Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4032,2,Mod(3583,4032)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4032, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4032.3583");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4032 = 2^{6} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4032.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: | \(32.1956820950\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | 16.0.29960650073923649536.7 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 7x^{12} + 40x^{8} - 112x^{4} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{30} \) |
Twist minimal: | no (minimal twist has level 2016) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3583.2 | ||
Root | \(-0.481610 + 1.32968i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4032.3583 |
Dual form | 4032.2.b.r.3583.13 |
$q$-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 \(\left(\mathbb{Z}/4032\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(1793\) | \(3781\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 3.33513i | − | 1.49152i | −0.666217 | − | 0.745758i | \(-0.732087\pi\) | ||
0.666217 | − | 0.745758i | \(-0.267913\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.662153 | + | 2.56155i | −0.250270 | + | 0.968176i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.03680i | 1.51865i | 0.650711 | + | 0.759326i | \(0.274471\pi\) | ||||
−0.650711 | + | 0.759326i | \(0.725529\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.04090i | 1.67544i | 0.546098 | + | 0.837722i | \(0.316113\pi\) | ||||
−0.546098 | + | 0.837722i | \(0.683887\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 5.20798i | − | 1.26312i | −0.775326 | − | 0.631561i | \(-0.782415\pi\) | ||
0.775326 | − | 0.631561i | \(-0.217585\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.71659 | 1.08206 | 0.541030 | − | 0.841003i | \(-0.318035\pi\) | ||||
0.541030 | + | 0.841003i | \(0.318035\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 2.20837i | − | 0.460477i | −0.973134 | − | 0.230238i | \(-0.926049\pi\) | ||
0.973134 | − | 0.230238i | \(-0.0739506\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −6.12311 | −1.22462 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.24517 | −1.34539 | −0.672697 | − | 0.739918i | \(-0.734864\pi\) | ||||
−0.672697 | + | 0.739918i | \(0.734864\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.04090 | −1.08498 | −0.542488 | − | 0.840063i | \(-0.682518\pi\) | ||||
−0.542488 | + | 0.840063i | \(0.682518\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 8.54312 | + | 2.20837i | 1.44405 | + | 0.373283i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.12311 | −0.842233 | −0.421117 | − | 0.907006i | \(-0.638362\pi\) | ||||
−0.421117 | + | 0.907006i | \(0.638362\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 5.20798i | − | 0.813351i | −0.913573 | − | 0.406675i | \(-0.866688\pi\) | ||
0.913573 | − | 0.406675i | \(-0.133312\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.12311i | 1.39126i | 0.718400 | + | 0.695630i | \(0.244875\pi\) | ||||
−0.718400 | + | 0.695630i | \(0.755125\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.74571 | −0.546367 | −0.273184 | − | 0.961962i | \(-0.588077\pi\) | ||||
−0.273184 | + | 0.961962i | \(0.588077\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.12311 | − | 3.39228i | −0.874729 | − | 0.484612i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.58831 | −0.218171 | −0.109086 | − | 0.994032i | \(-0.534792\pi\) | ||||
−0.109086 | + | 0.994032i | \(0.534792\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 16.7984 | 2.26509 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −13.3405 | −1.73679 | −0.868394 | − | 0.495874i | \(-0.834848\pi\) | ||||
−0.868394 | + | 0.495874i | \(0.834848\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 12.8255i | − | 1.64213i | −0.570833 | − | 0.821066i | \(-0.693380\pi\) | ||
0.570833 | − | 0.821066i | \(-0.306620\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 20.1472 | 2.49895 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 9.12311i | − | 1.11456i | −0.830323 | − | 0.557282i | \(-0.811844\pi\) | ||
0.830323 | − | 0.557282i | \(-0.188156\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 12.2820i | − | 1.45760i | −0.684726 | − | 0.728800i | \(-0.740078\pi\) | ||
0.684726 | − | 0.728800i | \(-0.259922\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.0818i | 1.41407i | 0.707180 | + | 0.707033i | \(0.249967\pi\) | ||||
−0.707180 | + | 0.707033i | \(0.750033\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −12.9020 | − | 3.33513i | −1.47032 | − | 0.380074i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 5.12311i | − | 0.576394i | −0.957571 | − | 0.288197i | \(-0.906944\pi\) | ||
0.957571 | − | 0.288197i | \(-0.0930559\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.74571 | 0.411145 | 0.205572 | − | 0.978642i | \(-0.434094\pi\) | ||||
0.205572 | + | 0.978642i | \(0.434094\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −17.3693 | −1.88397 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.46228i | 0.155001i | 0.996992 | + | 0.0775006i | \(0.0246940\pi\) | ||||
−0.996992 | + | 0.0775006i | \(0.975306\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −15.4741 | − | 4.00000i | −1.62212 | − | 0.419314i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 15.7304i | − | 1.61391i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 6.78456i | − | 0.688868i | −0.938811 | − | 0.344434i | \(-0.888071\pi\) | ||
