Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1792,2,Mod(897,1792)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1792, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1792.897");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1792 = 2^{8} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1792.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: | \(14.3091920422\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.399424.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} + 3x^{4} - 6x^{3} + 6x^{2} - 8x + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 896) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 897.4 | ||
Root | \(-0.671462 + 1.24464i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1792.897 |
Dual form | 1792.2.b.p.897.3 |
$q$-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 \(\left(\mathbb{Z}/1792\mathbb{Z}\right)^\times\).
\(n\) | \(1023\) | \(1025\) | \(1541\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.14637i | 0.661854i | 0.943656 | + | 0.330927i | \(0.107361\pi\) | ||||
−0.943656 | + | 0.330927i | \(0.892639\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.83221i | 1.71382i | 0.515468 | + | 0.856909i | \(0.327618\pi\) | ||||
−0.515468 | + | 0.856909i | \(0.672382\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.68585 | 0.561949 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 4.68585i | − 1.41284i | −0.707795 | − | 0.706418i | \(-0.750310\pi\) | ||||
0.707795 | − | 0.706418i | \(-0.249690\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.53948i | 1.53638i | 0.640225 | + | 0.768188i | \(0.278841\pi\) | ||||
−0.640225 | + | 0.768188i | \(0.721159\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.39312 | −1.13430 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.292731 | 0.0709977 | 0.0354988 | − | 0.999370i | \(-0.488698\pi\) | ||||
0.0354988 | + | 0.999370i | \(0.488698\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.14637i | 1.18066i | 0.807163 | + | 0.590329i | \(0.201002\pi\) | ||||
−0.807163 | + | 0.590329i | \(0.798998\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.14637i | 0.250157i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.97858 | 1.03811 | 0.519053 | − | 0.854742i | \(-0.326285\pi\) | ||||
0.519053 | + | 0.854742i | \(0.326285\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −9.68585 | −1.93717 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.37169i | 1.03378i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.29273i | 0.797140i | 0.917138 | + | 0.398570i | \(0.130493\pi\) | ||||
−0.917138 | + | 0.398570i | \(0.869507\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.66442 | 1.37657 | 0.688286 | − | 0.725440i | \(-0.258364\pi\) | ||||
0.688286 | + | 0.725440i | \(0.258364\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.37169 | 0.935092 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.83221i | 0.647762i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 9.66442i | − 1.58882i | −0.607381 | − | 0.794411i | \(-0.707780\pi\) | ||||
0.607381 | − | 0.794411i | \(-0.292220\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −6.35027 | −1.01686 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.70727 | −0.578978 | −0.289489 | − | 0.957181i | \(-0.593485\pi\) | ||||
−0.289489 | + | 0.957181i | \(0.593485\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.27131i | 0.803867i | 0.915669 | + | 0.401933i | \(0.131662\pi\) | ||||
−0.915669 | + | 0.401933i | \(0.868338\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 6.46052i | 0.963077i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.29273 | −0.334429 | −0.167215 | − | 0.985921i | \(-0.553477\pi\) | ||||
−0.167215 | + | 0.985921i | \(0.553477\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.335577i | 0.0469901i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.00000i | 0.274721i | 0.990521 | + | 0.137361i | \(0.0438619\pi\) | ||||
−0.990521 | + | 0.137361i | \(0.956138\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 17.9572 | 2.42134 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.89962 | −0.781423 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 9.93260i | − 1.29311i | −0.762866 | − | 0.646557i | \(-0.776208\pi\) | ||||
0.762866 | − | 0.646557i | \(-0.223792\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.16779i | 0.533631i | 0.963748 | + | 0.266815i | \(0.0859714\pi\) | ||||
−0.963748 | + | 0.266815i | \(0.914029\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.68585 | 0.212397 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −21.2285 | −2.63307 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 10.9786i | − 1.34125i | −0.741798 | − | 0.670623i | \(-0.766027\pi\) | ||||
0.741798 | − | 0.670623i | \(-0.233973\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.70727i | 0.687074i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.37169 | −0.862791 | −0.431396 | − | 0.902163i | \(-0.641979\pi\) | ||||
−0.431396 | + | 0.902163i | \(0.641979\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 11.1035i | − 1.28212i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 4.68585i | − 0.534002i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −13.9572 | −1.57030 | −0.785151 | − | 0.619304i | \(-0.787415\pi\) | ||||
−0.785151 | + | 0.619304i | \(0.787415\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.10038 | −0.122265 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.81079i | 0.528053i | 0.964515 | + | 0.264026i | \(0.0850506\pi\) | ||||
−0.964515 | + | 0.264026i | \(0.914949\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.12181i | 0.121677i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.92104 | −0.527591 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.58546 | 0.274058 | 0.137029 | − | 0.990567i | \(-0.456245\pi\) | ||||
0.137029 | + | 0.990567i | \(0.456245\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.53948i | 0.580695i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.78623i | 0.911090i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −19.7220 | −2.02343 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −14.2499 | −1.44686 | −0.723428 | − | 0.690399i | \(-0.757435\pi\) | ||||
−0.723428 | + | 0.690399i | \(0.757435\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − 7.89962i | − 0.793941i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 1.87506i | − 0.186575i | −0.995639 | − | 0.0932876i | \(-0.970262\pi\) | ||||
0.995639 | − | 0.0932876i | \(-0.0297376\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.66442 | −0.755198 | −0.377599 | − | 0.925969i | \(-0.623250\pi\) | ||||
