0.969690 | − | 0.244339i | \(-0.0785709\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.00000 | −0.240772 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.0000i | 1.17041i | 0.810885 | + | 0.585206i | \(0.198986\pi\) | ||||
−0.810885 | + | 0.585206i | \(0.801014\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.00000 | + | 3.00000i | 0.461880 | + | 0.346410i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 16.0000i | 1.75623i | 0.478451 | + | 0.878114i | \(0.341198\pi\) | ||||
−0.478451 | + | 0.878114i | \(0.658802\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.00000 | + | 4.00000i | 0.216930 | + | 0.433861i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 6.00000i | − | 0.643268i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.00000 | 0.847998 | 0.423999 | − | 0.905663i | \(-0.360626\pi\) | ||||
0.423999 | + | 0.905663i | \(0.360626\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.00000i | 0.207390i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 12.0000 | − | 6.00000i | 1.23117 | − | 0.615587i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.0000i | 1.01535i | 0.861550 | + | 0.507673i | \(0.169494\pi\) | ||||
−0.861550 | + | 0.507673i | \(0.830506\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.00000 | 0.402015 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −16.0000 | −1.59206 | −0.796030 | − | 0.605257i | \(-0.793070\pi\) | ||||
−0.796030 | + | 0.605257i | \(0.793070\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 16.0000i | − | 1.57653i | −0.615338 | − | 0.788263i | \(-0.710980\pi\) | ||
0.615338 | − | 0.788263i | \(-0.289020\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.00000i | 0.580042i | 0.957020 | + | 0.290021i | \(0.0936623\pi\) | ||||
−0.957020 | + | 0.290021i | \(0.906338\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.0000 | 1.34096 | 0.670478 | − | 0.741929i | \(-0.266089\pi\) | ||||
0.670478 | + | 0.741929i | \(0.266089\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.00000 | −0.379663 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 18.0000i | 1.69330i | 0.532152 | + | 0.846649i | \(0.321383\pi\) | ||||
−0.532152 | + | 0.846649i | \(0.678617\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.00000 | + | 4.00000i | 0.186501 | + | 0.373002i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 6.00000i | − | 0.554700i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.00000 | 0.454545 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 8.00000i | − | 0.721336i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.00000 | − | 11.0000i | 0.178885 | − | 0.983870i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.0000i | 1.41977i | 0.704317 | + | 0.709885i | \(0.251253\pi\) | ||||
−0.704317 | + | 0.709885i | \(0.748747\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.00000 | 0.352180 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.0000 | 1.04844 | 0.524222 | − | 0.851581i | \(-0.324356\pi\) | ||||
0.524222 | + | 0.851581i | \(0.324356\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.00000 | − | 2.00000i | −0.0860663 | − | 0.172133i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 18.0000i | − | 1.53784i | −0.639343 | − | 0.768922i | \(-0.720793\pi\) | ||
0.639343 | − | 0.768922i | \(-0.279207\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.0000 | 0.848189 | 0.424094 | − | 0.905618i | \(-0.360592\pi\) | ||||
0.424094 | + | 0.905618i | \(0.360592\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.00000 | −0.336861 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 24.0000i | − | 2.00698i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −12.0000 | + | 6.00000i | −0.996546 | + | 0.498273i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −22.0000 | −1.80231 | −0.901155 | − | 0.433497i | \(-0.857280\pi\) | ||||
−0.901155 | + | 0.433497i | \(0.857280\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16.0000 | 1.30206 | 0.651031 | − | 0.759051i | \(-0.274337\pi\) | ||||
0.651031 | + | 0.759051i | \(0.274337\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 2.00000i | − | 0.161690i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.00000 | − | 2.00000i | 0.321288 | − | 0.160644i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.0000i | 0.798087i | 0.916932 | + | 0.399043i | \(0.130658\pi\) | ||||
−0.916932 | + | 0.399043i | \(0.869342\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −6.00000 | −0.475831 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 8.00000i | − | 0.626608i | −0.949653 | − | 0.313304i | \(-0.898564\pi\) | ||
0.949653 | − | 0.313304i | \(-0.101436\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.00000 | − | 8.00000i | −0.311400 | − | 0.622799i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 24.0000i | 1.85718i | 0.371113 | + | 0.928588i | \(0.378976\pi\) | ||||
−0.371113 | + | 0.928588i | \(0.621024\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −23.0000 | −1.76923 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.00000 | −0.458831 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.00000i | 0.152057i | 0.997106 | + | 0.0760286i | \(0.0242240\pi\) | ||||
−0.997106 | + | 0.0760286i | \(0.975776\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.00000i | 0.300658i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.00000 | −0.298974 | −0.149487 | − | 0.988764i | \(-0.547762\pi\) | ||||
−0.149487 | + | 0.988764i | \(0.547762\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.0000 | 0.743294 | 0.371647 | − | 0.928374i | \(-0.378793\pi\) | ||||
