Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2646,2,Mod(2645,2646)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2646, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2646.2645");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2646.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: | \(21.1284163748\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\Q(\zeta_{48})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - x^{8} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{14} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2645.4 | ||
Root | \(0.793353 - 0.608761i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2646.2645 |
Dual form | 2646.2.d.f.2645.12 |
$q$-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 \(\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1081\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 1.00000i | − 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −0.115708 | −0.0517463 | −0.0258732 | − | 0.999665i | \(-0.508237\pi\) | ||||
−0.0258732 | + | 0.999665i | \(0.508237\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.115708i | 0.0365902i | ||||||||
\(11\) | − 3.52607i | − 1.06315i | −0.847011 | − | 0.531575i | \(-0.821601\pi\) | ||||
0.847011 | − | 0.531575i | \(-0.178399\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.01140i | 0.557861i | 0.960311 | + | 0.278930i | \(0.0899799\pi\) | ||||
−0.960311 | + | 0.278930i | \(0.910020\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.44949 | 0.594089 | 0.297044 | − | 0.954864i | \(-0.403999\pi\) | ||||
0.297044 | + | 0.954864i | \(0.403999\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.10030i | 1.17009i | 0.811001 | + | 0.585044i | \(0.198923\pi\) | ||||
−0.811001 | + | 0.585044i | \(0.801077\pi\) | |||||||
\(20\) | 0.115708 | 0.0258732 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.52607 | −0.751760 | ||||||||
\(23\) | 5.73987i | 1.19685i | 0.801181 | + | 0.598423i | \(0.204206\pi\) | ||||
−0.801181 | + | 0.598423i | \(0.795794\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.98661 | −0.997322 | ||||||||
\(26\) | 2.01140 | 0.394467 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.48938i | 0.833658i | 0.908985 | + | 0.416829i | \(0.136859\pi\) | ||||
−0.908985 | + | 0.416829i | \(0.863141\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.03446i | 0.185795i | 0.995676 | + | 0.0928976i | \(0.0296129\pi\) | ||||
−0.995676 | + | 0.0928976i | \(0.970387\pi\) | |||||||
\(32\) | − 1.00000i | − 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − 2.44949i | − 0.420084i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.69354 | 0.771613 | 0.385806 | − | 0.922580i | \(-0.373923\pi\) | ||||
0.385806 | + | 0.922580i | \(0.373923\pi\) | |||||||
\(38\) | 5.10030 | 0.827377 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | − 0.115708i | − 0.0182951i | ||||||||
\(41\) | −4.06047 | −0.634139 | −0.317070 | − | 0.948402i | \(-0.602699\pi\) | ||||
−0.317070 | + | 0.948402i | \(0.602699\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.70319 | −1.02223 | −0.511113 | − | 0.859513i | \(-0.670767\pi\) | ||||
−0.511113 | + | 0.859513i | \(0.670767\pi\) | |||||||
\(44\) | 3.52607i | 0.531575i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.73987 | 0.846297 | ||||||||
\(47\) | −2.96561 | −0.432579 | −0.216289 | − | 0.976329i | \(-0.569395\pi\) | ||||
−0.216289 | + | 0.976329i | \(0.569395\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 4.98661i | 0.705213i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − 2.01140i | − 0.278930i | ||||||||
\(53\) | − 9.17738i | − 1.26061i | −0.776348 | − | 0.630305i | \(-0.782930\pi\) | ||||
0.776348 | − | 0.630305i | \(-0.217070\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.407995i | 0.0550140i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.48938 | 0.589485 | ||||||||
\(59\) | 10.3422 | 1.34643 | 0.673217 | − | 0.739445i | \(-0.264912\pi\) | ||||
0.673217 | + | 0.739445i | \(0.264912\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.73420i | 0.350078i | 0.984562 | + | 0.175039i | \(0.0560051\pi\) | ||||
−0.984562 | + | 0.175039i | \(0.943995\pi\) | |||||||
\(62\) | 1.03446 | 0.131377 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | − 0.232735i | − 0.0288672i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.54910 | −0.311423 | −0.155711 | − | 0.987803i | \(-0.549767\pi\) | ||||
−0.155711 | + | 0.987803i | \(0.549767\pi\) | |||||||
\(68\) | −2.44949 | −0.297044 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.12150i | 0.607810i | 0.952702 | + | 0.303905i | \(0.0982906\pi\) | ||||
−0.952702 | + | 0.303905i | \(0.901709\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.60796i | 0.890445i | 0.895420 | + | 0.445222i | \(0.146875\pi\) | ||||
−0.895420 | + | 0.445222i | \(0.853125\pi\) | |||||||
\(74\) | − 4.69354i | − 0.545613i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − 5.10030i | − 0.585044i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.88030 | −0.549077 | −0.274539 | − | 0.961576i | \(-0.588525\pi\) | ||||
−0.274539 | + | 0.961576i | \(0.588525\pi\) | |||||||
\(80\) | −0.115708 | −0.0129366 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 4.06047i | 0.448404i | ||||||||
\(83\) | 17.9544 | 1.97075 | 0.985374 | − | 0.170408i | \(-0.0545085\pi\) | ||||
0.985374 | + | 0.170408i | \(0.0545085\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.283426 | −0.0307419 | ||||||||
\(86\) | 6.70319i | 0.722823i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.52607 | 0.375880 | ||||||||
\(89\) | 10.0274 | 1.06290 | 0.531449 | − | 0.847091i | \(-0.321648\pi\) | ||||
0.531449 | + | 0.847091i | \(0.321648\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − 5.73987i | − 0.598423i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 2.96561i | 0.305879i | ||||||||
\(95\) | − 0.590146i | − 0.0605477i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.2755i | 1.24639i | 0.782066 | + | 0.623195i | \(0.214166\pi\) | ||||
−0.782066 | + | 0.623195i | \(0.785834\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4.98661 | 0.498661 | ||||||||
\(101\) | 18.5530 | 1.84609 | 0.923044 | − | 0.384695i | \(-0.125693\pi\) | ||||
0.923044 | + | 0.384695i | \(0.125693\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.25440i | 0.911863i | 0.890015 | + | 0.455932i | \(0.150694\pi\) | ||||
−0.890015 | + | 0.455932i | \(0.849306\pi\) | |||||||
