Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3420,2,Mod(1369,3420)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3420, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3420.1369");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3420 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3420.f (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: | \(27.3088374913\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} - 2x^{8} + 18x^{7} - 7x^{6} - 48x^{5} - 35x^{4} + 450x^{3} - 250x^{2} - 1250x + 3125 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 1140) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1369.9 | ||
Root | \(1.16684 + 1.90748i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3420.1369 |
Dual form | 3420.2.f.e.1369.10 |
$q$-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 \(\left(\mathbb{Z}/3420\mathbb{Z}\right)^\times\).
\(n\) | \(1711\) | \(1901\) | \(2737\) | \(3061\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(5\) | 1.90748 | − | 1.16684i | 0.853052 | − | 0.521825i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.36950i | 0.517623i | 0.965928 | + | 0.258811i | \(0.0833308\pi\) | ||||
−0.965928 | + | 0.258811i | \(0.916669\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.469639 | 0.141602 | 0.0708008 | − | 0.997490i | \(-0.477445\pi\) | ||||
0.0708008 | + | 0.997490i | \(0.477445\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 1.03583i | − | 0.287287i | −0.989629 | − | 0.143644i | \(-0.954118\pi\) | ||
0.989629 | − | 0.143644i | \(-0.0458819\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.65411i | 1.37132i | 0.727921 | + | 0.685661i | \(0.240487\pi\) | ||||
−0.727921 | + | 0.685661i | \(0.759513\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.30950i | 0.481564i | 0.970579 | + | 0.240782i | \(0.0774038\pi\) | ||||
−0.970579 | + | 0.240782i | \(0.922596\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.27698 | − | 4.45144i | 0.455397 | − | 0.890288i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.21295 | −1.15372 | −0.576858 | − | 0.816845i | \(-0.695721\pi\) | ||||
−0.576858 | + | 0.816845i | \(0.695721\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.98778 | 1.79386 | 0.896929 | − | 0.442174i | \(-0.145793\pi\) | ||||
0.896929 | + | 0.442174i | \(0.145793\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.59798 | + | 2.61230i | 0.270109 | + | 0.441560i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.64245i | 1.42081i | 0.703793 | + | 0.710405i | \(0.251488\pi\) | ||||
−0.703793 | + | 0.710405i | \(0.748512\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.654673 | −0.102243 | −0.0511214 | − | 0.998692i | \(-0.516280\pi\) | ||||
−0.0511214 | + | 0.998692i | \(0.516280\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 8.26043i | − | 1.25970i | −0.776715 | − | 0.629852i | \(-0.783116\pi\) | ||
0.776715 | − | 0.629852i | \(-0.216884\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.39311i | 1.22426i | 0.790757 | + | 0.612131i | \(0.209687\pi\) | ||||
−0.790757 | + | 0.612131i | \(0.790313\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.12447 | 0.732066 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.24878i | 1.27042i | 0.772341 | + | 0.635209i | \(0.219086\pi\) | ||||
−0.772341 | + | 0.635209i | \(0.780914\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.895829 | − | 0.547992i | 0.120794 | − | 0.0738913i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.62993 | 0.732955 | 0.366477 | − | 0.930427i | \(-0.380564\pi\) | ||||
0.366477 | + | 0.930427i | \(0.380564\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.06374 | 1.16049 | 0.580247 | − | 0.814441i | \(-0.302956\pi\) | ||||
0.580247 | + | 0.814441i | \(0.302956\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.20864 | − | 1.97583i | −0.149914 | − | 0.245071i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 5.62993i | − | 0.687806i | −0.939005 | − | 0.343903i | \(-0.888251\pi\) | ||
0.939005 | − | 0.343903i | \(-0.111749\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.3456 | −1.22780 | −0.613900 | − | 0.789384i | \(-0.710400\pi\) | ||||
−0.613900 | + | 0.789384i | \(0.710400\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.89195i | 0.455518i | 0.973718 | + | 0.227759i | \(0.0731399\pi\) | ||||
−0.973718 | + | 0.227759i | \(0.926860\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.643172i | 0.0732962i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.5692 | −1.41415 | −0.707073 | − | 0.707140i | \(-0.749985\pi\) | ||||
−0.707073 | + | 0.707140i | \(0.749985\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.61884i | 0.397220i | 0.980079 | + | 0.198610i | \(0.0636427\pi\) | ||||
−0.980079 | + | 0.198610i | \(0.936357\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.59742 | + | 10.7851i | 0.715591 | + | 1.16981i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 11.8429 | 1.25534 | 0.627671 | − | 0.778478i | \(-0.284008\pi\) | ||||
0.627671 | + | 0.778478i | \(0.284008\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.41857 | 0.148706 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.90748 | − | 1.16684i | 0.195704 | − | 0.119715i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.65483i | 0.574161i | 0.957907 | + | 0.287080i | \(0.0926847\pi\) | ||||
−0.957907 | + | 0.287080i | \(0.907315\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 18.9865 | 1.88923 | 0.944614 | − | 0.328185i | \(-0.106437\pi\) | ||||
