Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5796,2,Mod(3725,5796)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5796, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 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("5796.3725");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5796 = 2^{2} \cdot 3^{2} \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5796.p (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: | \(46.2812930115\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3725.11 | ||
Character | \(\chi\) | \(=\) | 5796.3725 |
Dual form | 5796.2.p.a.3725.12 |
$q$-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 \(\left(\mathbb{Z}/5796\mathbb{Z}\right)^\times\).
\(n\) | \(829\) | \(1289\) | \(2899\) | \(4789\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(-1\) |
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 | ||||||||
\(5\) | −2.52995 | −1.13143 | −0.565713 | − | 0.824602i | \(-0.691399\pi\) | ||||
−0.565713 | + | 0.824602i | \(0.691399\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.00000i | − | 0.377964i | ||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.148938 | −0.0449064 | −0.0224532 | − | 0.999748i | \(-0.507148\pi\) | ||||
−0.0224532 | + | 0.999748i | \(0.507148\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.12072 | −1.14288 | −0.571441 | − | 0.820643i | \(-0.693616\pi\) | ||||
−0.571441 | + | 0.820643i | \(0.693616\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.48046 | 1.08667 | 0.543336 | − | 0.839516i | \(-0.317161\pi\) | ||||
0.543336 | + | 0.839516i | \(0.317161\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.775942i | 0.178013i | 0.996031 | + | 0.0890067i | \(0.0283692\pi\) | ||||
−0.996031 | + | 0.0890067i | \(0.971631\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.94061 | + | 2.73342i | 0.821675 | + | 0.569957i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.40063 | 0.280126 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 4.12003i | − | 0.765070i | −0.923941 | − | 0.382535i | \(-0.875051\pi\) | ||
0.923941 | − | 0.382535i | \(-0.124949\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.31955 | 0.775814 | 0.387907 | − | 0.921698i | \(-0.373198\pi\) | ||||
0.387907 | + | 0.921698i | \(0.373198\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.52995i | 0.427639i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.62073i | 0.759643i | 0.925060 | + | 0.379822i | \(0.124015\pi\) | ||||
−0.925060 | + | 0.379822i | \(0.875985\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 1.74012i | − | 0.271761i | −0.990725 | − | 0.135881i | \(-0.956614\pi\) | ||
0.990725 | − | 0.135881i | \(-0.0433863\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 1.88882i | − | 0.288042i | −0.989575 | − | 0.144021i | \(-0.953997\pi\) | ||
0.989575 | − | 0.144021i | \(-0.0460034\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 6.00777i | − | 0.876323i | −0.898896 | − | 0.438162i | \(-0.855630\pi\) | ||
0.898896 | − | 0.438162i | \(-0.144370\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.22127 | 0.167755 | 0.0838774 | − | 0.996476i | \(-0.473270\pi\) | ||||
0.0838774 | + | 0.996476i | \(0.473270\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.376804 | 0.0508083 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 12.6143i | − | 1.64225i | −0.570750 | − | 0.821124i | \(-0.693347\pi\) | ||
0.570750 | − | 0.821124i | \(-0.306653\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 0.327176i | − | 0.0418906i | −0.999781 | − | 0.0209453i | \(-0.993332\pi\) | ||
0.999781 | − | 0.0209453i | \(-0.00666758\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 10.4252 | 1.29309 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.77070i | 1.07151i | 0.844373 | + | 0.535755i | \(0.179973\pi\) | ||||
−0.844373 | + | 0.535755i | \(0.820027\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 9.70104i | − | 1.15130i | −0.817695 | − | 0.575651i | \(-0.804749\pi\) | ||
0.817695 | − | 0.575651i | \(-0.195251\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.80529 | −0.679458 | −0.339729 | − | 0.940523i | \(-0.610335\pi\) | ||||
−0.339729 | + | 0.940523i | \(0.610335\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.148938i | 0.0169730i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.3457i | 1.27649i | 0.769835 | + | 0.638243i | \(0.220339\pi\) | ||||
−0.769835 | + | 0.638243i | \(0.779661\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.932507 | 0.102356 | 0.0511779 | − | 0.998690i | \(-0.483702\pi\) | ||||
0.0511779 | + | 0.998690i | \(0.483702\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −11.3353 | −1.22949 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.18541 | −0.761652 | −0.380826 | − | 0.924647i | \(-0.624360\pi\) | ||||