−0.377599 | + | 0.925969i | \(0.623250\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −4.39312 | −0.428724 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.39312i | 0.231351i | 0.993287 | + | 0.115676i | \(0.0369033\pi\) | ||||
−0.993287 | + | 0.115676i | \(0.963097\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 1.07896i | − 0.103346i | −0.998664 | − | 0.0516729i | \(-0.983545\pi\) | ||||
0.998664 | − | 0.0516729i | \(-0.0164553\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 11.0790 | 1.05157 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.27131 | 0.872171 | 0.436086 | − | 0.899905i | \(-0.356364\pi\) | ||||
0.436086 | + | 0.899905i | \(0.356364\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 19.0790i | 1.77912i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 9.33871i | 0.863364i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.292731 | 0.0268346 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9572 | −0.996105 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 4.24989i | − 0.383199i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 17.9572i | − 1.60614i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.35027 | 0.563495 | 0.281748 | − | 0.959489i | \(-0.409086\pi\) | ||||
0.281748 | + | 0.959489i | \(0.409086\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −6.04285 | −0.532043 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 10.5181i | − 0.918967i | −0.888186 | − | 0.459483i | \(-0.848035\pi\) | ||||
0.888186 | − | 0.459483i | \(-0.151965\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.14637i | 0.446246i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −20.5855 | −1.77171 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 11.3717 | 0.971549 | 0.485775 | − | 0.874084i | \(-0.338538\pi\) | ||||
0.485775 | + | 0.874084i | \(0.338538\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 10.8536i | − 0.920593i | −0.887765 | − | 0.460297i | \(-0.847743\pi\) | ||||
0.887765 | − | 0.460297i | \(-0.152257\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 2.62831i | − 0.221343i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 25.9572 | 2.17065 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −16.4507 | −1.36615 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.14637i | 0.0945506i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.78623i | 0.228257i | 0.993466 | + | 0.114128i | \(0.0364075\pi\) | ||||
−0.993466 | + | 0.114128i | \(0.963592\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.56404 | −0.127280 | −0.0636398 | − | 0.997973i | \(-0.520271\pi\) | ||||
−0.0636398 | + | 0.997973i | \(0.520271\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.493499 | 0.0398971 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 29.3717i | 2.35919i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.7104i | 1.17402i | 0.809580 | + | 0.587009i | \(0.199695\pi\) | ||||
−0.809580 | + | 0.587009i | \(0.800305\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.29273 | −0.181825 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.97858 | 0.392367 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 0.100384i | − 0.00786270i | −0.999992 | − | 0.00393135i | \(-0.998749\pi\) | ||||
0.999992 | − | 0.00393135i | \(-0.00125139\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 20.5855i | 1.60258i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.70727 | 0.441642 | 0.220821 | − | 0.975314i | \(-0.429126\pi\) | ||||
0.220821 | + | 0.975314i | \(0.429126\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −17.6858 | −1.36045 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 8.67598i | 0.663469i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 12.8683i | 0.978361i | 0.872183 | + | 0.489180i | \(0.162704\pi\) | ||||
−0.872183 | + | 0.489180i | \(0.837296\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −9.68585 | −0.732181 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 11.3864 | 0.855853 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 26.3074i | − 1.96631i | −0.182776 | − | 0.983155i | \(-0.558508\pi\) | ||||
0.182776 | − | 0.983155i | \(-0.441492\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 3.24675i | − 0.241329i | −0.992693 | − | 0.120665i | \(-0.961497\pi\) | ||||
0.992693 | − | 0.120665i | \(-0.0385025\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.77781 | −0.353186 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 37.0361 | 2.72295 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 1.37169i | − 0.100308i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.37169i | 0.390733i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 17.3717 | 1.25697 | 0.628486 | − | 0.777821i | \(-0.283675\pi\) | ||||
0.628486 | + | 0.777821i | \(0.283675\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 27.4292 | 1.97440 | 0.987200 | − | 0.159490i | \(-0.0509848\pi\) | ||||
0.987200 | + | 0.159490i | \(0.0509848\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − 24.3356i | − 1.74271i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.0000i | 0.712470i | 0.934396 | + | 0.356235i | \(0.115940\pi\) | ||||
−0.934396 | + | 0.356235i | \(0.884060\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.24989 | 0.301266 | 0.150633 | − | 0.988590i | \(-0.451869\pi\) | ||||
0.150633 | + | 0.988590i | \(0.451869\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 12.5855 | 0.887710 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.29273i | 0.301291i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 14.2070i | − 0.992263i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 8.39312 | 0.583362 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 24.1151 | 1.66807 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.3503i | 1.40097i | 0.713667 | + | 0.700485i | \(0.247033\pi\) | ||||
−0.713667 | + | 0.700485i | \(0.752967\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −20.2008 | −1.37768 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.66442 | 0.520295 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 8.45065i | − 0.571042i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.62158i | 0.109079i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.786230 | −0.0526499 | −0.0263249 | − | 0.999653i | \(-0.508380\pi\) | ||||
−0.0263249 | + | 0.999653i | \(0.508380\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −16.3288 | −1.08859 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 10.8536i | − 0.720381i | −0.932879 | − | 0.360191i | \(-0.882712\pi\) | ||||
0.932879 | − | 0.360191i | \(-0.117288\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 10.1249i | − 0.669075i | −0.942382 | − | 0.334538i | \(-0.891420\pi\) | ||||
0.942382 | − | 0.334538i | \(-0.108580\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.37169 | 0.353431 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 18.7862 | 1.23073 | 0.615363 | − | 0.788244i | \(-0.289009\pi\) | ||||
