Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4032,2,Mod(2591,4032)]
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, 1, 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("4032.2591");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4032 = 2^{6} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4032.j (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(32.1956820950\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | 16.0.162447943996702457856.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - x^{12} - 15x^{8} - 16x^{4} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{23}]\) |
Coefficient ring index: | \( 2^{18} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2591.7 | ||
Root | \(-1.14839 - 0.825348i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4032.2591 |
Dual form | 4032.2.j.e.2591.6 |
$q$-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 | ||||||||
\(5\) | −0.646084 | −0.288937 | −0.144469 | − | 0.989509i | \(-0.546147\pi\) | ||||
−0.144469 | + | 0.989509i | \(0.546147\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.09557i | 0.933351i | 0.884429 | + | 0.466675i | \(0.154548\pi\) | ||||
−0.884429 | + | 0.466675i | \(0.845452\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 0.913701i | − 0.253415i | −0.991940 | − | 0.126707i | \(-0.959559\pi\) | ||||
0.991940 | − | 0.126707i | \(-0.0404409\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.77590i | 1.64340i | 0.569922 | + | 0.821699i | \(0.306974\pi\) | ||||
−0.569922 | + | 0.821699i | \(0.693026\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.29150 | 1.21395 | 0.606977 | − | 0.794719i | \(-0.292382\pi\) | ||||
0.606977 | + | 0.794719i | \(0.292382\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.53326 | 0.528222 | 0.264111 | − | 0.964492i | \(-0.414921\pi\) | ||||
0.264111 | + | 0.964492i | \(0.414921\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.58258 | −0.916515 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.93280 | 1.84448 | 0.922238 | − | 0.386623i | \(-0.126359\pi\) | ||||
0.922238 | + | 0.386623i | \(0.126359\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 9.16515i | − 1.64611i | −0.567962 | − | 0.823055i | \(-0.692268\pi\) | ||||
0.567962 | − | 0.823055i | \(-0.307732\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 0.646084i | − 0.109208i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.84190i | 1.28920i | 0.764520 | + | 0.644601i | \(0.222976\pi\) | ||||
−0.764520 | + | 0.644601i | \(0.777024\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 9.01400i | − 1.40775i | −0.710323 | − | 0.703875i | \(-0.751451\pi\) | ||||
0.710323 | − | 0.703875i | \(-0.248549\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −12.2197 | −1.86349 | −0.931744 | − | 0.363116i | \(-0.881713\pi\) | ||||
−0.931744 | + | 0.363116i | \(0.881713\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.65685 | −0.825137 | −0.412568 | − | 0.910927i | \(-0.635368\pi\) | ||||
−0.412568 | + | 0.910927i | \(0.635368\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.15732 | 0.158970 | 0.0794852 | − | 0.996836i | \(-0.474672\pi\) | ||||
0.0794852 | + | 0.996836i | \(0.474672\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 2.00000i | − 0.269680i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.92820i | 0.887066i | 0.896258 | + | 0.443533i | \(0.146275\pi\) | ||||
−0.896258 | + | 0.443533i | \(0.853725\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.590327i | 0.0732211i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.84190 | −0.958041 | −0.479021 | − | 0.877804i | \(-0.659008\pi\) | ||||
−0.479021 | + | 0.877804i | \(0.659008\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.36169 | −0.636316 | −0.318158 | − | 0.948038i | \(-0.603064\pi\) | ||||
−0.318158 | + | 0.948038i | \(0.603064\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.417424 | −0.0488558 | −0.0244279 | − | 0.999702i | \(-0.507776\pi\) | ||||
−0.0244279 | + | 0.999702i | \(0.507776\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.09557 | −0.352773 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.7477i | 1.20921i | 0.796524 | + | 0.604607i | \(0.206670\pi\) | ||||
−0.796524 | + | 0.604607i | \(0.793330\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 15.9891i | 1.75503i | 0.479547 | + | 0.877516i | \(0.340801\pi\) | ||||
−0.479547 | + | 0.877516i | \(0.659199\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 4.37780i | − 0.474839i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.01400i | 0.955483i | 0.878501 | + | 0.477741i | \(0.158544\pi\) | ||||
−0.878501 | + | 0.477741i | \(0.841456\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.913701 | 0.0957818 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.41875 | −0.350757 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −11.5826 | −1.17603 | −0.588016 | − | 0.808849i | \(-0.700091\pi\) | ||||
−0.588016 | + | 0.808849i | \(0.700091\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 14.0509 | 1.39811 | 0.699056 | − | 0.715067i | \(-0.253604\pi\) | ||||