0.371647 | + | 0.928374i | \(0.378793\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 14.0000i | − | 1.03491i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.00000 | + | 8.00000i | 0.294086 | + | 0.588172i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 8.00000i | − | 0.585018i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.00000i | 0.575853i | 0.957653 | + | 0.287926i | \(0.0929658\pi\) | ||||
−0.957653 | + | 0.287926i | \(0.907034\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −12.0000 | + | 6.00000i | −0.859338 | + | 0.429669i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 10.0000i | − | 0.712470i | −0.934396 | − | 0.356235i | \(-0.884060\pi\) | ||
0.934396 | − | 0.356235i | \(-0.115940\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 18.0000 | 1.27599 | 0.637993 | − | 0.770042i | \(-0.279765\pi\) | ||||
0.637993 | + | 0.770042i | \(0.279765\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.00000 | 0.282138 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −16.0000 | + | 8.00000i | −1.11749 | + | 0.558744i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 2.00000i | − | 0.139010i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −24.0000 | −1.66011 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −24.0000 | −1.65223 | −0.826114 | − | 0.563503i | \(-0.809453\pi\) | ||||
−0.826114 | + | 0.563503i | \(0.809453\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.00000 | − | 8.00000i | −0.272798 | − | 0.545595i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −10.0000 | −0.675737 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −12.0000 | −0.807207 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 16.0000i | 1.07144i | 0.844396 | + | 0.535720i | \(0.179960\pi\) | ||||
−0.844396 | + | 0.535720i | \(0.820040\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.00000 | + | 4.00000i | −0.200000 | + | 0.266667i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 20.0000i | 1.32745i | 0.747978 | + | 0.663723i | \(0.231025\pi\) | ||||
−0.747978 | + | 0.663723i | \(0.768975\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.00000 | 0.132164 | 0.0660819 | − | 0.997814i | \(-0.478950\pi\) | ||||
0.0660819 | + | 0.997814i | \(0.478950\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 26.0000i | − | 1.70332i | −0.524097 | − | 0.851658i | \(-0.675597\pi\) | ||
0.524097 | − | 0.851658i | \(-0.324403\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.00000 | + | 8.00000i | 0.260931 | + | 0.521862i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 16.0000 | 1.03495 | 0.517477 | − | 0.855697i | \(-0.326871\pi\) | ||||
0.517477 | + | 0.855697i | \(0.326871\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.0000 | −0.644157 | −0.322078 | − | 0.946713i | \(-0.604381\pi\) | ||||
−0.322078 | + | 0.946713i | \(0.604381\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 36.0000i | 2.29063i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −16.0000 | −1.01396 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.0000 | 0.757433 | 0.378717 | − | 0.925513i | \(-0.376365\pi\) | ||||
0.378717 | + | 0.925513i | \(0.376365\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 8.00000i | − | 0.502956i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −4.00000 | + | 2.00000i | −0.250490 | + | 0.125245i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.00000i | 0.374270i | 0.982334 | + | 0.187135i | \(0.0599201\pi\) | ||||
−0.982334 | + | 0.187135i | \(0.940080\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.00000 | 0.371391 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 10.0000i | − | 0.616626i | −0.951285 | − | 0.308313i | \(-0.900236\pi\) | ||
0.951285 | − | 0.308313i | \(-0.0997645\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.00000 | + | 12.0000i | 0.368577 | + | 0.737154i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.00000i | 0.489592i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −12.0000 | −0.731653 | −0.365826 | − | 0.930683i | \(-0.619214\pi\) | ||||
−0.365826 | + | 0.930683i | \(0.619214\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.0000 | 0.850439 | 0.425220 | − | 0.905090i | \(-0.360197\pi\) | ||||
0.425220 | + | 0.905090i | \(0.360197\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −12.0000 | + | 16.0000i | −0.723627 | + | 0.964836i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 28.0000i | 1.68236i | 0.540758 | + | 0.841178i | \(0.318138\pi\) | ||||
−0.540758 | + | 0.841178i | \(0.681862\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.00000 | −0.119737 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.00000 | −0.357930 | −0.178965 | − | 0.983855i | \(-0.557275\pi\) | ||||
−0.178965 | + | 0.983855i | \(0.557275\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 28.0000i | − | 1.66443i | −0.554455 | − | 0.832214i | \(-0.687073\pi\) | ||
0.554455 | − | 0.832214i | \(-0.312927\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 6.00000 | + | 12.0000i | 0.355409 | + | 0.710819i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.0000 | 0.764706 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −10.0000 | −0.586210 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.00000i | 0.350524i | 0.984522 | + | 0.175262i | \(0.0560772\pi\) | ||||
−0.984522 | + | 0.175262i | \(0.943923\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.00000 | − | 4.00000i | 0.465778 | − | 0.232889i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.00000i | 0.232104i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −12.0000 | −0.693978 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 16.0000i | − | 0.919176i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −28.0000 | + | 14.0000i | −1.60328 | + | 0.801638i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 12.0000i | − | 0.684876i | −0.939540 | − | 0.342438i | \(-0.888747\pi\) | ||
