Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8820,2,Mod(881,8820)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8820, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8820.881");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8820 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8820.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(70.4280545828\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2 x^{11} - 9 x^{10} + 58 x^{9} - 78 x^{8} - 298 x^{7} + 1341 x^{6} - 2086 x^{5} - 3822 x^{4} + 19894 x^{3} - 21609 x^{2} - 33614 x + 117649 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 1260) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 881.5 | ||
Root | \(1.75207 + 1.98249i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8820.881 |
Dual form | 8820.2.d.a.881.8 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/8820\mathbb{Z}\right)^\times\).
\(n\) | \(1081\) | \(4411\) | \(7057\) | \(7841\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 2.23292i | − 0.673252i | −0.941638 | − | 0.336626i | \(-0.890714\pi\) | ||||
0.941638 | − | 0.336626i | \(-0.109286\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 4.92905i | − 1.36707i | −0.729917 | − | 0.683536i | \(-0.760441\pi\) | ||||
0.729917 | − | 0.683536i | \(-0.239559\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.83953 | −0.931224 | −0.465612 | − | 0.884989i | \(-0.654166\pi\) | ||||
−0.465612 | + | 0.884989i | \(0.654166\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.96386i | 1.36820i | 0.729386 | + | 0.684102i | \(0.239806\pi\) | ||||
−0.729386 | + | 0.684102i | \(0.760194\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 4.24918i | − 0.886015i | −0.896518 | − | 0.443008i | \(-0.853911\pi\) | ||||
0.896518 | − | 0.443008i | \(-0.146089\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.73838i | 1.25129i | 0.780110 | + | 0.625643i | \(0.215163\pi\) | ||||
−0.780110 | + | 0.625643i | \(0.784837\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 1.80933i | − 0.324966i | −0.986711 | − | 0.162483i | \(-0.948050\pi\) | ||||
0.986711 | − | 0.162483i | \(-0.0519502\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.32755 | −0.711444 | −0.355722 | − | 0.934592i | \(-0.615765\pi\) | ||||
−0.355722 | + | 0.934592i | \(0.615765\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.50414 | −0.391080 | −0.195540 | − | 0.980696i | \(-0.562646\pi\) | ||||
−0.195540 | + | 0.980696i | \(0.562646\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.96414 | 0.757025 | 0.378512 | − | 0.925596i | \(-0.376436\pi\) | ||||
0.378512 | + | 0.925596i | \(0.376436\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −10.8837 | −1.58755 | −0.793773 | − | 0.608214i | \(-0.791886\pi\) | ||||
−0.793773 | + | 0.608214i | \(0.791886\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.50545i | 0.618872i | 0.950920 | + | 0.309436i | \(0.100140\pi\) | ||||
−0.950920 | + | 0.309436i | \(0.899860\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.23292i | 0.301088i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.99215 | 0.519733 | 0.259867 | − | 0.965645i | \(-0.416321\pi\) | ||||
0.259867 | + | 0.965645i | \(0.416321\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.25890i | 0.801369i | 0.916216 | + | 0.400685i | \(0.131228\pi\) | ||||
−0.916216 | + | 0.400685i | \(0.868772\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.92905i | 0.611373i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.1832 | −1.36625 | −0.683123 | − | 0.730303i | \(-0.739379\pi\) | ||||
−0.683123 | + | 0.730303i | \(0.739379\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 8.87665i | − 1.05347i | −0.850031 | − | 0.526733i | \(-0.823417\pi\) | ||||
0.850031 | − | 0.526733i | \(-0.176583\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 5.01716i | − 0.587214i | −0.955926 | − | 0.293607i | \(-0.905144\pi\) | ||||
0.955926 | − | 0.293607i | \(-0.0948557\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.2041 | 1.26056 | 0.630281 | − | 0.776367i | \(-0.282939\pi\) | ||||
0.630281 | + | 0.776367i | \(0.282939\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.295092 | −0.0323906 | −0.0161953 | − | 0.999869i | \(-0.505155\pi\) | ||||
−0.0161953 | + | 0.999869i | \(0.505155\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.83953 | 0.416456 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −14.1360 | −1.49842 | −0.749208 | − | 0.662335i | \(-0.769565\pi\) | ||||
−0.749208 | + | 0.662335i | \(0.769565\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − 5.96386i | − 0.611879i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.05218i | 0.106833i | 0.998572 | + | 0.0534165i | \(0.0170111\pi\) | ||||
−0.998572 | + | 0.0534165i | \(0.982989\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 17.4071 | 1.73207 | 0.866034 | − | 0.499985i | \(-0.166661\pi\) | ||||
