Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1850,2,Mod(149,1850)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1850, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1850.149");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1850 = 2 \cdot 5^{2} \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1850.b (of order \(2\), degree \(1\), not 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: | \(14.7723243739\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 149.1 | ||
Root | \(-1.22474 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1850.149 |
Dual form | 1850.2.b.k.149.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1850\mathbb{Z}\right)^\times\).
\(n\) | \(1001\) | \(1777\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | − 1.44949i | − 0.836863i | −0.908248 | − | 0.418432i | \(-0.862580\pi\) | ||||
0.908248 | − | 0.418432i | \(-0.137420\pi\) | |||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.44949 | −0.591752 | ||||||||
\(7\) | − 2.44949i | − 0.925820i | −0.886405 | − | 0.462910i | \(-0.846805\pi\) | ||||
0.886405 | − | 0.462910i | \(-0.153195\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0.898979 | 0.299660 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.44949 | 1.04006 | 0.520030 | − | 0.854148i | \(-0.325921\pi\) | ||||
0.520030 | + | 0.854148i | \(0.325921\pi\) | |||||||
\(12\) | 1.44949i | 0.418432i | ||||||||
\(13\) | − 0.449490i | − 0.124666i | −0.998055 | − | 0.0623330i | \(-0.980146\pi\) | ||||
0.998055 | − | 0.0623330i | \(-0.0198541\pi\) | |||||||
\(14\) | −2.44949 | −0.654654 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − 3.44949i | − 0.836624i | −0.908303 | − | 0.418312i | \(-0.862622\pi\) | ||||
0.908303 | − | 0.418312i | \(-0.137378\pi\) | |||||||
\(18\) | − 0.898979i | − 0.211891i | ||||||||
\(19\) | 5.00000 | 1.14708 | 0.573539 | − | 0.819178i | \(-0.305570\pi\) | ||||
0.573539 | + | 0.819178i | \(0.305570\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.55051 | −0.774785 | ||||||||
\(22\) | − 3.44949i | − 0.735434i | ||||||||
\(23\) | 2.00000i | 0.417029i | 0.978019 | + | 0.208514i | \(0.0668628\pi\) | ||||
−0.978019 | + | 0.208514i | \(0.933137\pi\) | |||||||
\(24\) | 1.44949 | 0.295876 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.449490 | −0.0881522 | ||||||||
\(27\) | − 5.65153i | − 1.08764i | ||||||||
\(28\) | 2.44949i | 0.462910i | ||||||||
\(29\) | 0.898979 | 0.166936 | 0.0834681 | − | 0.996510i | \(-0.473400\pi\) | ||||
0.0834681 | + | 0.996510i | \(0.473400\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.44949 | 0.799152 | 0.399576 | − | 0.916700i | \(-0.369157\pi\) | ||||
0.399576 | + | 0.916700i | \(0.369157\pi\) | |||||||
\(32\) | − 1.00000i | − 0.176777i | ||||||||
\(33\) | − 5.00000i | − 0.870388i | ||||||||
\(34\) | −3.44949 | −0.591583 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.898979 | −0.149830 | ||||||||
\(37\) | 1.00000i | 0.164399i | ||||||||
\(38\) | − 5.00000i | − 0.811107i | ||||||||
\(39\) | −0.651531 | −0.104328 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.00000 | 0.156174 | 0.0780869 | − | 0.996947i | \(-0.475119\pi\) | ||||
0.0780869 | + | 0.996947i | \(0.475119\pi\) | |||||||
\(42\) | 3.55051i | 0.547856i | ||||||||
\(43\) | − 1.10102i | − 0.167904i | −0.996470 | − | 0.0839520i | \(-0.973246\pi\) | ||||
0.996470 | − | 0.0839520i | \(-0.0267543\pi\) | |||||||
\(44\) | −3.44949 | −0.520030 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.00000 | 0.294884 | ||||||||
\(47\) | − 9.79796i | − 1.42918i | −0.699544 | − | 0.714590i | \(-0.746613\pi\) | ||||
0.699544 | − | 0.714590i | \(-0.253387\pi\) | |||||||
\(48\) | − 1.44949i | − 0.209216i | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.00000 | −0.700140 | ||||||||
\(52\) | 0.449490i | 0.0623330i | ||||||||
\(53\) | 6.00000i | 0.824163i | 0.911147 | + | 0.412082i | \(0.135198\pi\) | ||||
−0.911147 | + | 0.412082i | \(0.864802\pi\) | |||||||
\(54\) | −5.65153 | −0.769076 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.44949 | 0.327327 | ||||||||
\(57\) | − 7.24745i | − 0.959948i | ||||||||
\(58\) | − 0.898979i | − 0.118042i | ||||||||
\(59\) | 2.00000 | 0.260378 | 0.130189 | − | 0.991489i | \(-0.458442\pi\) | ||||
0.130189 | + | 0.991489i | \(0.458442\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.44949 | −0.825773 | −0.412886 | − | 0.910783i | \(-0.635479\pi\) | ||||
−0.412886 | + | 0.910783i | \(0.635479\pi\) | |||||||
\(62\) | − 4.44949i | − 0.565086i | ||||||||
\(63\) | − 2.20204i | − 0.277431i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −5.00000 | −0.615457 | ||||||||
\(67\) | − 4.55051i | − 0.555933i | −0.960591 | − | 0.277967i | \(-0.910340\pi\) | ||||
0.960591 | − | 0.277967i | \(-0.0896605\pi\) | |||||||
\(68\) | 3.44949i | 0.418312i | ||||||||
\(69\) | 2.89898 | 0.348996 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.55051 | −0.896081 | −0.448040 | − | 0.894013i | \(-0.647878\pi\) | ||||
−0.448040 | + | 0.894013i | \(0.647878\pi\) | |||||||
\(72\) | 0.898979i | 0.105946i | ||||||||
\(73\) | 12.7980i | 1.49789i | 0.662633 | + | 0.748944i | \(0.269439\pi\) | ||||
−0.662633 | + | 0.748944i | \(0.730561\pi\) | |||||||
\(74\) | 1.00000 | 0.116248 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −5.00000 | −0.573539 | ||||||||
\(77\) | − 8.44949i | − 0.962909i | ||||||||
\(78\) | 0.651531i | 0.0737713i | ||||||||
\(79\) | −7.79796 | −0.877339 | −0.438669 | − | 0.898648i | \(-0.644550\pi\) | ||||
−0.438669 | + | 0.898648i | \(0.644550\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.49490 | −0.610544 | ||||||||
\(82\) | − 1.00000i | − 0.110432i | ||||||||
\(83\) | 3.44949i | 0.378631i | 0.981916 | + | 0.189315i | \(0.0606268\pi\) | ||||
−0.981916 | + | 0.189315i | \(0.939373\pi\) | |||||||
\(84\) | 3.55051 | 0.387392 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.10102 | −0.118726 | ||||||||
\(87\) | − 1.30306i | − 0.139703i | ||||||||
\(88\) | 3.44949i | 0.367717i | ||||||||
\(89\) | −14.3485 | −1.52093 | −0.760467 | − | 0.649376i | \(-0.775030\pi\) | ||||
−0.760467 | + | 0.649376i | \(0.775030\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.10102 | −0.115418 | ||||||||
\(92\) | − 2.00000i | − 0.208514i | ||||||||
\(93\) | − 6.44949i | − 0.668781i | ||||||||
\(94\) | −9.79796 | −1.01058 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.44949 | −0.147938 | ||||||||
\(97\) | − 14.0000i | − 1.42148i | −0.703452 | − | 0.710742i | \(-0.748359\pi\) | ||||
0.703452 | − | 0.710742i | \(-0.251641\pi\) | |||||||
\(98\) | − 1.00000i | − 0.101015i | ||||||||
\(99\) | 3.10102 | 0.311664 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.10102 | 0.109556 | 0.0547778 | − | 0.998499i | \(-0.482555\pi\) | ||||
0.0547778 | + | 0.998499i | \(0.482555\pi\) | |||||||
\(102\) | 5.00000i | 0.495074i | ||||||||
\(103\) | 6.44949i | 0.635487i | 0.948177 | + | 0.317744i | \(0.102925\pi\) | ||||
−0.948177 | + | 0.317744i | \(0.897075\pi\) | |||||||
\(104\) | 0.449490 | 0.0440761 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.00000 | 0.582772 | ||||||||
\(107\) | 8.55051i | 0.826609i | 0.910593 | + | 0.413305i | \(0.135625\pi\) | ||||