0.939540 | − | 0.342438i | \(-0.111253\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 16.0000 | 0.910208 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −12.0000 | −0.680458 | −0.340229 | − | 0.940343i | \(-0.610505\pi\) | ||||
−0.340229 | + | 0.940343i | \(0.610505\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 14.0000i | − | 0.791327i | −0.918396 | − | 0.395663i | \(-0.870515\pi\) | ||
0.918396 | − | 0.395663i | \(-0.129485\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 14.0000i | − | 0.786318i | −0.919470 | − | 0.393159i | \(-0.871382\pi\) | ||
0.919470 | − | 0.393159i | \(-0.128618\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 24.0000 | 1.34374 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.00000 | −0.334887 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 12.0000i | 0.667698i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 24.0000 | + | 18.0000i | 1.33128 | + | 0.998460i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 14.0000i | 0.774202i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.00000 | −0.439720 | −0.219860 | − | 0.975531i | \(-0.570560\pi\) | ||||
−0.219860 | + | 0.975531i | \(0.570560\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 4.00000i | − | 0.219199i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.00000 | − | 8.00000i | −0.218543 | − | 0.437087i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 8.00000i | − | 0.435788i | −0.975972 | − | 0.217894i | \(-0.930081\pi\) | ||
0.975972 | − | 0.217894i | \(-0.0699187\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −18.0000 | −0.977626 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8.00000 | −0.433224 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4.00000 | + | 2.00000i | −0.215353 | + | 0.107676i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 18.0000i | − | 0.966291i | −0.875540 | − | 0.483145i | \(-0.839494\pi\) | ||
0.875540 | − | 0.483145i | \(-0.160506\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 22.0000 | 1.17763 | 0.588817 | − | 0.808267i | \(-0.299594\pi\) | ||||
0.588817 | + | 0.808267i | \(0.299594\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.00000 | 0.320256 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.00000i | 0.106449i | 0.998583 | + | 0.0532246i | \(0.0169499\pi\) | ||||
−0.998583 | + | 0.0532246i | \(0.983050\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.0000 | 0.894737 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5.00000i | 0.262432i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10.0000 | + | 20.0000i | 0.523424 | + | 1.04685i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 16.0000i | − | 0.835193i | −0.908633 | − | 0.417597i | \(-0.862873\pi\) | ||
0.908633 | − | 0.417597i | \(-0.137127\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8.00000 | 0.416463 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 24.0000i | − | 1.24267i | −0.783544 | − | 0.621336i | \(-0.786590\pi\) | ||
0.783544 | − | 0.621336i | \(-0.213410\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 11.0000 | + | 2.00000i | 0.568038 | + | 0.103280i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 36.0000i | − | 1.85409i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 28.0000 | 1.43826 | 0.719132 | − | 0.694874i | \(-0.244540\pi\) | ||||
0.719132 | + | 0.694874i | \(0.244540\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −16.0000 | −0.819705 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 28.0000i | − | 1.43073i | −0.698749 | − | 0.715367i | \(-0.746260\pi\) | ||
0.698749 | − | 0.715367i | \(-0.253740\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.00000i | 0.203331i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.00000 | −0.101404 | −0.0507020 | − | 0.998714i | \(-0.516146\pi\) | ||||
−0.0507020 | + | 0.998714i | \(0.516146\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.00000 | −0.202289 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 12.0000i | 0.605320i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 10.0000i | − | 0.501886i | −0.968002 | − | 0.250943i | \(-0.919259\pi\) | ||
0.968002 | − | 0.250943i | \(-0.0807406\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 22.0000 | 1.09863 | 0.549314 | − | 0.835616i | \(-0.314889\pi\) | ||||
0.549314 | + | 0.835616i | \(0.314889\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 12.0000i | 0.597763i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.00000 | − | 1.00000i | 0.0993808 | − | 0.0496904i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 16.0000i | − | 0.793091i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.0000 | −0.494468 | −0.247234 | − | 0.968956i | \(-0.579522\pi\) | ||||
−0.247234 | + | 0.968956i | \(0.579522\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 18.0000 | 0.887875 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 16.0000 | + | 32.0000i | 0.785409 | + | 1.57082i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 10.0000i | 0.489702i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −40.0000 | −1.95413 | −0.977064 | − | 0.212946i | \(-0.931694\pi\) | ||||
−0.977064 | + | 0.212946i | \(0.931694\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.00000 | −0.0974740 | −0.0487370 | − | 0.998812i | \(-0.515520\pi\) | ||||
−0.0487370 | + | 0.998812i | \(0.515520\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 4.00000i | − | 0.194487i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 8.00000 | + | 6.00000i | 0.388057 | + | 0.291043i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 24.0000 | 1.15873 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −16.0000 | −0.770693 | −0.385346 | − | 0.922772i | \(-0.625918\pi\) | ||||