0.866034 | + | 0.499985i | \(0.166661\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.5384i | 1.23544i | 0.786397 | + | 0.617721i | \(0.211944\pi\) | ||||
−0.786397 | + | 0.617721i | \(0.788056\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.92932i | 0.476535i | 0.971200 | + | 0.238268i | \(0.0765795\pi\) | ||||
−0.971200 | + | 0.238268i | \(0.923420\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.0223 | 1.24731 | 0.623656 | − | 0.781699i | \(-0.285647\pi\) | ||||
0.623656 | + | 0.781699i | \(0.285647\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 7.82363i | − 0.735985i | −0.929829 | − | 0.367993i | \(-0.880045\pi\) | ||||
0.929829 | − | 0.367993i | \(-0.119955\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.24918i | 0.396238i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.01405 | 0.546731 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.53736 | −0.580097 | −0.290048 | − | 0.957012i | \(-0.593671\pi\) | ||||
−0.290048 | + | 0.957012i | \(0.593671\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.315665 | 0.0275798 | 0.0137899 | − | 0.999905i | \(-0.495610\pi\) | ||||
0.0137899 | + | 0.999905i | \(0.495610\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 22.2097i | 1.89750i | 0.316026 | + | 0.948751i | \(0.397651\pi\) | ||||
−0.316026 | + | 0.948751i | \(0.602349\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.8183i | 1.25687i | 0.777862 | + | 0.628435i | \(0.216304\pi\) | ||||
−0.777862 | + | 0.628435i | \(0.783696\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −11.0062 | −0.920384 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − 6.73838i | − 0.559592i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.10602i | 0.336379i | 0.985755 | + | 0.168189i | \(0.0537920\pi\) | ||||
−0.985755 | + | 0.168189i | \(0.946208\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.5675 | 0.941352 | 0.470676 | − | 0.882306i | \(-0.344010\pi\) | ||||
0.470676 | + | 0.882306i | \(0.344010\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.80933i | 0.145329i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 1.92814i | − 0.153883i | −0.997036 | − | 0.0769413i | \(-0.975485\pi\) | ||||
0.997036 | − | 0.0769413i | \(-0.0245154\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 16.3345 | 1.27942 | 0.639709 | − | 0.768617i | \(-0.279055\pi\) | ||||
0.639709 | + | 0.768617i | \(0.279055\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −16.2112 | −1.25446 | −0.627231 | − | 0.778834i | \(-0.715812\pi\) | ||||
−0.627231 | + | 0.778834i | \(0.715812\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.2955 | −0.868885 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 21.5331 | 1.63713 | 0.818564 | − | 0.574415i | \(-0.194770\pi\) | ||||
0.818564 | + | 0.574415i | \(0.194770\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 21.7519i | − 1.62581i | −0.582393 | − | 0.812907i | \(-0.697884\pi\) | ||||
0.582393 | − | 0.812907i | \(-0.302116\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.4316i | 0.775378i | 0.921790 | + | 0.387689i | \(0.126726\pi\) | ||||
−0.921790 | + | 0.387689i | \(0.873274\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.32755 | 0.318167 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.57339i | 0.626949i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 23.6063i | 1.70809i | 0.520201 | + | 0.854044i | \(0.325857\pi\) | ||||
−0.520201 | + | 0.854044i | \(0.674143\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 16.3226 | 1.17493 | 0.587464 | − | 0.809250i | \(-0.300126\pi\) | ||||
0.587464 | + | 0.809250i | \(0.300126\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 7.03368i | − 0.501129i | −0.968100 | − | 0.250565i | \(-0.919384\pi\) | ||||
0.968100 | − | 0.250565i | \(-0.0806162\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.43512i | 0.456173i | 0.973641 | + | 0.228087i | \(0.0732470\pi\) | ||||
−0.973641 | + | 0.228087i | \(0.926753\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.50414 | 0.174896 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 13.3169 | 0.921146 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.59463 | −0.109779 | −0.0548895 | − | 0.998492i | \(-0.517481\pi\) | ||||
−0.0548895 | + | 0.998492i | \(0.517481\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.96414 | −0.338552 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 18.9252i | 1.27305i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 20.8137i | − 1.39379i | −0.717174 | − | 0.696894i | \(-0.754565\pi\) | ||||
0.717174 | − | 0.696894i | \(-0.245435\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −9.89554 | −0.656790 | −0.328395 | − | 0.944540i | \(-0.606508\pi\) | ||||
−0.328395 | + | 0.944540i | \(0.606508\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 20.2219i | − 1.33630i | −0.744025 | − | 0.668152i | \(-0.767086\pi\) | ||||