0.699056 | + | 0.715067i | \(0.253604\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.00000i | 0.197066i | 0.995134 | + | 0.0985329i | \(0.0314150\pi\) | ||||
−0.995134 | + | 0.0985329i | \(0.968585\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.70239i | 0.647944i | 0.946067 | + | 0.323972i | \(0.105018\pi\) | ||||
−0.946067 | + | 0.323972i | \(0.894982\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 5.29150i | − 0.506834i | −0.967357 | − | 0.253417i | \(-0.918446\pi\) | ||||
0.967357 | − | 0.253417i | \(-0.0815545\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.89949i | 0.931266i | 0.884978 | + | 0.465633i | \(0.154173\pi\) | ||||
−0.884978 | + | 0.465633i | \(0.845827\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.63670 | −0.152623 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6.77590 | −0.621146 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.41742 | 0.128857 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.19115 | 0.553753 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 4.41742i | − 0.391983i | −0.980606 | − | 0.195992i | \(-0.937207\pi\) | ||||
0.980606 | − | 0.195992i | \(-0.0627925\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.0901i | 0.968949i | 0.874805 | + | 0.484474i | \(0.160989\pi\) | ||||
−0.874805 | + | 0.484474i | \(0.839011\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.29150i | 0.458831i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.89041i | 0.503252i | 0.967825 | + | 0.251626i | \(0.0809653\pi\) | ||||
−0.967825 | + | 0.251626i | \(0.919035\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.82740 | 0.154998 | 0.0774991 | − | 0.996992i | \(-0.475307\pi\) | ||||
0.0774991 | + | 0.996992i | \(0.475307\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.82843 | 0.236525 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.41742 | −0.532938 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 19.7308 | 1.61641 | 0.808204 | − | 0.588903i | \(-0.200440\pi\) | ||||
0.808204 | + | 0.588903i | \(0.200440\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 23.1652i | − 1.88515i | −0.333990 | − | 0.942577i | \(-0.608395\pi\) | ||||
0.333990 | − | 0.942577i | \(-0.391605\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.92146i | 0.475623i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.6838i | 1.25170i | 0.779942 | + | 0.625852i | \(0.215249\pi\) | ||||
−0.779942 | + | 0.625852i | \(0.784751\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.53326i | 0.199649i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −13.3241 | −1.04362 | −0.521812 | − | 0.853060i | \(-0.674744\pi\) | ||||
−0.521812 | + | 0.853060i | \(0.674744\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −7.89495 | −0.610930 | −0.305465 | − | 0.952203i | \(-0.598812\pi\) | ||||
−0.305465 | + | 0.952203i | \(0.598812\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.1652 | 0.935781 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.85971 | 0.597562 | 0.298781 | − | 0.954322i | \(-0.403420\pi\) | ||||
0.298781 | + | 0.954322i | \(0.403420\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 4.58258i | − 0.346410i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 11.6014i | 0.867127i | 0.901123 | + | 0.433563i | \(0.142744\pi\) | ||||
−0.901123 | + | 0.433563i | \(0.857256\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.66930i | 0.718714i | 0.933200 | + | 0.359357i | \(0.117004\pi\) | ||||
−0.933200 | + | 0.359357i | \(0.882996\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − 5.06653i | − 0.372498i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −20.9753 | −1.53387 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −20.5613 | −1.48776 | −0.743881 | − | 0.668312i | \(-0.767017\pi\) | ||||
−0.743881 | + | 0.668312i | \(0.767017\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.74773 | 0.485712 | 0.242856 | − | 0.970062i | \(-0.421916\pi\) | ||||
0.242856 | + | 0.970062i | \(0.421916\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −24.8994 | −1.77401 | −0.887006 | − | 0.461759i | \(-0.847219\pi\) | ||||
−0.887006 | + | 0.461759i | \(0.847219\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19.1652i | 1.35858i | 0.733869 | + | 0.679291i | \(0.237712\pi\) | ||||
−0.733869 | + | 0.679291i | \(0.762288\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 9.93280i | 0.697146i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.82380i | 0.406752i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 16.3802i | 1.13304i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.190700 | 0.0131284 | 0.00656418 | − | 0.999978i | \(-0.497911\pi\) | ||||
0.00656418 | + | 0.999978i | \(0.497911\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 7.89495 | 0.538431 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.16515 | 0.622171 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.19115 | 0.416462 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 20.0000i | − 1.33930i | −0.742677 | − | 0.669650i | \(-0.766444\pi\) | ||||
0.742677 | − | 0.669650i | \(-0.233556\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 11.0901i | − 0.736078i | −0.929810 | − | 0.368039i | \(-0.880029\pi\) | ||||