−0.910593 | + | 0.413305i | \(0.864375\pi\) | |||||||
\(108\) | 5.65153i | 0.543819i | ||||||||
\(109\) | −14.0000 | −1.34096 | −0.670478 | − | 0.741929i | \(-0.733911\pi\) | ||||
−0.670478 | + | 0.741929i | \(0.733911\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.44949 | 0.137579 | ||||||||
\(112\) | − 2.44949i | − 0.231455i | ||||||||
\(113\) | − 4.55051i | − 0.428076i | −0.976825 | − | 0.214038i | \(-0.931338\pi\) | ||||
0.976825 | − | 0.214038i | \(-0.0686616\pi\) | |||||||
\(114\) | −7.24745 | −0.678786 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.898979 | −0.0834681 | ||||||||
\(117\) | − 0.404082i | − 0.0373574i | ||||||||
\(118\) | − 2.00000i | − 0.184115i | ||||||||
\(119\) | −8.44949 | −0.774563 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.898979 | 0.0817254 | ||||||||
\(122\) | 6.44949i | 0.583909i | ||||||||
\(123\) | − 1.44949i | − 0.130696i | ||||||||
\(124\) | −4.44949 | −0.399576 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −2.20204 | −0.196173 | ||||||||
\(127\) | 16.2474i | 1.44173i | 0.693077 | + | 0.720864i | \(0.256255\pi\) | ||||
−0.693077 | + | 0.720864i | \(0.743745\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | −1.59592 | −0.140513 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.69694 | 0.759855 | 0.379928 | − | 0.925016i | \(-0.375949\pi\) | ||||
0.379928 | + | 0.925016i | \(0.375949\pi\) | |||||||
\(132\) | 5.00000i | 0.435194i | ||||||||
\(133\) | − 12.2474i | − 1.06199i | ||||||||
\(134\) | −4.55051 | −0.393104 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.44949 | 0.295791 | ||||||||
\(137\) | − 9.69694i | − 0.828465i | −0.910171 | − | 0.414233i | \(-0.864050\pi\) | ||||
0.910171 | − | 0.414233i | \(-0.135950\pi\) | |||||||
\(138\) | − 2.89898i | − 0.246778i | ||||||||
\(139\) | 12.5505 | 1.06452 | 0.532260 | − | 0.846581i | \(-0.321343\pi\) | ||||
0.532260 | + | 0.846581i | \(0.321343\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −14.2020 | −1.19603 | ||||||||
\(142\) | 7.55051i | 0.633625i | ||||||||
\(143\) | − 1.55051i | − 0.129660i | ||||||||
\(144\) | 0.898979 | 0.0749150 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 12.7980 | 1.05917 | ||||||||
\(147\) | − 1.44949i | − 0.119552i | ||||||||
\(148\) | − 1.00000i | − 0.0821995i | ||||||||
\(149\) | 4.65153 | 0.381068 | 0.190534 | − | 0.981681i | \(-0.438978\pi\) | ||||
0.190534 | + | 0.981681i | \(0.438978\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.0000 | −1.13930 | −0.569652 | − | 0.821886i | \(-0.692922\pi\) | ||||
−0.569652 | + | 0.821886i | \(0.692922\pi\) | |||||||
\(152\) | 5.00000i | 0.405554i | ||||||||
\(153\) | − 3.10102i | − 0.250703i | ||||||||
\(154\) | −8.44949 | −0.680879 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0.651531 | 0.0521642 | ||||||||
\(157\) | − 16.4495i | − 1.31281i | −0.754408 | − | 0.656406i | \(-0.772076\pi\) | ||||
0.754408 | − | 0.656406i | \(-0.227924\pi\) | |||||||
\(158\) | 7.79796i | 0.620372i | ||||||||
\(159\) | 8.69694 | 0.689712 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.89898 | 0.386094 | ||||||||
\(162\) | 5.49490i | 0.431720i | ||||||||
\(163\) | 10.1010i | 0.791173i | 0.918429 | + | 0.395586i | \(0.129459\pi\) | ||||
−0.918429 | + | 0.395586i | \(0.870541\pi\) | |||||||
\(164\) | −1.00000 | −0.0780869 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.44949 | 0.267732 | ||||||||
\(167\) | 10.4495i | 0.808606i | 0.914625 | + | 0.404303i | \(0.132486\pi\) | ||||
−0.914625 | + | 0.404303i | \(0.867514\pi\) | |||||||
\(168\) | − 3.55051i | − 0.273928i | ||||||||
\(169\) | 12.7980 | 0.984458 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.49490 | 0.343733 | ||||||||
\(172\) | 1.10102i | 0.0839520i | ||||||||
\(173\) | − 6.69694i | − 0.509159i | −0.967052 | − | 0.254579i | \(-0.918063\pi\) | ||||
0.967052 | − | 0.254579i | \(-0.0819370\pi\) | |||||||
\(174\) | −1.30306 | −0.0987848 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.44949 | 0.260015 | ||||||||
\(177\) | − 2.89898i | − 0.217901i | ||||||||
\(178\) | 14.3485i | 1.07546i | ||||||||
\(179\) | 0.797959 | 0.0596423 | 0.0298211 | − | 0.999555i | \(-0.490506\pi\) | ||||
0.0298211 | + | 0.999555i | \(0.490506\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.89898 | 0.512797 | 0.256399 | − | 0.966571i | \(-0.417464\pi\) | ||||
0.256399 | + | 0.966571i | \(0.417464\pi\) | |||||||
\(182\) | 1.10102i | 0.0816131i | ||||||||
\(183\) | 9.34847i | 0.691059i | ||||||||
\(184\) | −2.00000 | −0.147442 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −6.44949 | −0.472900 | ||||||||
\(187\) | − 11.8990i | − 0.870140i | ||||||||
\(188\) | 9.79796i | 0.714590i | ||||||||
\(189\) | −13.8434 | −1.00696 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.79796 | −0.564241 | −0.282120 | − | 0.959379i | \(-0.591038\pi\) | ||||
−0.282120 | + | 0.959379i | \(0.591038\pi\) | |||||||
\(192\) | 1.44949i | 0.104608i | ||||||||
\(193\) | − 2.55051i | − 0.183590i | −0.995778 | − | 0.0917949i | \(-0.970740\pi\) | ||||
0.995778 | − | 0.0917949i | \(-0.0292604\pi\) | |||||||
\(194\) | −14.0000 | −1.00514 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.00000 | −0.0714286 | ||||||||
\(197\) | 17.3485i | 1.23603i | 0.786167 | + | 0.618014i | \(0.212062\pi\) | ||||
−0.786167 | + | 0.618014i | \(0.787938\pi\) | |||||||
\(198\) | − 3.10102i | − 0.220380i | ||||||||
\(199\) | 15.5959 | 1.10557 | 0.552783 | − | 0.833325i | \(-0.313566\pi\) | ||||
0.552783 | + | 0.833325i | \(0.313566\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −6.59592 | −0.465240 | ||||||||
\(202\) | − 1.10102i | − 0.0774675i | ||||||||
\(203\) | − 2.20204i | − 0.154553i | ||||||||
\(204\) | 5.00000 | 0.350070 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 6.44949 | 0.449357 | ||||||||
\(207\) | 1.79796i | 0.124967i | ||||||||
\(208\) | − 0.449490i | − 0.0311665i | ||||||||
\(209\) | 17.2474 | 1.19303 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.55051 | −0.313270 | −0.156635 | − | 0.987657i | \(-0.550065\pi\) | ||||
−0.156635 | + | 0.987657i | \(0.550065\pi\) | |||||||
\(212\) | − 6.00000i | − 0.412082i | ||||||||
\(213\) | 10.9444i | 0.749897i | ||||||||
\(214\) | 8.55051 | 0.584501 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 5.65153 | 0.384538 | ||||||||
\(217\) | − 10.8990i | − 0.739871i | ||||||||
\(218\) | 14.0000i | 0.948200i | ||||||||
\(219\) | 18.5505 | 1.25353 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.55051 | −0.104299 | ||||||||
\(222\) | − 1.44949i | − 0.0972834i | ||||||||
\(223\) | 21.7980i | 1.45970i | 0.683608 | + | 0.729850i | \(0.260410\pi\) | ||||
−0.683608 | + | 0.729850i | \(0.739590\pi\) | |||||||
\(224\) | −2.44949 | −0.163663 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4.55051 | −0.302695 | ||||||||
\(227\) | 16.6969i | 1.10821i | 0.832445 | + | 0.554107i | \(0.186940\pi\) | ||||
−0.832445 | + | 0.554107i | \(0.813060\pi\) | |||||||
\(228\) | 7.24745i | 0.479974i | ||||||||
\(229\) | −5.79796 | −0.383140 | −0.191570 | − | 0.981479i | \(-0.561358\pi\) | ||||
−0.191570 | + | 0.981479i | \(0.561358\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −12.2474 | −0.805823 | ||||||||