0.938811 | − | 0.344434i | \(-0.111929\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.08084i | 0.704570i | 0.935893 | + | 0.352285i | \(0.114595\pi\) | ||||
−0.935893 | + | 0.352285i | \(0.885405\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.8255 | −1.26373 | −0.631865 | − | 0.775078i | \(-0.717710\pi\) | ||||
−0.631865 | + | 0.775078i | \(0.717710\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.79668i | 0.367039i | 0.983016 | + | 0.183519i | \(0.0587490\pi\) | ||||
−0.983016 | + | 0.183519i | \(0.941251\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.24621 | −0.789844 | −0.394922 | − | 0.918715i | \(-0.629228\pi\) | ||||
−0.394922 | + | 0.918715i | \(0.629228\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.65685 | −0.532152 | −0.266076 | − | 0.963952i | \(-0.585727\pi\) | ||||
−0.266076 | + | 0.963952i | \(0.585727\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.36520 | −0.686809 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 13.3405 | + | 3.44849i | 1.22292 | + | 0.316122i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −14.3693 | −1.30630 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.74571i | 0.335026i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.87689i | 0.255283i | 0.991820 | + | 0.127642i | \(0.0407407\pi\) | ||||
−0.991820 | + | 0.127642i | \(0.959259\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.3405 | 1.16557 | 0.582784 | − | 0.812627i | \(-0.301963\pi\) | ||||
0.582784 | + | 0.812627i | \(0.301963\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.12311 | + | 12.0818i | −0.270808 | + | 1.04762i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.17662 | 0.271397 | 0.135699 | − | 0.990750i | \(-0.456672\pi\) | ||||
0.135699 | + | 0.990750i | \(0.456672\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.29723 | 0.449305 | 0.224652 | − | 0.974439i | \(-0.427875\pi\) | ||||
0.224652 | + | 0.974439i | \(0.427875\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −30.4268 | −2.54441 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 24.1636i | 2.00668i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.58831 | 0.130120 | 0.0650598 | − | 0.997881i | \(-0.479276\pi\) | ||||
0.0650598 | + | 0.997881i | \(0.479276\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 2.87689i | − | 0.234118i | −0.993125 | − | 0.117059i | \(-0.962653\pi\) | ||
0.993125 | − | 0.117059i | \(-0.0373467\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 20.1472i | 1.61826i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.3381i | 0.904881i | 0.891795 | + | 0.452440i | \(0.149446\pi\) | ||||
−0.891795 | + | 0.452440i | \(0.850554\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.65685 | + | 1.46228i | 0.445823 | + | 0.115244i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 1.12311i | − | 0.0879684i | −0.999032 | − | 0.0439842i | \(-0.985995\pi\) | ||
0.999032 | − | 0.0439842i | \(-0.0140051\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −23.4924 | −1.80711 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 20.4214i | 1.55261i | 0.630359 | + | 0.776304i | \(0.282908\pi\) | ||||
−0.630359 | + | 0.776304i | \(0.717092\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.05444 | − | 15.6847i | 0.306487 | − | 1.18565i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 22.0074i | 1.64491i | 0.568832 | + | 0.822454i | \(0.307395\pi\) | ||||
−0.568832 | + | 0.822454i | \(0.692605\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.04090i | 0.449016i | 0.974472 | + | 0.224508i | \(0.0720775\pi\) | ||||
−0.974472 | + | 0.224508i | \(0.927922\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 17.0862i | 1.25620i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 26.2316 | 1.91824 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.10534i | 0.658839i | 0.944184 | + | 0.329420i | \(0.106853\pi\) | ||||
−0.944184 | + | 0.329420i | \(0.893147\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.3693 | −0.818381 | −0.409191 | − | 0.912449i | \(-0.634189\pi\) | ||||
−0.409191 | + | 0.912449i | \(0.634189\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −7.24517 | −0.516197 | −0.258098 | − | 0.966119i | \(-0.583096\pi\) | ||||
−0.258098 | + | 0.966119i | \(0.583096\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.10887 | −0.574823 | −0.287411 | − | 0.957807i | \(-0.592795\pi\) | ||||
−0.287411 | + | 0.957807i | \(0.592795\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.79741 | − | 18.5589i | 0.336712 | − | 1.30258i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −17.3693 | −1.21313 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 23.7565i | 1.64327i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 3.36932i | − | 0.231953i | −0.993252 | − | 0.115977i | \(-0.963000\pi\) | ||
0.993252 | − | 0.115977i | \(-0.0369998\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 30.4268 | 2.07509 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.00000 | − | 15.4741i | 0.271538 | − | 1.05045i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 31.4609 | 2.11629 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.97292 | −0.266046 | −0.133023 | − | 0.991113i | \(-0.542468\pi\) | ||||
−0.133023 | + | 0.991113i | \(0.542468\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −9.59482 | −0.636831 | −0.318415 | − | 0.947951i | \(-0.603151\pi\) | ||||