0.744025 | − | 0.668152i | \(-0.232914\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 8.65346i | 0.566907i | 0.958986 | + | 0.283454i | \(0.0914802\pi\) | ||||
−0.958986 | + | 0.283454i | \(0.908520\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 10.8837 | 0.709972 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 17.9691i | 1.16233i | 0.813787 | + | 0.581163i | \(0.197402\pi\) | ||||
−0.813787 | + | 0.581163i | \(0.802598\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 26.0955i | 1.68096i | 0.541846 | + | 0.840478i | \(0.317726\pi\) | ||||
−0.541846 | + | 0.840478i | \(0.682274\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 29.3962 | 1.87043 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.97721 | 0.251039 | 0.125520 | − | 0.992091i | \(-0.459940\pi\) | ||||
0.125520 | + | 0.992091i | \(0.459940\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.48810 | −0.596512 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6.31927 | −0.394185 | −0.197093 | − | 0.980385i | \(-0.563150\pi\) | ||||
−0.197093 | + | 0.980385i | \(0.563150\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 18.4861i | 1.13990i | 0.821678 | + | 0.569952i | \(0.193038\pi\) | ||||
−0.821678 | + | 0.569952i | \(0.806962\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − 4.50545i | − 0.276768i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −14.5950 | −0.889872 | −0.444936 | − | 0.895562i | \(-0.646774\pi\) | ||||
−0.444936 | + | 0.895562i | \(0.646774\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.6470i | 1.25422i | 0.778931 | + | 0.627109i | \(0.215762\pi\) | ||||
−0.778931 | + | 0.627109i | \(0.784238\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 2.23292i | − 0.134650i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 24.3484 | 1.46295 | 0.731477 | − | 0.681866i | \(-0.238831\pi\) | ||||
0.731477 | + | 0.681866i | \(0.238831\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 30.6625i | − 1.82917i | −0.404393 | − | 0.914585i | \(-0.632517\pi\) | ||||
0.404393 | − | 0.914585i | \(-0.367483\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.44821i | 0.264419i | 0.991222 | + | 0.132209i | \(0.0422071\pi\) | ||||
−0.991222 | + | 0.132209i | \(0.957793\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.25797 | −0.132822 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −32.7139 | −1.91117 | −0.955583 | − | 0.294721i | \(-0.904773\pi\) | ||||
−0.955583 | + | 0.294721i | \(0.904773\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.99215 | −0.232432 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −20.9444 | −1.21125 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − 6.25890i | − 0.358383i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.37826i | 0.135735i | 0.997694 | + | 0.0678673i | \(0.0216195\pi\) | ||||
−0.997694 | + | 0.0678673i | \(0.978381\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.47133 | −0.423660 | −0.211830 | − | 0.977306i | \(-0.567942\pi\) | ||||
−0.211830 | + | 0.977306i | \(0.567942\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 19.3497i | 1.09371i | 0.837228 | + | 0.546854i | \(0.184175\pi\) | ||||
−0.837228 | + | 0.546854i | \(0.815825\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.38007i | 0.358341i | 0.983818 | + | 0.179170i | \(0.0573413\pi\) | ||||
−0.983818 | + | 0.179170i | \(0.942659\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 15.0463 | 0.842431 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 22.8985i | − 1.27410i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 4.92905i | − 0.273414i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.654466 | 0.0359727 | 0.0179863 | − | 0.999838i | \(-0.494274\pi\) | ||||
0.0179863 | + | 0.999838i | \(0.494274\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 11.1832 | 0.611004 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −20.4752 | −1.11536 | −0.557679 | − | 0.830057i | \(-0.688308\pi\) | ||||
−0.557679 | + | 0.830057i | \(0.688308\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.04010 | −0.218784 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 15.6077i | 0.837863i | 0.908018 | + | 0.418931i | \(0.137595\pi\) | ||||
−0.908018 | + | 0.418931i | \(0.862405\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 22.4320i | 1.20076i | 0.799715 | + | 0.600380i | \(0.204984\pi\) | ||||
−0.799715 | + | 0.600380i | \(0.795016\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −32.5208 | −1.73091 | −0.865453 | − | 0.500990i | \(-0.832969\pi\) | ||||
−0.865453 | + | 0.500990i | \(0.832969\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.87665i | 0.471124i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 15.6380i | 0.825344i | 0.910880 | + | 0.412672i | \(0.135405\pi\) | ||||