−0.385346 | + | 0.922772i | \(0.625918\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 10.0000i | 0.480569i | 0.970702 | + | 0.240285i | \(0.0772408\pi\) | ||||
−0.970702 | + | 0.240285i | \(0.922759\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −6.00000 | − | 12.0000i | −0.287678 | − | 0.575356i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 12.0000i | 0.574038i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −30.0000 | −1.43182 | −0.715911 | − | 0.698192i | \(-0.753988\pi\) | ||||
−0.715911 | + | 0.698192i | \(0.753988\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 30.0000i | − | 1.42534i | −0.701498 | − | 0.712672i | \(-0.747485\pi\) | ||
0.701498 | − | 0.712672i | \(-0.252515\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 16.0000 | − | 8.00000i | 0.758473 | − | 0.379236i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 22.0000i | − | 1.04056i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −18.0000 | −0.849473 | −0.424736 | − | 0.905317i | \(-0.639633\pi\) | ||||
−0.424736 | + | 0.905317i | \(0.639633\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 32.0000 | 1.50682 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 16.0000i | 0.751746i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 20.0000i | − | 0.935561i | −0.883845 | − | 0.467780i | \(-0.845054\pi\) | ||
0.883845 | − | 0.467780i | \(-0.154946\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.00000 | 0.0933520 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 24.0000i | − | 1.11537i | −0.830051 | − | 0.557687i | \(-0.811689\pi\) | ||
0.830051 | − | 0.557687i | \(-0.188311\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.00000 | + | 4.00000i | 0.0927478 | + | 0.185496i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 12.0000i | 0.555294i | 0.960683 | + | 0.277647i | \(0.0895545\pi\) | ||||
−0.960683 | + | 0.277647i | \(0.910445\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −10.0000 | −0.460776 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 16.0000i | 0.735681i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 18.0000 | − | 24.0000i | 0.825897 | − | 1.10120i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 6.00000i | − | 0.274721i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.00000 | −0.182765 | −0.0913823 | − | 0.995816i | \(-0.529129\pi\) | ||||
−0.0913823 | + | 0.995816i | \(0.529129\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −24.0000 | −1.09431 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 10.0000 | + | 20.0000i | 0.454077 | + | 0.908153i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12.0000i | 0.543772i | 0.962329 | + | 0.271886i | \(0.0876473\pi\) | ||||
−0.962329 | + | 0.271886i | \(0.912353\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 8.00000 | 0.361773 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.0000 | 0.541552 | 0.270776 | − | 0.962642i | \(-0.412720\pi\) | ||||
0.270776 | + | 0.962642i | \(0.412720\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 12.0000i | − | 0.540453i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 8.00000 | − | 4.00000i | 0.359573 | − | 0.179787i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 36.0000 | 1.61158 | 0.805791 | − | 0.592200i | \(-0.201741\pi\) | ||||
0.805791 | + | 0.592200i | \(0.201741\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −24.0000 | −1.07224 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 36.0000i | − | 1.60516i | −0.596544 | − | 0.802580i | \(-0.703460\pi\) | ||
0.596544 | − | 0.802580i | \(-0.296540\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −32.0000 | + | 16.0000i | −1.42398 | + | 0.711991i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 23.0000i | − | 1.02147i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 12.0000 | 0.531891 | 0.265945 | − | 0.963988i | \(-0.414316\pi\) | ||||
0.265945 | + | 0.963988i | \(0.414316\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 6.00000i | − | 0.264906i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −16.0000 | − | 32.0000i | −0.705044 | − | 1.41009i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 16.0000i | − | 0.703679i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.00000 | −0.0877903 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 44.0000 | 1.92767 | 0.963837 | − | 0.266491i | \(-0.0858642\pi\) | ||||
0.963837 | + | 0.266491i | \(0.0858642\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 20.0000i | 0.874539i | 0.899331 | + | 0.437269i | \(0.144054\pi\) | ||||
−0.899331 | + | 0.437269i | \(0.855946\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.00000i | 0.174243i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19.0000 | 0.826087 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.00000 | −0.173585 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 48.0000i | − | 2.07911i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.00000 | + | 12.0000i | 0.259403 | + | 0.518805i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 4.00000i | − | 0.172613i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10.0000 | 0.429934 | 0.214967 | − | 0.976621i | \(-0.431036\pi\) | ||||
0.214967 | + | 0.976621i | \(0.431036\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 10.0000i | 0.429141i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 28.0000 | − | 14.0000i | 1.19939 | − | 0.599694i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 20.0000i | − | 0.855138i | −0.903983 | − | 0.427569i | \(-0.859370\pi\) | ||