0.615363 | + | 0.788244i | \(0.289009\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 8.78623i | − 0.573150i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 16.0000i | − 1.03931i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.02142 | −0.454178 | −0.227089 | − | 0.973874i | \(-0.572921\pi\) | ||||
−0.227089 | + | 0.973874i | \(0.572921\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −28.4078 | −1.82991 | −0.914954 | − | 0.403558i | \(-0.867773\pi\) | ||||
−0.914954 | + | 0.403558i | \(0.867773\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 14.8536i | 0.952861i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.83221i | 0.244831i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −28.5082 | −1.81393 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5.51492 | −0.349494 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 2.51806i | − 0.158938i | −0.996837 | − | 0.0794692i | \(-0.974677\pi\) | ||||
0.996837 | − | 0.0794692i | \(-0.0253225\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 23.3288i | − 1.46667i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.28600 | −0.0805325 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.41454 | −0.0882365 | −0.0441182 | − | 0.999026i | \(-0.514048\pi\) | ||||
−0.0441182 | + | 0.999026i | \(0.514048\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 9.66442i | − 0.600518i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.23688i | 0.447952i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 27.9143 | 1.72127 | 0.860635 | − | 0.509222i | \(-0.170067\pi\) | ||||
0.860635 | + | 0.509222i | \(0.170067\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.66442 | −0.470822 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.96388i | 0.181387i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 18.1249i | 1.10510i | 0.833481 | + | 0.552549i | \(0.186345\pi\) | ||||
−0.833481 | + | 0.552549i | \(0.813655\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −24.1151 | −1.46489 | −0.732443 | − | 0.680828i | \(-0.761620\pi\) | ||||
−0.732443 | + | 0.680828i | \(0.761620\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −6.35027 | −0.384336 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 45.3864i | 2.73690i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 0.628308i | − 0.0377513i | −0.999822 | − | 0.0188757i | \(-0.993991\pi\) | ||||
0.999822 | − | 0.0188757i | \(-0.00600867\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 12.9210 | 0.773562 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.743385 | −0.0443466 | −0.0221733 | − | 0.999754i | \(-0.507059\pi\) | ||||
−0.0221733 | + | 0.999754i | \(0.507059\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.475212i | 0.0282484i | 0.999900 | + | 0.0141242i | \(0.00449603\pi\) | ||||
−0.999900 | + | 0.0141242i | \(0.995504\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 22.6086i | − 1.33922i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.70727 | −0.218833 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.9143 | −0.994959 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 16.3356i | − 0.957608i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.53948i | 0.0899374i | 0.998988 | + | 0.0449687i | \(0.0143188\pi\) | ||||
−0.998988 | + | 0.0449687i | \(0.985681\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 38.0638 | 2.21616 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 25.1709 | 1.46057 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 27.5787i | 1.59492i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.27131i | 0.303833i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.14950 | 0.123486 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −15.9718 | −0.914545 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 21.2614i | − 1.21345i | −0.794910 | − | 0.606727i | \(-0.792482\pi\) | ||||
0.794910 | − | 0.606727i | \(-0.207518\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − 8.78623i | − 0.499831i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −15.3288 | −0.869219 | −0.434610 | − | 0.900619i | \(-0.643114\pi\) | ||||
−0.434610 | + | 0.900619i | \(0.643114\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.70727 | −0.209547 | −0.104774 | − | 0.994496i | \(-0.533412\pi\) | ||||
−0.104774 | + | 0.994496i | \(0.533412\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 6.46052i | 0.364009i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 22.5855i | − 1.26853i | −0.773117 | − | 0.634263i | \(-0.781304\pi\) | ||||
0.773117 | − | 0.634263i | \(-0.218696\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 20.1151 | 1.12623 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.74338 | −0.153121 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.50650i | 0.0838239i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 53.6546i | − 2.97622i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.23688 | 0.0683998 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.29273 | −0.126402 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 14.6430i | − 0.804852i | −0.915452 | − | 0.402426i | \(-0.868167\pi\) | ||||
0.915452 | − | 0.402426i | \(-0.131833\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 16.2927i | − 0.892836i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 42.0722 | 2.29865 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 21.4721 | 1.16966 | 0.584829 | − | 0.811156i | \(-0.301162\pi\) | ||||
0.584829 | + | 0.811156i | \(0.301162\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 10.6283i | 0.577250i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 35.9143i | − 1.94487i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −21.8715 | −1.17752 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 28.6002i | 1.53534i | 0.640847 | + | 0.767668i | \(0.278583\pi\) | ||||
−0.640847 | + | 0.767668i | \(0.721417\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 23.8322i | 1.27571i | 0.770157 | + | 0.637855i | \(0.220178\pi\) | ||||
−0.770157 | + | 0.637855i | \(0.779822\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −29.7564 | −1.58828 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 35.2860 | 1.87808 | 0.939042 | − | 0.343802i | \(-0.111715\pi\) | ||||
0.939042 | + | 0.343802i | \(0.111715\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.335577i | 0.0177606i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0.393115 | 0.0207478 | 0.0103739 | − | 0.999946i | \(-0.496698\pi\) | ||||