\(232\) | 0.898979i | 0.0590209i | ||||||||
\(233\) | − 28.4949i | − 1.86676i | −0.358886 | − | 0.933381i | \(-0.616843\pi\) | ||||
0.358886 | − | 0.933381i | \(-0.383157\pi\) | |||||||
\(234\) | −0.404082 | −0.0264157 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −2.00000 | −0.130189 | ||||||||
\(237\) | 11.3031i | 0.734213i | ||||||||
\(238\) | 8.44949i | 0.547699i | ||||||||
\(239\) | −0.898979 | −0.0581501 | −0.0290751 | − | 0.999577i | \(-0.509256\pi\) | ||||
−0.0290751 | + | 0.999577i | \(0.509256\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.55051 | −0.164293 | −0.0821464 | − | 0.996620i | \(-0.526178\pi\) | ||||
−0.0821464 | + | 0.996620i | \(0.526178\pi\) | |||||||
\(242\) | − 0.898979i | − 0.0577886i | ||||||||
\(243\) | − 8.98979i | − 0.576696i | ||||||||
\(244\) | 6.44949 | 0.412886 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.44949 | −0.0924161 | ||||||||
\(247\) | − 2.24745i | − 0.143002i | ||||||||
\(248\) | 4.44949i | 0.282543i | ||||||||
\(249\) | 5.00000 | 0.316862 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −30.7980 | −1.94395 | −0.971975 | − | 0.235084i | \(-0.924463\pi\) | ||||
−0.971975 | + | 0.235084i | \(0.924463\pi\) | |||||||
\(252\) | 2.20204i | 0.138716i | ||||||||
\(253\) | 6.89898i | 0.433735i | ||||||||
\(254\) | 16.2474 | 1.01946 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 6.89898i | 0.430347i | 0.976576 | + | 0.215173i | \(0.0690316\pi\) | ||||
−0.976576 | + | 0.215173i | \(0.930968\pi\) | |||||||
\(258\) | 1.59592i | 0.0993575i | ||||||||
\(259\) | 2.44949 | 0.152204 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.808164 | 0.0500241 | ||||||||
\(262\) | − 8.69694i | − 0.537299i | ||||||||
\(263\) | 0.202041i | 0.0124584i | 0.999981 | + | 0.00622919i | \(0.00198283\pi\) | ||||
−0.999981 | + | 0.00622919i | \(0.998017\pi\) | |||||||
\(264\) | 5.00000 | 0.307729 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −12.2474 | −0.750939 | ||||||||
\(267\) | 20.7980i | 1.27281i | ||||||||
\(268\) | 4.55051i | 0.277967i | ||||||||
\(269\) | −4.00000 | −0.243884 | −0.121942 | − | 0.992537i | \(-0.538912\pi\) | ||||
−0.121942 | + | 0.992537i | \(0.538912\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 30.0454 | 1.82513 | 0.912564 | − | 0.408933i | \(-0.134099\pi\) | ||||
0.912564 | + | 0.408933i | \(0.134099\pi\) | |||||||
\(272\) | − 3.44949i | − 0.209156i | ||||||||
\(273\) | 1.59592i | 0.0965893i | ||||||||
\(274\) | −9.69694 | −0.585813 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −2.89898 | −0.174498 | ||||||||
\(277\) | − 5.79796i | − 0.348366i | −0.984713 | − | 0.174183i | \(-0.944272\pi\) | ||||
0.984713 | − | 0.174183i | \(-0.0557284\pi\) | |||||||
\(278\) | − 12.5505i | − 0.752730i | ||||||||
\(279\) | 4.00000 | 0.239474 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.89898 | 0.530869 | 0.265434 | − | 0.964129i | \(-0.414485\pi\) | ||||
0.265434 | + | 0.964129i | \(0.414485\pi\) | |||||||
\(282\) | 14.2020i | 0.845719i | ||||||||
\(283\) | − 11.6969i | − 0.695311i | −0.937622 | − | 0.347655i | \(-0.886978\pi\) | ||||
0.937622 | − | 0.347655i | \(-0.113022\pi\) | |||||||
\(284\) | 7.55051 | 0.448040 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.55051 | −0.0916836 | ||||||||
\(287\) | − 2.44949i | − 0.144589i | ||||||||
\(288\) | − 0.898979i | − 0.0529729i | ||||||||
\(289\) | 5.10102 | 0.300060 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −20.2929 | −1.18959 | ||||||||
\(292\) | − 12.7980i | − 0.748944i | ||||||||
\(293\) | − 28.0454i | − 1.63843i | −0.573486 | − | 0.819215i | \(-0.694409\pi\) | ||||
0.573486 | − | 0.819215i | \(-0.305591\pi\) | |||||||
\(294\) | −1.44949 | −0.0845360 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1.00000 | −0.0581238 | ||||||||
\(297\) | − 19.4949i | − 1.13121i | ||||||||
\(298\) | − 4.65153i | − 0.269456i | ||||||||
\(299\) | 0.898979 | 0.0519893 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.69694 | −0.155449 | ||||||||
\(302\) | 14.0000i | 0.805609i | ||||||||
\(303\) | − 1.59592i | − 0.0916831i | ||||||||
\(304\) | 5.00000 | 0.286770 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −3.10102 | −0.177274 | ||||||||
\(307\) | − 7.65153i | − 0.436696i | −0.975871 | − | 0.218348i | \(-0.929933\pi\) | ||||
0.975871 | − | 0.218348i | \(-0.0700668\pi\) | |||||||
\(308\) | 8.44949i | 0.481454i | ||||||||
\(309\) | 9.34847 | 0.531816 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.44949 | −0.479127 | −0.239563 | − | 0.970881i | \(-0.577004\pi\) | ||||
−0.239563 | + | 0.970881i | \(0.577004\pi\) | |||||||
\(312\) | − 0.651531i | − 0.0368857i | ||||||||
\(313\) | 8.89898i | 0.503000i | 0.967857 | + | 0.251500i | \(0.0809239\pi\) | ||||
−0.967857 | + | 0.251500i | \(0.919076\pi\) | |||||||
\(314\) | −16.4495 | −0.928298 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7.79796 | 0.438669 | ||||||||
\(317\) | 9.55051i | 0.536410i | 0.963362 | + | 0.268205i | \(0.0864305\pi\) | ||||
−0.963362 | + | 0.268205i | \(0.913570\pi\) | |||||||
\(318\) | − 8.69694i | − 0.487700i | ||||||||
\(319\) | 3.10102 | 0.173624 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 12.3939 | 0.691759 | ||||||||
\(322\) | − 4.89898i | − 0.273009i | ||||||||
\(323\) | − 17.2474i | − 0.959674i | ||||||||
\(324\) | 5.49490 | 0.305272 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 10.1010 | 0.559444 | ||||||||
\(327\) | 20.2929i | 1.12220i | ||||||||
\(328\) | 1.00000i | 0.0552158i | ||||||||
\(329\) | −24.0000 | −1.32316 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 19.8990 | 1.09375 | 0.546873 | − | 0.837215i | \(-0.315818\pi\) | ||||
0.546873 | + | 0.837215i | \(0.315818\pi\) | |||||||
\(332\) | − 3.44949i | − 0.189315i | ||||||||
\(333\) | 0.898979i | 0.0492638i | ||||||||
\(334\) | 10.4495 | 0.571771 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −3.55051 | −0.193696 | ||||||||
\(337\) | − 15.6969i | − 0.855067i | −0.904000 | − | 0.427533i | \(-0.859383\pi\) | ||||
0.904000 | − | 0.427533i | \(-0.140617\pi\) | |||||||
\(338\) | − 12.7980i | − 0.696117i | ||||||||
\(339\) | −6.59592 | −0.358241 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 15.3485 | 0.831166 | ||||||||
\(342\) | − 4.49490i | − 0.243056i | ||||||||
\(343\) | − 19.5959i | − 1.05808i | ||||||||
\(344\) | 1.10102 | 0.0593630 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −6.69694 | −0.360030 | ||||||||
\(347\) | 18.7980i | 1.00913i | 0.863374 | + | 0.504564i | \(0.168347\pi\) | ||||
−0.863374 | + | 0.504564i | \(0.831653\pi\) | |||||||
\(348\) | 1.30306i | 0.0698514i | ||||||||
\(349\) | 12.4495 | 0.666406 | 0.333203 | − | 0.942855i | \(-0.391871\pi\) | ||||
0.333203 | + | 0.942855i | \(0.391871\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.54031 | −0.135591 | ||||||||
\(352\) | − 3.44949i | − 0.183858i | ||||||||
\(353\) | 14.8990i | 0.792993i | 0.918036 | + | 0.396496i | \(0.129774\pi\) | ||||
−0.918036 | + | 0.396496i | \(0.870226\pi\) | |||||||
\(354\) | −2.89898 | −0.154079 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 14.3485 | 0.760467 | ||||||||
\(357\) | 12.2474i | 0.648204i | ||||||||
\(358\) | − 0.797959i | − 0.0421734i | ||||||||