−0.380826 | + | 0.924647i | \(0.624360\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.12072i | 0.431969i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 1.96309i | − | 0.201409i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.77969i | 0.586838i | 0.955984 | + | 0.293419i | \(0.0947931\pi\) | ||||
−0.955984 | + | 0.293419i | \(0.905207\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 4.61101i | − | 0.458813i | −0.973331 | − | 0.229406i | \(-0.926321\pi\) | ||
0.973331 | − | 0.229406i | \(-0.0736785\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.67463i | 0.559138i | 0.960126 | + | 0.279569i | \(0.0901916\pi\) | ||||
−0.960126 | + | 0.279569i | \(0.909808\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.71675 | −0.359312 | −0.179656 | − | 0.983730i | \(-0.557498\pi\) | ||||
−0.179656 | + | 0.983730i | \(0.557498\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.85947i | 0.657018i | 0.944501 | + | 0.328509i | \(0.106546\pi\) | ||||
−0.944501 | + | 0.328509i | \(0.893454\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.84409 | −0.737910 | −0.368955 | − | 0.929447i | \(-0.620284\pi\) | ||||
−0.368955 | + | 0.929447i | \(0.620284\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −9.96954 | − | 6.91540i | −0.929664 | − | 0.644864i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 4.48046i | − | 0.410723i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9778 | −0.997983 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.10622 | 0.814485 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.23880 | 0.642340 | 0.321170 | − | 0.947022i | \(-0.395924\pi\) | ||||
0.321170 | + | 0.947022i | \(0.395924\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.53804i | 0.571231i | 0.958344 | + | 0.285616i | \(0.0921981\pi\) | ||||
−0.958344 | + | 0.285616i | \(0.907802\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.775942 | 0.0672827 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −19.8768 | −1.69819 | −0.849097 | − | 0.528237i | \(-0.822853\pi\) | ||||
−0.849097 | + | 0.528237i | \(0.822853\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −17.6989 | −1.50120 | −0.750602 | − | 0.660755i | \(-0.770236\pi\) | ||||
−0.750602 | + | 0.660755i | \(0.770236\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.613731 | 0.0513227 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 10.4235i | 0.865621i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −20.9157 | −1.71348 | −0.856739 | − | 0.515750i | \(-0.827513\pi\) | ||||
−0.856739 | + | 0.515750i | \(0.827513\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.51755 | 0.449012 | 0.224506 | − | 0.974473i | \(-0.427923\pi\) | ||||
0.224506 | + | 0.974473i | \(0.427923\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −10.9282 | −0.877777 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 23.2541i | − | 1.85588i | −0.372731 | − | 0.927939i | \(-0.621579\pi\) | ||
0.372731 | − | 0.927939i | \(-0.378421\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.73342 | − | 3.94061i | 0.215423 | − | 0.310564i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −23.1465 | −1.81297 | −0.906487 | − | 0.422233i | \(-0.861246\pi\) | ||||
−0.906487 | + | 0.422233i | \(0.861246\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 11.9199i | 0.922393i | 0.887298 | + | 0.461196i | \(0.152580\pi\) | ||||
−0.887298 | + | 0.461196i | \(0.847420\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.98035 | 0.306181 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 4.55899i | − | 0.346613i | −0.984868 | − | 0.173307i | \(-0.944555\pi\) | ||
0.984868 | − | 0.173307i | \(-0.0554452\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 1.40063i | − | 0.105878i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 4.80276i | − | 0.358975i | −0.983760 | − | 0.179488i | \(-0.942556\pi\) | ||
0.983760 | − | 0.179488i | \(-0.0574440\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.32081i | 0.246834i | 0.992355 | + | 0.123417i | \(0.0393852\pi\) | ||||
−0.992355 | + | 0.123417i | \(0.960615\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 11.6902i | − | 0.859481i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.667309 | −0.0487985 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 19.9748 | 1.44533 | 0.722663 | − | 0.691201i | \(-0.242918\pi\) | ||||
0.722663 | + | 0.691201i | \(0.242918\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.6553 | 0.838969 | 0.419484 | − | 0.907763i | \(-0.362211\pi\) | ||||
0.419484 | + | 0.907763i | \(0.362211\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 21.4947i | 1.53144i | 0.643176 | + | 0.765718i | \(0.277616\pi\) | ||||
−0.643176 | + | 0.765718i | \(0.722384\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 17.2960i | 1.22608i | 0.790052 | + | 0.613040i | \(0.210053\pi\) | ||||