0.0103739 | + | 0.999946i | \(0.496698\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.48508 | −0.393951 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 12.5609i | − 0.659276i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 28.2499i | − 1.47867i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.62831 | 0.137197 | 0.0685983 | − | 0.997644i | \(-0.478147\pi\) | ||||
0.0685983 | + | 0.997644i | \(0.478147\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −6.24989 | −0.325356 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.00000i | 0.103835i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 14.7862i | − 0.765602i | −0.923831 | − | 0.382801i | \(-0.874959\pi\) | ||||
0.923831 | − | 0.382801i | \(-0.125041\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 20.5855 | 1.06303 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −23.7795 | −1.22471 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.10038i | 0.210623i | 0.994439 | + | 0.105311i | \(0.0335839\pi\) | ||||
−0.994439 | + | 0.105311i | \(0.966416\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.27973i | 0.372952i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 11.4637 | 0.585765 | 0.292883 | − | 0.956148i | \(-0.405385\pi\) | ||||
0.292883 | + | 0.956148i | \(0.405385\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 17.9572 | 0.915181 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 8.88661i | 0.451732i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 24.9933i | − 1.26721i | −0.773657 | − | 0.633605i | \(-0.781575\pi\) | ||||
0.773657 | − | 0.633605i | \(-0.218425\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.45738 | 0.0737031 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 12.0575 | 0.608222 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 53.4868i | − 2.69121i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.83221i | 0.393087i | 0.980495 | + | 0.196544i | \(0.0629718\pi\) | ||||
−0.980495 | + | 0.196544i | \(0.937028\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −5.89962 | −0.295350 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 37.3864 | 1.86699 | 0.933493 | − | 0.358594i | \(-0.116744\pi\) | ||||
0.933493 | + | 0.358594i | \(0.116744\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 42.4569i | 2.11493i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 4.21691i | − 0.209540i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −45.2860 | −2.24474 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.24989 | 0.309037 | 0.154518 | − | 0.987990i | \(-0.450617\pi\) | ||||
0.154518 | + | 0.987990i | \(0.450617\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 13.0361i | 0.643024i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 9.93260i | − 0.488751i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −18.4360 | −0.904986 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 12.4422 | 0.609299 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 19.4391i | − 0.949662i | −0.880077 | − | 0.474831i | \(-0.842509\pi\) | ||||
0.880077 | − | 0.474831i | \(-0.157491\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 35.2860i | 1.71973i | 0.510518 | + | 0.859867i | \(0.329454\pi\) | ||||
−0.510518 | + | 0.859867i | \(0.670546\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.86519 | −0.187932 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.83535 | −0.137535 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.16779i | 0.201693i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 29.7564i | 1.43665i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7.80765 | −0.376081 | −0.188041 | − | 0.982161i | \(-0.560214\pi\) | ||||
−0.188041 | + | 0.982161i | \(0.560214\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 17.4637 | 0.839250 | 0.419625 | − | 0.907698i | \(-0.362162\pi\) | ||||
0.419625 | + | 0.907698i | \(0.362162\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 18.8585i | − 0.904194i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 25.6216i | 1.22565i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 32.7862 | 1.56480 | 0.782401 | − | 0.622775i | \(-0.213995\pi\) | ||||
0.782401 | + | 0.622775i | \(0.213995\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.68585 | 0.0802784 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 34.5082i | 1.63953i | 0.572697 | + | 0.819767i | \(0.305897\pi\) | ||||
−0.572697 | + | 0.819767i | \(0.694103\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9.90804i | 0.469686i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.19404 | −0.151073 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 22.7862 | 1.07535 | 0.537674 | − | 0.843153i | \(-0.319303\pi\) | ||||
0.537674 | + | 0.843153i | \(0.319303\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 17.3717i | 0.818001i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 1.79296i | − 0.0842406i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −21.2285 | −0.995206 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.01469 | 0.374912 | 0.187456 | − | 0.982273i | \(-0.439976\pi\) | ||||
0.187456 | + | 0.982273i | \(0.439976\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.57246i | 0.0733962i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 31.4966i | − 1.46694i | −0.679719 | − | 0.733472i | \(-0.737898\pi\) | ||||
0.679719 | − | 0.733472i | \(-0.262102\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −28.7862 | −1.33781 | −0.668905 | − | 0.743348i | \(-0.733237\pi\) | ||||
−0.668905 | + | 0.743348i | \(0.733237\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −33.6707 | −1.56144 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 16.5609i | 0.766347i | 0.923676 | + | 0.383174i | \(0.125169\pi\) | ||||
−0.923676 | + | 0.383174i | \(0.874831\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 10.9786i | − 0.506944i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −16.8635 | −0.777029 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 24.7005 | 1.13573 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 49.8469i | − 2.28713i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.37169i | 0.154379i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −15.6644 | −0.715726 | −0.357863 | − | 0.933774i | \(-0.616494\pi\) | ||||
−0.357863 | + | 0.933774i | \(0.616494\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 53.5359 | 2.44103 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 5.70727i | 0.259690i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 54.6086i | − 2.47965i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 31.7220 | 1.43746 | 0.718730 | − | 0.695290i | \(-0.244724\pi\) | ||||
0.718730 | + | 0.695290i | \(0.244724\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.115077 | 0.00520396 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 35.4783i | − 1.60112i | −0.599256 | − | 0.800558i | \(-0.704537\pi\) | ||||