−0.318415 | + | 0.947951i | \(0.603151\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.3381i | 0.749244i | 0.927178 | + | 0.374622i | \(0.122228\pi\) | ||||
−0.927178 | + | 0.374622i | \(0.877772\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 16.9706 | 1.11178 | 0.555889 | − | 0.831256i | \(-0.312378\pi\) | ||||
0.555889 | + | 0.831256i | \(0.312378\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.4924i | 0.814916i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 21.1154i | 1.36584i | 0.730491 | + | 0.682922i | \(0.239291\pi\) | ||||
−0.730491 | + | 0.682922i | \(0.760709\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 18.8664i | − | 1.21529i | −0.794209 | − | 0.607644i | \(-0.792115\pi\) | ||
0.794209 | − | 0.607644i | \(-0.207885\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −11.3137 | + | 20.4214i | −0.722806 | + | 1.30467i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 28.4924i | 1.81293i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −17.0862 | −1.07847 | −0.539237 | − | 0.842154i | \(-0.681287\pi\) | ||||
−0.539237 | + | 0.842154i | \(0.681287\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 11.1231 | 0.699304 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 14.8028i | − | 0.923374i | −0.887043 | − | 0.461687i | \(-0.847244\pi\) | ||
0.887043 | − | 0.461687i | \(-0.152756\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.39228 | − | 13.1231i | 0.210786 | − | 0.815430i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 14.7622i | − | 0.910276i | −0.890421 | − | 0.455138i | \(-0.849590\pi\) | ||
0.890421 | − | 0.455138i | \(-0.150410\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.29723i | 0.325406i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 17.4968i | − | 1.06680i | −0.845863 | − | 0.533400i | \(-0.820914\pi\) | ||
0.845863 | − | 0.533400i | \(-0.179086\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.743668 | 0.0451746 | 0.0225873 | − | 0.999745i | \(-0.492810\pi\) | ||||
0.0225873 | + | 0.999745i | \(0.492810\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 30.8408i | − | 1.85977i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −23.3693 | −1.40413 | −0.702063 | − | 0.712115i | \(-0.747738\pi\) | ||||
−0.702063 | + | 0.712115i | \(0.747738\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.65685 | −0.337460 | −0.168730 | − | 0.985662i | \(-0.553967\pi\) | ||||
−0.168730 | + | 0.985662i | \(0.553967\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.36520 | 0.437816 | 0.218908 | − | 0.975746i | \(-0.429751\pi\) | ||||
0.218908 | + | 0.975746i | \(0.429751\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 13.3405 | + | 3.44849i | 0.787466 | + | 0.203558i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.1231 | −0.595477 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 4.15628i | − | 0.242812i | −0.992603 | − | 0.121406i | \(-0.961260\pi\) | ||
0.992603 | − | 0.121406i | \(-0.0387404\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 44.4924i | 2.59045i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 13.3405 | 0.771503 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −23.3693 | − | 6.04090i | −1.34699 | − | 0.348191i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −42.7746 | −2.44927 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −12.6624 | −0.722683 | −0.361342 | − | 0.932434i | \(-0.617681\pi\) | ||||
−0.361342 | + | 0.932434i | \(0.617681\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −22.9354 | −1.30054 | −0.650272 | − | 0.759701i | \(-0.725345\pi\) | ||||
−0.650272 | + | 0.759701i | \(0.725345\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −24.2157 | −1.36009 | −0.680045 | − | 0.733170i | \(-0.738040\pi\) | ||||
−0.680045 | + | 0.733170i | \(0.738040\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 36.4924i | − | 2.04318i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 24.5639i | − | 1.36677i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 36.9890i | − | 2.05178i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.48023 | − | 9.59482i | 0.136740 | − | 0.528980i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 29.6155i | 1.62782i | 0.580993 | + | 0.813908i | \(0.302664\pi\) | ||||
−0.580993 | + | 0.813908i | \(0.697336\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −30.4268 | −1.66239 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.24621 | −0.449200 | −0.224600 | − | 0.974451i | \(-0.572108\pi\) | ||||
−0.224600 | + | 0.974451i | \(0.572108\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 30.4268i | − | 1.64770i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 12.7439 | − | 13.4384i | 0.688108 | − | 0.725608i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 6.97330i | − | 0.374347i | −0.982327 | − | 0.187173i | \(-0.940067\pi\) | ||
0.982327 | − | 0.187173i | \(-0.0599326\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 0.743668i | − | 0.0398076i | −0.999802 | − | 0.0199038i | \(-0.993664\pi\) | ||
0.999802 | − | 0.0199038i | \(-0.00633600\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 11.8782i | − | 0.632215i | −0.948723 | − | 0.316108i | \(-0.897624\pi\) | ||
0.948723 | − | 0.316108i | \(-0.102376\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −40.9620 | −2.17404 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 33.6693i | 1.77700i | 0.458881 | + | 0.888498i | \(0.348251\pi\) | ||||