−0.790052 | + | 0.613040i | \(0.789947\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.12003 | −0.289169 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.40241i | 0.307478i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 0.115567i | − | 0.00799394i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.0305 | −0.690530 | −0.345265 | − | 0.938505i | \(-0.612211\pi\) | ||||
−0.345265 | + | 0.938505i | \(0.612211\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.77862i | 0.325899i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 4.31955i | − | 0.293230i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −18.4627 | −1.24194 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.09800 | −0.408352 | −0.204176 | − | 0.978934i | \(-0.565451\pi\) | ||||
−0.204176 | + | 0.978934i | \(0.565451\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −20.5885 | −1.36651 | −0.683254 | − | 0.730181i | \(-0.739436\pi\) | ||||
−0.683254 | + | 0.730181i | \(0.739436\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 16.0052i | − | 1.05765i | −0.848730 | − | 0.528827i | \(-0.822632\pi\) | ||
0.848730 | − | 0.528827i | \(-0.177368\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 24.7086i | 1.61871i | 0.587318 | + | 0.809356i | \(0.300184\pi\) | ||||
−0.587318 | + | 0.809356i | \(0.699816\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 15.1993i | 0.991495i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 14.2201i | − | 0.919822i | −0.887965 | − | 0.459911i | \(-0.847881\pi\) | ||
0.887965 | − | 0.459911i | \(-0.152119\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 6.99000i | − | 0.450265i | −0.974328 | − | 0.225133i | \(-0.927718\pi\) | ||
0.974328 | − | 0.225133i | \(-0.0722815\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.52995 | 0.161632 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 3.19744i | − | 0.203448i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7.51447 | −0.474309 | −0.237155 | − | 0.971472i | \(-0.576215\pi\) | ||||
−0.237155 | + | 0.971472i | \(0.576215\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.586906 | − | 0.407109i | −0.0368984 | − | 0.0255947i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 22.4100i | − | 1.39790i | −0.715172 | − | 0.698948i | \(-0.753652\pi\) | ||
0.715172 | − | 0.698948i | \(-0.246348\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.62073 | 0.287118 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.87715 | 0.115750 | 0.0578750 | − | 0.998324i | \(-0.481568\pi\) | ||||
0.0578750 | + | 0.998324i | \(0.481568\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.08976 | −0.189802 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 6.99760i | − | 0.426651i | −0.976981 | − | 0.213326i | \(-0.931570\pi\) | ||
0.976981 | − | 0.213326i | \(-0.0684295\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.82619 | −0.353916 | −0.176958 | − | 0.984218i | \(-0.556626\pi\) | ||||
−0.176958 | + | 0.984218i | \(0.556626\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.208606 | −0.0125794 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −23.3172 | −1.40100 | −0.700498 | − | 0.713654i | \(-0.747039\pi\) | ||||
−0.700498 | + | 0.713654i | \(0.747039\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.02569 | 0.120843 | 0.0604214 | − | 0.998173i | \(-0.480756\pi\) | ||||
0.0604214 | + | 0.998173i | \(0.480756\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.0762i | 0.658410i | 0.944258 | + | 0.329205i | \(0.106781\pi\) | ||||
−0.944258 | + | 0.329205i | \(0.893219\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.74012 | −0.102716 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.07453 | 0.180855 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −0.0960819 | −0.00561316 | −0.00280658 | − | 0.999996i | \(-0.500893\pi\) | ||||
−0.00280658 | + | 0.999996i | \(0.500893\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 31.9136i | 1.85808i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −16.2382 | − | 11.2637i | −0.939078 | − | 0.651394i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.88882 | −0.108870 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.827737i | 0.0473961i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.91870 | 0.451944 | 0.225972 | − | 0.974134i | \(-0.427444\pi\) | ||||
0.225972 | + | 0.974134i | \(0.427444\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 16.8699i | − | 0.956603i | −0.878196 | − | 0.478301i | \(-0.841253\pi\) | ||
0.878196 | − | 0.478301i | \(-0.158747\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 25.1608i | − | 1.42217i | −0.703106 | − | 0.711085i | \(-0.748204\pi\) | ||