0.929810 | − | 0.368039i | \(-0.119971\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.4967i | 0.759724i | 0.925043 | + | 0.379862i | \(0.124028\pi\) | ||||
−0.925043 | + | 0.379862i | \(0.875972\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.07107i | 0.463241i | 0.972806 | + | 0.231621i | \(0.0744028\pi\) | ||||
−0.972806 | + | 0.231621i | \(0.925597\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.65480 | 0.238413 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5.95202 | −0.385004 | −0.192502 | − | 0.981297i | \(-0.561660\pi\) | ||||
−0.192502 | + | 0.981297i | \(0.561660\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −20.4174 | −1.31520 | −0.657601 | − | 0.753366i | \(-0.728429\pi\) | ||||
−0.657601 | + | 0.753366i | \(0.728429\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.646084 | 0.0412768 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 4.83485i | − 0.307634i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.02248i | 0.0645381i | 0.999479 | + | 0.0322691i | \(0.0102733\pi\) | ||||
−0.999479 | + | 0.0322691i | \(0.989727\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.84190i | 0.493016i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 10.1947i | 0.635925i | 0.948103 | + | 0.317963i | \(0.102999\pi\) | ||||
−0.948103 | + | 0.317963i | \(0.897001\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.84190 | −0.487272 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.94294 | 0.119807 | 0.0599033 | − | 0.998204i | \(-0.480921\pi\) | ||||
0.0599033 | + | 0.998204i | \(0.480921\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.747727 | −0.0459325 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 25.1410 | 1.53287 | 0.766436 | − | 0.642320i | \(-0.222028\pi\) | ||||
0.766436 | + | 0.642320i | \(0.222028\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 5.16515i | − 0.313761i | −0.987618 | − | 0.156880i | \(-0.949856\pi\) | ||||
0.987618 | − | 0.156880i | \(-0.0501437\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 14.1857i | − 0.855430i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.9608i | 0.898908i | 0.893304 | + | 0.449454i | \(0.148381\pi\) | ||||
−0.893304 | + | 0.449454i | \(0.851619\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 20.6229i | − 1.23026i | −0.788427 | − | 0.615129i | \(-0.789104\pi\) | ||||
0.788427 | − | 0.615129i | \(-0.210896\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 17.3205 | 1.02960 | 0.514799 | − | 0.857311i | \(-0.327867\pi\) | ||||
0.514799 | + | 0.857311i | \(0.327867\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 9.01400 | 0.532080 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −28.9129 | −1.70076 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 14.3205 | 0.836615 | 0.418308 | − | 0.908305i | \(-0.362623\pi\) | ||||
0.418308 | + | 0.908305i | \(0.362623\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 2.31464i | − 0.133859i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 12.2197i | − 0.704332i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − 4.47620i | − 0.256306i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −22.8027 | −1.30142 | −0.650710 | − | 0.759327i | \(-0.725529\pi\) | ||||
−0.650710 | + | 0.759327i | \(0.725529\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.47620 | 0.253822 | 0.126911 | − | 0.991914i | \(-0.459494\pi\) | ||||
0.126911 | + | 0.991914i | \(0.459494\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.16515 | 0.518045 | 0.259022 | − | 0.965871i | \(-0.416600\pi\) | ||||
0.259022 | + | 0.965871i | \(0.416600\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −0.134846 | −0.00757368 | −0.00378684 | − | 0.999993i | \(-0.501205\pi\) | ||||
−0.00378684 | + | 0.999993i | \(0.501205\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 30.7477i | 1.72154i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 35.8547i | 1.99501i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.18710i | 0.232259i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − 5.65685i | − 0.311872i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.94630 | 0.491733 | 0.245867 | − | 0.969304i | \(-0.420927\pi\) | ||||
0.245867 | + | 0.969304i | \(0.420927\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5.06653 | 0.276814 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −22.3303 | −1.21641 | −0.608205 | − | 0.793780i | \(-0.708110\pi\) | ||||
−0.608205 | + | 0.793780i | \(0.708110\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 28.3714 | 1.53640 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 1.00000i | − 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 31.4670i | 1.68924i | 0.535370 | + | 0.844618i | \(0.320172\pi\) | ||||
−0.535370 | + | 0.844618i | \(0.679828\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 21.1660i | − 1.13299i | −0.824065 | − | 0.566495i | \(-0.808299\pi\) | ||||
0.824065 | − | 0.566495i | \(-0.191701\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 34.4698i | 1.83464i | 0.398145 | + | 0.917322i | \(0.369654\pi\) | ||||