0.944614 | + | 0.328185i | \(0.106437\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 15.3082i | − | 1.50836i | −0.656666 | − | 0.754182i | \(-0.728034\pi\) | ||
0.656666 | − | 0.754182i | \(-0.271966\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 9.23656i | − | 0.892932i | −0.894801 | − | 0.446466i | \(-0.852682\pi\) | ||
0.894801 | − | 0.446466i | \(-0.147318\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.2489 | 0.981670 | 0.490835 | − | 0.871253i | \(-0.336692\pi\) | ||||
0.490835 | + | 0.871253i | \(0.336692\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 11.1771i | 1.05146i | 0.850653 | + | 0.525728i | \(0.176207\pi\) | ||||
−0.850653 | + | 0.525728i | \(0.823793\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.69481 | + | 4.40533i | 0.251292 | + | 0.410799i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −7.74331 | −0.709828 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.7794 | −0.979949 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −0.850795 | − | 11.1479i | −0.0760974 | − | 0.997100i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 4.20028i | − | 0.372714i | −0.982482 | − | 0.186357i | \(-0.940332\pi\) | ||
0.982482 | − | 0.186357i | \(-0.0596681\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.87599 | −0.513388 | −0.256694 | − | 0.966493i | \(-0.582633\pi\) | ||||
−0.256694 | + | 0.966493i | \(0.582633\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.36950i | 0.118751i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 10.2355i | − | 0.874481i | −0.899345 | − | 0.437241i | \(-0.855956\pi\) | ||
0.899345 | − | 0.437241i | \(-0.144044\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.56491 | 0.811285 | 0.405642 | − | 0.914032i | \(-0.367048\pi\) | ||||
0.405642 | + | 0.914032i | \(0.367048\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 0.486466i | − | 0.0406803i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −11.8511 | + | 7.24950i | −0.984180 | + | 0.602038i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.26763 | −0.267694 | −0.133847 | − | 0.991002i | \(-0.542733\pi\) | ||||
−0.133847 | + | 0.991002i | \(0.542733\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.57050 | 0.290563 | 0.145281 | − | 0.989390i | \(-0.453591\pi\) | ||||
0.145281 | + | 0.989390i | \(0.453591\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 19.0515 | − | 11.6541i | 1.53026 | − | 0.936080i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 16.2740i | 1.29880i | 0.760445 | + | 0.649402i | \(0.224981\pi\) | ||||
−0.760445 | + | 0.649402i | \(0.775019\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.16286 | −0.249268 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13.0114i | 1.01913i | 0.860432 | + | 0.509565i | \(0.170194\pi\) | ||||
−0.860432 | + | 0.509565i | \(0.829806\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 17.4174i | 1.34780i | 0.738822 | + | 0.673901i | \(0.235383\pi\) | ||||
−0.738822 | + | 0.673901i | \(0.764617\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.9271 | 0.917466 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 3.93943i | − | 0.299509i | −0.988723 | − | 0.149755i | \(-0.952152\pi\) | ||
0.988723 | − | 0.149755i | \(-0.0478484\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.09626 | + | 3.11833i | 0.460834 | + | 0.235724i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −18.7379 | −1.40053 | −0.700267 | − | 0.713881i | \(-0.746936\pi\) | ||||
−0.700267 | + | 0.713881i | \(0.746936\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 19.1384 | 1.42255 | 0.711274 | − | 0.702915i | \(-0.248119\pi\) | ||||
0.711274 | + | 0.702915i | \(0.248119\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 10.0843 | + | 16.4853i | 0.741415 | + | 1.21203i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.65539i | 0.194181i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.23195 | −0.0891408 | −0.0445704 | − | 0.999006i | \(-0.514192\pi\) | ||||
−0.0445704 | + | 0.999006i | \(0.514192\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.34404i | 0.312691i | 0.987702 | + | 0.156346i | \(0.0499713\pi\) | ||||
−0.987702 | + | 0.156346i | \(0.950029\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 22.8304i | − | 1.62660i | −0.581847 | − | 0.813298i | \(-0.697670\pi\) | ||
0.581847 | − | 0.813298i | \(-0.302330\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.05152 | 0.358093 | 0.179047 | − | 0.983841i | \(-0.442699\pi\) | ||||
0.179047 | + | 0.983841i | \(0.442699\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 8.50864i | − | 0.597190i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.24878 | + | 0.763896i | −0.0872184 | + | 0.0533528i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.469639 | 0.0324856 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.90390 | −0.681813 | −0.340906 | − | 0.940097i | \(-0.610734\pi\) | ||||
−0.340906 | + | 0.940097i | \(0.610734\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −9.63857 | − | 15.7566i | −0.657345 | − | 1.07459i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 13.6783i | 0.928542i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.85669 | 0.393963 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 16.1189i | − | 1.07940i | −0.841858 | − | 0.539700i | \(-0.818538\pi\) | ||