0.703106 | − | 0.711085i | \(-0.251796\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.20949i | 0.348760i | 0.984678 | + | 0.174380i | \(0.0557921\pi\) | ||||
−0.984678 | + | 0.174380i | \(0.944208\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.613628i | 0.0343566i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.47658i | 0.193442i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.77160 | −0.320151 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6.00777 | −0.331219 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −35.5936 | −1.95640 | −0.978201 | − | 0.207659i | \(-0.933416\pi\) | ||||
−0.978201 | + | 0.207659i | \(0.933416\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 22.1894i | − | 1.21234i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 0.673930i | − | 0.0367113i | −0.999832 | − | 0.0183557i | \(-0.994157\pi\) | ||
0.999832 | − | 0.0183557i | \(-0.00584312\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.643344 | −0.0348390 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 8.80190i | − | 0.472511i | −0.971691 | − | 0.236255i | \(-0.924080\pi\) | ||
0.971691 | − | 0.236255i | \(-0.0759202\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −28.4731 | −1.52413 | −0.762066 | − | 0.647499i | \(-0.775815\pi\) | ||||
−0.762066 | + | 0.647499i | \(0.775815\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 14.8208i | 0.788832i | 0.918932 | + | 0.394416i | \(0.129053\pi\) | ||||
−0.918932 | + | 0.394416i | \(0.870947\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 24.5431i | 1.30261i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 12.4115 | 0.655054 | 0.327527 | − | 0.944842i | \(-0.393785\pi\) | ||||
0.327527 | + | 0.944842i | \(0.393785\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.3979 | 0.968311 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 14.6871 | 0.768757 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 34.9854i | − | 1.82622i | −0.407713 | − | 0.913110i | \(-0.633673\pi\) | ||
0.407713 | − | 0.913110i | \(-0.366327\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 1.22127i | − | 0.0634053i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 7.84130i | − | 0.406007i | −0.979178 | − | 0.203004i | \(-0.934930\pi\) | ||
0.979178 | − | 0.203004i | \(-0.0650703\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 16.9775i | 0.874386i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.86934i | 0.506954i | 0.967341 | + | 0.253477i | \(0.0815742\pi\) | ||||
−0.967341 | + | 0.253477i | \(0.918426\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.57892 | −0.131776 | −0.0658882 | − | 0.997827i | \(-0.520988\pi\) | ||||
−0.0658882 | + | 0.997827i | \(0.520988\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 0.376804i | − | 0.0192037i | ||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.73943 | −0.189597 | −0.0947984 | − | 0.995496i | \(-0.530221\pi\) | ||||
−0.0947984 | + | 0.995496i | \(0.530221\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 17.6558 | + | 12.2470i | 0.892890 | + | 0.619356i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 28.7039i | − | 1.44425i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.50547 | 0.0755571 | 0.0377786 | − | 0.999286i | \(-0.487972\pi\) | ||||
0.0377786 | + | 0.999286i | \(0.487972\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.42987 | 0.0714043 | 0.0357021 | − | 0.999362i | \(-0.488633\pi\) | ||||
0.0357021 | + | 0.999362i | \(0.488633\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −17.7997 | −0.886665 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 0.688201i | − | 0.0341128i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −36.1330 | −1.78666 | −0.893330 | − | 0.449401i | \(-0.851637\pi\) | ||||
−0.893330 | + | 0.449401i | \(0.851637\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −12.6143 | −0.620712 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.35919 | −0.115808 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −13.8636 | −0.677282 | −0.338641 | − | 0.940916i | \(-0.609967\pi\) | ||||
−0.338641 | + | 0.940916i | \(0.609967\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 24.0942i | 1.17428i | 0.809485 | + | 0.587140i | \(0.199746\pi\) | ||||
−0.809485 | + | 0.587140i | \(0.800254\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.27546 | 0.304405 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.327176 | −0.0158331 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −25.8172 | −1.24357 | −0.621786 | − | 0.783187i | \(-0.713593\pi\) | ||||
−0.621786 | + | 0.783187i | \(0.713593\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 28.7807i | 1.38311i | 0.722323 | + | 0.691555i | \(0.243074\pi\) | ||||