−0.398145 | + | 0.917322i | \(0.630346\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.46410 | 0.183855 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4.18104 | −0.220667 | −0.110333 | − | 0.993895i | \(-0.535192\pi\) | ||||
−0.110333 | + | 0.993895i | \(0.535192\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.00000 | 0.473684 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.269691 | 0.0141163 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.834849i | 0.0435787i | 0.999763 | + | 0.0217894i | \(0.00693632\pi\) | ||||
−0.999763 | + | 0.0217894i | \(0.993064\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.15732i | 0.0600852i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 21.1660i | − 1.09593i | −0.836500 | − | 0.547967i | \(-0.815402\pi\) | ||||
0.836500 | − | 0.547967i | \(-0.184598\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 9.07561i | − 0.467418i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.01810 | −0.103663 | −0.0518315 | − | 0.998656i | \(-0.516506\pi\) | ||||
−0.0518315 | + | 0.998656i | \(0.516506\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −9.07561 | −0.463742 | −0.231871 | − | 0.972747i | \(-0.574485\pi\) | ||||
−0.231871 | + | 0.972747i | \(0.574485\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.00000 | 0.101929 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −23.3376 | −1.18326 | −0.591631 | − | 0.806209i | \(-0.701516\pi\) | ||||
−0.591631 | + | 0.806209i | \(0.701516\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 17.1652i | 0.868079i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 6.94393i | − 0.349387i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 8.75560i | − 0.439431i | −0.975564 | − | 0.219716i | \(-0.929487\pi\) | ||||
0.975564 | − | 0.219716i | \(-0.0705129\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 32.5269i | 1.62432i | 0.583437 | + | 0.812158i | \(0.301707\pi\) | ||||
−0.583437 | + | 0.812158i | \(0.698293\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.37420 | −0.417149 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −24.2752 | −1.20328 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.58258 | 0.374934 | 0.187467 | − | 0.982271i | \(-0.439972\pi\) | ||||
0.187467 | + | 0.982271i | \(0.439972\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 10.3303i | − 0.507095i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 19.8656i | − 0.970499i | −0.874376 | − | 0.485249i | \(-0.838729\pi\) | ||||
0.874376 | − | 0.485249i | \(-0.161271\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.3060i | 0.551021i | 0.961298 | + | 0.275510i | \(0.0888469\pi\) | ||||
−0.961298 | + | 0.275510i | \(0.911153\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − 31.0511i | − 1.50620i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.92820 | −0.335279 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −17.7328 | −0.854161 | −0.427081 | − | 0.904214i | \(-0.640458\pi\) | ||||
−0.427081 | + | 0.904214i | \(0.640458\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 21.1652 | 1.01713 | 0.508566 | − | 0.861023i | \(-0.330176\pi\) | ||||
0.508566 | + | 0.861023i | \(0.330176\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 13.4048 | 0.641237 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 18.3303i | − 0.874858i | −0.899253 | − | 0.437429i | \(-0.855889\pi\) | ||||
0.899253 | − | 0.437429i | \(-0.144111\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 22.9612i | − 1.09092i | −0.838137 | − | 0.545459i | \(-0.816355\pi\) | ||||
0.838137 | − | 0.545459i | \(-0.183645\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 5.82380i | − 0.276075i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 9.89949i | − 0.467186i | −0.972334 | − | 0.233593i | \(-0.924952\pi\) | ||||
0.972334 | − | 0.233593i | \(-0.0750483\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 27.9035 | 1.31393 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.590327 | −0.0276750 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.16515 | −0.148060 | −0.0740298 | − | 0.997256i | \(-0.523586\pi\) | ||||
−0.0740298 | + | 0.997256i | \(0.523586\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −31.6018 | −1.47184 | −0.735922 | − | 0.677067i | \(-0.763251\pi\) | ||||
−0.735922 | + | 0.677067i | \(0.763251\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 11.5826i | − 0.538288i | −0.963100 | − | 0.269144i | \(-0.913259\pi\) | ||||
0.963100 | − | 0.269144i | \(-0.0867407\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 33.5401i | − 1.55205i | −0.630703 | − | 0.776025i | \(-0.717233\pi\) | ||||
0.630703 | − | 0.776025i | \(-0.282767\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 7.84190i | − 0.362105i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 37.8270i | − 1.73929i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −24.2487 | −1.11261 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 35.5889 | 1.62610 | 0.813049 | − | 0.582195i | \(-0.197806\pi\) | ||||
0.813049 | + | 0.582195i | \(0.197806\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.16515 | 0.326703 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.48331 | 0.339800 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 22.3303i | − 1.01188i | −0.862568 | − | 0.505941i | \(-0.831145\pi\) | ||||