0.903983 | − | 0.427569i | \(-0.140630\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 14.0000 | 0.597505 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −36.0000 | −1.53365 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −8.00000 | + | 4.00000i | −0.339581 | + | 0.169791i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 6.00000i | − | 0.254228i | −0.991888 | − | 0.127114i | \(-0.959429\pi\) | ||
0.991888 | − | 0.127114i | \(-0.0405714\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 24.0000 | 1.01509 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.00000 | 0.337760 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 40.0000i | − | 1.68580i | −0.538071 | − | 0.842900i | \(-0.680847\pi\) | ||
0.538071 | − | 0.842900i | \(-0.319153\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 18.0000 | + | 36.0000i | 0.757266 | + | 1.51453i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 10.0000 | 0.419222 | 0.209611 | − | 0.977785i | \(-0.432780\pi\) | ||||
0.209611 | + | 0.977785i | \(0.432780\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.00000 | −0.334790 | −0.167395 | − | 0.985890i | \(-0.553535\pi\) | ||||
−0.167395 | + | 0.985890i | \(0.553535\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.00000 | + | 6.00000i | 0.333623 | + | 0.250217i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 38.0000i | 1.58196i | 0.611842 | + | 0.790980i | \(0.290429\pi\) | ||||
−0.611842 | + | 0.790980i | \(0.709571\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −8.00000 | −0.332469 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 24.0000i | − | 0.993978i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −6.00000 | − | 12.0000i | −0.248069 | − | 0.496139i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 12.0000 | 0.494451 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 10.0000 | 0.411345 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 18.0000i | − | 0.739171i | −0.929197 | − | 0.369586i | \(-0.879500\pi\) | ||
0.929197 | − | 0.369586i | \(-0.120500\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 18.0000i | 0.736691i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 34.0000 | 1.38689 | 0.693444 | − | 0.720510i | \(-0.256092\pi\) | ||||
0.693444 | + | 0.720510i | \(0.256092\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.00000i | 0.162893i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 10.0000 | − | 5.00000i | 0.406558 | − | 0.203279i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 40.0000i | 1.62355i | 0.583970 | + | 0.811775i | \(0.301498\pi\) | ||||
−0.583970 | + | 0.811775i | \(0.698502\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −24.0000 | −0.970936 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 44.0000i | 1.77714i | 0.458738 | + | 0.888572i | \(0.348302\pi\) | ||||
−0.458738 | + | 0.888572i | \(0.651698\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −8.00000 | − | 16.0000i | −0.322591 | − | 0.645182i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 34.0000i | 1.36879i | 0.729112 | + | 0.684394i | \(0.239933\pi\) | ||||
−0.729112 | + | 0.684394i | \(0.760067\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 26.0000 | 1.04503 | 0.522514 | − | 0.852631i | \(-0.324994\pi\) | ||||
0.522514 | + | 0.852631i | \(0.324994\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.00000 | 0.0802572 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.00000 | − | 24.0000i | −0.280000 | − | 0.960000i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 24.0000i | − | 0.958468i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −8.00000 | −0.318981 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.00000 | 0.318475 | 0.159237 | − | 0.987240i | \(-0.449096\pi\) | ||||
0.159237 | + | 0.987240i | \(0.449096\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 24.0000i | − | 0.953914i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 16.0000 | + | 32.0000i | 0.634941 | + | 1.26988i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.00000 | 0.0789953 | 0.0394976 | − | 0.999220i | \(-0.487424\pi\) | ||||
0.0394976 | + | 0.999220i | \(0.487424\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12.0000i | 0.473234i | 0.971603 | + | 0.236617i | \(0.0760386\pi\) | ||||
−0.971603 | + | 0.236617i | \(0.923961\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8.00000 | − | 4.00000i | 0.315000 | − | 0.157500i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 24.0000i | − | 0.943537i | −0.881722 | − | 0.471769i | \(-0.843616\pi\) | ||
0.881722 | − | 0.471769i | \(-0.156384\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −16.0000 | −0.628055 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 34.0000i | − | 1.33052i | −0.746611 | − | 0.665261i | \(-0.768320\pi\) | ||
0.746611 | − | 0.665261i | \(-0.231680\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 24.0000 | − | 12.0000i | 0.937758 | − | 0.468879i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 10.0000i | − | 0.390137i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.00000 | −0.155818 | −0.0779089 | − | 0.996960i | \(-0.524824\pi\) | ||||
−0.0779089 | + | 0.996960i | \(0.524824\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14.0000 | −0.544537 | −0.272268 | − | 0.962221i | \(-0.587774\pi\) | ||||
−0.272268 | + | 0.962221i | \(0.587774\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 12.0000i | − | 0.466041i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 12.0000i | − | 0.464642i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −16.0000 | −0.618596 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 56.0000 | 2.16186 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12.0000i | 0.462566i | 0.972887 | + | 0.231283i | \(0.0742923\pi\) | ||||