−0.722323 | + | 0.691555i | \(0.756926\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.12097 | + | 3.05769i | −0.101460 | + | 0.146269i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −23.5643 | −1.12466 | −0.562332 | − | 0.826911i | \(-0.690096\pi\) | ||||
−0.562332 | + | 0.826911i | \(0.690096\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 20.6291i | − | 0.980120i | −0.871689 | − | 0.490060i | \(-0.836975\pi\) | ||
0.871689 | − | 0.490060i | \(-0.163025\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 18.1787 | 0.861754 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 19.6011i | 0.925032i | 0.886611 | + | 0.462516i | \(0.153053\pi\) | ||||
−0.886611 | + | 0.462516i | \(0.846947\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.259169i | 0.0122038i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 10.4252i | − | 0.488741i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 4.70323i | − | 0.220008i | −0.993931 | − | 0.110004i | \(-0.964914\pi\) | ||
0.993931 | − | 0.110004i | \(-0.0350864\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 19.9401i | 0.928703i | 0.885651 | + | 0.464351i | \(0.153713\pi\) | ||||
−0.885651 | + | 0.464351i | \(0.846287\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.07647 | 0.142976 | 0.0714879 | − | 0.997441i | \(-0.477225\pi\) | ||||
0.0714879 | + | 0.997441i | \(0.477225\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 11.8091 | 0.546460 | 0.273230 | − | 0.961949i | \(-0.411908\pi\) | ||||
0.273230 | + | 0.961949i | \(0.411908\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.77070 | 0.404993 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.281317i | 0.0129349i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.08681i | 0.0498661i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 21.0311 | 0.960934 | 0.480467 | − | 0.877013i | \(-0.340467\pi\) | ||||
0.480467 | + | 0.877013i | \(0.340467\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 19.0407i | − | 0.868183i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 14.6223i | − | 0.663964i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.20875 | −0.371974 | −0.185987 | − | 0.982552i | \(-0.559548\pi\) | ||||
−0.185987 | + | 0.982552i | \(0.559548\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.58335i | 0.432491i | 0.976339 | + | 0.216245i | \(0.0693811\pi\) | ||||
−0.976339 | + | 0.216245i | \(0.930619\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 18.4596i | − | 0.831380i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −9.70104 | −0.435151 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −31.4415 | −1.40751 | −0.703757 | − | 0.710441i | \(-0.748496\pi\) | ||||
−0.703757 | + | 0.710441i | \(0.748496\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.21401 | 0.0541301 | 0.0270650 | − | 0.999634i | \(-0.491384\pi\) | ||||
0.0270650 | + | 0.999634i | \(0.491384\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 11.6656i | 0.519113i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 15.2568i | − | 0.676246i | −0.941102 | − | 0.338123i | \(-0.890208\pi\) | ||
0.941102 | − | 0.338123i | \(-0.109792\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.80529i | 0.256811i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 14.3565i | − | 0.632624i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.894783i | 0.0393525i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.03937 | 0.220779 | 0.110389 | − | 0.993888i | \(-0.464790\pi\) | ||||
0.110389 | + | 0.993888i | \(0.464790\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.11943i | 0.223857i | 0.993716 | + | 0.111929i | \(0.0357028\pi\) | ||||
−0.993716 | + | 0.111929i | \(0.964297\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 19.3536 | 0.843055 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.05687 | + | 21.5427i | 0.350299 | + | 0.936638i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7.17055i | 0.310591i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.40318 | 0.406535 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.148938 | 0.00641520 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 44.4139 | 1.90950 | 0.954752 | − | 0.297402i | \(-0.0961203\pi\) | ||||
0.954752 | + | 0.297402i | \(0.0961203\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 17.3541i | − | 0.743368i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −27.9106 | −1.19337 | −0.596686 | − | 0.802475i | \(-0.703516\pi\) | ||||
−0.596686 | + | 0.802475i | \(0.703516\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.19690 | 0.136193 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 11.3457 | 0.482467 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 27.6681 | 1.17233 | 0.586167 | − | 0.810190i | \(-0.300636\pi\) | ||||