−0.910880 | + | 0.412672i | \(0.864595\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.5676 | −0.871981 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.01716i | 0.262610i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 3.05166i | − 0.159295i | −0.996823 | − | 0.0796476i | \(-0.974620\pi\) | ||||
0.996823 | − | 0.0796476i | \(-0.0253795\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.9475 | 0.618619 | 0.309310 | − | 0.950961i | \(-0.399902\pi\) | ||||
0.309310 | + | 0.950961i | \(0.399902\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 33.2138 | 1.71060 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −34.8181 | −1.78848 | −0.894242 | − | 0.447584i | \(-0.852285\pi\) | ||||
−0.894242 | + | 0.447584i | \(0.852285\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.45814 | 0.0745076 | 0.0372538 | − | 0.999306i | \(-0.488139\pi\) | ||||
0.0372538 | + | 0.999306i | \(0.488139\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 20.1509i | 1.02169i | 0.859673 | + | 0.510845i | \(0.170667\pi\) | ||||
−0.859673 | + | 0.510845i | \(0.829333\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.3149i | 0.825079i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −11.2041 | −0.563741 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 19.3115i | 0.969215i | 0.874732 | + | 0.484607i | \(0.161038\pi\) | ||||
−0.874732 | + | 0.484607i | \(0.838962\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − 28.3691i | − 1.41669i | −0.705868 | − | 0.708343i | \(-0.749443\pi\) | ||||
0.705868 | − | 0.708343i | \(-0.250557\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.91828 | −0.444251 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9.66308i | 0.478981i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 15.8762i | 0.785026i | 0.919747 | + | 0.392513i | \(0.128394\pi\) | ||||
−0.919747 | + | 0.392513i | \(0.871606\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.295092 | 0.0144855 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.98073 | −0.0967652 | −0.0483826 | − | 0.998829i | \(-0.515407\pi\) | ||||
−0.0483826 | + | 0.998829i | \(0.515407\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −31.1448 | −1.51790 | −0.758952 | − | 0.651147i | \(-0.774288\pi\) | ||||
−0.758952 | + | 0.651147i | \(0.774288\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.83953 | −0.186245 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 25.5894i | 1.23260i | 0.787512 | + | 0.616300i | \(0.211369\pi\) | ||||
−0.787512 | + | 0.616300i | \(0.788631\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.90795i | 0.331975i | 0.986128 | + | 0.165987i | \(0.0530811\pi\) | ||||
−0.986128 | + | 0.165987i | \(0.946919\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 25.3415 | 1.21225 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 18.5663i | 0.886120i | 0.896492 | + | 0.443060i | \(0.146107\pi\) | ||||
−0.896492 | + | 0.443060i | \(0.853893\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12.0525i | 0.572633i | 0.958135 | + | 0.286317i | \(0.0924309\pi\) | ||||
−0.958135 | + | 0.286317i | \(0.907569\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 14.1360 | 0.670112 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 18.2147i | − 0.859604i | −0.902923 | − | 0.429802i | \(-0.858583\pi\) | ||||
0.902923 | − | 0.429802i | \(-0.141417\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.59155i | 0.263296i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −0.886209 | −0.0414551 | −0.0207276 | − | 0.999785i | \(-0.506598\pi\) | ||||
−0.0207276 | + | 0.999785i | \(0.506598\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.24276 | −0.0578811 | −0.0289405 | − | 0.999581i | \(-0.509213\pi\) | ||||
−0.0289405 | + | 0.999581i | \(0.509213\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 35.8986 | 1.66835 | 0.834176 | − | 0.551499i | \(-0.185944\pi\) | ||||
0.834176 | + | 0.551499i | \(0.185944\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 17.5952 | 0.814208 | 0.407104 | − | 0.913382i | \(-0.366539\pi\) | ||||
0.407104 | + | 0.913382i | \(0.366539\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 11.0846i | − 0.509668i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.96386i | 0.273641i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 23.5746 | 1.07715 | 0.538575 | − | 0.842578i | \(-0.318963\pi\) | ||||
0.538575 | + | 0.842578i | \(0.318963\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 21.3307i | 0.972595i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 1.05218i | − 0.0477772i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.54793 | 0.160772 | 0.0803861 | − | 0.996764i | \(-0.474385\pi\) | ||||
0.0803861 | + | 0.996764i | \(0.474385\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 41.3330i | 1.86533i | 0.360739 | + | 0.932667i | \(0.382525\pi\) | ||||
−0.360739 | + | 0.932667i | \(0.617475\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 25.8722i | − 1.16523i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 23.7292 | 1.06226 | 0.531132 | − | 0.847289i | \(-0.321767\pi\) | ||||