0.862568 | − | 0.505941i | \(-0.168855\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16.5003i | 0.744650i | 0.928102 | + | 0.372325i | \(0.121439\pi\) | ||||
−0.928102 | + | 0.372325i | \(0.878561\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 67.3037i | 3.03121i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 5.36169i | − 0.240505i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 22.4213 | 1.00372 | 0.501858 | − | 0.864950i | \(-0.332650\pi\) | ||||
0.501858 | + | 0.864950i | \(0.332650\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −27.6939 | −1.23481 | −0.617406 | − | 0.786645i | \(-0.711816\pi\) | ||||
−0.617406 | + | 0.786645i | \(0.711816\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9.07803 | −0.403967 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −24.1185 | −1.06903 | −0.534517 | − | 0.845158i | \(-0.679506\pi\) | ||||
−0.534517 | + | 0.845158i | \(0.679506\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 0.417424i | − 0.0184658i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 1.29217i | − 0.0569397i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 17.5112i | − 0.770142i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13.4902i | 0.591017i | 0.955340 | + | 0.295508i | \(0.0954890\pi\) | ||||
−0.955340 | + | 0.295508i | \(0.904511\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 40.5046 | 1.77114 | 0.885572 | − | 0.464503i | \(-0.153767\pi\) | ||||
0.885572 | + | 0.464503i | \(0.153767\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 62.1022 | 2.70521 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.5826 | −0.720982 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −8.23610 | −0.356745 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 4.33030i | − 0.187215i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 3.09557i | − 0.133336i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 16.7882i | 0.721781i | 0.932608 | + | 0.360891i | \(0.117527\pi\) | ||||
−0.932608 | + | 0.360891i | \(0.882473\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.41875i | 0.146443i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.46050 | −0.318988 | −0.159494 | − | 0.987199i | \(-0.550986\pi\) | ||||
−0.159494 | + | 0.987199i | \(0.550986\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 52.5595 | 2.23911 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −10.7477 | −0.457040 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −11.9778 | −0.507514 | −0.253757 | − | 0.967268i | \(-0.581666\pi\) | ||||
−0.253757 | + | 0.967268i | \(0.581666\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 11.1652i | 0.472236i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 14.4272i | − 0.608036i | −0.952666 | − | 0.304018i | \(-0.901672\pi\) | ||||
0.952666 | − | 0.304018i | \(-0.0983283\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 6.39590i | − 0.269078i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − 34.1747i | − 1.43268i | −0.697753 | − | 0.716339i | \(-0.745817\pi\) | ||||
0.697753 | − | 0.716339i | \(-0.254183\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −34.4901 | −1.44337 | −0.721683 | − | 0.692223i | \(-0.756631\pi\) | ||||
−0.721683 | + | 0.692223i | \(0.756631\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −11.6089 | −0.484123 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.16515 | 0.215028 | 0.107514 | − | 0.994204i | \(-0.465711\pi\) | ||||
0.107514 | + | 0.994204i | \(0.465711\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −15.9891 | −0.663340 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.58258i | 0.148375i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 28.6411i | 1.18214i | 0.806619 | + | 0.591072i | \(0.201295\pi\) | ||||
−0.806619 | + | 0.591072i | \(0.798705\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 48.4974i | − 1.99830i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 31.6414i | 1.29936i | 0.760209 | + | 0.649679i | \(0.225097\pi\) | ||||
−0.760209 | + | 0.649679i | \(0.774903\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.37780 | 0.179472 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −27.3988 | −1.11948 | −0.559742 | − | 0.828667i | \(-0.689100\pi\) | ||||
−0.559742 | + | 0.828667i | \(0.689100\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 25.1652 | 1.02651 | 0.513254 | − | 0.858237i | \(-0.328440\pi\) | ||||
0.513254 | + | 0.858237i | \(0.328440\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.915775 | −0.0372315 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14.3303i | 0.581649i | 0.956776 | + | 0.290825i | \(0.0939296\pi\) | ||||
−0.956776 | + | 0.290825i | \(0.906070\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.16867i | 0.209102i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 41.9506i | − 1.69437i | −0.531298 | − | 0.847185i | \(-0.678296\pi\) | ||||
0.531298 | − | 0.847185i | \(-0.321704\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 11.0801i | − 0.446070i | −0.974810 | − | 0.223035i | \(-0.928404\pi\) | ||||