0.586167 | + | 0.810190i | \(0.300636\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.78331i | 0.329199i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −27.2314 | −1.14767 | −0.573833 | − | 0.818972i | \(-0.694544\pi\) | ||||
−0.573833 | + | 0.818972i | \(0.694544\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 19.8451 | 0.834891 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5.12271 | 0.214755 | 0.107378 | − | 0.994218i | \(-0.465755\pi\) | ||||
0.107378 | + | 0.994218i | \(0.465755\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.56201i | 0.0653680i | 0.999466 | + | 0.0326840i | \(0.0104055\pi\) | ||||
−0.999466 | + | 0.0326840i | \(0.989595\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.51934 | + | 3.82850i | 0.230172 | + | 0.159660i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.94862 | −0.206014 | −0.103007 | − | 0.994681i | \(-0.532846\pi\) | ||||
−0.103007 | + | 0.994681i | \(0.532846\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 0.932507i | − | 0.0386869i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.181894 | −0.00753326 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 8.23518i | − | 0.339902i | −0.985452 | − | 0.169951i | \(-0.945639\pi\) | ||
0.985452 | − | 0.169951i | \(-0.0543610\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.35172i | 0.138105i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 35.8156i | − | 1.47077i | −0.677649 | − | 0.735386i | \(-0.737001\pi\) | ||
0.677649 | − | 0.735386i | \(-0.262999\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 11.3353i | 0.464703i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 22.8844i | − | 0.935031i | −0.883985 | − | 0.467515i | \(-0.845149\pi\) | ||
0.883985 | − | 0.467515i | \(-0.154851\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 34.7863 | 1.41896 | 0.709481 | − | 0.704725i | \(-0.248930\pi\) | ||||
0.709481 | + | 0.704725i | \(0.248930\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 27.7733 | 1.12914 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 10.7198 | 0.435104 | 0.217552 | − | 0.976049i | \(-0.430193\pi\) | ||||
0.217552 | + | 0.976049i | \(0.430193\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 24.7563i | 1.00153i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 29.5254i | − | 1.19252i | −0.802792 | − | 0.596260i | \(-0.796653\pi\) | ||
0.802792 | − | 0.596260i | \(-0.203347\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −9.60152 | −0.386543 | −0.193271 | − | 0.981145i | \(-0.561910\pi\) | ||||
−0.193271 | + | 0.981145i | \(0.561910\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 26.5651i | − | 1.06774i | −0.845566 | − | 0.533871i | \(-0.820737\pi\) | ||
0.845566 | − | 0.533871i | \(-0.179263\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7.18541i | 0.287878i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.0414 | −1.20166 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 20.7030i | 0.825483i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19.8921i | 0.791893i | 0.918274 | + | 0.395946i | \(0.129583\pi\) | ||||
−0.918274 | + | 0.395946i | \(0.870417\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −18.3138 | −0.726760 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.12072 | 0.163269 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 13.6329 | 0.538469 | 0.269234 | − | 0.963075i | \(-0.413229\pi\) | ||||
0.269234 | + | 0.963075i | \(0.413229\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.55297i | 0.258424i | 0.991617 | + | 0.129212i | \(0.0412448\pi\) | ||||
−0.991617 | + | 0.129212i | \(0.958755\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 15.4159i | − | 0.606062i | −0.952981 | − | 0.303031i | \(-0.902002\pi\) | ||
0.952981 | − | 0.303031i | \(-0.0979985\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.87875i | 0.0737474i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4.40349i | 0.172322i | 0.996281 | + | 0.0861610i | \(0.0274599\pi\) | ||||
−0.996281 | + | 0.0861610i | \(0.972540\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 16.5409i | − | 0.646306i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −15.3289 | −0.597131 | −0.298565 | − | 0.954389i | \(-0.596508\pi\) | ||||
−0.298565 | + | 0.954389i | \(0.596508\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.89302i | 0.229212i | 0.993411 | + | 0.114606i | \(0.0365605\pi\) | ||||
−0.993411 | + | 0.114606i | \(0.963439\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.96309 | −0.0761254 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 11.2618 | − | 16.2354i | 0.436057 | − | 0.628639i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.0487288i | 0.00188115i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 19.6865 | 0.758859 | 0.379430 | − | 0.925221i | \(-0.376120\pi\) | ||||