−0.458881 | + | 0.888498i | \(0.651749\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.24621 | 0.170853 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 40.2944 | 2.10910 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 26.9752 | 1.40810 | 0.704048 | − | 0.710153i | \(-0.251374\pi\) | ||||
0.704048 | + | 0.710153i | \(0.251374\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.05171 | − | 4.06854i | 0.0546018 | − | 0.211228i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.0000 | 0.517780 | 0.258890 | − | 0.965907i | \(-0.416643\pi\) | ||||
0.258890 | + | 0.965907i | \(0.416643\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 43.7673i | − | 2.25413i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 25.1231i | 1.29049i | 0.763977 | + | 0.645244i | \(0.223244\pi\) | ||||
−0.763977 | + | 0.645244i | \(0.776756\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 37.9182 | 1.93753 | 0.968764 | − | 0.247984i | \(-0.0797681\pi\) | ||||
0.968764 | + | 0.247984i | \(0.0797681\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −11.1231 | + | 43.0299i | −0.566886 | + | 2.19301i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 29.8726 | 1.51460 | 0.757300 | − | 0.653067i | \(-0.226518\pi\) | ||||
0.757300 | + | 0.653067i | \(0.226518\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −11.5012 | −0.581638 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −17.0862 | −0.859702 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.52823i | 0.377831i | 0.981993 | + | 0.188916i | \(0.0604973\pi\) | ||||
−0.981993 | + | 0.188916i | \(0.939503\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −32.1573 | −1.60586 | −0.802929 | − | 0.596075i | \(-0.796726\pi\) | ||||
−0.802929 | + | 0.596075i | \(0.796726\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 36.4924i | − | 1.81782i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 25.8040i | − | 1.27906i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 17.3790i | 0.859337i | 0.902987 | + | 0.429669i | \(0.141370\pi\) | ||||
−0.902987 | + | 0.429669i | \(0.858630\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.83348 | − | 34.1725i | 0.434667 | − | 1.68152i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 12.4924i | − | 0.613229i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −11.2371 | −0.548969 | −0.274485 | − | 0.961592i | \(-0.588507\pi\) | ||||
−0.274485 | + | 0.961592i | \(0.588507\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.12311 | 0.249685 | 0.124842 | − | 0.992177i | \(-0.460157\pi\) | ||||
0.124842 | + | 0.992177i | \(0.460157\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 31.8890i | 1.54685i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 32.8531 | + | 8.49242i | 1.58987 | + | 0.410977i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 21.6592i | − | 1.04329i | −0.853164 | − | 0.521643i | \(-0.825319\pi\) | ||
0.853164 | − | 0.521643i | \(-0.174681\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.48734i | 0.0714768i | 0.999361 | + | 0.0357384i | \(0.0113783\pi\) | ||||
−0.999361 | + | 0.0357384i | \(0.988622\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 10.4160i | − | 0.498263i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16.0547 | 0.766250 | 0.383125 | − | 0.923697i | \(-0.374848\pi\) | ||||
0.383125 | + | 0.923697i | \(0.374848\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 22.0074i | − | 1.04560i | −0.852455 | − | 0.522801i | \(-0.824887\pi\) | ||
0.852455 | − | 0.522801i | \(-0.175113\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.87689 | 0.231187 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8.83348 | −0.416878 | −0.208439 | − | 0.978035i | \(-0.566838\pi\) | ||||
−0.208439 | + | 0.978035i | \(0.566838\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 26.2316 | 1.23520 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −13.3405 | + | 51.6081i | −0.625414 | + | 2.41942i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 20.2462 | 0.947078 | 0.473539 | − | 0.880773i | \(-0.342976\pi\) | ||||
0.473539 | + | 0.880773i | \(0.342976\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 16.6757i | − | 0.776663i | −0.921520 | − | 0.388331i | \(-0.873052\pi\) | ||
0.921520 | − | 0.388331i | \(-0.126948\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 1.61553i | − | 0.0750800i | −0.999295 | − | 0.0375400i | \(-0.988048\pi\) | ||
0.999295 | − | 0.0375400i | \(-0.0119522\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 17.0862 | 0.790657 | 0.395328 | − | 0.918540i | \(-0.370631\pi\) | ||||
0.395328 | + | 0.918540i | \(0.370631\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 23.3693 | + | 6.04090i | 1.07909 | + | 0.278943i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −45.9512 | −2.11284 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −28.8802 | −1.32511 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 37.9182 | 1.73253 | 0.866263 | − | 0.499589i | \(-0.166515\pi\) | ||||
0.866263 | + | 0.499589i | \(0.166515\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 30.9481i | − | 1.41111i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −22.6274 | −1.02746 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.61553i | 0.435721i | 0.975980 | + | 0.217861i | \(0.0699078\pi\) | ||||
−0.975980 | + | 0.217861i | \(0.930092\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.10029i | 0.139914i | 0.997550 | + | 0.0699571i | \(0.0222862\pi\) | ||||