−0.972887 | + | 0.231283i | \(0.925708\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.00000 | − | 3.00000i | −0.153960 | − | 0.115470i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 38.0000i | 1.46046i | 0.683202 | + | 0.730229i | \(0.260587\pi\) | ||||
−0.683202 | + | 0.730229i | \(0.739413\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −20.0000 | −0.766402 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 26.0000i | 0.994862i | 0.867503 | + | 0.497431i | \(0.165723\pi\) | ||||
−0.867503 | + | 0.497431i | \(0.834277\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −18.0000 | − | 36.0000i | −0.687745 | − | 1.37549i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.00000i | 0.0763048i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −36.0000 | −1.37149 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.00000 | 0.0760836 | 0.0380418 | − | 0.999276i | \(-0.487888\pi\) | ||||
0.0380418 | + | 0.999276i | \(0.487888\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 20.0000 | − | 10.0000i | 0.758643 | − | 0.379322i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 16.0000i | − | 0.606043i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 26.0000 | 0.983410 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 38.0000 | 1.43524 | 0.717620 | − | 0.696435i | \(-0.245231\pi\) | ||||
0.717620 | + | 0.696435i | \(0.245231\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 24.0000i | 0.905177i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −8.00000 | + | 4.00000i | −0.301297 | + | 0.150649i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.00000 | 0.225335 | 0.112667 | − | 0.993633i | \(-0.464061\pi\) | ||||
0.112667 | + | 0.993633i | \(0.464061\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.00000i | 0.149801i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −24.0000 | − | 48.0000i | −0.897549 | − | 1.79510i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 16.0000i | 0.597531i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 44.0000 | 1.64092 | 0.820462 | − | 0.571702i | \(-0.193717\pi\) | ||||
0.820462 | + | 0.571702i | \(0.193717\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 10.0000i | − | 0.371904i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −18.0000 | + | 24.0000i | −0.668503 | + | 0.891338i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.00000 | 0.295891 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 34.0000i | − | 1.25582i | −0.778287 | − | 0.627909i | \(-0.783911\pi\) | ||
0.778287 | − | 0.627909i | \(-0.216089\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 16.0000i | 0.589368i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16.0000 | −0.588570 | −0.294285 | − | 0.955718i | \(-0.595081\pi\) | ||||
−0.294285 | + | 0.955718i | \(0.595081\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −36.0000 | −1.32249 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 54.0000i | − | 1.98107i | −0.137268 | − | 0.990534i | \(-0.543832\pi\) | ||
0.137268 | − | 0.990534i | \(-0.456168\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −44.0000 | + | 22.0000i | −1.61204 | + | 0.806018i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 16.0000i | − | 0.585409i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20.0000 | 0.729810 | 0.364905 | − | 0.931045i | \(-0.381101\pi\) | ||||
0.364905 | + | 0.931045i | \(0.381101\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 12.0000i | 0.437304i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 32.0000 | − | 16.0000i | 1.16460 | − | 0.582300i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 8.00000i | − | 0.290765i | −0.989376 | − | 0.145382i | \(-0.953559\pi\) | ||
0.989376 | − | 0.145382i | \(-0.0464413\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 8.00000 | 0.290382 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 24.0000 | 0.869999 | 0.435000 | − | 0.900431i | \(-0.356748\pi\) | ||||
0.435000 | + | 0.900431i | \(0.356748\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.00000 | − | 4.00000i | −0.0723102 | − | 0.144620i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 24.0000i | 0.866590i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 30.0000 | 1.08183 | 0.540914 | − | 0.841078i | \(-0.318079\pi\) | ||||
0.540914 | + | 0.841078i | \(0.318079\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.00000 | −0.216085 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6.00000i | 0.215805i | 0.994161 | + | 0.107903i | \(0.0344134\pi\) | ||||
−0.994161 | + | 0.107903i | \(0.965587\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.00000 | − | 8.00000i | 0.215526 | − | 0.287368i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −48.0000 | −1.71978 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 6.00000i | 0.214423i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 10.0000 | + | 20.0000i | 0.356915 | + | 0.713831i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 4.00000i | − | 0.142585i | −0.997455 | − | 0.0712923i | \(-0.977288\pi\) | ||
0.997455 | − | 0.0712923i | \(-0.0227123\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 10.0000 | 0.356009 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 84.0000i | − | 2.98293i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −12.0000 | + | 6.00000i | −0.425596 | + | 0.212798i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 34.0000i | − | 1.20434i | −0.798367 | − | 0.602171i | \(-0.794303\pi\) | ||
0.798367 | − | 0.602171i | \(-0.205697\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.00000 | −0.283020 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8.00000 | −0.282666 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 40.0000i | − | 1.41157i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 12.0000i | − | 0.422420i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 18.0000 | 0.632846 | 0.316423 | − | 0.948618i | \(-0.397518\pi\) | ||||