\(104\) | −2.01140 | −0.197234 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −9.17738 | −0.891386 | ||||||||
\(107\) | 18.3003i | 1.76916i | 0.466390 | + | 0.884579i | \(0.345554\pi\) | ||||
−0.466390 | + | 0.884579i | \(0.654446\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −14.7842 | −1.41607 | −0.708033 | − | 0.706180i | \(-0.750417\pi\) | ||||
−0.708033 | + | 0.706180i | \(0.750417\pi\) | |||||||
\(110\) | 0.407995 | 0.0389008 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 11.4294i | 1.07519i | 0.843204 | + | 0.537594i | \(0.180667\pi\) | ||||
−0.843204 | + | 0.537594i | \(0.819333\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 0.664150i | − 0.0619323i | ||||||||
\(116\) | − 4.48938i | − 0.416829i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − 10.3422i | − 0.952073i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.43315 | −0.130286 | ||||||||
\(122\) | 2.73420 | 0.247542 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − 1.03446i | − 0.0928976i | ||||||||
\(125\) | 1.15553 | 0.103354 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.0480 | 1.33530 | 0.667648 | − | 0.744477i | \(-0.267301\pi\) | ||||
0.667648 | + | 0.744477i | \(0.267301\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.232735 | −0.0204122 | ||||||||
\(131\) | 13.1615 | 1.14992 | 0.574962 | − | 0.818180i | \(-0.305017\pi\) | ||||
0.574962 | + | 0.818180i | \(0.305017\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 2.54910i | 0.220209i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.44949i | 0.210042i | ||||||||
\(137\) | − 13.3425i | − 1.13993i | −0.821669 | − | 0.569965i | \(-0.806957\pi\) | ||||
0.821669 | − | 0.569965i | \(-0.193043\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 21.8991i | 1.85746i | 0.370757 | + | 0.928730i | \(0.379098\pi\) | ||||
−0.370757 | + | 0.928730i | \(0.620902\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 5.12150 | 0.429787 | ||||||||
\(143\) | 7.09231 | 0.593089 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − 0.519459i | − 0.0431387i | ||||||||
\(146\) | 7.60796 | 0.629639 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.69354 | −0.385806 | ||||||||
\(149\) | 21.9423i | 1.79759i | 0.438372 | + | 0.898793i | \(0.355555\pi\) | ||||
−0.438372 | + | 0.898793i | \(0.644445\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.21380 | −0.180157 | −0.0900783 | − | 0.995935i | \(-0.528712\pi\) | ||||
−0.0900783 | + | 0.995935i | \(0.528712\pi\) | |||||||
\(152\) | −5.10030 | −0.413689 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 0.119696i | − 0.00961422i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 18.3494i | − 1.46444i | −0.681067 | − | 0.732221i | \(-0.738484\pi\) | ||||
0.681067 | − | 0.732221i | \(-0.261516\pi\) | |||||||
\(158\) | 4.88030i | 0.388256i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.115708i | 0.00914754i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.94438 | −0.778904 | −0.389452 | − | 0.921047i | \(-0.627336\pi\) | ||||
−0.389452 | + | 0.921047i | \(0.627336\pi\) | |||||||
\(164\) | 4.06047 | 0.317070 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − 17.9544i | − 1.39353i | ||||||||
\(167\) | −6.88516 | −0.532790 | −0.266395 | − | 0.963864i | \(-0.585833\pi\) | ||||
−0.266395 | + | 0.963864i | \(0.585833\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.95429 | 0.688791 | ||||||||
\(170\) | 0.283426i | 0.0217378i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 6.70319 | 0.511113 | ||||||||
\(173\) | −16.2961 | −1.23897 | −0.619485 | − | 0.785009i | \(-0.712658\pi\) | ||||
−0.619485 | + | 0.785009i | \(0.712658\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − 3.52607i | − 0.265787i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − 10.0274i | − 0.751582i | ||||||||
\(179\) | 3.56456i | 0.266427i | 0.991087 | + | 0.133214i | \(0.0425297\pi\) | ||||
−0.991087 | + | 0.133214i | \(0.957470\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 14.7498i | − 1.09634i | −0.836367 | − | 0.548170i | \(-0.815325\pi\) | ||||
0.836367 | − | 0.548170i | \(-0.184675\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −5.73987 | −0.423149 | ||||||||
\(185\) | −0.543081 | −0.0399281 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 8.63706i | − 0.631605i | ||||||||
\(188\) | 2.96561 | 0.216289 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.590146 | −0.0428137 | ||||||||
\(191\) | − 20.2251i | − 1.46344i | −0.681605 | − | 0.731720i | \(-0.738718\pi\) | ||||
0.681605 | − | 0.731720i | \(-0.261282\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.94557 | 0.284008 | 0.142004 | − | 0.989866i | \(-0.454645\pi\) | ||||
0.142004 | + | 0.989866i | \(0.454645\pi\) | |||||||
\(194\) | 12.2755 | 0.881331 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 2.29826i | − 0.163744i | −0.996643 | − | 0.0818720i | \(-0.973910\pi\) | ||||
0.996643 | − | 0.0818720i | \(-0.0260899\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 25.9021i | 1.83615i | 0.396408 | + | 0.918074i | \(0.370256\pi\) | ||||
−0.396408 | + | 0.918074i | \(0.629744\pi\) | |||||||
\(200\) | − 4.98661i | − 0.352607i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − 18.5530i | − 1.30538i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.469830 | 0.0328144 | ||||||||
\(206\) | 9.25440 | 0.644785 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.01140i | 0.139465i | ||||||||
\(209\) | 17.9840 | 1.24398 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.20067 | 0.151500 | 0.0757502 | − | 0.997127i | \(-0.475865\pi\) | ||||
0.0757502 | + | 0.997127i | \(0.475865\pi\) | |||||||
\(212\) | 9.17738i | 0.630305i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 18.3003 | 1.25098 | ||||||||
\(215\) | 0.775614 | 0.0528964 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 14.7842i | 1.00131i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | − 0.407995i | − 0.0275070i | ||||||||
\(221\) | 4.92689i | 0.331419i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.12818i | 0.343408i | 0.985149 | + | 0.171704i | \(0.0549273\pi\) | ||||
−0.985149 | + | 0.171704i | \(0.945073\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 11.4294 | 0.760273 | ||||||||
\(227\) | 18.1149 | 1.20233 | 0.601163 | − | 0.799127i | \(-0.294704\pi\) | ||||
0.601163 | + | 0.799127i | \(0.294704\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.45493i | 0.426554i | 0.976992 | + | 0.213277i | \(0.0684136\pi\) | ||||