0.531132 | + | 0.847289i | \(0.321767\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −24.4784 | −1.09144 | −0.545719 | − | 0.837968i | \(-0.683743\pi\) | ||||
−0.545719 | + | 0.837968i | \(0.683743\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −17.4071 | −0.774604 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −43.6140 | −1.93316 | −0.966579 | − | 0.256369i | \(-0.917474\pi\) | ||||
−0.966579 | + | 0.256369i | \(0.917474\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 12.5384i | − 0.552507i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 24.3024i | 1.06882i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10.1104 | 0.442947 | 0.221473 | − | 0.975166i | \(-0.428913\pi\) | ||||
0.221473 | + | 0.975166i | \(0.428913\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 19.1213i | 0.836118i | 0.908420 | + | 0.418059i | \(0.137289\pi\) | ||||
−0.908420 | + | 0.418059i | \(0.862711\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.94699i | 0.302616i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.94447 | 0.214977 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 12.3430i | 0.534635i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 4.92932i | − 0.213113i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 16.3125 | 0.701331 | 0.350665 | − | 0.936501i | \(-0.385955\pi\) | ||||
0.350665 | + | 0.936501i | \(0.385955\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −13.0223 | −0.557815 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 21.0498 | 0.900023 | 0.450012 | − | 0.893023i | \(-0.351420\pi\) | ||||
0.450012 | + | 0.893023i | \(0.351420\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −40.1868 | −1.71201 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 21.7778i | − 0.922754i | −0.887204 | − | 0.461377i | \(-0.847356\pi\) | ||||
0.887204 | − | 0.461377i | \(-0.152644\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 24.4685i | − 1.03491i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −18.8316 | −0.793656 | −0.396828 | − | 0.917893i | \(-0.629889\pi\) | ||||
−0.396828 | + | 0.917893i | \(0.629889\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.82363i | 0.329143i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 31.9438i | 1.33915i | 0.742742 | + | 0.669577i | \(0.233525\pi\) | ||||
−0.742742 | + | 0.669577i | \(0.766475\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19.7088 | −0.824789 | −0.412394 | − | 0.911005i | \(-0.635307\pi\) | ||||
−0.412394 | + | 0.911005i | \(0.635307\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 4.24918i | − 0.177203i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 15.7729i | 0.656633i | 0.944568 | + | 0.328317i | \(0.106481\pi\) | ||||
−0.944568 | + | 0.328317i | \(0.893519\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10.0603 | 0.416657 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −5.89811 | −0.243441 | −0.121721 | − | 0.992564i | \(-0.538841\pi\) | ||||
−0.121721 | + | 0.992564i | \(0.538841\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10.7906 | 0.444619 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −2.36373 | −0.0970669 | −0.0485335 | − | 0.998822i | \(-0.515455\pi\) | ||||
−0.0485335 | + | 0.998822i | \(0.515455\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 16.9286i | 0.691684i | 0.938293 | + | 0.345842i | \(0.112407\pi\) | ||||
−0.938293 | + | 0.345842i | \(0.887593\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − 20.7753i | − 0.847443i | −0.905793 | − | 0.423721i | \(-0.860724\pi\) | ||||
0.905793 | − | 0.423721i | \(-0.139276\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −6.01405 | −0.244506 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.75183i | 0.111693i | 0.998439 | + | 0.0558466i | \(0.0177858\pi\) | ||||
−0.998439 | + | 0.0558466i | \(0.982214\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 53.6461i | 2.17029i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 15.5628 | 0.628575 | 0.314287 | − | 0.949328i | \(-0.398234\pi\) | ||||
0.314287 | + | 0.949328i | \(0.398234\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.50012i | 0.0603925i | 0.999544 | + | 0.0301963i | \(0.00961323\pi\) | ||||
−0.999544 | + | 0.0301963i | \(0.990387\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 10.4623i | − 0.420513i | −0.977646 | − | 0.210257i | \(-0.932570\pi\) | ||||
0.977646 | − | 0.210257i | \(-0.0674300\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 16.6158 | 0.662514 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 42.9480 | 1.70973 | 0.854866 | − | 0.518849i | \(-0.173639\pi\) | ||||
0.854866 | + | 0.518849i | \(0.173639\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.53736 | 0.259427 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 43.1330i | 1.70365i | 0.523826 | + | 0.851825i | \(0.324504\pi\) | ||||