0.316423 | + | 0.948618i | \(0.397518\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −34.0000 | −1.19390 | −0.596951 | − | 0.802278i | \(-0.703621\pi\) | ||||
−0.596951 | + | 0.802278i | \(0.703621\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 14.0000i | 0.491001i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8.00000 | − | 16.0000i | −0.280228 | − | 0.560456i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 24.0000i | − | 0.839654i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 10.0000 | 0.349002 | 0.174501 | − | 0.984657i | \(-0.444169\pi\) | ||||
0.174501 | + | 0.984657i | \(0.444169\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24.0000i | 0.836587i | 0.908312 | + | 0.418294i | \(0.137372\pi\) | ||||
−0.908312 | + | 0.418294i | \(0.862628\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −16.0000 | − | 12.0000i | −0.557048 | − | 0.417786i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 22.0000i | 0.765015i | 0.923952 | + | 0.382507i | \(0.124939\pi\) | ||||
−0.923952 | + | 0.382507i | \(0.875061\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.00000 | 0.208389 | 0.104194 | − | 0.994557i | \(-0.466774\pi\) | ||||
0.104194 | + | 0.994557i | \(0.466774\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −28.0000 | −0.971309 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 24.0000 | + | 48.0000i | 0.830554 | + | 1.66111i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 2.00000i | − | 0.0691301i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −32.0000 | −1.10476 | −0.552381 | − | 0.833592i | \(-0.686281\pi\) | ||||
−0.552381 | + | 0.833592i | \(0.686281\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.00000 | 0.241379 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 6.00000i | − | 0.206651i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −46.0000 | + | 23.0000i | −1.58245 | + | 0.791224i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 28.0000 | 0.960958 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8.00000 | −0.274236 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.00000i | 0.0684787i | 0.999414 | + | 0.0342393i | \(0.0109009\pi\) | ||||
−0.999414 | + | 0.0342393i | \(0.989099\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −12.0000 | + | 6.00000i | −0.410391 | + | 0.205196i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 6.00000i | 0.204956i | 0.994735 | + | 0.102478i | \(0.0326771\pi\) | ||||
−0.994735 | + | 0.102478i | \(0.967323\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −46.0000 | −1.56950 | −0.784750 | − | 0.619813i | \(-0.787209\pi\) | ||||
−0.784750 | + | 0.619813i | \(0.787209\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 18.0000i | 0.612727i | 0.951915 | + | 0.306364i | \(0.0991123\pi\) | ||||
−0.951915 | + | 0.306364i | \(0.900888\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.00000 | + | 4.00000i | 0.0680020 | + | 0.136004i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 13.0000i | 0.441503i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 24.0000 | 0.813209 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 10.0000i | − | 0.338449i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 44.0000i | 1.48577i | 0.669417 | + | 0.742887i | \(0.266544\pi\) | ||||
−0.669417 | + | 0.742887i | \(0.733456\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −6.00000 | −0.202375 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −36.0000 | −1.21287 | −0.606435 | − | 0.795133i | \(-0.707401\pi\) | ||||
−0.606435 | + | 0.795133i | \(0.707401\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 24.0000i | − | 0.807664i | −0.914833 | − | 0.403832i | \(-0.867678\pi\) | ||
0.914833 | − | 0.403832i | \(-0.132322\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4.00000 | + | 8.00000i | 0.134459 | + | 0.268917i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 12.0000i | 0.402921i | 0.979497 | + | 0.201460i | \(0.0645687\pi\) | ||||
−0.979497 | + | 0.201460i | \(0.935431\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.00000 | −0.134005 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 24.0000i | 0.803129i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8.00000 | + | 4.00000i | −0.267411 | + | 0.133705i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 12.0000i | − | 0.400668i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −12.0000 | −0.400222 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −12.0000 | −0.399778 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 20.0000 | − | 10.0000i | 0.664822 | − | 0.332411i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 24.0000i | − | 0.796907i | −0.917189 | − | 0.398453i | \(-0.869547\pi\) | ||
0.917189 | − | 0.398453i | \(-0.130453\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 16.0000 | 0.530687 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −24.0000 | −0.795155 | −0.397578 | − | 0.917568i | \(-0.630149\pi\) | ||||
−0.397578 | + | 0.917568i | \(0.630149\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 64.0000i | − | 2.11809i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −14.0000 | − | 28.0000i | −0.462826 | − | 0.925651i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −36.0000 | −1.18753 | −0.593765 | − | 0.804638i | \(-0.702359\pi\) | ||||
−0.593765 | + | 0.804638i | \(0.702359\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 12.0000 | 0.395413 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 16.0000 | + | 12.0000i | 0.526077 | + | 0.394558i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 16.0000i | 0.525509i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 24.0000 | 0.787414 | 0.393707 | − | 0.919236i | \(-0.371192\pi\) | ||||