−0.976992 | + | 0.213277i | \(0.931586\pi\) | |||||||
\(230\) | −0.664150 | −0.0437928 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.48938 | −0.294743 | ||||||||
\(233\) | 12.0288i | 0.788035i | 0.919103 | + | 0.394018i | \(0.128915\pi\) | ||||
−0.919103 | + | 0.394018i | \(0.871085\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.343146 | 0.0223844 | ||||||||
\(236\) | −10.3422 | −0.673217 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.19342i | 0.0771962i | 0.999255 | + | 0.0385981i | \(0.0122892\pi\) | ||||
−0.999255 | + | 0.0385981i | \(0.987711\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − 11.9940i | − 0.772599i | −0.922373 | − | 0.386299i | \(-0.873753\pi\) | ||||
0.922373 | − | 0.386299i | \(-0.126247\pi\) | |||||||
\(242\) | 1.43315i | 0.0921262i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − 2.73420i | − 0.175039i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −10.2587 | −0.652746 | ||||||||
\(248\) | −1.03446 | −0.0656885 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | − 1.15553i | − 0.0730824i | ||||||||
\(251\) | −7.66816 | −0.484010 | −0.242005 | − | 0.970275i | \(-0.577805\pi\) | ||||
−0.242005 | + | 0.970275i | \(0.577805\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 20.2392 | 1.27242 | ||||||||
\(254\) | − 15.0480i | − 0.944197i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 1.49305 | 0.0931341 | 0.0465670 | − | 0.998915i | \(-0.485172\pi\) | ||||
0.0465670 | + | 0.998915i | \(0.485172\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0.232735i | 0.0144336i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − 13.1615i | − 0.813119i | ||||||||
\(263\) | − 14.9939i | − 0.924561i | −0.886734 | − | 0.462280i | \(-0.847031\pi\) | ||||
0.886734 | − | 0.462280i | \(-0.152969\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.06190i | 0.0652319i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2.54910 | 0.155711 | ||||||||
\(269\) | −12.2100 | −0.744455 | −0.372227 | − | 0.928142i | \(-0.621406\pi\) | ||||
−0.372227 | + | 0.928142i | \(0.621406\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 11.3211i | − 0.687709i | −0.939023 | − | 0.343854i | \(-0.888267\pi\) | ||||
0.939023 | − | 0.343854i | \(-0.111733\pi\) | |||||||
\(272\) | 2.44949 | 0.148522 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −13.3425 | −0.806053 | ||||||||
\(275\) | 17.5831i | 1.06030i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −19.6283 | −1.17935 | −0.589674 | − | 0.807641i | \(-0.700744\pi\) | ||||
−0.589674 | + | 0.807641i | \(0.700744\pi\) | |||||||
\(278\) | 21.8991 | 1.31342 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 9.26424i | − 0.552658i | −0.961063 | − | 0.276329i | \(-0.910882\pi\) | ||||
0.961063 | − | 0.276329i | \(-0.0891179\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.48744i | 0.385638i | 0.981234 | + | 0.192819i | \(0.0617631\pi\) | ||||
−0.981234 | + | 0.192819i | \(0.938237\pi\) | |||||||
\(284\) | − 5.12150i | − 0.303905i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − 7.09231i | − 0.419377i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11.0000 | −0.647059 | ||||||||
\(290\) | −0.519459 | −0.0305037 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − 7.60796i | − 0.445222i | ||||||||
\(293\) | −12.8799 | −0.752453 | −0.376226 | − | 0.926528i | \(-0.622779\pi\) | ||||
−0.376226 | + | 0.926528i | \(0.622779\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.19667 | −0.0696730 | ||||||||
\(296\) | 4.69354i | 0.272806i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 21.9423 | 1.27109 | ||||||||
\(299\) | −11.5451 | −0.667673 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 2.21380i | 0.127390i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 5.10030i | 0.292522i | ||||||||
\(305\) | − 0.316369i | − 0.0181152i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.1063i | 0.690945i | 0.938429 | + | 0.345472i | \(0.112281\pi\) | ||||
−0.938429 | + | 0.345472i | \(0.887719\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −0.119696 | −0.00679828 | ||||||||
\(311\) | −28.1723 | −1.59751 | −0.798753 | − | 0.601660i | \(-0.794506\pi\) | ||||
−0.798753 | + | 0.601660i | \(0.794506\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 24.9784i | − 1.41186i | −0.708280 | − | 0.705932i | \(-0.750528\pi\) | ||||
0.708280 | − | 0.705932i | \(-0.249472\pi\) | |||||||
\(314\) | −18.3494 | −1.03552 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.88030 | 0.274539 | ||||||||
\(317\) | − 28.0688i | − 1.57650i | −0.615356 | − | 0.788250i | \(-0.710988\pi\) | ||||
0.615356 | − | 0.788250i | \(-0.289012\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 15.8299 | 0.886303 | ||||||||
\(320\) | 0.115708 | 0.00646829 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 12.4931i | 0.695136i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 10.0300i | − 0.556367i | ||||||||
\(326\) | 9.94438i | 0.550768i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − 4.06047i | − 0.224202i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −30.4124 | −1.67162 | −0.835809 | − | 0.549020i | \(-0.815001\pi\) | ||||
−0.835809 | + | 0.549020i | \(0.815001\pi\) | |||||||
\(332\) | −17.9544 | −0.985374 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 6.88516i | 0.376739i | ||||||||
\(335\) | 0.294952 | 0.0161150 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 32.5762 | 1.77454 | 0.887268 | − | 0.461254i | \(-0.152600\pi\) | ||||
0.887268 | + | 0.461254i | \(0.152600\pi\) | |||||||
\(338\) | − 8.95429i | − 0.487049i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0.283426 | 0.0153709 | ||||||||
\(341\) | 3.64759 | 0.197528 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | − 6.70319i | − 0.361412i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 16.2961i | 0.876083i | ||||||||
\(347\) | − 12.5588i | − 0.674189i | −0.941471 | − | 0.337095i | \(-0.890556\pi\) | ||||
0.941471 | − | 0.337095i | \(-0.109444\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 17.1062i | 0.915676i | 0.889036 | + | 0.457838i | \(0.151376\pi\) | ||||
−0.889036 | + | 0.457838i | \(0.848624\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.52607 | −0.187940 | ||||||||
\(353\) | 9.61557 | 0.511785 | 0.255893 | − | 0.966705i | \(-0.417631\pi\) | ||||
0.255893 | + | 0.966705i | \(0.417631\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 0.592600i | − 0.0314519i | ||||||||