−0.997550 | + | 0.0699571i | \(0.977714\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 37.7327i | 1.69940i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 31.4609 | + | 8.13254i | 1.41121 | + | 0.364794i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 31.8617i | − | 1.42633i | −0.700998 | − | 0.713164i | \(-0.747262\pi\) | ||
0.700998 | − | 0.713164i | \(-0.252738\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3.74571 | 0.167013 | 0.0835064 | − | 0.996507i | \(-0.473388\pi\) | ||||
0.0835064 | + | 0.996507i | \(0.473388\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 23.6155 | 1.05088 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5.43854i | 0.241059i | 0.992710 | + | 0.120530i | \(0.0384593\pi\) | ||||
−0.992710 | + | 0.120530i | \(0.961541\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −30.9481 | − | 8.00000i | −1.36907 | − | 0.353899i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 42.7746i | 1.88487i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 18.8664i | − | 0.829741i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 8.13254i | − | 0.356293i | −0.984004 | − | 0.178147i | \(-0.942990\pi\) | ||
0.984004 | − | 0.178147i | \(-0.0570101\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −20.3537 | −0.890005 | −0.445002 | − | 0.895529i | \(-0.646797\pi\) | ||||
−0.445002 | + | 0.895529i | \(0.646797\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 31.4609i | 1.37046i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 18.1231 | 0.787961 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 31.4609 | 1.36272 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12.6624 | 0.547445 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 17.0862 | − | 30.8408i | 0.735956 | − | 1.32841i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.61553 | 0.413404 | 0.206702 | − | 0.978404i | \(-0.433727\pi\) | ||||
0.206702 | + | 0.978404i | \(0.433727\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 27.5022i | 1.17806i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 30.8769i | 1.32020i | 0.751177 | + | 0.660100i | \(0.229486\pi\) | ||||
−0.751177 | + | 0.660100i | \(0.770514\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −34.1725 | −1.45580 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 13.1231 | + | 3.39228i | 0.558051 | + | 0.144255i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6.54877 | 0.277480 | 0.138740 | − | 0.990329i | \(-0.455695\pi\) | ||||
0.138740 | + | 0.990329i | \(0.455695\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −55.1117 | −2.33098 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −37.9182 | −1.59806 | −0.799030 | − | 0.601291i | \(-0.794653\pi\) | ||||
−0.799030 | + | 0.601291i | \(0.794653\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 18.8664i | 0.793714i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −8.83348 | −0.370319 | −0.185159 | − | 0.982709i | \(-0.559280\pi\) | ||||
−0.185159 | + | 0.982709i | \(0.559280\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 33.1231i | − | 1.38616i | −0.720861 | − | 0.693079i | \(-0.756254\pi\) | ||
0.720861 | − | 0.693079i | \(-0.243746\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 13.5221i | 0.563910i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 22.6762i | − | 0.944025i | −0.881592 | − | 0.472012i | \(-0.843528\pi\) | ||
0.881592 | − | 0.472012i | \(-0.156472\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.48023 | + | 9.59482i | −0.102897 | + | 0.398060i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 8.00000i | − | 0.331326i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7.49141 | 0.309204 | 0.154602 | − | 0.987977i | \(-0.450591\pi\) | ||||
0.154602 | + | 0.987977i | \(0.450591\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −28.4924 | −1.17401 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 28.1433i | − | 1.15571i | −0.816140 | − | 0.577854i | \(-0.803890\pi\) | ||
0.816140 | − | 0.577854i | \(-0.196110\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 11.5012 | − | 44.4924i | 0.471501 | − | 1.82401i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 34.3657i | 1.40414i | 0.712107 | + | 0.702071i | \(0.247741\pi\) | ||||
−0.712107 | + | 0.702071i | \(0.752259\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.78456i | 0.276748i | 0.990380 | + | 0.138374i | \(0.0441876\pi\) | ||||
−0.990380 | + | 0.138374i | \(0.955812\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 47.9236i | 1.94837i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9.59621 | 0.389498 | 0.194749 | − | 0.980853i | \(-0.437611\pi\) | ||||
0.194749 | + | 0.980853i | \(0.437611\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 22.6274i | − | 0.915407i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 41.2311 | 1.66531 | 0.832653 | − | 0.553795i | \(-0.186821\pi\) | ||||
0.832653 | + | 0.553795i | \(0.186821\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −11.3137 | −0.455473 | −0.227736 | − | 0.973723i | \(-0.573132\pi\) | ||||
−0.227736 | + | 0.973723i | \(0.573132\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.27190 | −0.332476 | −0.166238 | − | 0.986086i | \(-0.553162\pi\) | ||||
−0.166238 | + | 0.986086i | \(0.553162\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.74571 | − | 0.968253i | −0.150069 | − | 0.0387922i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −18.1231 | −0.724924 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 26.6811i | 1.06384i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 39.3693i | 1.56727i | 0.621223 | + | 0.783634i | \(0.286636\pi\) | ||||