0.393707 | + | 0.919236i | \(0.371192\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 12.0000i | − | 0.392862i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −8.00000 | − | 16.0000i | −0.261628 | − | 0.523256i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 14.0000i | − | 0.457360i | −0.973502 | − | 0.228680i | \(-0.926559\pi\) | ||
0.973502 | − | 0.228680i | \(-0.0734410\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 14.0000 | 0.456873 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −44.0000 | −1.43436 | −0.717180 | − | 0.696888i | \(-0.754567\pi\) | ||||
−0.717180 | + | 0.696888i | \(0.754567\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 16.0000i | − | 0.521032i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 6.00000i | − | 0.194974i | −0.995237 | − | 0.0974869i | \(-0.968920\pi\) | ||
0.995237 | − | 0.0974869i | \(-0.0310804\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −60.0000 | −1.94768 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 14.0000 | 0.453981 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 14.0000i | − | 0.453504i | −0.973952 | − | 0.226752i | \(-0.927189\pi\) | ||
0.973952 | − | 0.226752i | \(-0.0728108\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 24.0000i | 0.775810i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.0000 | −0.870968 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 6.00000i | − | 0.193347i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 8.00000 | + | 16.0000i | 0.257529 | + | 0.515058i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 20.0000i | 0.643157i | 0.946883 | + | 0.321578i | \(0.104213\pi\) | ||||
−0.946883 | + | 0.321578i | \(0.895787\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −12.0000 | −0.385496 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 24.0000 | 0.770197 | 0.385098 | − | 0.922876i | \(-0.374168\pi\) | ||||
0.385098 | + | 0.922876i | \(0.374168\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −18.0000 | + | 24.0000i | −0.576461 | + | 0.768615i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 18.0000i | 0.575871i | 0.957650 | + | 0.287936i | \(0.0929689\pi\) | ||||
−0.957650 | + | 0.287936i | \(0.907031\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −32.0000 | −1.02272 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −14.0000 | −0.446986 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 8.00000i | 0.255160i | 0.991828 | + | 0.127580i | \(0.0407210\pi\) | ||||
−0.991828 | + | 0.127580i | \(0.959279\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −10.0000 | − | 20.0000i | −0.318626 | − | 0.637253i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8.00000 | 0.254385 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 52.0000 | 1.65183 | 0.825917 | − | 0.563791i | \(-0.190658\pi\) | ||||
0.825917 | + | 0.563791i | \(0.190658\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 8.00000i | − | 0.253872i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 36.0000 | − | 18.0000i | 1.14128 | − | 0.570638i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 18.0000i | − | 0.570066i | −0.958518 | − | 0.285033i | \(-0.907995\pi\) | ||
0.958518 | − | 0.285033i | \(-0.0920045\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.00000 | 0.126554 |
(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 | 2940.2.k.d.589.2 | 2 | ||
5.4 | even | 2 | inner | 2940.2.k.d.589.1 | 2 | ||
7.2 | even | 3 | 2940.2.bb.c.949.1 | 4 | |||
7.3 | odd | 6 | 2940.2.bb.h.1549.1 | 4 | |||
7.4 | even | 3 | 2940.2.bb.c.1549.2 | 4 | |||
7.5 | odd | 6 | 2940.2.bb.h.949.2 | 4 | |||
7.6 | odd | 2 | 420.2.k.a.169.1 | ✓ | 2 | ||
21.20 | even | 2 | 1260.2.k.d.1009.1 | 2 | |||
28.27 | even | 2 | 1680.2.t.a.1009.2 | 2 | |||
35.4 | even | 6 | 2940.2.bb.c.1549.1 | 4 | |||
35.9 | even | 6 | 2940.2.bb.c.949.2 | 4 | |||
35.13 | even | 4 | 2100.2.a.j.1.1 | 1 | |||
35.19 | odd | 6 | 2940.2.bb.h.949.1 | 4 | |||
35.24 | odd | 6 | 2940.2.bb.h.1549.2 | 4 | |||
35.27 | even | 4 | 2100.2.a.e.1.1 | 1 | |||
35.34 | odd | 2 | 420.2.k.a.169.2 | yes | 2 | ||
84.83 | odd | 2 | 5040.2.t.o.1009.1 | 2 | |||
105.62 | odd | 4 | 6300.2.a.bc.1.1 | 1 | |||
105.83 | odd | 4 | 6300.2.a.n.1.1 | 1 | |||
105.104 | even | 2 | 1260.2.k.d.1009.2 | 2 | |||
140.27 | odd | 4 | 8400.2.a.cd.1.1 | 1 | |||
140.83 | odd | 4 | 8400.2.a.bh.1.1 | 1 | |||
140.139 | even | 2 | 1680.2.t.a.1009.1 | 2 | |||
420.419 | odd | 2 | 5040.2.t.o.1009.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
420.2.k.a.169.1 | ✓ | 2 | 7.6 | odd | 2 | ||
420.2.k.a.169.2 | yes | 2 | 35.34 | odd | 2 | ||
1260.2.k.d.1009.1 | 2 | 21.20 | even | 2 | |||
1260.2.k.d.1009.2 | 2 | 105.104 | even | 2 | |||
1680.2.t.a.1009.1 | 2 | 140.139 | even | 2 | |||
1680.2.t.a.1009.2 | 2 | 28.27 | even | 2 | |||
2100.2.a.e.1.1 | 1 | 35.27 | even | 4 | |||
2100.2.a.j.1.1 | 1 | 35.13 | even | 4 | |||
2940.2.k.d.589.1 | 2 | 5.4 | even | 2 | inner | ||
2940.2.k.d.589.2 | 2 | 1.1 | even | 1 | trivial | ||
2940.2.bb.c.949.1 | 4 | 7.2 | even | 3 | |||
2940.2.bb.c.949.2 | 4 | 35.9 | even | 6 | |||
2940.2.bb.c.1549.1 | 4 | 35.4 | even | 6 | |||
2940.2.bb.c.1549.2 | 4 | 7.4 | even | 3 | |||
2940.2.bb.h.949.1 | 4 | 35.19 | odd | 6 | |||
2940.2.bb.h.949.2 | 4 | 7.5 | odd | 6 | |||
2940.2.bb.h.1549.1 | 4 | 7.3 | odd | 6 | |||
2940.2.bb.h.1549.2 | 4 | 35.24 | odd | 6 | |||
5040.2.t.o.1009.1 | 2 | 84.83 | odd | 2 | |||
5040.2.t.o.1009.2 | 2 | 420.419 | odd | 2 | |||
6300.2.a.n.1.1 | 1 | 105.83 | odd | 4 | |||
6300.2.a.bc.1.1 | 1 | 105.62 | odd | 4 | |||
8400.2.a.bh.1.1 | 1 | 140.83 | odd | 4 | |||
8400.2.a.cd.1.1 | 1 | 140.27 | odd | 4 |