\(356\) | −10.0274 | −0.531449 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3.56456 | 0.188393 | ||||||||
\(359\) | − 15.0521i | − 0.794421i | −0.917727 | − | 0.397211i | \(-0.869978\pi\) | ||||
0.917727 | − | 0.397211i | \(-0.130022\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.01303 | −0.369107 | ||||||||
\(362\) | −14.7498 | −0.775230 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 0.880304i | − 0.0460772i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.2943i | 0.589560i | 0.955565 | + | 0.294780i | \(0.0952464\pi\) | ||||
−0.955565 | + | 0.294780i | \(0.904754\pi\) | |||||||
\(368\) | 5.73987i | 0.299211i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0.543081i | 0.0282334i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.56600 | −0.288196 | −0.144098 | − | 0.989563i | \(-0.546028\pi\) | ||||
−0.144098 | + | 0.989563i | \(0.546028\pi\) | |||||||
\(374\) | −8.63706 | −0.446612 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − 2.96561i | − 0.152940i | ||||||||
\(377\) | −9.02993 | −0.465065 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.80720 | −0.298296 | −0.149148 | − | 0.988815i | \(-0.547653\pi\) | ||||
−0.149148 | + | 0.988815i | \(0.547653\pi\) | |||||||
\(380\) | 0.590146i | 0.0302739i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −20.2251 | −1.03481 | ||||||||
\(383\) | 7.28335 | 0.372162 | 0.186081 | − | 0.982534i | \(-0.440421\pi\) | ||||
0.186081 | + | 0.982534i | \(0.440421\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − 3.94557i | − 0.200824i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − 12.2755i | − 0.623195i | ||||||||
\(389\) | 23.7553i | 1.20444i | 0.798329 | + | 0.602221i | \(0.205717\pi\) | ||||
−0.798329 | + | 0.602221i | \(0.794283\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14.0597i | 0.711032i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2.29826 | −0.115785 | ||||||||
\(395\) | 0.564691 | 0.0284127 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 15.8429i | 0.795131i | 0.917574 | + | 0.397565i | \(0.130145\pi\) | ||||
−0.917574 | + | 0.397565i | \(0.869855\pi\) | |||||||
\(398\) | 25.9021 | 1.29835 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.98661 | −0.249331 | ||||||||
\(401\) | − 8.33412i | − 0.416186i | −0.978109 | − | 0.208093i | \(-0.933274\pi\) | ||||
0.978109 | − | 0.208093i | \(-0.0667257\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.08072 | −0.103648 | ||||||||
\(404\) | −18.5530 | −0.923044 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 16.5497i | − 0.820339i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − 28.1151i | − 1.39020i | −0.718913 | − | 0.695100i | \(-0.755360\pi\) | ||||
0.718913 | − | 0.695100i | \(-0.244640\pi\) | |||||||
\(410\) | − 0.469830i | − 0.0232033i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − 9.25440i | − 0.455932i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.07747 | −0.101979 | ||||||||
\(416\) | 2.01140 | 0.0986168 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − 17.9840i | − 0.879626i | ||||||||
\(419\) | −15.3664 | −0.750700 | −0.375350 | − | 0.926883i | \(-0.622478\pi\) | ||||
−0.375350 | + | 0.926883i | \(0.622478\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.33930 | −0.114010 | −0.0570052 | − | 0.998374i | \(-0.518155\pi\) | ||||
−0.0570052 | + | 0.998374i | \(0.518155\pi\) | |||||||
\(422\) | − 2.20067i | − 0.107127i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 9.17738 | 0.445693 | ||||||||
\(425\) | −12.2147 | −0.592498 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | − 18.3003i | − 0.884579i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | − 0.775614i | − 0.0374034i | ||||||||
\(431\) | 24.4954i | 1.17990i | 0.807438 | + | 0.589952i | \(0.200853\pi\) | ||||
−0.807438 | + | 0.589952i | \(0.799147\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.66332i | 0.224105i | 0.993702 | + | 0.112052i | \(0.0357424\pi\) | ||||
−0.993702 | + | 0.112052i | \(0.964258\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 14.7842 | 0.708033 | ||||||||
\(437\) | −29.2750 | −1.40041 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16.9027i | 0.806722i | 0.915041 | + | 0.403361i | \(0.132158\pi\) | ||||
−0.915041 | + | 0.403361i | \(0.867842\pi\) | |||||||
\(440\) | −0.407995 | −0.0194504 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 4.92689 | 0.234348 | ||||||||
\(443\) | − 34.2190i | − 1.62579i | −0.582407 | − | 0.812897i | \(-0.697889\pi\) | ||||
0.582407 | − | 0.812897i | \(-0.302111\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.16025 | −0.0550010 | ||||||||
\(446\) | 5.12818 | 0.242826 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 1.38574i | − 0.0653970i | −0.999465 | − | 0.0326985i | \(-0.989590\pi\) | ||||
0.999465 | − | 0.0326985i | \(-0.0104101\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 14.3175i | 0.674184i | ||||||||
\(452\) | − 11.4294i | − 0.537594i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − 18.1149i | − 0.850172i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 30.3990 | 1.42201 | 0.711004 | − | 0.703188i | \(-0.248241\pi\) | ||||
0.711004 | + | 0.703188i | \(0.248241\pi\) | |||||||
\(458\) | 6.45493 | 0.301619 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0.664150i | 0.0309662i | ||||||||
\(461\) | 16.3888 | 0.763303 | 0.381651 | − | 0.924306i | \(-0.375355\pi\) | ||||
0.381651 | + | 0.924306i | \(0.375355\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.18677 | −0.333997 | −0.166999 | − | 0.985957i | \(-0.553408\pi\) | ||||
−0.166999 | + | 0.985957i | \(0.553408\pi\) | |||||||
\(464\) | 4.48938i | 0.208414i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 12.0288 | 0.557225 | ||||||||
\(467\) | −13.7962 | −0.638412 | −0.319206 | − | 0.947685i | \(-0.603416\pi\) | ||||
−0.319206 | + | 0.947685i | \(0.603416\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | − 0.343146i | − 0.0158281i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 10.3422i | 0.476036i | ||||||||
\(473\) | 23.6359i | 1.08678i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 25.4332i | − 1.16696i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.19342 | 0.0545860 | ||||||||
\(479\) | −14.1443 | −0.646267 | −0.323134 | − | 0.946353i | \(-0.604736\pi\) | ||||
−0.323134 | + | 0.946353i | \(0.604736\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.44056i | 0.430452i | ||||||||
\(482\) | −11.9940 | −0.546310 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.43315 | 0.0651431 | ||||||||