\(359\) | 31.3939 | 1.65691 | 0.828453 | − | 0.560059i | \(-0.189222\pi\) | ||||
0.828453 | + | 0.560059i | \(0.189222\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.00000 | 0.315789 | ||||||||
\(362\) | − 6.89898i | − 0.362602i | ||||||||
\(363\) | − 1.30306i | − 0.0683930i | ||||||||
\(364\) | 1.10102 | 0.0577092 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 9.34847 | 0.488652 | ||||||||
\(367\) | 14.2474i | 0.743711i | 0.928291 | + | 0.371855i | \(0.121278\pi\) | ||||
−0.928291 | + | 0.371855i | \(0.878722\pi\) | |||||||
\(368\) | 2.00000i | 0.104257i | ||||||||
\(369\) | 0.898979 | 0.0467990 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 14.6969 | 0.763027 | ||||||||
\(372\) | 6.44949i | 0.334390i | ||||||||
\(373\) | − 20.0454i | − 1.03791i | −0.854801 | − | 0.518956i | \(-0.826321\pi\) | ||||
0.854801 | − | 0.518956i | \(-0.173679\pi\) | |||||||
\(374\) | −11.8990 | −0.615282 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 9.79796 | 0.505291 | ||||||||
\(377\) | − 0.404082i | − 0.0208113i | ||||||||
\(378\) | 13.8434i | 0.712026i | ||||||||
\(379\) | 21.0454 | 1.08103 | 0.540515 | − | 0.841334i | \(-0.318229\pi\) | ||||
0.540515 | + | 0.841334i | \(0.318229\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 23.5505 | 1.20653 | ||||||||
\(382\) | 7.79796i | 0.398978i | ||||||||
\(383\) | − 5.34847i | − 0.273294i | −0.990620 | − | 0.136647i | \(-0.956367\pi\) | ||||
0.990620 | − | 0.136647i | \(-0.0436326\pi\) | |||||||
\(384\) | 1.44949 | 0.0739690 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.55051 | −0.129818 | ||||||||
\(387\) | − 0.989795i | − 0.0503141i | ||||||||
\(388\) | 14.0000i | 0.710742i | ||||||||
\(389\) | −13.1464 | −0.666550 | −0.333275 | − | 0.942830i | \(-0.608154\pi\) | ||||
−0.333275 | + | 0.942830i | \(0.608154\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.89898 | 0.348896 | ||||||||
\(392\) | 1.00000i | 0.0505076i | ||||||||
\(393\) | − 12.6061i | − 0.635895i | ||||||||
\(394\) | 17.3485 | 0.874003 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −3.10102 | −0.155832 | ||||||||
\(397\) | 15.3485i | 0.770318i | 0.922850 | + | 0.385159i | \(0.125853\pi\) | ||||
−0.922850 | + | 0.385159i | \(0.874147\pi\) | |||||||
\(398\) | − 15.5959i | − 0.781753i | ||||||||
\(399\) | −17.7526 | −0.888739 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 15.9444 | 0.796225 | 0.398112 | − | 0.917337i | \(-0.369665\pi\) | ||||
0.398112 | + | 0.917337i | \(0.369665\pi\) | |||||||
\(402\) | 6.59592i | 0.328974i | ||||||||
\(403\) | − 2.00000i | − 0.0996271i | ||||||||
\(404\) | −1.10102 | −0.0547778 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.20204 | −0.109285 | ||||||||
\(407\) | 3.44949i | 0.170985i | ||||||||
\(408\) | − 5.00000i | − 0.247537i | ||||||||
\(409\) | 34.1464 | 1.68843 | 0.844216 | − | 0.536003i | \(-0.180066\pi\) | ||||
0.844216 | + | 0.536003i | \(0.180066\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −14.0556 | −0.693312 | ||||||||
\(412\) | − 6.44949i | − 0.317744i | ||||||||
\(413\) | − 4.89898i | − 0.241063i | ||||||||
\(414\) | 1.79796 | 0.0883649 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −0.449490 | −0.0220380 | ||||||||
\(417\) | − 18.1918i | − 0.890858i | ||||||||
\(418\) | − 17.2474i | − 0.843600i | ||||||||
\(419\) | 21.4495 | 1.04788 | 0.523938 | − | 0.851756i | \(-0.324462\pi\) | ||||
0.523938 | + | 0.851756i | \(0.324462\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 32.8990 | 1.60340 | 0.801699 | − | 0.597728i | \(-0.203930\pi\) | ||||
0.801699 | + | 0.597728i | \(0.203930\pi\) | |||||||
\(422\) | 4.55051i | 0.221515i | ||||||||
\(423\) | − 8.80816i | − 0.428268i | ||||||||
\(424\) | −6.00000 | −0.291386 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 10.9444 | 0.530257 | ||||||||
\(427\) | 15.7980i | 0.764517i | ||||||||
\(428\) | − 8.55051i | − 0.413305i | ||||||||
\(429\) | −2.24745 | −0.108508 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −20.6969 | −0.996936 | −0.498468 | − | 0.866908i | \(-0.666104\pi\) | ||||
−0.498468 | + | 0.866908i | \(0.666104\pi\) | |||||||
\(432\) | − 5.65153i | − 0.271909i | ||||||||
\(433\) | 19.0000i | 0.913082i | 0.889702 | + | 0.456541i | \(0.150912\pi\) | ||||
−0.889702 | + | 0.456541i | \(0.849088\pi\) | |||||||
\(434\) | −10.8990 | −0.523168 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 14.0000 | 0.670478 | ||||||||
\(437\) | 10.0000i | 0.478365i | ||||||||
\(438\) | − 18.5505i | − 0.886378i | ||||||||
\(439\) | 19.5959 | 0.935262 | 0.467631 | − | 0.883924i | \(-0.345108\pi\) | ||||
0.467631 | + | 0.883924i | \(0.345108\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.898979 | 0.0428085 | ||||||||
\(442\) | 1.55051i | 0.0737503i | ||||||||
\(443\) | − 17.4495i | − 0.829050i | −0.910038 | − | 0.414525i | \(-0.863948\pi\) | ||||
0.910038 | − | 0.414525i | \(-0.136052\pi\) | |||||||
\(444\) | −1.44949 | −0.0687897 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 21.7980 | 1.03216 | ||||||||
\(447\) | − 6.74235i | − 0.318902i | ||||||||
\(448\) | 2.44949i | 0.115728i | ||||||||
\(449\) | −33.2474 | −1.56904 | −0.784522 | − | 0.620101i | \(-0.787092\pi\) | ||||
−0.784522 | + | 0.620101i | \(0.787092\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.44949 | 0.162430 | ||||||||
\(452\) | 4.55051i | 0.214038i | ||||||||
\(453\) | 20.2929i | 0.953442i | ||||||||
\(454\) | 16.6969 | 0.783626 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 7.24745 | 0.339393 | ||||||||
\(457\) | − 15.2474i | − 0.713246i | −0.934248 | − | 0.356623i | \(-0.883928\pi\) | ||||
0.934248 | − | 0.356623i | \(-0.116072\pi\) | |||||||
\(458\) | 5.79796i | 0.270921i | ||||||||
\(459\) | −19.4949 | −0.909944 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9.30306 | 0.433287 | 0.216643 | − | 0.976251i | \(-0.430489\pi\) | ||||
0.216643 | + | 0.976251i | \(0.430489\pi\) | |||||||
\(462\) | 12.2474i | 0.569803i | ||||||||
\(463\) | 9.55051i | 0.443850i | 0.975064 | + | 0.221925i | \(0.0712340\pi\) | ||||
−0.975064 | + | 0.221925i | \(0.928766\pi\) | |||||||
\(464\) | 0.898979 | 0.0417341 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −28.4949 | −1.32000 | ||||||||
\(467\) | 12.0000i | 0.555294i | 0.960683 | + | 0.277647i | \(0.0895545\pi\) | ||||
−0.960683 | + | 0.277647i | \(0.910445\pi\) | |||||||
\(468\) | 0.404082i | 0.0186787i | ||||||||
\(469\) | −11.1464 | −0.514694 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −23.8434 | −1.09864 | ||||||||
\(472\) | 2.00000i | 0.0920575i | ||||||||
\(473\) | − 3.79796i | − 0.174630i | ||||||||
\(474\) | 11.3031 | 0.519167 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 8.44949 | 0.387282 | ||||||||
\(477\) | 5.39388i | 0.246969i | ||||||||
\(478\) | 0.898979i | 0.0411184i | ||||||||
\(479\) | −6.24745 | −0.285453 | −0.142727 | − | 0.989762i | \(-0.545587\pi\) | ||||
−0.142727 | + | 0.989762i | \(0.545587\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.449490 | 0.0204950 | ||||||||
\(482\) | 2.55051i | 0.116173i | ||||||||
\(483\) | − 7.10102i | − 0.323108i | ||||||||
\(484\) | −0.898979 | −0.0408627 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −8.98979 | −0.407785 | ||||||||