0.599256 | − | 0.800558i | \(-0.295463\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.25662i | 0.0565951i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 30.2730 | 1.36067 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 15.6497i | 0.700578i | 0.936642 | + | 0.350289i | \(0.113917\pi\) | ||||
−0.936642 | + | 0.350289i | \(0.886083\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.54262i | 0.292303i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 37.3717 | 1.66632 | 0.833161 | − | 0.553031i | \(-0.186529\pi\) | ||||
0.833161 | + | 0.553031i | \(0.186529\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.18562 | 0.319756 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 20.2744i | − 0.900420i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 18.5756i | 0.823349i | 0.911331 | + | 0.411674i | \(0.135056\pi\) | ||||
−0.911331 | + | 0.411674i | \(0.864944\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.37169 | −0.326104 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −27.6447 | −1.22054 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 29.3717i | − 1.29427i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10.7434i | 0.472494i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −14.7518 | −0.647532 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −17.5787 | −0.770138 | −0.385069 | − | 0.922888i | \(-0.625822\pi\) | ||||
−0.385069 | + | 0.922888i | \(0.625822\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 14.5181i | − 0.634830i | −0.948287 | − | 0.317415i | \(-0.897185\pi\) | ||||
0.948287 | − | 0.317415i | \(-0.102815\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − 11.1035i | − 0.484597i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.24361 | 0.0977334 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.78623 | 0.0776622 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 16.7448i | − 0.726664i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 20.5363i | − 0.889528i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −9.17092 | −0.396494 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 30.1579 | 1.30141 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 4.68585i | − 0.201834i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.5426i | 0.539249i | 0.962966 | + | 0.269625i | \(0.0868996\pi\) | ||||
−0.962966 | + | 0.269625i | \(0.913100\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.72196 | 0.159725 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.13481 | 0.177116 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 0.771538i | − 0.0329886i | −0.999864 | − | 0.0164943i | \(-0.994749\pi\) | ||||
0.999864 | − | 0.0164943i | \(-0.00525053\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 7.02625i | 0.299873i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −22.0920 | −0.941149 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −13.9572 | −0.593519 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 42.4569i | 1.80220i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 28.7434i | − 1.21790i | −0.793210 | − | 0.608948i | \(-0.791592\pi\) | ||||
0.793210 | − | 0.608948i | \(-0.208408\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −29.2003 | −1.23504 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.57246 | 0.0663893 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 5.34713i | − 0.225355i | −0.993632 | − | 0.112677i | \(-0.964057\pi\) | ||||
0.993632 | − | 0.112677i | \(-0.0359427\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 35.5296i | 1.49474i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.10038 | −0.0462118 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 31.2285 | 1.30917 | 0.654583 | − | 0.755990i | \(-0.272844\pi\) | ||||
0.654583 | + | 0.755990i | \(0.272844\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 18.7287i | − 0.783771i | −0.920014 | − | 0.391886i | \(-0.871823\pi\) | ||||
0.920014 | − | 0.391886i | \(-0.128177\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 19.9143i | 0.831932i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −48.2217 | −2.01099 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0.542616 | 0.0225894 | 0.0112947 | − | 0.999936i | \(-0.496405\pi\) | ||||
0.0112947 | + | 0.999936i | \(0.496405\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 31.4439i | 1.30676i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.81079i | 0.199585i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.37169 | 0.388136 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −35.7879 | −1.47965 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 7.43910i | − 0.307044i | −0.988145 | − | 0.153522i | \(-0.950938\pi\) | ||||
0.988145 | − | 0.153522i | \(-0.0490617\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 39.4439i | 1.62526i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −11.4637 | −0.471552 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −9.91431 | −0.407132 | −0.203566 | − | 0.979061i | \(-0.565253\pi\) | ||||
−0.203566 | + | 0.979061i | \(0.565253\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.12181i | 0.0459896i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4.87192i | 0.199394i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 29.4868 | 1.20480 | 0.602398 | − | 0.798196i | \(-0.294212\pi\) | ||||
0.602398 | + | 0.798196i | \(0.294212\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 33.2432 | 1.35602 | 0.678008 | − | 0.735054i | \(-0.262843\pi\) | ||||
0.678008 | + | 0.735054i | \(0.262843\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 18.5082i | − 0.753712i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 41.9901i | − 1.70714i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 18.0722 | 0.733529 | 0.366765 | − | 0.930314i | \(-0.380465\pi\) | ||||
0.366765 | + | 0.930314i | \(0.380465\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4.92104 | −0.199411 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 12.7005i | − 0.513809i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 37.7795i | 1.52590i | 0.646458 | + | 0.762950i | \(0.276250\pi\) | ||||
−0.646458 | + | 0.762950i | \(0.723750\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 16.2865 | 0.656733 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 16.4851 | 0.663664 | 0.331832 | − | 0.943338i | \(-0.392333\pi\) | ||||
0.331832 | + | 0.943338i | \(0.392333\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 22.1825i | − 0.891589i | −0.895135 | − | 0.445795i | \(-0.852921\pi\) | ||||