0.841858 | − | 0.539700i | \(-0.181462\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.55812i | 0.169789i | 0.996390 | + | 0.0848943i | \(0.0270553\pi\) | ||||
−0.996390 | + | 0.0848943i | \(0.972945\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −16.3268 | −1.07890 | −0.539452 | − | 0.842016i | \(-0.681369\pi\) | ||||
−0.539452 | + | 0.842016i | \(0.681369\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.71468i | 0.636430i | 0.948019 | + | 0.318215i | \(0.103083\pi\) | ||||
−0.948019 | + | 0.318215i | \(0.896917\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.79339 | + | 16.0097i | 0.638850 | + | 1.04436i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5.53036 | −0.357729 | −0.178865 | − | 0.983874i | \(-0.557242\pi\) | ||||
−0.178865 | + | 0.983874i | \(0.557242\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.60806 | −0.232416 | −0.116208 | − | 0.993225i | \(-0.537074\pi\) | ||||
−0.116208 | + | 0.993225i | \(0.537074\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 9.77483 | − | 5.97941i | 0.624491 | − | 0.382011i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 1.03583i | − | 0.0659082i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 15.0084 | 0.947320 | 0.473660 | − | 0.880708i | \(-0.342933\pi\) | ||||
0.473660 | + | 0.880708i | \(0.342933\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.08463i | 0.0681902i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.91612i | 0.119525i | 0.998213 | + | 0.0597623i | \(0.0190343\pi\) | ||||
−0.998213 | + | 0.0597623i | \(0.980966\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −11.8359 | −0.735444 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 12.3448i | 0.761211i | 0.924738 | + | 0.380605i | \(0.124284\pi\) | ||||
−0.924738 | + | 0.380605i | \(0.875716\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.7918 | + | 17.6419i | 0.662936 | + | 1.08373i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0.701891 | 0.0427951 | 0.0213975 | − | 0.999771i | \(-0.493188\pi\) | ||||
0.0213975 | + | 0.999771i | \(0.493188\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 26.2159 | 1.59250 | 0.796251 | − | 0.604967i | \(-0.206814\pi\) | ||||
0.796251 | + | 0.604967i | \(0.206814\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.06936 | − | 2.09057i | 0.0644849 | − | 0.126066i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 6.11410i | − | 0.367360i | −0.982986 | − | 0.183680i | \(-0.941199\pi\) | ||
0.982986 | − | 0.183680i | \(-0.0588011\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 22.4838 | 1.34127 | 0.670634 | − | 0.741788i | \(-0.266022\pi\) | ||||
0.670634 | + | 0.741788i | \(0.266022\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 28.4861i | − | 1.69332i | −0.532134 | − | 0.846660i | \(-0.678610\pi\) | ||
0.532134 | − | 0.846660i | \(-0.321390\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 0.896575i | − | 0.0529232i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.9689 | −0.880525 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 8.55699i | − | 0.499905i | −0.968258 | − | 0.249952i | \(-0.919585\pi\) | ||
0.968258 | − | 0.249952i | \(-0.0804150\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10.7390 | − | 6.56921i | 0.625249 | − | 0.382474i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.39224 | 0.138347 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11.3127 | 0.652052 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 17.2889 | − | 10.5759i | 0.989962 | − | 0.605575i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.85352i | 0.448224i | 0.974563 | + | 0.224112i | \(0.0719481\pi\) | ||||
−0.974563 | + | 0.224112i | \(0.928052\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 31.8265 | 1.80472 | 0.902358 | − | 0.430988i | \(-0.141835\pi\) | ||||
0.902358 | + | 0.430988i | \(0.141835\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.1991i | 0.576490i | 0.957557 | + | 0.288245i | \(0.0930717\pi\) | ||||
−0.957557 | + | 0.288245i | \(0.906928\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 17.9130i | − | 1.00609i | −0.864260 | − | 0.503046i | \(-0.832213\pi\) | ||
0.864260 | − | 0.503046i | \(-0.167787\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.91785 | −0.163368 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.65411i | 0.314603i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.61093 | − | 2.35857i | −0.255768 | − | 0.130830i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −11.4944 | −0.633706 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −17.1674 | −0.943604 | −0.471802 | − | 0.881704i | \(-0.656396\pi\) | ||||
−0.471802 | + | 0.881704i | \(0.656396\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −6.56921 | − | 10.7390i | −0.358914 | − | 0.586734i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.4010i | 0.893420i | 0.894679 | + | 0.446710i | \(0.147404\pi\) | ||||
−0.894679 | + | 0.446710i | \(0.852596\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.69065 | 0.254013 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.6045i | 0.896557i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 18.4648i | − | 0.991241i | −0.868539 | − | 0.495620i | \(-0.834941\pi\) | ||
0.868539 | − | 0.495620i | \(-0.165059\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.6561 | 0.784524 | 0.392262 | − | 0.919854i | \(-0.371693\pi\) | ||||