−0.523826 | + | 0.851825i | \(0.675496\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11.6402i | 0.459045i | 0.973303 | + | 0.229523i | \(0.0737165\pi\) | ||||
−0.973303 | + | 0.229523i | \(0.926284\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 37.0432 | 1.45632 | 0.728159 | − | 0.685408i | \(-0.240376\pi\) | ||||
0.728159 | + | 0.685408i | \(0.240376\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − 8.91416i | − 0.349912i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 31.7308i | − 1.24172i | −0.783921 | − | 0.620861i | \(-0.786783\pi\) | ||||
0.783921 | − | 0.620861i | \(-0.213217\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.315665 | −0.0123341 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 1.01969i | − 0.0397216i | −0.999803 | − | 0.0198608i | \(-0.993678\pi\) | ||||
0.999803 | − | 0.0198608i | \(-0.00632231\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 40.9457i | − 1.59260i | −0.604899 | − | 0.796302i | \(-0.706787\pi\) | ||||
0.604899 | − | 0.796302i | \(-0.293213\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 28.6326 | 1.10866 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 13.9756 | 0.539524 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16.2023 | −0.624552 | −0.312276 | − | 0.949992i | \(-0.601091\pi\) | ||||
−0.312276 | + | 0.949992i | \(0.601091\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −8.48419 | −0.326074 | −0.163037 | − | 0.986620i | \(-0.552129\pi\) | ||||
−0.163037 | + | 0.986620i | \(0.552129\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 32.8128i | − 1.25555i | −0.778396 | − | 0.627773i | \(-0.783967\pi\) | ||||
0.778396 | − | 0.627773i | \(-0.216033\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 22.2097i | − 0.848588i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 22.2076 | 0.846042 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 34.5459i | − 1.31419i | −0.753809 | − | 0.657094i | \(-0.771786\pi\) | ||||
0.753809 | − | 0.657094i | \(-0.228214\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 14.8183i | − 0.562089i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.61472 | 0.364183 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 14.0470i | 0.530547i | 0.964173 | + | 0.265274i | \(0.0854623\pi\) | ||||
−0.964173 | + | 0.265274i | \(0.914538\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 25.8089i | − 0.973401i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −42.3730 | −1.59135 | −0.795676 | − | 0.605722i | \(-0.792884\pi\) | ||||
−0.795676 | + | 0.605722i | \(0.792884\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −7.68818 | −0.287924 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 11.0062 | 0.411608 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 28.3385 | 1.05685 | 0.528424 | − | 0.848981i | \(-0.322783\pi\) | ||||
0.528424 | + | 0.848981i | \(0.322783\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 6.73838i | 0.250257i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.2471i | 0.528395i | 0.964469 | + | 0.264197i | \(0.0851070\pi\) | ||||
−0.964469 | + | 0.264197i | \(0.914893\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −19.0600 | −0.704959 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 28.7599i | 1.06227i | 0.847287 | + | 0.531136i | \(0.178234\pi\) | ||||
−0.847287 | + | 0.531136i | \(0.821766\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 24.9713i | 0.919828i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 21.3948 | 0.787022 | 0.393511 | − | 0.919320i | \(-0.371260\pi\) | ||||
0.393511 | + | 0.919320i | \(0.371260\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 11.2869i | − 0.414077i | −0.978333 | − | 0.207039i | \(-0.933617\pi\) | ||||
0.978333 | − | 0.207039i | \(-0.0663826\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − 4.10602i | − 0.150433i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.85438 | −0.0676672 | −0.0338336 | − | 0.999427i | \(-0.510772\pi\) | ||||
−0.0338336 | + | 0.999427i | \(0.510772\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −11.5675 | −0.420986 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 25.3114 | 0.919958 | 0.459979 | − | 0.887930i | \(-0.347857\pi\) | ||||
0.459979 | + | 0.887930i | \(0.347857\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6.45702 | 0.234067 | 0.117033 | − | 0.993128i | \(-0.462662\pi\) | ||||
0.117033 | + | 0.993128i | \(0.462662\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 19.6775i | − 0.710513i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − 28.0248i | − 1.01060i | −0.862943 | − | 0.505301i | \(-0.831382\pi\) | ||||
0.862943 | − | 0.505301i | \(-0.168618\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 11.2519 | 0.404703 | 0.202352 | − | 0.979313i | \(-0.435142\pi\) | ||||