0.895135 | − | 0.445795i | \(-0.147079\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 26.7434i | 1.07318i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.58546 | 0.103584 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 20.3864 | 0.815455 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 27.6447i | 1.10402i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 2.82908i | − 0.112803i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.9870 | 0.517004 | 0.258502 | − | 0.966011i | \(-0.416771\pi\) | ||||
0.258502 | + | 0.966011i | \(0.416771\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −23.3288 | −0.927238 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 24.3356i | 0.965728i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.53948i | 0.219482i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.72869 | 0.265767 | 0.132884 | − | 0.991132i | \(-0.457576\pi\) | ||||
0.132884 | + | 0.991132i | \(0.457576\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 45.1758i | − 1.78156i | −0.454437 | − | 0.890779i | \(-0.650160\pi\) | ||||
0.454437 | − | 0.890779i | \(-0.349840\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − 23.1575i | − 0.911824i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −34.4078 | −1.35271 | −0.676355 | − | 0.736576i | \(-0.736442\pi\) | ||||
−0.676355 | + | 0.736576i | \(0.736442\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −46.5426 | −1.82696 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8.78623i | 0.344360i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 15.0361i | 0.588409i | 0.955743 | + | 0.294204i | \(0.0950546\pi\) | ||||
−0.955743 | + | 0.294204i | \(0.904945\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 40.3074 | 1.57494 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −12.4275 | −0.484844 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 20.8866i | 0.813627i | 0.913511 | + | 0.406813i | \(0.133360\pi\) | ||||
−0.913511 | + | 0.406813i | \(0.866640\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.79610i | 0.264337i | 0.991227 | + | 0.132169i | \(0.0421941\pi\) | ||||
−0.991227 | + | 0.132169i | \(0.957806\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.85892 | −0.0721945 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −19.7220 | −0.764785 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 21.3717i | 0.827515i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 0.901307i | − 0.0348466i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 19.5296 | 0.753932 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.15792 | −0.314465 | −0.157232 | − | 0.987562i | \(-0.550257\pi\) | ||||
−0.157232 | + | 0.987562i | \(0.550257\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 52.0294i | − 2.00261i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 5.58860i | − 0.214787i | −0.994217 | − | 0.107394i | \(-0.965749\pi\) | ||||
0.994217 | − | 0.107394i | \(-0.0342505\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −14.2499 | −0.546860 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 12.4422 | 0.476787 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 6.30742i | 0.241347i | 0.992692 | + | 0.120673i | \(0.0385054\pi\) | ||||
−0.992692 | + | 0.120673i | \(0.961495\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 43.5787i | 1.66506i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 11.6069 | 0.442830 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −11.0790 | −0.422075 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 0.945597i | − 0.0359722i | −0.999838 | − | 0.0179861i | \(-0.994275\pi\) | ||||
0.999838 | − | 0.0179861i | \(-0.00572546\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 7.89962i | − 0.300082i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 41.5934 | 1.57773 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.08523 | −0.0411061 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 21.5359i | 0.814562i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 12.2070i | − 0.461054i | −0.973066 | − | 0.230527i | \(-0.925955\pi\) | ||||
0.973066 | − | 0.230527i | \(-0.0740449\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 49.7367 | 1.87585 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 10.0722 | 0.379342 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 1.87506i | − 0.0705188i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 34.2499i | 1.28628i | 0.765748 | + | 0.643141i | \(0.222369\pi\) | ||||
−0.765748 | + | 0.643141i | \(0.777631\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −23.5296 | −0.882430 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 38.1579 | 1.42903 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 99.4733i | 3.72009i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 8.04912i | − 0.300600i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −25.1218 | −0.936885 | −0.468443 | − | 0.883494i | \(-0.655185\pi\) | ||||
−0.468443 | + | 0.883494i | \(0.655185\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.66442 | −0.285438 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 32.5657i | − 1.21113i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 41.5787i | − 1.54420i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −31.2797 | −1.16010 | −0.580050 | − | 0.814581i | \(-0.696967\pi\) | ||||
−0.580050 | + | 0.814581i | \(0.696967\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −20.3288 | −0.752920 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.54308i | 0.0570727i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 21.0031i | − 0.775769i | −0.921708 | − | 0.387884i | \(-0.873206\pi\) | ||||
0.921708 | − | 0.387884i | \(-0.126794\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −4.39312 | −0.162042 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −51.4439 | −1.89496 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 37.3864i | 1.37528i | 0.726052 | + | 0.687640i | \(0.241353\pi\) | ||||
−0.726052 | + | 0.687640i | \(0.758647\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 32.6808i | − 1.20056i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −19.9227 | −0.730894 | −0.365447 | − | 0.930832i | \(-0.619084\pi\) | ||||
−0.365447 | + | 0.930832i | \(0.619084\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −10.6774 | −0.391191 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 8.11025i | 0.296739i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.39312i | 0.0874425i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −44.8929 | −1.63816 | −0.819082 | − | 0.573676i | \(-0.805517\pi\) | ||||
−0.819082 | + | 0.573676i | \(0.805517\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.88661 | 0.105194 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 5.99373i | − 0.218134i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.46365i | 0.343962i | 0.985100 | + | 0.171981i | \(0.0550168\pi\) | ||||