0.392262 | + | 0.919854i | \(0.371693\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 21.7986i | 1.16022i | 0.814537 | + | 0.580111i | \(0.196991\pi\) | ||||
−0.814537 | + | 0.580111i | \(0.803009\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −19.7341 | + | 12.0717i | −1.04738 | + | 0.640697i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −16.1494 | −0.852331 | −0.426165 | − | 0.904645i | \(-0.640136\pi\) | ||||
−0.426165 | + | 0.904645i | \(0.640136\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.54127 | + | 7.42383i | 0.237701 | + | 0.388581i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 7.33454i | − | 0.382860i | −0.981506 | − | 0.191430i | \(-0.938687\pi\) | ||
0.981506 | − | 0.191430i | \(-0.0613125\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −12.6662 | −0.657597 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 28.2727i | 1.46390i | 0.681356 | + | 0.731952i | \(0.261391\pi\) | ||||
−0.681356 | + | 0.731952i | \(0.738609\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.43555i | 0.331448i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −24.9357 | −1.28086 | −0.640430 | − | 0.768017i | \(-0.721244\pi\) | ||||
−0.640430 | + | 0.768017i | \(0.721244\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 33.0435i | 1.68844i | 0.535995 | + | 0.844221i | \(0.319936\pi\) | ||||
−0.535995 | + | 0.844221i | \(0.680064\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.750476 | + | 1.22684i | 0.0382478 | + | 0.0625255i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 10.0087 | 0.507460 | 0.253730 | − | 0.967275i | \(-0.418343\pi\) | ||||
0.253730 | + | 0.967275i | \(0.418343\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −13.0582 | −0.660379 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −23.9756 | + | 14.6662i | −1.20634 | + | 0.737937i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 20.8784i | − | 1.04786i | −0.851762 | − | 0.523930i | \(-0.824465\pi\) | ||
0.851762 | − | 0.523930i | \(-0.175535\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 14.1327 | 0.705752 | 0.352876 | − | 0.935670i | \(-0.385204\pi\) | ||||
0.352876 | + | 0.935670i | \(0.385204\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 10.3456i | − | 0.515352i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.05884i | 0.201189i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.23452 | −0.258830 | −0.129415 | − | 0.991590i | \(-0.541310\pi\) | ||||
−0.129415 | + | 0.991590i | \(0.541310\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7.71020i | 0.379394i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.22260 | + | 6.90288i | 0.207279 | + | 0.338849i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7.46737 | 0.364805 | 0.182402 | − | 0.983224i | \(-0.441613\pi\) | ||||
0.182402 | + | 0.983224i | \(0.441613\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17.9502 | −0.874840 | −0.437420 | − | 0.899257i | \(-0.644108\pi\) | ||||
−0.437420 | + | 0.899257i | \(0.644108\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 25.1689 | + | 12.8743i | 1.22087 | + | 0.624496i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12.4128i | 0.600698i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7.79859 | −0.375645 | −0.187823 | − | 0.982203i | \(-0.560143\pi\) | ||||
−0.187823 | + | 0.982203i | \(0.560143\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 27.7020i | − | 1.33128i | −0.746275 | − | 0.665638i | \(-0.768160\pi\) | ||
0.746275 | − | 0.665638i | \(-0.231840\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.30950i | 0.110478i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −13.2513 | −0.632448 | −0.316224 | − | 0.948685i | \(-0.602415\pi\) | ||||
−0.316224 | + | 0.948685i | \(0.602415\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 21.0107i | 0.998247i | 0.866531 | + | 0.499124i | \(0.166345\pi\) | ||||
−0.866531 | + | 0.499124i | \(0.833655\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 22.5901 | − | 13.8187i | 1.07087 | − | 0.655070i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −22.1295 | −1.04436 | −0.522178 | − | 0.852836i | \(-0.674880\pi\) | ||||
−0.522178 | + | 0.852836i | \(0.674880\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.307460 | −0.0144777 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.70590 | − | 1.65524i | 0.126854 | − | 0.0775988i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.05857i | 0.283408i | 0.989909 | + | 0.141704i | \(0.0452581\pi\) | ||||
−0.989909 | + | 0.141704i | \(0.954742\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −25.6858 | −1.19631 | −0.598154 | − | 0.801381i | \(-0.704099\pi\) | ||||
−0.598154 | + | 0.801381i | \(0.704099\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.2858i | 0.756864i | 0.925629 | + | 0.378432i | \(0.123537\pi\) | ||||
−0.925629 | + | 0.378432i | \(0.876463\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 22.1537i | − | 1.02515i | −0.858642 | − | 0.512576i | \(-0.828691\pi\) | ||
0.858642 | − | 0.512576i | \(-0.171309\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.71020 | 0.356024 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 3.87942i | − | 0.178376i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.27698 | − | 4.45144i | 0.104475 | − | 0.204246i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −41.0475 | −1.87551 | −0.937755 | − | 0.347299i | \(-0.887099\pi\) | ||||