−0.621223 | + | 0.783634i | \(0.713364\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 9.59482 | 0.380759 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 20.4924 | − | 36.9890i | 0.811939 | − | 1.46556i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −8.13709 | −0.321396 | −0.160698 | − | 0.987004i | \(-0.551374\pi\) | ||||
−0.160698 | + | 0.987004i | \(0.551374\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 33.0161 | 1.30203 | 0.651014 | − | 0.759065i | \(-0.274344\pi\) | ||||
0.651014 | + | 0.759065i | \(0.274344\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −7.49141 | −0.294518 | −0.147259 | − | 0.989098i | \(-0.547045\pi\) | ||||
−0.147259 | + | 0.989098i | \(0.547045\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 67.1935i | − | 2.63758i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −21.0391 | −0.823324 | −0.411662 | − | 0.911337i | \(-0.635052\pi\) | ||||
−0.411662 | + | 0.911337i | \(0.635052\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 44.4924i | − | 1.73846i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 5.03680i | − | 0.196206i | −0.995176 | − | 0.0981029i | \(-0.968723\pi\) | ||
0.995176 | − | 0.0981029i | \(-0.0312774\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.743668i | 0.0289253i | 0.999895 | + | 0.0144627i | \(0.00460377\pi\) | ||||
−0.999895 | + | 0.0144627i | \(0.995396\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 40.2944 | + | 10.4160i | 1.56255 | + | 0.403914i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 16.0000i | 0.619522i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 64.5992 | 2.49383 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 29.6155 | 1.14159 | 0.570797 | − | 0.821091i | \(-0.306634\pi\) | ||||
0.570797 | + | 0.821091i | \(0.306634\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 26.2705i | − | 1.00966i | −0.863220 | − | 0.504828i | \(-0.831556\pi\) | ||
0.863220 | − | 0.504828i | \(-0.168444\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 17.3790 | + | 4.49242i | 0.666946 | + | 0.172403i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 23.2475i | 0.889540i | 0.895645 | + | 0.444770i | \(0.146715\pi\) | ||||
−0.895645 | + | 0.444770i | \(0.853285\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 10.5945i | − | 0.404793i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 9.59482i | − | 0.365534i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.78456 | 0.258097 | 0.129048 | − | 0.991638i | \(-0.458808\pi\) | ||||
0.129048 | + | 0.991638i | \(0.458808\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 17.6670i | − | 0.670146i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −27.1231 | −1.02736 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −12.9020 | −0.487303 | −0.243651 | − | 0.969863i | \(-0.578345\pi\) | ||||
−0.243651 | + | 0.969863i | \(0.578345\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −24.1636 | −0.911347 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −18.1379 | − | 4.68860i | −0.682147 | − | 0.176333i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.00000 | 0.225335 | 0.112667 | − | 0.993633i | \(-0.464061\pi\) | ||||
0.112667 | + | 0.993633i | \(0.464061\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 13.3405i | 0.499607i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 101.477i | 3.79503i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −30.4268 | −1.13473 | −0.567363 | − | 0.823468i | \(-0.692036\pi\) | ||||
−0.567363 | + | 0.823468i | \(0.692036\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.49242 | − | 32.8531i | 0.316274 | − | 1.22351i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 44.3629 | 1.64760 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −24.9073 | −0.923759 | −0.461879 | − | 0.886943i | \(-0.652825\pi\) | ||||
−0.461879 | + | 0.886943i | \(0.652825\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 47.5130 | 1.75733 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0.743668i | 0.0274680i | 0.999906 | + | 0.0137340i | \(0.00437181\pi\) | ||||
−0.999906 | + | 0.0137340i | \(0.995628\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 45.9512 | 1.69264 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 25.1231i | − | 0.924168i | −0.886836 | − | 0.462084i | \(-0.847102\pi\) | ||
0.886836 | − | 0.462084i | \(-0.152898\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 16.0023i | − | 0.587068i | −0.955949 | − | 0.293534i | \(-0.905169\pi\) | ||
0.955949 | − | 0.293534i | \(-0.0948314\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 5.29723i | − | 0.194075i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −9.72540 | − | 2.51398i | −0.355358 | − | 0.0918590i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.630683i | 0.0230140i | 0.999934 | + | 0.0115070i | \(0.00366287\pi\) | ||||
−0.999934 | + | 0.0115070i | \(0.996337\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −9.59482 | −0.349191 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 30.9848 | 1.12616 | 0.563082 | − | 0.826401i | \(-0.309616\pi\) | ||||
0.563082 | + | 0.826401i | \(0.309616\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 42.3050i | 1.53356i | 0.641913 | + | 0.766778i | \(0.278141\pi\) | ||||