0.974810 | − | 0.223035i | \(-0.0715964\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.381401 | −0.0153298 | −0.00766490 | − | 0.999971i | \(-0.502440\pi\) | ||||
−0.00766490 | + | 0.999971i | \(0.502440\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −9.01400 | −0.361138 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 18.9129 | 0.756515 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −53.1360 | −2.11867 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13.9129i | 0.553863i | 0.960890 | + | 0.276931i | \(0.0893175\pi\) | ||||
−0.960890 | + | 0.276931i | \(0.910682\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.85403i | 0.113259i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.913701i | 0.0362021i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 38.0606i | 1.50330i | 0.659561 | + | 0.751651i | \(0.270742\pi\) | ||||
−0.659561 | + | 0.751651i | \(0.729258\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 20.5939 | 0.812145 | 0.406072 | − | 0.913841i | \(-0.366898\pi\) | ||||
0.406072 | + | 0.913841i | \(0.366898\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 20.3893 | 0.801587 | 0.400793 | − | 0.916168i | \(-0.368735\pi\) | ||||
0.400793 | + | 0.916168i | \(0.368735\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 37.0120 | 1.44839 | 0.724196 | − | 0.689594i | \(-0.242211\pi\) | ||||
0.724196 | + | 0.689594i | \(0.242211\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 7.16515i | − 0.279966i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.07310i | 0.0807564i | 0.999184 | + | 0.0403782i | \(0.0128563\pi\) | ||||
−0.999184 | + | 0.0403782i | \(0.987144\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 12.4104i | − 0.482709i | −0.970437 | − | 0.241354i | \(-0.922408\pi\) | ||||
0.970437 | − | 0.241354i | \(-0.0775916\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − 3.41875i | − 0.132574i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 25.1624 | 0.974292 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −21.4468 | −0.827943 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.91288 | 0.227925 | 0.113962 | − | 0.993485i | \(-0.463646\pi\) | ||||
0.113962 | + | 0.993485i | \(0.463646\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 16.9049 | 0.649707 | 0.324854 | − | 0.945764i | \(-0.394685\pi\) | ||||
0.324854 | + | 0.945764i | \(0.394685\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 11.5826i | − 0.444498i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 36.9053i | − 1.41214i | −0.708140 | − | 0.706072i | \(-0.750466\pi\) | ||||
0.708140 | − | 0.706072i | \(-0.249534\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 3.80570i | − 0.145408i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 1.05745i | − 0.0402855i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16.0652 | −0.611149 | −0.305575 | − | 0.952168i | \(-0.598849\pi\) | ||||
−0.305575 | + | 0.952168i | \(0.598849\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.18065 | −0.0447848 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 61.0780 | 2.31350 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −30.8209 | −1.16409 | −0.582044 | − | 0.813157i | \(-0.697747\pi\) | ||||
−0.582044 | + | 0.813157i | \(0.697747\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 41.4955i | 1.56503i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 14.0509i | 0.528437i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 29.7309i | 1.11657i | 0.829650 | + | 0.558284i | \(0.188540\pi\) | ||||
−0.829650 | + | 0.558284i | \(0.811460\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 23.2177i | − 0.869511i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.82740 | −0.0683409 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −22.5042 | −0.839265 | −0.419633 | − | 0.907694i | \(-0.637841\pi\) | ||||
−0.419633 | + | 0.907694i | \(0.637841\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.00000 | −0.0744839 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −45.5178 | −1.69049 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 19.4955i | 0.723046i | 0.932363 | + | 0.361523i | \(0.117743\pi\) | ||||
−0.932363 | + | 0.361523i | \(0.882257\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 82.7996i | − 3.06245i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 2.35970i | − 0.0871575i | −0.999050 | − | 0.0435788i | \(-0.986124\pi\) | ||||
0.999050 | − | 0.0435788i | \(-0.0138759\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 24.2752i | − 0.894188i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7.84190 | 0.288469 | 0.144235 | − | 0.989544i | \(-0.453928\pi\) | ||||
0.144235 | + | 0.989544i | \(0.453928\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 43.1887 | 1.58444 | 0.792220 | − | 0.610236i | \(-0.208925\pi\) | ||||
0.792220 | + | 0.610236i | \(0.208925\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −12.7477 | −0.467041 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.70239 | −0.244900 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 35.1652i | 1.28319i | 0.767042 | + | 0.641597i | \(0.221728\pi\) | ||||