−0.937755 | + | 0.347299i | \(0.887099\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.95210 | 0.408181 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6.59826 | + | 10.7865i | 0.299611 | + | 0.489789i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 8.51686i | − | 0.385936i | −0.981205 | − | 0.192968i | \(-0.938189\pi\) | ||
0.981205 | − | 0.192968i | \(-0.0618113\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 18.8706 | 0.851616 | 0.425808 | − | 0.904814i | \(-0.359990\pi\) | ||||
0.425808 | + | 0.904814i | \(0.359990\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 35.1287i | − | 1.58212i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 14.1684i | − | 0.635538i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.426482 | −0.0190920 | −0.00954598 | − | 0.999954i | \(-0.503039\pi\) | ||||
−0.00954598 | + | 0.999954i | \(0.503039\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0.950368i | 0.0423748i | 0.999776 | + | 0.0211874i | \(0.00674466\pi\) | ||||
−0.999776 | + | 0.0211874i | \(0.993255\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 36.2164 | − | 22.1541i | 1.61161 | − | 0.985846i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −7.69412 | −0.341036 | −0.170518 | − | 0.985355i | \(-0.554544\pi\) | ||||
−0.170518 | + | 0.985355i | \(0.554544\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.33003 | −0.235787 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −17.8622 | − | 29.2002i | −0.787102 | − | 1.28671i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.94173i | 0.173357i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −29.2578 | −1.28181 | −0.640905 | − | 0.767620i | \(-0.721441\pi\) | ||||
−0.640905 | + | 0.767620i | \(0.721441\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 21.3885i | − | 0.935253i | −0.883926 | − | 0.467627i | \(-0.845109\pi\) | ||
0.883926 | − | 0.467627i | \(-0.154891\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 56.4720i | 2.45996i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 17.6662 | 0.768096 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.678129i | 0.0293730i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −10.7776 | − | 17.6186i | −0.465954 | − | 0.761718i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.40665 | 0.103662 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13.7453 | −0.590959 | −0.295479 | − | 0.955349i | \(-0.595479\pi\) | ||||
−0.295479 | + | 0.955349i | \(0.595479\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 19.5497 | − | 11.9588i | 0.837416 | − | 0.512260i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 11.2613i | − | 0.481499i | −0.970587 | − | 0.240749i | \(-0.922607\pi\) | ||
0.970587 | − | 0.240749i | \(-0.0773932\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.21295 | −0.264681 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 17.2136i | − | 0.731995i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 15.1412i | 0.641552i | 0.947155 | + | 0.320776i | \(0.103944\pi\) | ||||
−0.947155 | + | 0.320776i | \(0.896056\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.55639 | −0.361897 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 32.2672i | − | 1.35990i | −0.733258 | − | 0.679950i | \(-0.762001\pi\) | ||
0.733258 | − | 0.679950i | \(-0.237999\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 13.0419 | + | 21.3202i | 0.548676 | + | 0.896946i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −19.5476 | −0.819480 | −0.409740 | − | 0.912202i | \(-0.634381\pi\) | ||||
−0.409740 | + | 0.912202i | \(0.634381\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.19023 | 0.175356 | 0.0876778 | − | 0.996149i | \(-0.472055\pi\) | ||||
0.0876778 | + | 0.996149i | \(0.472055\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 10.2806 | + | 5.25869i | 0.428731 | + | 0.219303i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 26.1553i | 1.08886i | 0.838807 | + | 0.544429i | \(0.183254\pi\) | ||||
−0.838807 | + | 0.544429i | \(0.816746\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.95601 | −0.205610 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.34359i | 0.179893i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 25.3145i | 1.04484i | 0.852688 | + | 0.522421i | \(0.174971\pi\) | ||||
−0.852688 | + | 0.522421i | \(0.825029\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.98778 | 0.411539 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 38.2001i | − | 1.56869i | −0.620326 | − | 0.784344i | \(-0.713000\pi\) | ||
0.620326 | − | 0.784344i | \(-0.287000\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −14.7702 | + | 9.03518i | −0.605521 | + | 0.370406i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −9.23255 | −0.377232 | −0.188616 | − | 0.982051i | \(-0.560400\pi\) | ||||
−0.188616 | + | 0.982051i | \(0.560400\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −40.1997 | −1.63978 | −0.819891 | − | 0.572520i | \(-0.805966\pi\) | ||||
−0.819891 | + | 0.572520i | \(0.805966\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −20.5616 | + | 12.5778i | −0.835948 | + | 0.511362i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 46.1042i | − | 1.87131i | −0.352915 | − | 0.935655i | \(-0.614809\pi\) | ||
0.352915 | − | 0.935655i | \(-0.385191\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.69382 | 0.351714 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 26.4347i | − | 1.06769i | −0.845583 | − | 0.533843i | \(-0.820747\pi\) | ||