\(485\) | − 1.42038i | − 0.0644961i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.92664 | −0.449819 | −0.224909 | − | 0.974380i | \(-0.572209\pi\) | ||||
−0.224909 | + | 0.974380i | \(0.572209\pi\) | |||||||
\(488\) | −2.73420 | −0.123771 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.46802i | 0.0662510i | 0.999451 | + | 0.0331255i | \(0.0105461\pi\) | ||||
−0.999451 | + | 0.0331255i | \(0.989454\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 10.9967i | 0.495267i | ||||||||
\(494\) | 10.2587i | 0.461561i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.03446i | 0.0464488i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.29707 | 0.371428 | 0.185714 | − | 0.982604i | \(-0.440540\pi\) | ||||
0.185714 | + | 0.982604i | \(0.440540\pi\) | |||||||
\(500\) | −1.15553 | −0.0516770 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 7.66816i | 0.342247i | ||||||||
\(503\) | −28.1114 | −1.25343 | −0.626714 | − | 0.779250i | \(-0.715600\pi\) | ||||
−0.626714 | + | 0.779250i | \(0.715600\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.14673 | −0.0955282 | ||||||||
\(506\) | − 20.2392i | − 0.899740i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −15.0480 | −0.667648 | ||||||||
\(509\) | 43.9940 | 1.95000 | 0.975000 | − | 0.222204i | \(-0.0713252\pi\) | ||||
0.975000 | + | 0.222204i | \(0.0713252\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − 1.00000i | − 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − 1.49305i | − 0.0658557i | ||||||||
\(515\) | − 1.07081i | − 0.0471856i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10.4569i | 0.459896i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0.232735 | 0.0102061 | ||||||||
\(521\) | −31.8306 | −1.39452 | −0.697262 | − | 0.716816i | \(-0.745599\pi\) | ||||
−0.697262 | + | 0.716816i | \(0.745599\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 18.8678i | − 0.825029i | −0.910951 | − | 0.412515i | \(-0.864651\pi\) | ||||
0.910951 | − | 0.412515i | \(-0.135349\pi\) | |||||||
\(524\) | −13.1615 | −0.574962 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −14.9939 | −0.653763 | ||||||||
\(527\) | 2.53391i | 0.110379i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.94608 | −0.432438 | ||||||||
\(530\) | 1.06190 | 0.0461259 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 8.16721i | − 0.353761i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 2.11750i | − 0.0915474i | ||||||||
\(536\) | − 2.54910i | − 0.110105i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 12.2100i | 0.526409i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 28.4031 | 1.22115 | 0.610573 | − | 0.791960i | \(-0.290939\pi\) | ||||
0.610573 | + | 0.791960i | \(0.290939\pi\) | |||||||
\(542\) | −11.3211 | −0.486283 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − 2.44949i | − 0.105021i | ||||||||
\(545\) | 1.71065 | 0.0732762 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.64525 | −0.241373 | −0.120687 | − | 0.992691i | \(-0.538510\pi\) | ||||
−0.120687 | + | 0.992691i | \(0.538510\pi\) | |||||||
\(548\) | 13.3425i | 0.569965i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 17.5831 | 0.749747 | ||||||||
\(551\) | −22.8972 | −0.975453 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 19.6283i | 0.833925i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − 21.8991i | − 0.928730i | ||||||||
\(557\) | 25.8164i | 1.09387i | 0.837173 | + | 0.546937i | \(0.184206\pi\) | ||||
−0.837173 | + | 0.546937i | \(0.815794\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 13.4828i | − 0.570260i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −9.26424 | −0.390788 | ||||||||
\(563\) | −28.1008 | −1.18431 | −0.592153 | − | 0.805826i | \(-0.701722\pi\) | ||||
−0.592153 | + | 0.805826i | \(0.701722\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 1.32248i | − 0.0556370i | ||||||||
\(566\) | 6.48744 | 0.272688 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −5.12150 | −0.214893 | ||||||||
\(569\) | − 31.0489i | − 1.30164i | −0.759233 | − | 0.650819i | \(-0.774426\pi\) | ||||
0.759233 | − | 0.650819i | \(-0.225574\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 45.0250 | 1.88424 | 0.942119 | − | 0.335278i | \(-0.108830\pi\) | ||||
0.942119 | + | 0.335278i | \(0.108830\pi\) | |||||||
\(572\) | −7.09231 | −0.296545 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 28.6225i | − 1.19364i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 12.5714i | − 0.523354i | −0.965156 | − | 0.261677i | \(-0.915725\pi\) | ||||
0.965156 | − | 0.261677i | \(-0.0842754\pi\) | |||||||
\(578\) | 11.0000i | 0.457540i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0.519459i | 0.0215694i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −32.3600 | −1.34022 | ||||||||
\(584\) | −7.60796 | −0.314820 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 12.8799i | 0.532065i | ||||||||
\(587\) | 11.1722 | 0.461125 | 0.230562 | − | 0.973058i | \(-0.425943\pi\) | ||||
0.230562 | + | 0.973058i | \(0.425943\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.27607 | −0.217397 | ||||||||
\(590\) | 1.19667i | 0.0492662i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4.69354 | 0.192903 | ||||||||
\(593\) | 10.1941 | 0.418623 | 0.209311 | − | 0.977849i | \(-0.432878\pi\) | ||||
0.209311 | + | 0.977849i | \(0.432878\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − 21.9423i | − 0.898793i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 11.5451i | 0.472116i | ||||||||
\(599\) | 31.6315i | 1.29243i | 0.763156 | + | 0.646214i | \(0.223649\pi\) | ||||
−0.763156 | + | 0.646214i | \(0.776351\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − 26.4742i | − 1.07990i | −0.841696 | − | 0.539952i | \(-0.818442\pi\) | ||||
0.841696 | − | 0.539952i | \(-0.181558\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 2.21380 | 0.0900783 | ||||||||
\(605\) | 0.165827 | 0.00674183 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 24.2960i | 0.986144i | 0.869988 | + | 0.493072i | \(0.164126\pi\) | ||||
−0.869988 | + | 0.493072i | \(0.835874\pi\) | |||||||
\(608\) | 5.10030 | 0.206844 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −0.316369 | −0.0128094 | ||||||||
\(611\) | − 5.96502i | − 0.241319i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −42.5646 | −1.71917 | −0.859584 | − | 0.510995i | \(-0.829277\pi\) | ||||
−0.859584 | + | 0.510995i | \(0.829277\pi\) | |||||||