\(487\) | 30.7423i | 1.39307i | 0.717523 | + | 0.696534i | \(0.245276\pi\) | ||||
−0.717523 | + | 0.696534i | \(0.754724\pi\) | |||||||
\(488\) | − 6.44949i | − 0.291955i | ||||||||
\(489\) | 14.6413 | 0.662104 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −41.7980 | −1.88632 | −0.943158 | − | 0.332345i | \(-0.892160\pi\) | ||||
−0.943158 | + | 0.332345i | \(0.892160\pi\) | |||||||
\(492\) | 1.44949i | 0.0653480i | ||||||||
\(493\) | − 3.10102i | − 0.139663i | ||||||||
\(494\) | −2.24745 | −0.101117 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.44949 | 0.199788 | ||||||||
\(497\) | 18.4949i | 0.829610i | ||||||||
\(498\) | − 5.00000i | − 0.224055i | ||||||||
\(499\) | −22.0000 | −0.984855 | −0.492428 | − | 0.870353i | \(-0.663890\pi\) | ||||
−0.492428 | + | 0.870353i | \(0.663890\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 15.1464 | 0.676693 | ||||||||
\(502\) | 30.7980i | 1.37458i | ||||||||
\(503\) | 9.79796i | 0.436869i | 0.975852 | + | 0.218435i | \(0.0700951\pi\) | ||||
−0.975852 | + | 0.218435i | \(0.929905\pi\) | |||||||
\(504\) | 2.20204 | 0.0980867 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 6.89898 | 0.306697 | ||||||||
\(507\) | − 18.5505i | − 0.823857i | ||||||||
\(508\) | − 16.2474i | − 0.720864i | ||||||||
\(509\) | −29.3485 | −1.30085 | −0.650424 | − | 0.759571i | \(-0.725409\pi\) | ||||
−0.650424 | + | 0.759571i | \(0.725409\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 31.3485 | 1.38677 | ||||||||
\(512\) | − 1.00000i | − 0.0441942i | ||||||||
\(513\) | − 28.2577i | − 1.24761i | ||||||||
\(514\) | 6.89898 | 0.304301 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 1.59592 | 0.0702564 | ||||||||
\(517\) | − 33.7980i | − 1.48643i | ||||||||
\(518\) | − 2.44949i | − 0.107624i | ||||||||
\(519\) | −9.70714 | −0.426096 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10.1010 | 0.442534 | 0.221267 | − | 0.975213i | \(-0.428981\pi\) | ||||
0.221267 | + | 0.975213i | \(0.428981\pi\) | |||||||
\(522\) | − 0.808164i | − 0.0353724i | ||||||||
\(523\) | − 18.3939i | − 0.804308i | −0.915572 | − | 0.402154i | \(-0.868262\pi\) | ||||
0.915572 | − | 0.402154i | \(-0.131738\pi\) | |||||||
\(524\) | −8.69694 | −0.379928 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0.202041 | 0.00880941 | ||||||||
\(527\) | − 15.3485i | − 0.668590i | ||||||||
\(528\) | − 5.00000i | − 0.217597i | ||||||||
\(529\) | 19.0000 | 0.826087 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.79796 | 0.0780248 | ||||||||
\(532\) | 12.2474i | 0.530994i | ||||||||
\(533\) | − 0.449490i | − 0.0194696i | ||||||||
\(534\) | 20.7980 | 0.900016 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 4.55051 | 0.196552 | ||||||||
\(537\) | − 1.15663i | − 0.0499124i | ||||||||
\(538\) | 4.00000i | 0.172452i | ||||||||
\(539\) | 3.44949 | 0.148580 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 25.3485 | 1.08982 | 0.544908 | − | 0.838496i | \(-0.316565\pi\) | ||||
0.544908 | + | 0.838496i | \(0.316565\pi\) | |||||||
\(542\) | − 30.0454i | − 1.29056i | ||||||||
\(543\) | − 10.0000i | − 0.429141i | ||||||||
\(544\) | −3.44949 | −0.147896 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 1.59592 | 0.0682990 | ||||||||
\(547\) | − 3.69694i | − 0.158070i | −0.996872 | − | 0.0790348i | \(-0.974816\pi\) | ||||
0.996872 | − | 0.0790348i | \(-0.0251838\pi\) | |||||||
\(548\) | 9.69694i | 0.414233i | ||||||||
\(549\) | −5.79796 | −0.247451 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.49490 | 0.191489 | ||||||||
\(552\) | 2.89898i | 0.123389i | ||||||||
\(553\) | 19.1010i | 0.812258i | ||||||||
\(554\) | −5.79796 | −0.246332 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −12.5505 | −0.532260 | ||||||||
\(557\) | 21.7980i | 0.923609i | 0.886982 | + | 0.461805i | \(0.152798\pi\) | ||||
−0.886982 | + | 0.461805i | \(0.847202\pi\) | |||||||
\(558\) | − 4.00000i | − 0.169334i | ||||||||
\(559\) | −0.494897 | −0.0209319 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −17.2474 | −0.728188 | ||||||||
\(562\) | − 8.89898i | − 0.375381i | ||||||||
\(563\) | 37.5959i | 1.58448i | 0.610210 | + | 0.792240i | \(0.291085\pi\) | ||||
−0.610210 | + | 0.792240i | \(0.708915\pi\) | |||||||
\(564\) | 14.2020 | 0.598014 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −11.6969 | −0.491659 | ||||||||
\(567\) | 13.4597i | 0.565254i | ||||||||
\(568\) | − 7.55051i | − 0.316812i | ||||||||
\(569\) | −27.0454 | −1.13380 | −0.566901 | − | 0.823786i | \(-0.691858\pi\) | ||||
−0.566901 | + | 0.823786i | \(0.691858\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.0000 | 0.502184 | 0.251092 | − | 0.967963i | \(-0.419210\pi\) | ||||
0.251092 | + | 0.967963i | \(0.419210\pi\) | |||||||
\(572\) | 1.55051i | 0.0648301i | ||||||||
\(573\) | 11.3031i | 0.472192i | ||||||||
\(574\) | −2.44949 | −0.102240 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.898979 | −0.0374575 | ||||||||
\(577\) | − 21.0454i | − 0.876132i | −0.898943 | − | 0.438066i | \(-0.855664\pi\) | ||||
0.898943 | − | 0.438066i | \(-0.144336\pi\) | |||||||
\(578\) | − 5.10102i | − 0.212174i | ||||||||
\(579\) | −3.69694 | −0.153640 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.44949 | 0.350544 | ||||||||
\(582\) | 20.2929i | 0.841166i | ||||||||
\(583\) | 20.6969i | 0.857180i | ||||||||
\(584\) | −12.7980 | −0.529583 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −28.0454 | −1.15855 | ||||||||
\(587\) | 6.30306i | 0.260155i | 0.991504 | + | 0.130078i | \(0.0415226\pi\) | ||||
−0.991504 | + | 0.130078i | \(0.958477\pi\) | |||||||
\(588\) | 1.44949i | 0.0597759i | ||||||||
\(589\) | 22.2474 | 0.916690 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 25.1464 | 1.03439 | ||||||||
\(592\) | 1.00000i | 0.0410997i | ||||||||
\(593\) | 46.3939i | 1.90517i | 0.304275 | + | 0.952584i | \(0.401586\pi\) | ||||
−0.304275 | + | 0.952584i | \(0.598414\pi\) | |||||||
\(594\) | −19.4949 | −0.799885 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −4.65153 | −0.190534 | ||||||||
\(597\) | − 22.6061i | − 0.925207i | ||||||||
\(598\) | − 0.898979i | − 0.0367620i | ||||||||
\(599\) | −38.9444 | −1.59122 | −0.795612 | − | 0.605806i | \(-0.792851\pi\) | ||||
−0.795612 | + | 0.605806i | \(0.792851\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.00000 | −0.285536 | −0.142768 | − | 0.989756i | \(-0.545600\pi\) | ||||
−0.142768 | + | 0.989756i | \(0.545600\pi\) | |||||||
\(602\) | 2.69694i | 0.109919i | ||||||||
\(603\) | − 4.09082i | − 0.166591i | ||||||||
\(604\) | 14.0000 | 0.569652 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1.59592 | −0.0648297 | ||||||||
\(607\) | 28.7423i | 1.16662i | 0.812251 | + | 0.583308i | \(0.198242\pi\) | ||||
−0.812251 | + | 0.583308i | \(0.801758\pi\) | |||||||
\(608\) | − 5.00000i | − 0.202777i | ||||||||
\(609\) | −3.19184 | −0.129340 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.40408 | −0.178170 | ||||||||
\(612\) | 3.10102i | 0.125351i | ||||||||
\(613\) | − 34.4949i | − 1.39324i | −0.717442 | − | 0.696618i | \(-0.754687\pi\) | ||||
0.717442 | − | 0.696618i | \(-0.245313\pi\) | |||||||