0.845583 | − | 0.533843i | \(-0.179253\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 15.8944i | − | 0.639885i | −0.947437 | − | 0.319943i | \(-0.896336\pi\) | ||
0.947437 | − | 0.319943i | \(-0.103664\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −15.7102 | −0.631446 | −0.315723 | − | 0.948851i | \(-0.602247\pi\) | ||||
−0.315723 | + | 0.948851i | \(0.602247\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 16.2188i | 0.649794i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −14.6307 | − | 20.2717i | −0.585227 | − | 0.810869i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −48.8654 | −1.94839 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −15.9822 | −0.636241 | −0.318120 | − | 0.948050i | \(-0.603052\pi\) | ||||
−0.318120 | + | 0.948050i | \(0.603052\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4.90103 | − | 8.01196i | −0.194492 | − | 0.317945i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 5.30807i | − | 0.210313i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12.8015 | −0.505627 | −0.252814 | − | 0.967515i | \(-0.581356\pi\) | ||||
−0.252814 | + | 0.967515i | \(0.581356\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11.1413i | 0.439370i | 0.975571 | + | 0.219685i | \(0.0705030\pi\) | ||||
−0.975571 | + | 0.219685i | \(0.929497\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 32.1287i | − | 1.26311i | −0.775332 | − | 0.631554i | \(-0.782417\pi\) | ||
0.775332 | − | 0.631554i | \(-0.217583\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.64404 | 0.103788 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 26.2685i | − | 1.02797i | −0.857800 | − | 0.513983i | \(-0.828169\pi\) | ||
0.857800 | − | 0.513983i | \(-0.171831\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −11.2084 | + | 6.85632i | −0.437946 | + | 0.267899i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5.37783 | −0.209491 | −0.104745 | − | 0.994499i | \(-0.533403\pi\) | ||||
−0.104745 | + | 0.994499i | \(0.533403\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 42.3710 | 1.64804 | 0.824020 | − | 0.566561i | \(-0.191726\pi\) | ||||
0.824020 | + | 0.566561i | \(0.191726\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.59798 | + | 2.61230i | 0.0619672 | + | 0.101301i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 14.3488i | − | 0.555588i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.25669 | 0.164328 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 46.4252i | − | 1.78956i | −0.446507 | − | 0.894780i | \(-0.647332\pi\) | ||
0.446507 | − | 0.894780i | \(-0.352668\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 37.9124i | − | 1.45709i | −0.684996 | − | 0.728546i | \(-0.740196\pi\) | ||
0.684996 | − | 0.728546i | \(-0.259804\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.74429 | −0.297199 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 17.0932i | − | 0.654055i | −0.945015 | − | 0.327027i | \(-0.893953\pi\) | ||
0.945015 | − | 0.327027i | \(-0.106047\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −11.9432 | − | 19.5241i | −0.456326 | − | 0.745978i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 9.58015 | 0.364975 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.07279 | 0.345145 | 0.172573 | − | 0.984997i | \(-0.444792\pi\) | ||||
0.172573 | + | 0.984997i | \(0.444792\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 18.2449 | − | 11.1607i | 0.692068 | − | 0.423349i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 3.70159i | − | 0.140208i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −29.9511 | −1.13124 | −0.565619 | − | 0.824667i | \(-0.691363\pi\) | ||||
−0.565619 | + | 0.824667i | \(0.691363\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.64245i | 0.325956i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 26.0020i | 0.977907i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −26.6347 | −1.00029 | −0.500143 | − | 0.865943i | \(-0.666719\pi\) | ||||
−0.500143 | + | 0.865943i | \(0.666719\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 23.0668i | 0.863857i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.567626 | − | 0.927925i | −0.0212280 | − | 0.0347024i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −10.5194 | −0.392308 | −0.196154 | − | 0.980573i | \(-0.562845\pi\) | ||||
−0.196154 | + | 0.980573i | \(0.562845\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 20.9646 | 0.780763 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −14.1468 | + | 27.6566i | −0.525399 | + | 1.02714i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 24.0343i | − | 0.891382i | −0.895187 | − | 0.445691i | \(-0.852958\pi\) | ||
0.895187 | − | 0.445691i | \(-0.147042\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 46.7054 | 1.72746 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 17.5589i | 0.648552i | 0.945963 | + | 0.324276i | \(0.105121\pi\) | ||||
−0.945963 | + | 0.324276i | \(0.894879\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 2.64404i | − | 0.0973944i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −30.7753 | −1.13209 | −0.566044 | − | 0.824375i | \(-0.691527\pi\) | ||||
−0.566044 | + | 0.824375i | \(0.691527\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 30.6409i | − | 1.12410i | −0.827102 | − | 0.562052i | \(-0.810012\pi\) | ||