−0.641913 | + | 0.766778i | \(0.721859\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.46026 | − | 21.1231i | 0.197675 | − | 0.764708i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 80.5887i | − | 2.90989i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 43.0299i | 1.55170i | 0.630918 | + | 0.775850i | \(0.282678\pi\) | ||||
−0.630918 | + | 0.775850i | \(0.717322\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0.410574i | 0.0147673i | 0.999973 | + | 0.00738365i | \(0.00235031\pi\) | ||||
−0.999973 | + | 0.00738365i | \(0.997650\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 36.9890 | 1.32869 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 24.5639i | − | 0.880094i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 61.8617 | 2.21359 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 37.8141 | 1.34964 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −46.8398 | −1.66966 | −0.834830 | − | 0.550508i | \(-0.814434\pi\) | ||||
−0.834830 | + | 0.550508i | \(0.814434\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.74571 | − | 14.4903i | 0.133182 | − | 0.515217i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 77.4773 | 2.75130 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 12.9300i | − | 0.458002i | −0.973426 | − | 0.229001i | \(-0.926454\pi\) | ||
0.973426 | − | 0.229001i | \(-0.0735460\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 19.5076i | 0.690128i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −60.8535 | −2.14747 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.87689 | − | 18.8664i | 0.171888 | − | 0.664952i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −54.0883 | −1.90164 | −0.950822 | − | 0.309738i | \(-0.899759\pi\) | ||||
−0.950822 | + | 0.309738i | \(0.899759\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 41.5426 | 1.45876 | 0.729379 | − | 0.684110i | \(-0.239809\pi\) | ||||
0.729379 | + | 0.684110i | \(0.239809\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.74571 | −0.131206 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 43.0299i | 1.50543i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −53.1964 | −1.85657 | −0.928283 | − | 0.371874i | \(-0.878716\pi\) | ||||
−0.928283 | + | 0.371874i | \(0.878716\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 19.8617i | 0.692337i | 0.938172 | + | 0.346168i | \(0.112517\pi\) | ||||
−0.938172 | + | 0.346168i | \(0.887483\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 37.1941i | 1.29336i | 0.762759 | + | 0.646682i | \(0.223844\pi\) | ||||
−0.762759 | + | 0.646682i | \(0.776156\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 11.3381i | − | 0.393789i | −0.980425 | − | 0.196895i | \(-0.936914\pi\) | ||
0.980425 | − | 0.196895i | \(-0.0630857\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −17.6670 | + | 31.8890i | −0.612124 | + | 1.10489i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −34.1725 | −1.17976 | −0.589882 | − | 0.807489i | \(-0.700826\pi\) | ||||
−0.589882 | + | 0.807489i | \(0.700826\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 23.4924 | 0.810084 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 78.3503i | 2.69533i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.51469 | − | 36.8078i | 0.326929 | − | 1.26473i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 11.3137i | 0.387829i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 35.5017i | − | 1.21556i | −0.794107 | − | 0.607778i | \(-0.792061\pi\) | ||
0.794107 | − | 0.607778i | \(-0.207939\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 27.3222i | 0.933308i | 0.884440 | + | 0.466654i | \(0.154541\pi\) | ||||
−0.884440 | + | 0.466654i | \(0.845459\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −38.3134 | −1.30723 | −0.653617 | − | 0.756825i | \(-0.726749\pi\) | ||||
−0.653617 | + | 0.756825i | \(0.726749\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 20.4190i | 0.695072i | 0.937667 | + | 0.347536i | \(0.112982\pi\) | ||||
−0.937667 | + | 0.347536i | \(0.887018\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 68.1080 | 2.31574 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 25.8040 | 0.875342 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 55.1117 | 1.86739 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −9.59482 | − | 2.48023i | −0.324364 | − | 0.0838471i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8.24621 | 0.278455 | 0.139227 | − | 0.990260i | \(-0.455538\pi\) | ||||
0.139227 | + | 0.990260i | \(0.455538\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 20.6519i | 0.695781i | 0.937535 | + | 0.347891i | \(0.113102\pi\) | ||||
−0.937535 | + | 0.347891i | \(0.886898\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 7.86174i | − | 0.264569i | −0.991212 | − | 0.132284i | \(-0.957769\pi\) | ||
0.991212 | − | 0.132284i | \(-0.0422312\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −34.1725 | −1.14740 | −0.573700 | − | 0.819066i | \(-0.694492\pi\) | ||||
−0.573700 | + | 0.819066i | \(0.694492\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7.36932 | − | 1.90495i | −0.247159 | − | 0.0638898i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −17.6670 | −0.591202 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 73.3974 | 2.45341 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 43.7673 | 1.45972 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.27190i | 0.275577i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 20.1472 | 0.669715 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 18.1080i | 0.601265i | 0.953740 | + | 0.300632i | \(0.0971977\pi\) | ||||