0.202352 | + | 0.979313i | \(0.435142\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 1.80933i | − 0.0649931i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 14.9343i | − 0.535078i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −19.8209 | −0.709248 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.92814i | 0.0688184i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 45.7781i | 1.63181i | 0.578185 | + | 0.815906i | \(0.303761\pi\) | ||||
−0.578185 | + | 0.815906i | \(0.696239\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 30.8504 | 1.09553 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 5.50164 | 0.194878 | 0.0974390 | − | 0.995241i | \(-0.468935\pi\) | ||||
0.0974390 | + | 0.995241i | \(0.468935\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 41.7882 | 1.47836 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −11.2029 | −0.395343 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − 28.9201i | − 1.01678i | −0.861128 | − | 0.508389i | \(-0.830241\pi\) | ||||
0.861128 | − | 0.508389i | \(-0.169759\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 39.1672i | 1.37535i | 0.726021 | + | 0.687673i | \(0.241368\pi\) | ||||
−0.726021 | + | 0.687673i | \(0.758632\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −16.3345 | −0.572173 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 29.6055i | 1.03576i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 19.5583i | − 0.682589i | −0.939956 | − | 0.341295i | \(-0.889135\pi\) | ||||
0.939956 | − | 0.341295i | \(-0.110865\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 51.2087 | 1.78502 | 0.892511 | − | 0.451026i | \(-0.148942\pi\) | ||||
0.892511 | + | 0.451026i | \(0.148942\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 21.2391i | − 0.738555i | −0.929319 | − | 0.369277i | \(-0.879605\pi\) | ||||
0.929319 | − | 0.369277i | \(-0.120395\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 22.5901i | − 0.784585i | −0.919841 | − | 0.392292i | \(-0.871682\pi\) | ||||
0.919841 | − | 0.392292i | \(-0.128318\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 16.2112 | 0.561012 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −7.06207 | −0.243810 | −0.121905 | − | 0.992542i | \(-0.538900\pi\) | ||||
−0.121905 | + | 0.992542i | \(0.538900\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16.4058 | −0.565716 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 11.2955 | 0.388577 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 18.3885i | 0.630350i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 32.2255i | − 1.10338i | −0.834050 | − | 0.551689i | \(-0.813983\pi\) | ||||
0.834050 | − | 0.551689i | \(-0.186017\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −16.4202 | −0.560902 | −0.280451 | − | 0.959868i | \(-0.590484\pi\) | ||||
−0.280451 | + | 0.959868i | \(0.590484\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 28.1679i | 0.961076i | 0.876974 | + | 0.480538i | \(0.159559\pi\) | ||||
−0.876974 | + | 0.480538i | \(0.840441\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 34.1063i | 1.16099i | 0.814264 | + | 0.580495i | \(0.197141\pi\) | ||||
−0.814264 | + | 0.580495i | \(0.802859\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −21.5331 | −0.732146 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 25.0180i | − 0.848677i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 55.1225i | 1.86776i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −34.7964 | −1.17499 | −0.587495 | − | 0.809227i | \(-0.699886\pi\) | ||||
−0.587495 | + | 0.809227i | \(0.699886\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 39.6838 | 1.33698 | 0.668491 | − | 0.743721i | \(-0.266941\pi\) | ||||
0.668491 | + | 0.743721i | \(0.266941\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.50323 | 0.151546 | 0.0757728 | − | 0.997125i | \(-0.475858\pi\) | ||||
0.0757728 | + | 0.997125i | \(0.475858\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −26.2075 | −0.879961 | −0.439981 | − | 0.898007i | \(-0.645015\pi\) | ||||
−0.439981 | + | 0.898007i | \(0.645015\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 64.9087i | − 2.17209i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 21.7519i | 0.727086i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 12.1920 | 0.406625 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 17.2988i | − 0.576308i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − 10.4316i | − 0.346759i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −45.1884 | −1.50046 | −0.750229 | − | 0.661178i | \(-0.770057\pi\) | ||||
−0.750229 | + | 0.661178i | \(0.770057\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 21.4888i | 0.711956i | 0.934494 | + | 0.355978i | \(0.115852\pi\) | ||||
−0.934494 | + | 0.355978i | \(0.884148\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.658919i | 0.0218070i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −9.56919 | −0.315659 | −0.157829 | − | 0.987466i | \(-0.550450\pi\) | ||||