−0.767042 | + | 0.641597i | \(0.778272\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 14.9666i | 0.544691i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 41.7599i | − 1.51779i | −0.651213 | − | 0.758895i | \(-0.725740\pi\) | ||||
0.651213 | − | 0.758895i | \(-0.274260\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5.00492i | 0.181428i | 0.995877 | + | 0.0907142i | \(0.0289150\pi\) | ||||
−0.995877 | + | 0.0907142i | \(0.971085\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.29150 | 0.191565 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −14.0000 | −0.504853 | −0.252426 | − | 0.967616i | \(-0.581229\pi\) | ||||
−0.252426 | + | 0.967616i | \(0.581229\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 47.3212 | 1.70203 | 0.851013 | − | 0.525144i | \(-0.175989\pi\) | ||||
0.851013 | + | 0.525144i | \(0.175989\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 42.0000i | 1.50868i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 47.6976i | − 1.70894i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 16.5975i | − 0.593906i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 10.1331i | − 0.361664i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 53.9796 | 1.92417 | 0.962083 | − | 0.272757i | \(-0.0879355\pi\) | ||||
0.962083 | + | 0.272757i | \(0.0879355\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9.89949 | −0.351986 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.33030 | 0.224796 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.39887 | −0.0495505 | −0.0247752 | − | 0.999693i | \(-0.507887\pi\) | ||||
−0.0247752 | + | 0.999693i | \(0.507887\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 38.3303i | − 1.35603i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 1.29217i | − 0.0455996i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 1.63670i | − 0.0576861i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − 47.7265i | − 1.67797i | −0.544151 | − | 0.838987i | \(-0.683148\pi\) | ||||
0.544151 | − | 0.838987i | \(-0.316852\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.48220 | 0.192506 | 0.0962531 | − | 0.995357i | \(-0.469314\pi\) | ||||
0.0962531 | + | 0.995357i | \(0.469314\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 8.60849 | 0.301542 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −64.6606 | −2.26219 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3.74166 | −0.130585 | −0.0652924 | − | 0.997866i | \(-0.520798\pi\) | ||||
−0.0652924 | + | 0.997866i | \(0.520798\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.91288i | 0.0666788i | 0.999444 | + | 0.0333394i | \(0.0106142\pi\) | ||||
−0.999444 | + | 0.0333394i | \(0.989386\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 30.7142i | − 1.06804i | −0.845473 | − | 0.534018i | \(-0.820681\pi\) | ||||
0.845473 | − | 0.534018i | \(-0.179319\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 30.8353i | − 1.07095i | −0.844550 | − | 0.535477i | \(-0.820132\pi\) | ||||
0.844550 | − | 0.535477i | \(-0.179868\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 6.77590i | − 0.234771i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.10080 | 0.176521 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 39.0077 | 1.34669 | 0.673347 | − | 0.739327i | \(-0.264856\pi\) | ||||
0.673347 | + | 0.739327i | \(0.264856\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 69.6606 | 2.40209 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −7.85971 | −0.270382 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.41742i | 0.0487033i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 19.8656i | 0.680984i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 35.0224i | 1.19914i | 0.800321 | + | 0.599572i | \(0.204663\pi\) | ||||
−0.800321 | + | 0.599572i | \(0.795337\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 13.0231i | 0.444860i | 0.974949 | + | 0.222430i | \(0.0713989\pi\) | ||||
−0.974949 | + | 0.222430i | \(0.928601\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 48.6881 | 1.66122 | 0.830609 | − | 0.556857i | \(-0.187993\pi\) | ||||
0.830609 | + | 0.556857i | \(0.187993\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 16.6754 | 0.567637 | 0.283819 | − | 0.958878i | \(-0.408399\pi\) | ||||
0.283819 | + | 0.958878i | \(0.408399\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.07803 | −0.172658 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −33.2704 | −1.12862 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.16515i | 0.242782i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 6.19115i | 0.209299i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7.30960i | 0.246828i | 0.992355 | + | 0.123414i | \(0.0393843\pi\) | ||||
−0.992355 | + | 0.123414i | \(0.960616\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 18.0896i | − 0.609455i | −0.952440 | − | 0.304727i | \(-0.901435\pi\) | ||||
0.952440 | − | 0.304727i | \(-0.0985653\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −24.2487 | −0.816034 | −0.408017 | − | 0.912974i | \(-0.633780\pi\) | ||||
−0.408017 | + | 0.912974i | \(0.633780\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −22.5042 | −0.755617 | −0.377809 | − | 0.925884i | \(-0.623322\pi\) | ||||