\(614\) | −7.65153 | −0.308791 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 8.44949 | 0.340440 | ||||||||
\(617\) | 4.89898i | 0.197225i | 0.995126 | + | 0.0986127i | \(0.0314405\pi\) | ||||
−0.995126 | + | 0.0986127i | \(0.968559\pi\) | |||||||
\(618\) | − 9.34847i | − 0.376051i | ||||||||
\(619\) | 32.8990 | 1.32232 | 0.661161 | − | 0.750244i | \(-0.270064\pi\) | ||||
0.661161 | + | 0.750244i | \(0.270064\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 11.3031 | 0.453576 | ||||||||
\(622\) | 8.44949i | 0.338794i | ||||||||
\(623\) | 35.1464i | 1.40811i | ||||||||
\(624\) | −0.651531 | −0.0260821 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 8.89898 | 0.355675 | ||||||||
\(627\) | − 25.0000i | − 0.998404i | ||||||||
\(628\) | 16.4495i | 0.656406i | ||||||||
\(629\) | 3.44949 | 0.137540 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.00000 | 0.0796187 | 0.0398094 | − | 0.999207i | \(-0.487325\pi\) | ||||
0.0398094 | + | 0.999207i | \(0.487325\pi\) | |||||||
\(632\) | − 7.79796i | − 0.310186i | ||||||||
\(633\) | 6.59592i | 0.262164i | ||||||||
\(634\) | 9.55051 | 0.379299 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −8.69694 | −0.344856 | ||||||||
\(637\) | − 0.449490i | − 0.0178094i | ||||||||
\(638\) | − 3.10102i | − 0.122771i | ||||||||
\(639\) | −6.78775 | −0.268519 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 21.5959 | 0.852987 | 0.426494 | − | 0.904491i | \(-0.359749\pi\) | ||||
0.426494 | + | 0.904491i | \(0.359749\pi\) | |||||||
\(642\) | − 12.3939i | − 0.489147i | ||||||||
\(643\) | 32.2929i | 1.27351i | 0.771068 | + | 0.636753i | \(0.219723\pi\) | ||||
−0.771068 | + | 0.636753i | \(0.780277\pi\) | |||||||
\(644\) | −4.89898 | −0.193047 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −17.2474 | −0.678592 | ||||||||
\(647\) | 40.2474i | 1.58229i | 0.611628 | + | 0.791145i | \(0.290515\pi\) | ||||
−0.611628 | + | 0.791145i | \(0.709485\pi\) | |||||||
\(648\) | − 5.49490i | − 0.215860i | ||||||||
\(649\) | 6.89898 | 0.270809 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −15.7980 | −0.619171 | ||||||||
\(652\) | − 10.1010i | − 0.395586i | ||||||||
\(653\) | − 10.0454i | − 0.393107i | −0.980493 | − | 0.196554i | \(-0.937025\pi\) | ||||
0.980493 | − | 0.196554i | \(-0.0629750\pi\) | |||||||
\(654\) | 20.2929 | 0.793513 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.00000 | 0.0390434 | ||||||||
\(657\) | 11.5051i | 0.448857i | ||||||||
\(658\) | 24.0000i | 0.935617i | ||||||||
\(659\) | −6.55051 | −0.255172 | −0.127586 | − | 0.991828i | \(-0.540723\pi\) | ||||
−0.127586 | + | 0.991828i | \(0.540723\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 25.7980 | 1.00342 | 0.501712 | − | 0.865035i | \(-0.332704\pi\) | ||||
0.501712 | + | 0.865035i | \(0.332704\pi\) | |||||||
\(662\) | − 19.8990i | − 0.773396i | ||||||||
\(663\) | 2.24745i | 0.0872837i | ||||||||
\(664\) | −3.44949 | −0.133866 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.898979 | 0.0348347 | ||||||||
\(667\) | 1.79796i | 0.0696172i | ||||||||
\(668\) | − 10.4495i | − 0.404303i | ||||||||
\(669\) | 31.5959 | 1.22157 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −22.2474 | −0.858853 | ||||||||
\(672\) | 3.55051i | 0.136964i | ||||||||
\(673\) | 5.79796i | 0.223495i | 0.993737 | + | 0.111747i | \(0.0356448\pi\) | ||||
−0.993737 | + | 0.111747i | \(0.964355\pi\) | |||||||
\(674\) | −15.6969 | −0.604623 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.7980 | −0.492229 | ||||||||
\(677\) | 43.5959i | 1.67553i | 0.546033 | + | 0.837764i | \(0.316137\pi\) | ||||
−0.546033 | + | 0.837764i | \(0.683863\pi\) | |||||||
\(678\) | 6.59592i | 0.253315i | ||||||||
\(679\) | −34.2929 | −1.31604 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 24.2020 | 0.927424 | ||||||||
\(682\) | − 15.3485i | − 0.587723i | ||||||||
\(683\) | − 7.00000i | − 0.267848i | −0.990992 | − | 0.133924i | \(-0.957242\pi\) | ||||
0.990992 | − | 0.133924i | \(-0.0427577\pi\) | |||||||
\(684\) | −4.49490 | −0.171867 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −19.5959 | −0.748176 | ||||||||
\(687\) | 8.40408i | 0.320636i | ||||||||
\(688\) | − 1.10102i | − 0.0419760i | ||||||||
\(689\) | 2.69694 | 0.102745 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 29.6515 | 1.12800 | 0.563999 | − | 0.825776i | \(-0.309262\pi\) | ||||
0.563999 | + | 0.825776i | \(0.309262\pi\) | |||||||
\(692\) | 6.69694i | 0.254579i | ||||||||
\(693\) | − 7.59592i | − 0.288545i | ||||||||
\(694\) | 18.7980 | 0.713561 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1.30306 | 0.0493924 | ||||||||
\(697\) | − 3.44949i | − 0.130659i | ||||||||
\(698\) | − 12.4495i | − 0.471220i | ||||||||
\(699\) | −41.3031 | −1.56223 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −34.2474 | −1.29351 | −0.646754 | − | 0.762699i | \(-0.723874\pi\) | ||||
−0.646754 | + | 0.762699i | \(0.723874\pi\) | |||||||
\(702\) | 2.54031i | 0.0958776i | ||||||||
\(703\) | 5.00000i | 0.188579i | ||||||||
\(704\) | −3.44949 | −0.130008 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 14.8990 | 0.560730 | ||||||||
\(707\) | − 2.69694i | − 0.101429i | ||||||||
\(708\) | 2.89898i | 0.108950i | ||||||||
\(709\) | −16.8990 | −0.634654 | −0.317327 | − | 0.948316i | \(-0.602785\pi\) | ||||
−0.317327 | + | 0.948316i | \(0.602785\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −7.01021 | −0.262903 | ||||||||
\(712\) | − 14.3485i | − 0.537732i | ||||||||
\(713\) | 8.89898i | 0.333269i | ||||||||
\(714\) | 12.2474 | 0.458349 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −0.797959 | −0.0298211 | ||||||||
\(717\) | 1.30306i | 0.0486637i | ||||||||
\(718\) | − 31.3939i | − 1.17161i | ||||||||
\(719\) | 0.651531 | 0.0242980 | 0.0121490 | − | 0.999926i | \(-0.496133\pi\) | ||||
0.0121490 | + | 0.999926i | \(0.496133\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.7980 | 0.588347 | ||||||||
\(722\) | − 6.00000i | − 0.223297i | ||||||||
\(723\) | 3.69694i | 0.137491i | ||||||||
\(724\) | −6.89898 | −0.256399 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −1.30306 | −0.0483611 | ||||||||
\(727\) | − 36.0000i | − 1.33517i | −0.744535 | − | 0.667583i | \(-0.767329\pi\) | ||||
0.744535 | − | 0.667583i | \(-0.232671\pi\) | |||||||
\(728\) | − 1.10102i | − 0.0408065i | ||||||||
\(729\) | −29.5153 | −1.09316 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.79796 | −0.140473 | ||||||||
\(732\) | − 9.34847i | − 0.345529i | ||||||||
\(733\) | − 15.5959i | − 0.576048i | −0.957623 | − | 0.288024i | \(-0.907002\pi\) | ||||
0.957623 | − | 0.288024i | \(-0.0929984\pi\) | |||||||
\(734\) | 14.2474 | 0.525883 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.00000 | 0.0737210 | ||||||||
\(737\) | − 15.6969i | − 0.578204i | ||||||||
\(738\) | − 0.898979i | − 0.0330919i | ||||||||
\(739\) | 31.5959 | 1.16227 | 0.581137 | − | 0.813806i | \(-0.302608\pi\) | ||||
0.581137 | + | 0.813806i | \(0.302608\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.25765 | −0.119673 | ||||||||
\(742\) | − 14.6969i | − 0.539542i | ||||||||
\(743\) | − 6.40408i | − 0.234943i | −0.993076 | − | 0.117471i | \(-0.962521\pi\) | ||||