−0.157829 | + | 0.987466i | \(0.550450\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −43.7535 | −1.44016 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.32755 | −0.142289 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 18.2534 | 0.598874 | 0.299437 | − | 0.954116i | \(-0.403201\pi\) | ||||
0.299437 | + | 0.954116i | \(0.403201\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 8.57339i | − 0.280380i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 30.4878i | − 0.995992i | −0.867179 | − | 0.497996i | \(-0.834069\pi\) | ||||
0.867179 | − | 0.497996i | \(-0.165931\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 51.0256 | 1.66339 | 0.831694 | − | 0.555234i | \(-0.187371\pi\) | ||||
0.831694 | + | 0.555234i | \(0.187371\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 10.6405i | 0.346503i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 55.5343i | − 1.80462i | −0.431087 | − | 0.902311i | \(-0.641870\pi\) | ||||
0.431087 | − | 0.902311i | \(-0.358130\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −24.7298 | −0.802764 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 40.0901i | − 1.29865i | −0.760512 | − | 0.649323i | \(-0.775052\pi\) | ||||
0.760512 | − | 0.649323i | \(-0.224948\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 23.6063i | − 0.763880i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 27.7263 | 0.894397 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −16.3226 | −0.525444 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −37.7974 | −1.21548 | −0.607740 | − | 0.794136i | \(-0.707924\pi\) | ||||
−0.607740 | + | 0.794136i | \(0.707924\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −32.7876 | −1.05220 | −0.526102 | − | 0.850422i | \(-0.676347\pi\) | ||||
−0.526102 | + | 0.850422i | \(0.676347\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 29.4856i | 0.943328i | 0.881778 | + | 0.471664i | \(0.156346\pi\) | ||||
−0.881778 | + | 0.471664i | \(0.843654\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 31.5647i | 1.00881i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −38.3639 | −1.22362 | −0.611810 | − | 0.791005i | \(-0.709558\pi\) | ||||
−0.611810 | + | 0.791005i | \(0.709558\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7.03368i | 0.224112i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 21.0935i | − 0.670735i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9.63794 | 0.306159 | 0.153080 | − | 0.988214i | \(-0.451081\pi\) | ||||
0.153080 | + | 0.988214i | \(0.451081\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 6.43512i | − 0.204007i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8.07296i | 0.255673i | 0.991795 | + | 0.127837i | \(0.0408033\pi\) | ||||
−0.991795 | + | 0.127837i | \(0.959197\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8820.2.d.a.881.5 | 12 | ||
3.2 | odd | 2 | 8820.2.d.b.881.8 | 12 | |||
7.2 | even | 3 | 1260.2.cg.b.521.5 | yes | 12 | ||
7.3 | odd | 6 | 1260.2.cg.a.341.5 | ✓ | 12 | ||
7.6 | odd | 2 | 8820.2.d.b.881.5 | 12 | |||
21.2 | odd | 6 | 1260.2.cg.a.521.5 | yes | 12 | ||
21.17 | even | 6 | 1260.2.cg.b.341.5 | yes | 12 | ||
21.20 | even | 2 | inner | 8820.2.d.a.881.8 | 12 | ||
35.2 | odd | 12 | 6300.2.dd.b.4049.3 | 24 | |||
35.3 | even | 12 | 6300.2.dd.c.1349.3 | 24 | |||
35.9 | even | 6 | 6300.2.ch.b.4301.2 | 12 | |||
35.17 | even | 12 | 6300.2.dd.c.1349.10 | 24 | |||
35.23 | odd | 12 | 6300.2.dd.b.4049.10 | 24 | |||
35.24 | odd | 6 | 6300.2.ch.c.1601.2 | 12 | |||
105.2 | even | 12 | 6300.2.dd.c.4049.3 | 24 | |||
105.17 | odd | 12 | 6300.2.dd.b.1349.10 | 24 | |||
105.23 | even | 12 | 6300.2.dd.c.4049.10 | 24 | |||
105.38 | odd | 12 | 6300.2.dd.b.1349.3 | 24 | |||
105.44 | odd | 6 | 6300.2.ch.c.4301.2 | 12 | |||
105.59 | even | 6 | 6300.2.ch.b.1601.2 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1260.2.cg.a.341.5 | ✓ | 12 | 7.3 | odd | 6 | ||
1260.2.cg.a.521.5 | yes | 12 | 21.2 | odd | 6 | ||
1260.2.cg.b.341.5 | yes | 12 | 21.17 | even | 6 | ||
1260.2.cg.b.521.5 | yes | 12 | 7.2 | even | 3 | ||
6300.2.ch.b.1601.2 | 12 | 105.59 | even | 6 | |||
6300.2.ch.b.4301.2 | 12 | 35.9 | even | 6 | |||
6300.2.ch.c.1601.2 | 12 | 35.24 | odd | 6 | |||
6300.2.ch.c.4301.2 | 12 | 105.44 | odd | 6 | |||
6300.2.dd.b.1349.3 | 24 | 105.38 | odd | 12 | |||
6300.2.dd.b.1349.10 | 24 | 105.17 | odd | 12 | |||
6300.2.dd.b.4049.3 | 24 | 35.2 | odd | 12 | |||
6300.2.dd.b.4049.10 | 24 | 35.23 | odd | 12 | |||
6300.2.dd.c.1349.3 | 24 | 35.3 | even | 12 | |||
6300.2.dd.c.1349.10 | 24 | 35.17 | even | 12 | |||
6300.2.dd.c.4049.3 | 24 | 105.2 | even | 12 | |||
6300.2.dd.c.4049.10 | 24 | 105.23 | even | 12 | |||
8820.2.d.a.881.5 | 12 | 1.1 | even | 1 | trivial | ||
8820.2.d.a.881.8 | 12 | 21.20 | even | 2 | inner | ||
8820.2.d.b.881.5 | 12 | 7.6 | odd | 2 | |||
8820.2.d.b.881.8 | 12 | 3.2 | odd | 2 |