−0.377809 | + | 0.925884i | \(0.623322\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.41742 | 0.148156 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −29.9333 | −1.00168 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 7.49545i | − 0.250545i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 91.0357i | − 3.03621i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.84190i | 0.261252i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − 6.24718i | − 0.207663i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −13.6657 | −0.453762 | −0.226881 | − | 0.973922i | \(-0.572853\pi\) | ||||
−0.226881 | + | 0.973922i | \(0.572853\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 13.2566 | 0.439212 | 0.219606 | − | 0.975589i | \(-0.429523\pi\) | ||||
0.219606 | + | 0.975589i | \(0.429523\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −49.4955 | −1.63806 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −11.0901 | −0.366228 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 12.8348i | 0.423383i | 0.977337 | + | 0.211691i | \(0.0678971\pi\) | ||||
−0.977337 | + | 0.211691i | \(0.932103\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4.89898i | 0.161252i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 35.9361i | − 1.18157i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.11905i | 0.0367148i | 0.999831 | + | 0.0183574i | \(0.00584368\pi\) | ||||
−0.999831 | + | 0.0183574i | \(0.994156\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.29150 | −0.173422 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 13.5518 | 0.443192 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 39.4955 | 1.29026 | 0.645130 | − | 0.764073i | \(-0.276803\pi\) | ||||
0.645130 | + | 0.764073i | \(0.276803\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 12.7587 | 0.415921 | 0.207961 | − | 0.978137i | \(-0.433317\pi\) | ||||
0.207961 | + | 0.978137i | \(0.433317\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 22.8348i | − 0.743605i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.34279i | 0.0761304i | 0.999275 | + | 0.0380652i | \(0.0121195\pi\) | ||||
−0.999275 | + | 0.0380652i | \(0.987881\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.381401i | 0.0123808i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 27.4604i | − 0.889529i | −0.895648 | − | 0.444765i | \(-0.853287\pi\) | ||||
0.895648 | − | 0.444765i | \(-0.146713\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 13.2843 | 0.429870 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5.89041 | −0.190211 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −53.0000 | −1.70968 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −4.35960 | −0.140340 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 13.0780i | − 0.420561i | −0.977641 | − | 0.210281i | \(-0.932562\pi\) | ||||
0.977641 | − | 0.210281i | \(-0.0674377\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 9.52827i | − 0.305777i | −0.988243 | − | 0.152888i | \(-0.951143\pi\) | ||||
0.988243 | − | 0.152888i | \(-0.0488575\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.82740i | 0.0585838i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 6.01362i | − 0.192393i | −0.995362 | − | 0.0961964i | \(-0.969332\pi\) | ||||
0.995362 | − | 0.0961964i | \(-0.0306677\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −27.9035 | −0.891800 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −27.5707 | −0.879370 | −0.439685 | − | 0.898152i | \(-0.644910\pi\) | ||||
−0.439685 | + | 0.898152i | \(0.644910\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 16.0871 | 0.512578 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −30.9557 | −0.984335 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 20.0000i | − 0.635321i | −0.948205 | − | 0.317660i | \(-0.897103\pi\) | ||||
0.948205 | − | 0.317660i | \(-0.102897\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 12.3823i | − 0.392545i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 6.54680i | 0.207339i | 0.994612 | + | 0.103670i | \(0.0330585\pi\) | ||||
−0.994612 | + | 0.103670i | \(0.966942\pi\) | |||||||
\(998\) | 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.j.e.2591.7 | yes | 16 | |
3.2 | odd | 2 | inner | 4032.2.j.e.2591.11 | yes | 16 | |
4.3 | odd | 2 | inner | 4032.2.j.e.2591.5 | ✓ | 16 | |
8.3 | odd | 2 | inner | 4032.2.j.e.2591.10 | yes | 16 | |
8.5 | even | 2 | inner | 4032.2.j.e.2591.12 | yes | 16 | |
12.11 | even | 2 | inner | 4032.2.j.e.2591.9 | yes | 16 | |
24.5 | odd | 2 | inner | 4032.2.j.e.2591.8 | yes | 16 | |
24.11 | even | 2 | inner | 4032.2.j.e.2591.6 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4032.2.j.e.2591.5 | ✓ | 16 | 4.3 | odd | 2 | inner | |
4032.2.j.e.2591.6 | yes | 16 | 24.11 | even | 2 | inner | |
4032.2.j.e.2591.7 | yes | 16 | 1.1 | even | 1 | trivial | |
4032.2.j.e.2591.8 | yes | 16 | 24.5 | odd | 2 | inner | |
4032.2.j.e.2591.9 | yes | 16 | 12.11 | even | 2 | inner | |
4032.2.j.e.2591.10 | yes | 16 | 8.3 | odd | 2 | inner | |
4032.2.j.e.2591.11 | yes | 16 | 3.2 | odd | 2 | inner | |
4032.2.j.e.2591.12 | yes | 16 | 8.5 | even | 2 | inner |