0.993076 | − | 0.117471i | \(-0.0374789\pi\) | |||||||
\(744\) | 6.44949 | 0.236450 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −20.0454 | −0.733915 | ||||||||
\(747\) | 3.10102i | 0.113460i | ||||||||
\(748\) | 11.8990i | 0.435070i | ||||||||
\(749\) | 20.9444 | 0.765291 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −30.6969 | −1.12015 | −0.560074 | − | 0.828443i | \(-0.689227\pi\) | ||||
−0.560074 | + | 0.828443i | \(0.689227\pi\) | |||||||
\(752\) | − 9.79796i | − 0.357295i | ||||||||
\(753\) | 44.6413i | 1.62682i | ||||||||
\(754\) | −0.404082 | −0.0147158 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 13.8434 | 0.503478 | ||||||||
\(757\) | 13.7980i | 0.501495i | 0.968052 | + | 0.250748i | \(0.0806764\pi\) | ||||
−0.968052 | + | 0.250748i | \(0.919324\pi\) | |||||||
\(758\) | − 21.0454i | − 0.764404i | ||||||||
\(759\) | 10.0000 | 0.362977 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −14.3031 | −0.518486 | −0.259243 | − | 0.965812i | \(-0.583473\pi\) | ||||
−0.259243 | + | 0.965812i | \(0.583473\pi\) | |||||||
\(762\) | − 23.5505i | − 0.853145i | ||||||||
\(763\) | 34.2929i | 1.24148i | ||||||||
\(764\) | 7.79796 | 0.282120 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −5.34847 | −0.193248 | ||||||||
\(767\) | − 0.898979i | − 0.0324603i | ||||||||
\(768\) | − 1.44949i | − 0.0523040i | ||||||||
\(769\) | −53.2474 | −1.92015 | −0.960076 | − | 0.279739i | \(-0.909752\pi\) | ||||
−0.960076 | + | 0.279739i | \(0.909752\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.0000 | 0.360141 | ||||||||
\(772\) | 2.55051i | 0.0917949i | ||||||||
\(773\) | 22.0454i | 0.792918i | 0.918052 | + | 0.396459i | \(0.129761\pi\) | ||||
−0.918052 | + | 0.396459i | \(0.870239\pi\) | |||||||
\(774\) | −0.989795 | −0.0355774 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 14.0000 | 0.502571 | ||||||||
\(777\) | − 3.55051i | − 0.127374i | ||||||||
\(778\) | 13.1464i | 0.471322i | ||||||||
\(779\) | 5.00000 | 0.179144 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −26.0454 | −0.931978 | ||||||||
\(782\) | − 6.89898i | − 0.246707i | ||||||||
\(783\) | − 5.08061i | − 0.181566i | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −12.6061 | −0.449646 | ||||||||
\(787\) | − 30.6969i | − 1.09423i | −0.837058 | − | 0.547114i | \(-0.815726\pi\) | ||||
0.837058 | − | 0.547114i | \(-0.184274\pi\) | |||||||
\(788\) | − 17.3485i | − 0.618014i | ||||||||
\(789\) | 0.292856 | 0.0104260 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −11.1464 | −0.396321 | ||||||||
\(792\) | 3.10102i | 0.110190i | ||||||||
\(793\) | 2.89898i | 0.102946i | ||||||||
\(794\) | 15.3485 | 0.544697 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −15.5959 | −0.552783 | ||||||||
\(797\) | − 4.24745i | − 0.150452i | −0.997166 | − | 0.0752262i | \(-0.976032\pi\) | ||||
0.997166 | − | 0.0752262i | \(-0.0239679\pi\) | |||||||
\(798\) | 17.7526i | 0.628434i | ||||||||
\(799\) | −33.7980 | −1.19569 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −12.8990 | −0.455763 | ||||||||
\(802\) | − 15.9444i | − 0.563016i | ||||||||
\(803\) | 44.1464i | 1.55789i | ||||||||
\(804\) | 6.59592 | 0.232620 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −2.00000 | −0.0704470 | ||||||||
\(807\) | 5.79796i | 0.204098i | ||||||||
\(808\) | 1.10102i | 0.0387338i | ||||||||
\(809\) | 39.3939 | 1.38501 | 0.692507 | − | 0.721411i | \(-0.256506\pi\) | ||||
0.692507 | + | 0.721411i | \(0.256506\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.79796 | 0.203594 | 0.101797 | − | 0.994805i | \(-0.467541\pi\) | ||||
0.101797 | + | 0.994805i | \(0.467541\pi\) | |||||||
\(812\) | 2.20204i | 0.0772765i | ||||||||
\(813\) | − 43.5505i | − 1.52738i | ||||||||
\(814\) | 3.44949 | 0.120905 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −5.00000 | −0.175035 | ||||||||
\(817\) | − 5.50510i | − 0.192599i | ||||||||
\(818\) | − 34.1464i | − 1.19390i | ||||||||
\(819\) | −0.989795 | −0.0345862 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4.04541 | 0.141186 | 0.0705929 | − | 0.997505i | \(-0.477511\pi\) | ||||
0.0705929 | + | 0.997505i | \(0.477511\pi\) | |||||||
\(822\) | 14.0556i | 0.490246i | ||||||||
\(823\) | 33.8434i | 1.17971i | 0.807511 | + | 0.589853i | \(0.200814\pi\) | ||||
−0.807511 | + | 0.589853i | \(0.799186\pi\) | |||||||
\(824\) | −6.44949 | −0.224679 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −4.89898 | −0.170457 | ||||||||
\(827\) | − 27.0000i | − 0.938882i | −0.882964 | − | 0.469441i | \(-0.844455\pi\) | ||||
0.882964 | − | 0.469441i | \(-0.155545\pi\) | |||||||
\(828\) | − 1.79796i | − 0.0624834i | ||||||||
\(829\) | −21.3485 | −0.741463 | −0.370731 | − | 0.928740i | \(-0.620893\pi\) | ||||
−0.370731 | + | 0.928740i | \(0.620893\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8.40408 | −0.291534 | ||||||||
\(832\) | 0.449490i | 0.0155833i | ||||||||
\(833\) | − 3.44949i | − 0.119518i | ||||||||
\(834\) | −18.1918 | −0.629932 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −17.2474 | −0.596515 | ||||||||
\(837\) | − 25.1464i | − 0.869188i | ||||||||
\(838\) | − 21.4495i | − 0.740960i | ||||||||
\(839\) | 1.34847 | 0.0465543 | 0.0232772 | − | 0.999729i | \(-0.492590\pi\) | ||||
0.0232772 | + | 0.999729i | \(0.492590\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.1918 | −0.972132 | ||||||||
\(842\) | − 32.8990i | − 1.13377i | ||||||||
\(843\) | − 12.8990i | − 0.444264i | ||||||||
\(844\) | 4.55051 | 0.156635 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −8.80816 | −0.302831 | ||||||||
\(847\) | − 2.20204i | − 0.0756630i | ||||||||
\(848\) | 6.00000i | 0.206041i | ||||||||
\(849\) | −16.9546 | −0.581880 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.00000 | −0.0685591 | ||||||||
\(852\) | − 10.9444i | − 0.374949i | ||||||||
\(853\) | − 19.3485i | − 0.662479i | −0.943547 | − | 0.331239i | \(-0.892533\pi\) | ||||
0.943547 | − | 0.331239i | \(-0.107467\pi\) | |||||||
\(854\) | 15.7980 | 0.540595 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −8.55051 | −0.292250 | ||||||||
\(857\) | 32.1464i | 1.09810i | 0.835789 | + | 0.549051i | \(0.185011\pi\) | ||||
−0.835789 | + | 0.549051i | \(0.814989\pi\) | |||||||
\(858\) | 2.24745i | 0.0767266i | ||||||||
\(859\) | 9.49490 | 0.323962 | 0.161981 | − | 0.986794i | \(-0.448212\pi\) | ||||
0.161981 | + | 0.986794i | \(0.448212\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.55051 | −0.121001 | ||||||||
\(862\) | 20.6969i | 0.704941i | ||||||||
\(863\) | 18.2474i | 0.621150i | 0.950549 | + | 0.310575i | \(0.100522\pi\) | ||||
−0.950549 | + | 0.310575i | \(0.899478\pi\) | |||||||
\(864\) | −5.65153 | −0.192269 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 19.0000 | 0.645646 | ||||||||
\(867\) | − 7.39388i | − 0.251109i | ||||||||
\(868\) | 10.8990i | 0.369935i | ||||||||
\(869\) | −26.8990 | −0.912485 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.04541 | −0.0693060 | ||||||||
\(872\) | − 14.0000i | − 0.474100i | ||||||||
\(873\) | − 12.5857i | − 0.425962i | ||||||||
\(874\) | 10.0000 | 0.338255 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −18.5505 | −0.626764 | ||||||||