0.827102 | − | 0.562052i | \(-0.189988\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.23294 | + | 3.81279i | −0.228357 | + | 0.139690i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 12.6495 | 0.462202 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.83299 | −0.212849 | −0.106424 | − | 0.994321i | \(-0.533940\pi\) | ||||
−0.106424 | + | 0.994321i | \(0.533940\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 6.81066 | − | 4.16618i | 0.247865 | − | 0.151623i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 46.8068i | 1.70122i | 0.525796 | + | 0.850611i | \(0.323768\pi\) | ||||
−0.525796 | + | 0.850611i | \(0.676232\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.40317 | −0.0871150 | −0.0435575 | − | 0.999051i | \(-0.513869\pi\) | ||||
−0.0435575 | + | 0.999051i | \(0.513869\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 14.0359i | 0.508135i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 5.83165i | − | 0.210569i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −52.3618 | −1.88821 | −0.944107 | − | 0.329639i | \(-0.893073\pi\) | ||||
−0.944107 | + | 0.329639i | \(0.893073\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 0.420892i | − | 0.0151384i | −0.999971 | − | 0.00756922i | \(-0.997591\pi\) | ||
0.999971 | − | 0.00756922i | \(-0.00240938\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 22.7420 | − | 44.4600i | 0.816918 | − | 1.59705i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.654673 | −0.0234561 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.85871 | −0.173858 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 18.9891 | + | 31.0423i | 0.677749 | + | 1.10795i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 49.5598i | − | 1.76662i | −0.468794 | − | 0.883308i | \(-0.655311\pi\) | ||
0.468794 | − | 0.883308i | \(-0.344689\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −15.3071 | −0.544257 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 9.38848i | − | 0.333395i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 39.1979i | 1.38846i | 0.719753 | + | 0.694230i | \(0.244255\pi\) | ||||
−0.719753 | + | 0.694230i | \(0.755745\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −47.4556 | −1.67886 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.82781i | 0.0645021i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.03311 | + | 3.69054i | −0.212639 | + | 0.130075i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −54.1920 | −1.90529 | −0.952644 | − | 0.304087i | \(-0.901649\pi\) | ||||
−0.952644 | + | 0.304087i | \(0.901649\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.44752 | −0.0508294 | −0.0254147 | − | 0.999677i | \(-0.508091\pi\) | ||||
−0.0254147 | + | 0.999677i | \(0.508091\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 15.1822 | + | 24.8190i | 0.531808 | + | 0.869372i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 8.26043i | − | 0.288996i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 51.6786 | 1.80360 | 0.901798 | − | 0.432158i | \(-0.142248\pi\) | ||||
0.901798 | + | 0.432158i | \(0.142248\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 19.4492i | − | 0.677958i | −0.940794 | − | 0.338979i | \(-0.889918\pi\) | ||
0.940794 | − | 0.338979i | \(-0.110082\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 19.5628i | − | 0.680265i | −0.940378 | − | 0.340132i | \(-0.889528\pi\) | ||
0.940378 | − | 0.340132i | \(-0.110472\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7.55828 | 0.262510 | 0.131255 | − | 0.991349i | \(-0.458099\pi\) | ||||
0.131255 | + | 0.991349i | \(0.458099\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 28.9743i | 1.00390i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 20.3233 | + | 33.2235i | 0.703317 | + | 1.14975i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −43.3540 | −1.49675 | −0.748373 | − | 0.663278i | \(-0.769165\pi\) | ||||
−0.748373 | + | 0.663278i | \(0.769165\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.60073 | 0.331060 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 22.7507 | − | 13.9169i | 0.782647 | − | 0.478757i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 14.7625i | − | 0.507244i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −19.9597 | −0.684211 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 20.8731i | 0.714680i | 0.933974 | + | 0.357340i | \(0.116316\pi\) | ||||
−0.933974 | + | 0.357340i | \(0.883684\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 38.1539i | 1.30331i | 0.758515 | + | 0.651656i | \(0.225925\pi\) | ||||
−0.758515 | + | 0.651656i | \(0.774075\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.36607 | 0.114849 | 0.0574244 | − | 0.998350i | \(-0.481711\pi\) | ||||
0.0574244 | + | 0.998350i | \(0.481711\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 37.7606i | − | 1.28539i | −0.766124 | − | 0.642693i | \(-0.777817\pi\) | ||
0.766124 | − | 0.642693i | \(-0.222183\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.59667 | − | 7.51440i | −0.156292 | − | 0.255497i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5.90300 | −0.200245 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.83165 | −0.197598 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 15.2671 | − | 1.16517i | 0.516122 | − | 0.0393898i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 10.1910i | − | 0.344125i | −0.985086 | − | 0.172063i | \(-0.944957\pi\) | ||
0.985086 | − | 0.172063i | \(-0.0550431\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −32.8786 | −1.10771 | −0.553853 | − | 0.832614i | \(-0.686843\pi\) | ||||