\(614\) | 12.1063 | 0.488572 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 45.9424i | − 1.84957i | −0.380490 | − | 0.924785i | \(-0.624245\pi\) | ||||
0.380490 | − | 0.924785i | \(-0.375755\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 21.6196i | 0.868964i | 0.900680 | + | 0.434482i | \(0.143069\pi\) | ||||
−0.900680 | + | 0.434482i | \(0.856931\pi\) | |||||||
\(620\) | 0.119696i | 0.00480711i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 28.1723i | 1.12961i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.7994 | 0.991974 | ||||||||
\(626\) | −24.9784 | −0.998338 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 18.3494i | 0.732221i | ||||||||
\(629\) | 11.4968 | 0.458406 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −46.4078 | −1.84747 | −0.923733 | − | 0.383036i | \(-0.874879\pi\) | ||||
−0.923733 | + | 0.383036i | \(0.874879\pi\) | |||||||
\(632\) | − 4.88030i | − 0.194128i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −28.0688 | −1.11475 | ||||||||
\(635\) | −1.74118 | −0.0690967 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | − 15.8299i | − 0.626711i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | − 0.115708i | − 0.00457377i | ||||||||
\(641\) | − 0.107493i | − 0.00424573i | −0.999998 | − | 0.00212287i | \(-0.999324\pi\) | ||||
0.999998 | − | 0.00212287i | \(-0.000675730\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 16.3117i | 0.643270i | 0.946864 | + | 0.321635i | \(0.104232\pi\) | ||||
−0.946864 | + | 0.321635i | \(0.895768\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 12.4931 | 0.491535 | ||||||||
\(647\) | −27.2436 | −1.07106 | −0.535528 | − | 0.844518i | \(-0.679887\pi\) | ||||
−0.535528 | + | 0.844518i | \(0.679887\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − 36.4671i | − 1.43146i | ||||||||
\(650\) | −10.0300 | −0.393411 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 9.94438 | 0.389452 | ||||||||
\(653\) | − 3.85546i | − 0.150876i | −0.997151 | − | 0.0754379i | \(-0.975965\pi\) | ||||
0.997151 | − | 0.0754379i | \(-0.0240355\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.52289 | −0.0595043 | ||||||||
\(656\) | −4.06047 | −0.158535 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.47215i | 0.135256i | 0.997711 | + | 0.0676279i | \(0.0215431\pi\) | ||||
−0.997711 | + | 0.0676279i | \(0.978457\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 6.78526i | − 0.263916i | −0.991255 | − | 0.131958i | \(-0.957874\pi\) | ||||
0.991255 | − | 0.131958i | \(-0.0421264\pi\) | |||||||
\(662\) | 30.4124i | 1.18201i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 17.9544i | 0.696764i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −25.7685 | −0.997759 | ||||||||
\(668\) | 6.88516 | 0.266395 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | − 0.294952i | − 0.0113950i | ||||||||
\(671\) | 9.64095 | 0.372185 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 22.2776 | 0.858739 | 0.429370 | − | 0.903129i | \(-0.358736\pi\) | ||||
0.429370 | + | 0.903129i | \(0.358736\pi\) | |||||||
\(674\) | − 32.5762i | − 1.25479i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −8.95429 | −0.344396 | ||||||||
\(677\) | −38.0215 | −1.46129 | −0.730643 | − | 0.682760i | \(-0.760780\pi\) | ||||
−0.730643 | + | 0.682760i | \(0.760780\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | − 0.283426i | − 0.0108689i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − 3.64759i | − 0.139673i | ||||||||
\(683\) | − 12.9592i | − 0.495871i | −0.968777 | − | 0.247935i | \(-0.920248\pi\) | ||||
0.968777 | − | 0.247935i | \(-0.0797520\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.54384i | 0.0589872i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −6.70319 | −0.255557 | ||||||||
\(689\) | 18.4593 | 0.703244 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 49.4231i | 1.88014i | 0.340978 | + | 0.940071i | \(0.389242\pi\) | ||||
−0.340978 | + | 0.940071i | \(0.610758\pi\) | |||||||
\(692\) | 16.2961 | 0.619485 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −12.5588 | −0.476724 | ||||||||
\(695\) | − 2.53391i | − 0.0961167i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.94608 | −0.376735 | ||||||||
\(698\) | 17.1062 | 0.647481 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 4.29078i | − 0.162060i | −0.996712 | − | 0.0810302i | \(-0.974179\pi\) | ||||
0.996712 | − | 0.0810302i | \(-0.0258210\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 23.9384i | 0.902855i | ||||||||
\(704\) | 3.52607i | 0.132894i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − 9.61557i | − 0.361887i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 47.6242 | 1.78856 | 0.894282 | − | 0.447504i | \(-0.147687\pi\) | ||||
0.894282 | + | 0.447504i | \(0.147687\pi\) | |||||||
\(710\) | −0.592600 | −0.0222399 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 10.0274i | 0.375791i | ||||||||
\(713\) | −5.93769 | −0.222368 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.820639 | −0.0306902 | ||||||||
\(716\) | − 3.56456i | − 0.133214i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −15.0521 | −0.561741 | ||||||||
\(719\) | 11.5753 | 0.431685 | 0.215842 | − | 0.976428i | \(-0.430750\pi\) | ||||
0.215842 | + | 0.976428i | \(0.430750\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 7.01303i | 0.260998i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 14.7498i | 0.548170i | ||||||||
\(725\) | − 22.3868i | − 0.831425i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 25.4165i | 0.942646i | 0.881961 | + | 0.471323i | \(0.156223\pi\) | ||||
−0.881961 | + | 0.471323i | \(0.843777\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −0.880304 | −0.0325815 | ||||||||
\(731\) | −16.4194 | −0.607293 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 52.2922i | 1.93146i | 0.259557 | + | 0.965728i | \(0.416423\pi\) | ||||
−0.259557 | + | 0.965728i | \(0.583577\pi\) | |||||||
\(734\) | 11.2943 | 0.416882 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.73987 | 0.211574 | ||||||||
\(737\) | 8.98831i | 0.331089i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −13.1369 | −0.483250 | −0.241625 | − | 0.970370i | \(-0.577680\pi\) | ||||
−0.241625 | + | 0.970370i | \(0.577680\pi\) | |||||||
\(740\) | 0.543081 | 0.0199641 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5.94789i | 0.218207i | 0.994030 | + | 0.109103i | \(0.0347980\pi\) | ||||