\(877\) | − 4.65153i | − 0.157071i | −0.996911 | − | 0.0785355i | \(-0.974976\pi\) | ||||
0.996911 | − | 0.0785355i | \(-0.0250244\pi\) | |||||||
\(878\) | − 19.5959i | − 0.661330i | ||||||||
\(879\) | −40.6515 | −1.37114 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 34.2929 | 1.15536 | 0.577678 | − | 0.816265i | \(-0.303959\pi\) | ||||
0.577678 | + | 0.816265i | \(0.303959\pi\) | |||||||
\(882\) | − 0.898979i | − 0.0302702i | ||||||||
\(883\) | 26.1010i | 0.878369i | 0.898397 | + | 0.439185i | \(0.144733\pi\) | ||||
−0.898397 | + | 0.439185i | \(0.855267\pi\) | |||||||
\(884\) | 1.55051 | 0.0521493 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −17.4495 | −0.586227 | ||||||||
\(887\) | − 50.6969i | − 1.70224i | −0.524974 | − | 0.851118i | \(-0.675925\pi\) | ||||
0.524974 | − | 0.851118i | \(-0.324075\pi\) | |||||||
\(888\) | 1.44949i | 0.0486417i | ||||||||
\(889\) | 39.7980 | 1.33478 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −18.9546 | −0.635003 | ||||||||
\(892\) | − 21.7980i | − 0.729850i | ||||||||
\(893\) | − 48.9898i | − 1.63938i | ||||||||
\(894\) | −6.74235 | −0.225498 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2.44949 | 0.0818317 | ||||||||
\(897\) | − 1.30306i | − 0.0435080i | ||||||||
\(898\) | 33.2474i | 1.10948i | ||||||||
\(899\) | 4.00000 | 0.133407 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 20.6969 | 0.689515 | ||||||||
\(902\) | − 3.44949i | − 0.114855i | ||||||||
\(903\) | 3.90918i | 0.130090i | ||||||||
\(904\) | 4.55051 | 0.151348 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 20.2929 | 0.674185 | ||||||||
\(907\) | 34.8990i | 1.15880i | 0.815043 | + | 0.579401i | \(0.196713\pi\) | ||||
−0.815043 | + | 0.579401i | \(0.803287\pi\) | |||||||
\(908\) | − 16.6969i | − 0.554107i | ||||||||
\(909\) | 0.989795 | 0.0328294 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −16.2474 | −0.538302 | −0.269151 | − | 0.963098i | \(-0.586743\pi\) | ||||
−0.269151 | + | 0.963098i | \(0.586743\pi\) | |||||||
\(912\) | − 7.24745i | − 0.239987i | ||||||||
\(913\) | 11.8990i | 0.393799i | ||||||||
\(914\) | −15.2474 | −0.504341 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 5.79796 | 0.191570 | ||||||||
\(917\) | − 21.3031i | − 0.703489i | ||||||||
\(918\) | 19.4949i | 0.643427i | ||||||||
\(919\) | 51.7980 | 1.70866 | 0.854329 | − | 0.519733i | \(-0.173969\pi\) | ||||
0.854329 | + | 0.519733i | \(0.173969\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −11.0908 | −0.365455 | ||||||||
\(922\) | − 9.30306i | − 0.306380i | ||||||||
\(923\) | 3.39388i | 0.111711i | ||||||||
\(924\) | 12.2474 | 0.402911 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 9.55051 | 0.313849 | ||||||||
\(927\) | 5.79796i | 0.190430i | ||||||||
\(928\) | − 0.898979i | − 0.0295104i | ||||||||
\(929\) | 5.79796 | 0.190225 | 0.0951124 | − | 0.995467i | \(-0.469679\pi\) | ||||
0.0951124 | + | 0.995467i | \(0.469679\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.00000 | 0.163868 | ||||||||
\(932\) | 28.4949i | 0.933381i | ||||||||
\(933\) | 12.2474i | 0.400963i | ||||||||
\(934\) | 12.0000 | 0.392652 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0.404082 | 0.0132078 | ||||||||
\(937\) | − 14.5959i | − 0.476828i | −0.971164 | − | 0.238414i | \(-0.923373\pi\) | ||||
0.971164 | − | 0.238414i | \(-0.0766275\pi\) | |||||||
\(938\) | 11.1464i | 0.363944i | ||||||||
\(939\) | 12.8990 | 0.420942 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −41.3939 | −1.34940 | −0.674701 | − | 0.738091i | \(-0.735727\pi\) | ||||
−0.674701 | + | 0.738091i | \(0.735727\pi\) | |||||||
\(942\) | 23.8434i | 0.776859i | ||||||||
\(943\) | 2.00000i | 0.0651290i | ||||||||
\(944\) | 2.00000 | 0.0650945 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.79796 | −0.123482 | ||||||||
\(947\) | − 32.0000i | − 1.03986i | −0.854209 | − | 0.519930i | \(-0.825958\pi\) | ||||
0.854209 | − | 0.519930i | \(-0.174042\pi\) | |||||||
\(948\) | − 11.3031i | − 0.367106i | ||||||||
\(949\) | 5.75255 | 0.186736 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 13.8434 | 0.448902 | ||||||||
\(952\) | − 8.44949i | − 0.273850i | ||||||||
\(953\) | 25.4949i | 0.825861i | 0.910763 | + | 0.412930i | \(0.135495\pi\) | ||||
−0.910763 | + | 0.412930i | \(0.864505\pi\) | |||||||
\(954\) | 5.39388 | 0.174633 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0.898979 | 0.0290751 | ||||||||
\(957\) | − 4.49490i | − 0.145299i | ||||||||
\(958\) | 6.24745i | 0.201846i | ||||||||
\(959\) | −23.7526 | −0.767010 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11.2020 | −0.361356 | ||||||||
\(962\) | − 0.449490i | − 0.0144921i | ||||||||
\(963\) | 7.68673i | 0.247702i | ||||||||
\(964\) | 2.55051 | 0.0821464 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −7.10102 | −0.228472 | ||||||||
\(967\) | 44.0000i | 1.41494i | 0.706741 | + | 0.707472i | \(0.250165\pi\) | ||||
−0.706741 | + | 0.707472i | \(0.749835\pi\) | |||||||
\(968\) | 0.898979i | 0.0288943i | ||||||||
\(969\) | −25.0000 | −0.803116 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −53.5403 | −1.71819 | −0.859095 | − | 0.511816i | \(-0.828973\pi\) | ||||
−0.859095 | + | 0.511816i | \(0.828973\pi\) | |||||||
\(972\) | 8.98979i | 0.288348i | ||||||||
\(973\) | − 30.7423i | − 0.985554i | ||||||||
\(974\) | 30.7423 | 0.985048 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −6.44949 | −0.206443 | ||||||||
\(977\) | 23.7423i | 0.759585i | 0.925072 | + | 0.379792i | \(0.124005\pi\) | ||||
−0.925072 | + | 0.379792i | \(0.875995\pi\) | |||||||
\(978\) | − 14.6413i | − 0.468178i | ||||||||
\(979\) | −49.4949 | −1.58186 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −12.5857 | −0.401831 | ||||||||
\(982\) | 41.7980i | 1.33383i | ||||||||
\(983\) | 18.4949i | 0.589896i | 0.955513 | + | 0.294948i | \(0.0953023\pi\) | ||||
−0.955513 | + | 0.294948i | \(0.904698\pi\) | |||||||
\(984\) | 1.44949 | 0.0462080 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −3.10102 | −0.0987566 | ||||||||
\(987\) | 34.7878i | 1.10731i | ||||||||
\(988\) | 2.24745i | 0.0715009i | ||||||||
\(989\) | 2.20204 | 0.0700208 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16.4495 | −0.522535 | −0.261268 | − | 0.965266i | \(-0.584141\pi\) | ||||
−0.261268 | + | 0.965266i | \(0.584141\pi\) | |||||||
\(992\) | − 4.44949i | − 0.141271i | ||||||||
\(993\) | − 28.8434i | − 0.915317i | ||||||||
\(994\) | 18.4949 | 0.586623 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −5.00000 | −0.158431 | ||||||||
\(997\) | − 39.5505i | − 1.25258i | −0.779591 | − | 0.626289i | \(-0.784573\pi\) | ||||
0.779591 | − | 0.626289i | \(-0.215427\pi\) | |||||||
\(998\) | 22.0000i | 0.696398i | ||||||||
\(999\) | 5.65153 | 0.178807 |
(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 | 1850.2.b.k.149.1 | 4 | ||
5.2 | odd | 4 | 1850.2.a.w.1.1 | yes | 2 | ||
5.3 | odd | 4 | 1850.2.a.r.1.2 | ✓ | 2 | ||
5.4 | even | 2 | inner | 1850.2.b.k.149.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1850.2.a.r.1.2 | ✓ | 2 | 5.3 | odd | 4 | ||
1850.2.a.w.1.1 | yes | 2 | 5.2 | odd | 4 | ||
1850.2.b.k.149.1 | 4 | 1.1 | even | 1 | trivial | ||
1850.2.b.k.149.4 | 4 | 5.4 | even | 2 | inner |