0.379430 | + | 0.925221i | \(0.376120\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 31.1163 | 1.19590 | 0.597948 | − | 0.801535i | \(-0.295983\pi\) | ||||
0.597948 | + | 0.801535i | \(0.295983\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.77969 | 0.221804 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 9.57583i | 0.366409i | 0.983075 | + | 0.183204i | \(0.0586470\pi\) | ||||
−0.983075 | + | 0.183204i | \(0.941353\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 50.2874 | 1.92138 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −5.03253 | −0.191724 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −25.2991 | −0.962424 | −0.481212 | − | 0.876604i | \(-0.659803\pi\) | ||||
−0.481212 | + | 0.876604i | \(0.659803\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 44.7773 | 1.69850 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 7.79654i | − | 0.295315i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 23.0197 | 0.869443 | 0.434722 | − | 0.900565i | \(-0.356847\pi\) | ||||
0.434722 | + | 0.900565i | \(0.356847\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.58542 | −0.135227 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4.61101 | −0.173415 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.68502i | 0.100838i | 0.998728 | + | 0.0504191i | \(0.0160557\pi\) | ||||
−0.998728 | + | 0.0504191i | \(0.983944\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 17.0217 | + | 11.8071i | 0.637467 | + | 0.442181i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.55271 | −0.0580679 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 3.08498i | 0.115050i | 0.998344 | + | 0.0575252i | \(0.0183210\pi\) | ||||
−0.998344 | + | 0.0575252i | \(0.981679\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.67463 | 0.211334 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 5.77064i | − | 0.214316i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 9.05394i | 0.335792i | 0.985805 | + | 0.167896i | \(0.0536973\pi\) | ||||
−0.985805 | + | 0.167896i | \(0.946303\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 8.46279i | − | 0.313008i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 6.63913i | − | 0.245222i | −0.992455 | − | 0.122611i | \(-0.960873\pi\) | ||
0.992455 | − | 0.122611i | \(-0.0391267\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 1.30629i | − | 0.0481177i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.24877 | 0.303436 | 0.151718 | − | 0.988424i | \(-0.451519\pi\) | ||||
0.151718 | + | 0.988424i | \(0.451519\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −7.93170 | −0.290986 | −0.145493 | − | 0.989359i | \(-0.546477\pi\) | ||||
−0.145493 | + | 0.989359i | \(0.546477\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 52.9155 | 1.93868 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.71675i | 0.135807i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 32.6877i | 1.19279i | 0.802690 | + | 0.596396i | \(0.203401\pi\) | ||||
−0.802690 | + | 0.596396i | \(0.796599\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −13.9591 | −0.508024 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 0.710487i | − | 0.0258231i | −0.999917 | − | 0.0129115i | \(-0.995890\pi\) | ||
0.999917 | − | 0.0129115i | \(-0.00410998\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 8.26317i | − | 0.299540i | −0.988721 | − | 0.149770i | \(-0.952147\pi\) | ||
0.988721 | − | 0.149770i | \(-0.0478532\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.85947 | 0.248330 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 51.9802i | 1.87690i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 20.6049i | 0.743033i | 0.928426 | + | 0.371516i | \(0.121162\pi\) | ||||
−0.928426 | + | 0.371516i | \(0.878838\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 36.8271 | 1.32458 | 0.662290 | − | 0.749248i | \(-0.269585\pi\) | ||||
0.662290 | + | 0.749248i | \(0.269585\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.05009 | 0.217326 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.35023 | 0.0483771 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.44485i | 0.0517008i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 58.8316i | 2.09979i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 11.8097i | 0.420972i | 0.977597 | + | 0.210486i | \(0.0675046\pi\) | ||||
−0.977597 | + | 0.210486i | \(0.932495\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7.84409i | 0.278904i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.34820i | 0.0478760i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −39.5755 | −1.40183 | −0.700917 | − | 0.713243i | \(-0.747226\pi\) | ||||