−0.953740 | + | 0.300632i | \(0.902802\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 12.2820i | − | 0.406920i | −0.979083 | − | 0.203460i | \(-0.934781\pi\) | ||
0.979083 | − | 0.203460i | \(-0.0652186\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 18.8664i | 0.624385i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −8.83348 | + | 34.1725i | −0.291707 | + | 1.12847i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 49.6155i | 1.63667i | 0.574745 | + | 0.818333i | \(0.305101\pi\) | ||||
−0.574745 | + | 0.818333i | \(0.694899\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 74.1941 | 2.44213 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 31.3693 | 1.03142 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 52.7210i | − | 1.72972i | −0.502014 | − | 0.864860i | \(-0.667407\pi\) | ||
0.502014 | − | 0.864860i | \(-0.332593\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −28.8802 | − | 16.0000i | −0.946509 | − | 0.524379i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 87.4857i | − | 2.86109i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 8.27190i | 0.270231i | 0.990830 | + | 0.135116i | \(0.0431406\pi\) | ||||
−0.990830 | + | 0.135116i | \(0.956859\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 27.9128i | − | 0.909931i | −0.890509 | − | 0.454965i | \(-0.849652\pi\) | ||
0.890509 | − | 0.454965i | \(-0.150348\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −11.5012 | −0.374529 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 46.0276i | 1.49569i | 0.663871 | + | 0.747847i | \(0.268912\pi\) | ||||
−0.663871 | + | 0.747847i | \(0.731088\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −72.9848 | −2.36919 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 25.8040 | 0.835875 | 0.417937 | − | 0.908476i | \(-0.362753\pi\) | ||||
0.417937 | + | 0.908476i | \(0.362753\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 30.3675 | 0.982670 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.10341 | + | 8.13709i | −0.0679227 | + | 0.262760i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.49242 | 0.177175 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 37.9182i | 1.22063i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 47.3693i | 1.52329i | 0.647992 | + | 0.761647i | \(0.275609\pi\) | ||||
−0.647992 | + | 0.761647i | \(0.724391\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −36.2759 | −1.16415 | −0.582074 | − | 0.813136i | \(-0.697759\pi\) | ||||
−0.582074 | + | 0.813136i | \(0.697759\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.50758 | + | 13.5691i | −0.112448 | + | 0.435006i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 49.1278 | 1.57174 | 0.785870 | − | 0.618392i | \(-0.212216\pi\) | ||||
0.785870 | + | 0.618392i | \(0.212216\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7.36520 | −0.235393 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 45.8707 | 1.46305 | 0.731524 | − | 0.681816i | \(-0.238809\pi\) | ||||
0.731524 | + | 0.681816i | \(0.238809\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 24.1636i | 0.769916i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 20.1472 | 0.640643 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 39.3693i | − | 1.25061i | −0.780381 | − | 0.625304i | \(-0.784975\pi\) | ||
0.780381 | − | 0.625304i | \(-0.215025\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 27.0442i | 0.857357i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 50.5582i | 1.60119i | 0.599204 | + | 0.800597i | \(0.295484\pi\) | ||||
−0.599204 | + | 0.800597i | \(0.704516\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 4032.2.b.r.3583.2 | 16 | ||
3.2 | odd | 2 | inner | 4032.2.b.r.3583.14 | 16 | ||
4.3 | odd | 2 | inner | 4032.2.b.r.3583.3 | 16 | ||
7.6 | odd | 2 | inner | 4032.2.b.r.3583.16 | 16 | ||
8.3 | odd | 2 | 2016.2.b.d.1567.15 | yes | 16 | ||
8.5 | even | 2 | 2016.2.b.d.1567.14 | yes | 16 | ||
12.11 | even | 2 | inner | 4032.2.b.r.3583.15 | 16 | ||
21.20 | even | 2 | inner | 4032.2.b.r.3583.4 | 16 | ||
24.5 | odd | 2 | 2016.2.b.d.1567.2 | yes | 16 | ||
24.11 | even | 2 | 2016.2.b.d.1567.3 | yes | 16 | ||
28.27 | even | 2 | inner | 4032.2.b.r.3583.13 | 16 | ||
56.13 | odd | 2 | 2016.2.b.d.1567.4 | yes | 16 | ||
56.27 | even | 2 | 2016.2.b.d.1567.1 | ✓ | 16 | ||
84.83 | odd | 2 | inner | 4032.2.b.r.3583.1 | 16 | ||
168.83 | odd | 2 | 2016.2.b.d.1567.13 | yes | 16 | ||
168.125 | even | 2 | 2016.2.b.d.1567.16 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2016.2.b.d.1567.1 | ✓ | 16 | 56.27 | even | 2 | ||
2016.2.b.d.1567.2 | yes | 16 | 24.5 | odd | 2 | ||
2016.2.b.d.1567.3 | yes | 16 | 24.11 | even | 2 | ||
2016.2.b.d.1567.4 | yes | 16 | 56.13 | odd | 2 | ||
2016.2.b.d.1567.13 | yes | 16 | 168.83 | odd | 2 | ||
2016.2.b.d.1567.14 | yes | 16 | 8.5 | even | 2 | ||
2016.2.b.d.1567.15 | yes | 16 | 8.3 | odd | 2 | ||
2016.2.b.d.1567.16 | yes | 16 | 168.125 | even | 2 | ||
4032.2.b.r.3583.1 | 16 | 84.83 | odd | 2 | inner | ||
4032.2.b.r.3583.2 | 16 | 1.1 | even | 1 | trivial | ||
4032.2.b.r.3583.3 | 16 | 4.3 | odd | 2 | inner | ||
4032.2.b.r.3583.4 | 16 | 21.20 | even | 2 | inner | ||
4032.2.b.r.3583.13 | 16 | 28.27 | even | 2 | inner | ||
4032.2.b.r.3583.14 | 16 | 3.2 | odd | 2 | inner | ||
4032.2.b.r.3583.15 | 16 | 12.11 | even | 2 | inner | ||
4032.2.b.r.3583.16 | 16 | 7.6 | odd | 2 | inner |