−0.553853 | + | 0.832614i | \(0.686843\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 53.1963i | 1.79020i | 0.445867 | + | 0.895099i | \(0.352896\pi\) | ||||
−0.445867 | + | 0.895099i | \(0.647104\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 22.2768i | − | 0.747983i | −0.927432 | − | 0.373992i | \(-0.877989\pi\) | ||
0.927432 | − | 0.373992i | \(-0.122011\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.75228 | 0.192925 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 8.39311i | 0.280865i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −35.7422 | + | 21.8640i | −1.19473 | + | 0.730834i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −62.0536 | −2.06960 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −52.2936 | −1.74215 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 36.5062 | − | 22.3314i | 1.21351 | − | 0.742321i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 25.4129i | − | 0.843822i | −0.906637 | − | 0.421911i | \(-0.861359\pi\) | ||
0.906637 | − | 0.421911i | \(-0.138641\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 15.4450 | 0.511714 | 0.255857 | − | 0.966715i | \(-0.417642\pi\) | ||||
0.255857 | + | 0.966715i | \(0.417642\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.69955i | 0.0562469i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 8.04718i | − | 0.265741i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −15.8354 | −0.522362 | −0.261181 | − | 0.965290i | \(-0.584112\pi\) | ||||
−0.261181 | + | 0.965290i | \(0.584112\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 10.7163i | 0.352731i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 38.4714 | + | 19.6787i | 1.26493 | + | 0.647033i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −33.1079 | −1.08624 | −0.543118 | − | 0.839656i | \(-0.682756\pi\) | ||||
−0.543118 | + | 0.839656i | \(0.682756\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.12447 | 0.167948 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3.09841 | + | 5.06511i | 0.101329 | + | 0.165647i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 8.90605i | − | 0.290948i | −0.989362 | − | 0.145474i | \(-0.953529\pi\) | ||
0.989362 | − | 0.145474i | \(-0.0464707\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 30.0334 | 0.979061 | 0.489531 | − | 0.871986i | \(-0.337168\pi\) | ||||
0.489531 | + | 0.871986i | \(0.337168\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 1.51197i | − | 0.0492364i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 47.2376i | − | 1.53502i | −0.641040 | − | 0.767508i | \(-0.721497\pi\) | ||
0.641040 | − | 0.767508i | \(-0.278503\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.03139 | 0.130865 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 24.0163i | − | 0.777964i | −0.921245 | − | 0.388982i | \(-0.872827\pi\) | ||
0.921245 | − | 0.388982i | \(-0.127173\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.34993 | + | 1.43749i | −0.0760418 | + | 0.0465159i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 14.0176 | 0.452651 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 68.7558 | 2.21793 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5.06879 | + | 8.28619i | 0.163170 | + | 0.266742i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 22.7242i | − | 0.730760i | −0.930859 | − | 0.365380i | \(-0.880939\pi\) | ||
0.930859 | − | 0.365380i | \(-0.119061\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 12.8708 | 0.413043 | 0.206522 | − | 0.978442i | \(-0.433786\pi\) | ||||
0.206522 | + | 0.978442i | \(0.433786\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 13.0992i | 0.419940i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 48.7912i | − | 1.56097i | −0.625175 | − | 0.780485i | \(-0.714972\pi\) | ||
0.625175 | − | 0.780485i | \(-0.285028\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.56188 | 0.177759 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 4.87123i | − | 0.155368i | −0.996978 | − | 0.0776840i | \(-0.975247\pi\) | ||
0.996978 | − | 0.0776840i | \(-0.0247525\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −26.6393 | − | 43.5485i | −0.848799 | − | 1.38757i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 19.0775 | 0.606628 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −42.8104 | −1.35992 | −0.679959 | − | 0.733250i | \(-0.738003\pi\) | ||||
−0.679959 | + | 0.733250i | \(0.738003\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 9.63570 | − | 5.89430i | 0.305472 | − | 0.186862i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 38.0563i | 1.20526i | 0.798022 | + | 0.602628i | \(0.205880\pi\) | ||||
−0.798022 | + | 0.602628i | \(0.794120\pi\) | |||||||
\(998\) | 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 | 3420.2.f.e.1369.9 | 10 | ||
3.2 | odd | 2 | 1140.2.f.b.229.1 | ✓ | 10 | ||
5.4 | even | 2 | inner | 3420.2.f.e.1369.10 | 10 | ||
15.2 | even | 4 | 5700.2.a.bc.1.2 | 5 | |||
15.8 | even | 4 | 5700.2.a.bd.1.4 | 5 | |||
15.14 | odd | 2 | 1140.2.f.b.229.6 | yes | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1140.2.f.b.229.1 | ✓ | 10 | 3.2 | odd | 2 | ||
1140.2.f.b.229.6 | yes | 10 | 15.14 | odd | 2 | ||
3420.2.f.e.1369.9 | 10 | 1.1 | even | 1 | trivial | ||
3420.2.f.e.1369.10 | 10 | 5.4 | even | 2 | inner | ||
5700.2.a.bc.1.2 | 5 | 15.2 | even | 4 | |||
5700.2.a.bd.1.4 | 5 | 15.8 | even | 4 |