−0.994030 | + | 0.109103i | \(0.965202\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − 2.53891i | − 0.0930185i | ||||||||
\(746\) | 5.56600i | 0.203786i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 8.63706i | 0.315802i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.68990 | 0.171137 | 0.0855685 | − | 0.996332i | \(-0.472729\pi\) | ||||
0.0855685 | + | 0.996332i | \(0.472729\pi\) | |||||||
\(752\) | −2.96561 | −0.108145 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 9.02993i | 0.328851i | ||||||||
\(755\) | 0.256155 | 0.00932244 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −32.9356 | −1.19706 | −0.598532 | − | 0.801099i | \(-0.704249\pi\) | ||||
−0.598532 | + | 0.801099i | \(0.704249\pi\) | |||||||
\(758\) | 5.80720i | 0.210927i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0.590146 | 0.0214069 | ||||||||
\(761\) | −41.4163 | −1.50134 | −0.750669 | − | 0.660678i | \(-0.770269\pi\) | ||||
−0.750669 | + | 0.660678i | \(0.770269\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 20.2251i | 0.731720i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − 7.28335i | − 0.263158i | ||||||||
\(767\) | 20.8022i | 0.751123i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − 19.2896i | − 0.695601i | −0.937569 | − | 0.347801i | \(-0.886929\pi\) | ||||
0.937569 | − | 0.347801i | \(-0.113071\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −3.94557 | −0.142004 | ||||||||
\(773\) | 20.8000 | 0.748125 | 0.374062 | − | 0.927404i | \(-0.377965\pi\) | ||||
0.374062 | + | 0.927404i | \(0.377965\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 5.15847i | − 0.185298i | ||||||||
\(776\) | −12.2755 | −0.440666 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 23.7553 | 0.851669 | ||||||||
\(779\) | − 20.7096i | − 0.741999i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 18.0588 | 0.646193 | ||||||||
\(782\) | 14.0597 | 0.502776 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.12318i | 0.0757795i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 38.5833i | 1.37535i | 0.726020 | + | 0.687674i | \(0.241368\pi\) | ||||
−0.726020 | + | 0.687674i | \(0.758632\pi\) | |||||||
\(788\) | 2.29826i | 0.0818720i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | − 0.564691i | − 0.0200908i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.49955 | −0.195295 | ||||||||
\(794\) | 15.8429 | 0.562242 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − 25.9021i | − 0.918074i | ||||||||
\(797\) | −42.3609 | −1.50050 | −0.750250 | − | 0.661155i | \(-0.770067\pi\) | ||||
−0.750250 | + | 0.661155i | \(0.770067\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7.26424 | −0.256990 | ||||||||
\(800\) | 4.98661i | 0.176303i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −8.33412 | −0.294288 | ||||||||
\(803\) | 26.8262 | 0.946675 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 2.08072i | 0.0732901i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 18.5530i | 0.652691i | ||||||||
\(809\) | 11.0315i | 0.387847i | 0.981017 | + | 0.193923i | \(0.0621213\pi\) | ||||
−0.981017 | + | 0.193923i | \(0.937879\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.99413i | 0.105138i | 0.998617 | + | 0.0525691i | \(0.0167410\pi\) | ||||
−0.998617 | + | 0.0525691i | \(0.983259\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −16.5497 | −0.580068 | ||||||||
\(815\) | 1.15065 | 0.0403054 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 34.1882i | − 1.19609i | ||||||||
\(818\) | −28.1151 | −0.983020 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.469830 | −0.0164072 | ||||||||
\(821\) | 5.01543i | 0.175040i | 0.996163 | + | 0.0875198i | \(0.0278941\pi\) | ||||
−0.996163 | + | 0.0875198i | \(0.972106\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 46.2889 | 1.61353 | 0.806765 | − | 0.590873i | \(-0.201217\pi\) | ||||
0.806765 | + | 0.590873i | \(0.201217\pi\) | |||||||
\(824\) | −9.25440 | −0.322392 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 14.2511i | − 0.495559i | −0.968816 | − | 0.247780i | \(-0.920299\pi\) | ||||
0.968816 | − | 0.247780i | \(-0.0797009\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 43.4959i | − 1.51068i | −0.655336 | − | 0.755338i | \(-0.727473\pi\) | ||||
0.655336 | − | 0.755338i | \(-0.272527\pi\) | |||||||
\(830\) | 2.07747i | 0.0721100i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − 2.01140i | − 0.0697326i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.796670 | 0.0275699 | ||||||||
\(836\) | −17.9840 | −0.621989 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 15.3664i | 0.530825i | ||||||||
\(839\) | 24.1805 | 0.834802 | 0.417401 | − | 0.908722i | \(-0.362941\pi\) | ||||
0.417401 | + | 0.908722i | \(0.362941\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8.84543 | 0.305015 | ||||||||
\(842\) | 2.33930i | 0.0806176i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −2.20067 | −0.0757502 | ||||||||
\(845\) | −1.03609 | −0.0356424 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − 9.17738i | − 0.315152i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 12.2147i | 0.418959i | ||||||||
\(851\) | 26.9403i | 0.923501i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 31.9963i | − 1.09553i | −0.836632 | − | 0.547766i | \(-0.815478\pi\) | ||||
0.836632 | − | 0.547766i | \(-0.184522\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −18.3003 | −0.625492 | ||||||||
\(857\) | −53.7174 | −1.83495 | −0.917476 | − | 0.397790i | \(-0.869777\pi\) | ||||
−0.917476 | + | 0.397790i | \(0.869777\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 17.3109i | 0.590640i | 0.955398 | + | 0.295320i | \(0.0954263\pi\) | ||||
−0.955398 | + | 0.295320i | \(0.904574\pi\) | |||||||
\(860\) | −0.775614 | −0.0264482 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 24.4954 | 0.834318 | ||||||||
\(863\) | − 2.08650i | − 0.0710252i | −0.999369 | − | 0.0355126i | \(-0.988694\pi\) | ||||
0.999369 | − | 0.0355126i | \(-0.0113064\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.88559 | 0.0641121 | ||||||||
\(866\) | 4.66332 | 0.158466 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 17.2083i | 0.583751i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 5.12726i | − 0.173730i | ||||||||
\(872\) | − 14.7842i | − 0.500655i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 29.2750i | 0.990243i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11.9004 | 0.401847 | 0.200924 | − | 0.979607i | \(-0.435606\pi\) | ||||
0.200924 | + | 0.979607i | \(0.435606\pi\) | |||||||