−0.985100 | + | 0.171981i | \(0.944983\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 26.7434 | 0.970723 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 25.7795 | 0.934506 | 0.467253 | − | 0.884124i | \(-0.345244\pi\) | ||||
0.467253 | + | 0.884124i | \(0.345244\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 1.07896i | − 0.0390610i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.89119i | 0.0683763i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 55.0214 | 1.98671 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −19.5065 | −0.703422 | −0.351711 | − | 0.936109i | \(-0.614400\pi\) | ||||
−0.351711 | + | 0.936109i | \(0.614400\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 1.62158i | − 0.0583997i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 44.6676i | − 1.60658i | −0.595588 | − | 0.803290i | \(-0.703081\pi\) | ||||
0.595588 | − | 0.803290i | \(-0.296919\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −74.2364 | −2.66665 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 11.0790 | 0.397456 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 19.0790i | − 0.683575i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −23.0592 | −0.824070 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −56.3734 | −2.01205 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 34.1825i | − 1.21847i | −0.792988 | − | 0.609237i | \(-0.791476\pi\) | ||||
0.792988 | − | 0.609237i | \(-0.208524\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 32.0000i | 1.13923i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.27131 | 0.329650 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −23.0874 | −0.819857 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 8.78623i | − 0.311615i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 24.6184i | − 0.872030i | −0.899939 | − | 0.436015i | \(-0.856389\pi\) | ||||
0.899939 | − | 0.436015i | \(-0.143611\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.671153 | −0.0237437 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.35869 | 0.154007 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 34.5426i | 1.21898i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 19.0790i | 0.672445i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −20.7778 | −0.731414 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −31.8139 | −1.11852 | −0.559259 | − | 0.828993i | \(-0.688914\pi\) | ||||
−0.559259 | + | 0.828993i | \(0.688914\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 43.9389i | − 1.54290i | −0.636289 | − | 0.771451i | \(-0.719531\pi\) | ||||
0.636289 | − | 0.771451i | \(-0.280469\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 27.6447i | − 0.969542i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.384694 | 0.0134752 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −27.1281 | −0.949091 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 9.33871i | 0.326321i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 45.1281i | 1.57498i | 0.616327 | + | 0.787490i | \(0.288620\pi\) | ||||
−0.616327 | + | 0.787490i | \(0.711380\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −14.1579 | −0.493514 | −0.246757 | − | 0.969077i | \(-0.579365\pi\) | ||||
−0.246757 | + | 0.969077i | \(0.579365\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −52.0294 | −1.81143 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 14.5082i | − 0.504499i | −0.967662 | − | 0.252250i | \(-0.918830\pi\) | ||||
0.967662 | − | 0.252250i | \(-0.0811704\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 15.7465i | − 0.546899i | −0.961886 | − | 0.273450i | \(-0.911835\pi\) | ||||
0.961886 | − | 0.273450i | \(-0.0881647\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.720270 | 0.0249859 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.292731 | 0.0101425 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 21.8715i | 0.756893i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 41.1709i | 1.42308i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 7.66442 | 0.264605 | 0.132303 | − | 0.991209i | \(-0.457763\pi\) | ||||
0.132303 | + | 0.991209i | \(0.457763\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.5725 | 0.364568 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 0.852191i | − 0.0293510i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 67.7759i | − 2.33156i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −10.9572 | −0.376492 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −0.544767 | −0.0186963 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 48.1151i | − 1.64936i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 16.9540i | − 0.580495i | −0.956952 | − | 0.290247i | \(-0.906262\pi\) | ||||
0.956952 | − | 0.290247i | \(-0.0937376\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −33.2482 | −1.13706 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −17.0790 | −0.583406 | −0.291703 | − | 0.956509i | \(-0.594222\pi\) | ||||
−0.291703 | + | 0.956509i | \(0.594222\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 10.5181i | − 0.358872i | −0.983770 | − | 0.179436i | \(-0.942573\pi\) | ||||
0.983770 | − | 0.179436i | \(-0.0574272\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − 4.24989i | − 0.144836i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −36.1151 | −1.22937 | −0.614686 | − | 0.788772i | \(-0.710717\pi\) | ||||
−0.614686 | + | 0.788772i | \(0.710717\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −49.3142 | −1.67673 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 19.3900i | − 0.658518i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 65.4011i | 2.21858i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 60.8156 | 2.06066 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −24.0231 | −0.813059 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 17.9572i | − 0.607063i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 0.177654i | − 0.00599895i | −0.999996 | − | 0.00299947i | \(-0.999045\pi\) | ||||
0.999996 | − | 0.00299947i | \(-0.000954764\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.76481 | −0.0595255 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.52962 | −0.0515340 | −0.0257670 | − | 0.999668i | \(-0.508203\pi\) | ||||
−0.0257670 | + | 0.999668i | \(0.508203\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 43.7942i | 1.47379i | 0.676006 | + | 0.736896i | \(0.263709\pi\) | ||||
−0.676006 | + | 0.736896i | \(0.736291\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 43.6350i | 1.46678i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 35.6938 | 1.19848 | 0.599240 | − | 0.800569i | \(-0.295469\pi\) | ||||