\(878\) | 16.9027 | 0.570439 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0.407995i | 0.0137535i | ||||||||
\(881\) | −31.5992 | −1.06460 | −0.532302 | − | 0.846554i | \(-0.678673\pi\) | ||||
−0.532302 | + | 0.846554i | \(0.678673\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −35.5159 | −1.19521 | −0.597603 | − | 0.801792i | \(-0.703880\pi\) | ||||
−0.597603 | + | 0.801792i | \(0.703880\pi\) | |||||||
\(884\) | − 4.92689i | − 0.165709i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −34.2190 | −1.14961 | ||||||||
\(887\) | −8.49754 | −0.285319 | −0.142660 | − | 0.989772i | \(-0.545565\pi\) | ||||
−0.142660 | + | 0.989772i | \(0.545565\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 1.16025i | 0.0388916i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − 5.12818i | − 0.171704i | ||||||||
\(893\) | − 15.1255i | − 0.506156i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 0.412448i | − 0.0137866i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1.38574 | −0.0462426 | ||||||||
\(899\) | −4.64411 | −0.154890 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 22.4799i | − 0.748914i | ||||||||
\(902\) | 14.3175 | 0.476720 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −11.4294 | −0.380136 | ||||||||
\(905\) | 1.70667i | 0.0567316i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 10.4395 | 0.346639 | 0.173320 | − | 0.984866i | \(-0.444551\pi\) | ||||
0.173320 | + | 0.984866i | \(0.444551\pi\) | |||||||
\(908\) | −18.1149 | −0.601163 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 0.0955475i | − 0.00316563i | −0.999999 | − | 0.00158282i | \(-0.999496\pi\) | ||||
0.999999 | − | 0.00158282i | \(-0.000503826\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 63.3083i | − 2.09520i | ||||||||
\(914\) | − 30.3990i | − 1.00551i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − 6.45493i | − 0.213277i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 14.0845 | 0.464603 | 0.232302 | − | 0.972644i | \(-0.425374\pi\) | ||||
0.232302 | + | 0.972644i | \(0.425374\pi\) | |||||||
\(920\) | 0.664150 | 0.0218964 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − 16.3888i | − 0.539737i | ||||||||
\(923\) | −10.3014 | −0.339074 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −23.4048 | −0.769547 | ||||||||
\(926\) | 7.18677i | 0.236172i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 4.48938 | 0.147371 | ||||||||
\(929\) | 40.3080 | 1.32246 | 0.661232 | − | 0.750182i | \(-0.270034\pi\) | ||||
0.661232 | + | 0.750182i | \(0.270034\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | − 12.0288i | − 0.394018i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 13.7962i | 0.451426i | ||||||||
\(935\) | 0.999380i | 0.0326832i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 33.1386i | − 1.08259i | −0.840833 | − | 0.541295i | \(-0.817934\pi\) | ||||
0.840833 | − | 0.541295i | \(-0.182066\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −0.343146 | −0.0111922 | ||||||||
\(941\) | −2.92082 | −0.0952161 | −0.0476081 | − | 0.998866i | \(-0.515160\pi\) | ||||
−0.0476081 | + | 0.998866i | \(0.515160\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 23.3066i | − 0.758966i | ||||||||
\(944\) | 10.3422 | 0.336609 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 23.6359 | 0.768469 | ||||||||
\(947\) | 33.2988i | 1.08207i | 0.841002 | + | 0.541033i | \(0.181966\pi\) | ||||
−0.841002 | + | 0.541033i | \(0.818034\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −15.3026 | −0.496744 | ||||||||
\(950\) | −25.4332 | −0.825162 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 19.2086i | 0.622228i | 0.950373 | + | 0.311114i | \(0.100702\pi\) | ||||
−0.950373 | + | 0.311114i | \(0.899298\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.34022i | 0.0757276i | ||||||||
\(956\) | − 1.19342i | − 0.0385981i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 14.1443i | 0.456980i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 29.9299 | 0.965480 | ||||||||
\(962\) | 9.44056 | 0.304376 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 11.9940i | 0.386299i | ||||||||
\(965\) | −0.456535 | −0.0146964 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −13.2334 | −0.425556 | −0.212778 | − | 0.977101i | \(-0.568251\pi\) | ||||
−0.212778 | + | 0.977101i | \(0.568251\pi\) | |||||||
\(968\) | − 1.43315i | − 0.0460631i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −1.42038 | −0.0456056 | ||||||||
\(971\) | 14.4446 | 0.463548 | 0.231774 | − | 0.972770i | \(-0.425547\pi\) | ||||
0.231774 | + | 0.972770i | \(0.425547\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 9.92664i | 0.318070i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.73420i | 0.0875195i | ||||||||
\(977\) | − 25.1431i | − 0.804400i | −0.915552 | − | 0.402200i | \(-0.868246\pi\) | ||||
0.915552 | − | 0.402200i | \(-0.131754\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 35.3571i | − 1.13002i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1.46802 | 0.0468465 | ||||||||
\(983\) | 55.0721 | 1.75653 | 0.878263 | − | 0.478178i | \(-0.158702\pi\) | ||||
0.878263 | + | 0.478178i | \(0.158702\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.265927i | 0.00847315i | ||||||||
\(986\) | 10.9967 | 0.350206 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 10.2587 | 0.326373 | ||||||||
\(989\) | − 38.4754i | − 1.22345i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 49.2537 | 1.56459 | 0.782297 | − | 0.622905i | \(-0.214048\pi\) | ||||
0.782297 | + | 0.622905i | \(0.214048\pi\) | |||||||
\(992\) | 1.03446 | 0.0328443 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 2.99708i | − 0.0950139i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 35.6075i | 1.12770i | 0.825877 | + | 0.563850i | \(0.190681\pi\) | ||||
−0.825877 | + | 0.563850i | \(0.809319\pi\) | |||||||
\(998\) | − 8.29707i | − 0.262639i | ||||||||
\(999\) | 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 | 2646.2.d.f.2645.4 | ✓ | 16 | |
3.2 | odd | 2 | inner | 2646.2.d.f.2645.13 | yes | 16 | |
7.6 | odd | 2 | inner | 2646.2.d.f.2645.5 | yes | 16 | |
21.20 | even | 2 | inner | 2646.2.d.f.2645.12 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2646.2.d.f.2645.4 | ✓ | 16 | 1.1 | even | 1 | trivial | |
2646.2.d.f.2645.5 | yes | 16 | 7.6 | odd | 2 | inner | |
2646.2.d.f.2645.12 | yes | 16 | 21.20 | even | 2 | inner | |
2646.2.d.f.2645.13 | yes | 16 | 3.2 | odd | 2 | inner |