0.599240 | + | 0.800569i | \(0.295469\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.35027 | 0.212981 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.15623i | 0.172740i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 11.7992i | − 0.394846i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 100.816 | 3.36989 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −31.6153 | −1.05560 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 32.9013i | 1.09732i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.585462i | 0.0195046i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −6.04285 | −0.201093 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 12.4422 | 0.413594 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 33.3373i | 1.10695i | 0.832867 | + | 0.553473i | \(0.186698\pi\) | ||||
−0.832867 | + | 0.553473i | \(0.813302\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 3.16106i | − 0.104846i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 45.5640 | 1.50960 | 0.754802 | − | 0.655953i | \(-0.227733\pi\) | ||||
0.754802 | + | 0.655953i | \(0.227733\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 22.5426 | 0.746052 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 18.3096i | − 0.605296i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 10.5181i | − 0.347337i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6.15792 | −0.203131 | −0.101566 | − | 0.994829i | \(-0.532385\pi\) | ||||
−0.101566 | + | 0.994829i | \(0.532385\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 24.3734 | 0.803130 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 93.6081i | 3.07782i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −12.9210 | −0.424383 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −42.9504 | −1.40916 | −0.704579 | − | 0.709626i | \(-0.748864\pi\) | ||||
−0.704579 | + | 0.709626i | \(0.748864\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.14637i | 0.168665i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 17.5725i | − 0.575297i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5.25662 | 0.171910 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 41.1281 | 1.34360 | 0.671798 | − | 0.740735i | \(-0.265522\pi\) | ||||
0.671798 | + | 0.740735i | \(0.265522\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 4.24989i | − 0.138690i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.61844i | 0.150557i | 0.997163 | + | 0.0752785i | \(0.0239846\pi\) | ||||
−0.997163 | + | 0.0752785i | \(0.976015\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −18.4569 | −0.601040 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −20.5855 | −0.669645 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0.800923i | 0.0260265i | 0.999915 | + | 0.0130133i | \(0.00414236\pi\) | ||||
−0.999915 | + | 0.0130133i | \(0.995858\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 40.8353i | − 1.32557i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 25.8912 | 0.839579 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −13.9143 | −0.450729 | −0.225364 | − | 0.974275i | \(-0.572357\pi\) | ||||
−0.225364 | + | 0.974275i | \(0.572357\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 66.5720i | 2.15422i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 23.0592i | 0.745399i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 11.3717 | 0.367211 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 27.7434 | 0.894948 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4.03442i | 0.130007i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 105.115i | 3.38376i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 27.6363 | 0.888723 | 0.444361 | − | 0.895848i | \(-0.353431\pi\) | ||||
0.444361 | + | 0.895848i | \(0.353431\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.72700 | −0.0554792 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0.810789i | 0.0260195i | 0.999915 | + | 0.0130097i | \(0.00414124\pi\) | ||||
−0.999915 | + | 0.0130097i | \(0.995859\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 10.8536i | − 0.347952i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 61.5077 | 1.96982 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −4.62831 | −0.148073 | −0.0740363 | − | 0.997256i | \(-0.523588\pi\) | ||||
−0.0740363 | + | 0.997256i | \(0.523588\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 12.1151i | − 0.387200i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 1.81896i | − 0.0580750i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −5.42081 | −0.172897 | −0.0864485 | − | 0.996256i | \(-0.527552\pi\) | ||||
−0.0864485 | + | 0.996256i | \(0.527552\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −38.3221 | −1.22104 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 2.62831i | − 0.0836600i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 26.2436i | 0.834498i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16.2008 | −0.514634 | −0.257317 | − | 0.966327i | \(-0.582839\pi\) | ||||
−0.257317 | + | 0.966327i | \(0.582839\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 16.7862 | 0.532695 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 16.2865i | 0.516315i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 17.9901i | 0.569753i | 0.958564 | + | 0.284877i | \(0.0919526\pi\) | ||||
−0.958564 | + | 0.284877i | \(0.908047\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 51.9143 | 1.64250 |
(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 | 1792.2.b.p.897.4 | 6 | ||
4.3 | odd | 2 | 1792.2.b.o.897.3 | 6 | |||
8.3 | odd | 2 | 1792.2.b.o.897.4 | 6 | |||
8.5 | even | 2 | inner | 1792.2.b.p.897.3 | 6 | ||
16.3 | odd | 4 | 896.2.a.k.1.2 | yes | 3 | ||
16.5 | even | 4 | 896.2.a.l.1.2 | yes | 3 | ||
16.11 | odd | 4 | 896.2.a.j.1.2 | yes | 3 | ||
16.13 | even | 4 | 896.2.a.i.1.2 | ✓ | 3 | ||
48.5 | odd | 4 | 8064.2.a.bu.1.3 | 3 | |||
48.11 | even | 4 | 8064.2.a.cb.1.3 | 3 | |||
48.29 | odd | 4 | 8064.2.a.ce.1.1 | 3 | |||
48.35 | even | 4 | 8064.2.a.ch.1.1 | 3 | |||
112.13 | odd | 4 | 6272.2.a.x.1.2 | 3 | |||
112.27 | even | 4 | 6272.2.a.w.1.2 | 3 | |||
112.69 | odd | 4 | 6272.2.a.u.1.2 | 3 | |||
112.83 | even | 4 | 6272.2.a.v.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
896.2.a.i.1.2 | ✓ | 3 | 16.13 | even | 4 | ||
896.2.a.j.1.2 | yes | 3 | 16.11 | odd | 4 | ||
896.2.a.k.1.2 | yes | 3 | 16.3 | odd | 4 | ||
896.2.a.l.1.2 | yes | 3 | 16.5 | even | 4 | ||
1792.2.b.o.897.3 | 6 | 4.3 | odd | 2 | |||
1792.2.b.o.897.4 | 6 | 8.3 | odd | 2 | |||
1792.2.b.p.897.3 | 6 | 8.5 | even | 2 | inner | ||
1792.2.b.p.897.4 | 6 | 1.1 | even | 1 | trivial | ||
6272.2.a.u.1.2 | 3 | 112.69 | odd | 4 | |||
6272.2.a.v.1.2 | 3 | 112.83 | even | 4 | |||
6272.2.a.w.1.2 | 3 | 112.27 | even | 4 | |||
6272.2.a.x.1.2 | 3 | 112.13 | odd | 4 | |||
8064.2.a.bu.1.3 | 3 | 48.5 | odd | 4 | |||
8064.2.a.cb.1.3 | 3 | 48.11 | even | 4 | |||
8064.2.a.ce.1.1 | 3 | 48.29 | odd | 4 | |||
8064.2.a.ch.1.1 | 3 | 48.35 | even | 4 |