−0.700917 | + | 0.713243i | \(0.747226\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 26.9176i | − | 0.952275i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.864626 | 0.0305120 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.91540 | + | 9.96954i | −0.243736 | + | 0.351380i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 6.43666i | − | 0.226301i | −0.993578 | − | 0.113150i | \(-0.963906\pi\) | ||
0.993578 | − | 0.113150i | \(-0.0360942\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −43.8629 | −1.54023 | −0.770117 | − | 0.637903i | \(-0.779802\pi\) | ||||
−0.770117 | + | 0.637903i | \(0.779802\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 58.5594 | 2.05125 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.46562 | 0.0512754 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 3.63643i | − | 0.126912i | −0.997985 | − | 0.0634561i | \(-0.979788\pi\) | ||
0.997985 | − | 0.0634561i | \(-0.0202123\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.32577 | 0.220502 | 0.110251 | − | 0.993904i | \(-0.464834\pi\) | ||||
0.110251 | + | 0.993904i | \(0.464834\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −37.1316 | −1.29119 | −0.645596 | − | 0.763679i | \(-0.723391\pi\) | ||||
−0.645596 | + | 0.763679i | \(0.723391\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −33.5445 | −1.16505 | −0.582524 | − | 0.812814i | \(-0.697935\pi\) | ||||
−0.582524 | + | 0.812814i | \(0.697935\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.48046 | −0.155239 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 30.1568i | − | 1.04362i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 7.07428 | 0.244231 | 0.122116 | − | 0.992516i | \(-0.461032\pi\) | ||||
0.122116 | + | 0.992516i | \(0.461032\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.0253 | 0.414667 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −10.0701 | −0.346421 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.9778i | 0.377202i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −12.6304 | + | 18.2085i | −0.432964 | + | 0.624180i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −6.09610 | −0.208726 | −0.104363 | − | 0.994539i | \(-0.533280\pi\) | ||||
−0.104363 | + | 0.994539i | \(0.533280\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 9.33970i | − | 0.319038i | −0.987195 | − | 0.159519i | \(-0.949006\pi\) | ||
0.987195 | − | 0.159519i | \(-0.0509943\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 24.1222 | 0.823040 | 0.411520 | − | 0.911401i | \(-0.364998\pi\) | ||||
0.411520 | + | 0.911401i | \(0.364998\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 16.1279i | − | 0.548998i | −0.961587 | − | 0.274499i | \(-0.911488\pi\) | ||
0.961587 | − | 0.274499i | \(-0.0885121\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 11.5340i | 0.392167i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 1.68980i | − | 0.0573224i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 36.1416i | − | 1.22461i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 9.10622i | − | 0.307846i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 16.7922 | 0.567031 | 0.283516 | − | 0.958968i | \(-0.408499\pi\) | ||||
0.283516 | + | 0.958968i | \(0.408499\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8.88554 | 0.299361 | 0.149681 | − | 0.988734i | \(-0.452175\pi\) | ||||
0.149681 | + | 0.988734i | \(0.452175\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 35.8056 | 1.20496 | 0.602478 | − | 0.798136i | \(-0.294180\pi\) | ||||
0.602478 | + | 0.798136i | \(0.294180\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 4.99655i | 0.167768i | 0.996476 | + | 0.0838839i | \(0.0267325\pi\) | ||||
−0.996476 | + | 0.0838839i | \(0.973267\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 7.23880i | − | 0.242782i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.66168 | 0.155997 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 12.1507i | 0.406154i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 17.7967i | − | 0.593553i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.47187 | 0.182294 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 8.40146i | − | 0.279274i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 27.7345i | 0.920909i | 0.887683 | + | 0.460454i | \(0.152314\pi\) | ||||
−0.887683 | + | 0.460454i | \(0.847686\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −55.2253 | −1.82970 | −0.914848 | − | 0.403799i | \(-0.867690\pi\) | ||||
−0.914848 | + | 0.403799i | \(0.867690\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.138885 | −0.00459643 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 6.53804 | 0.215905 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 23.9880i | − | 0.791290i | −0.918404 | − | 0.395645i | \(-0.870521\pi\) | ||
0.918404 | − | 0.395645i | \(-0.129479\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 39.9753i | 1.31580i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.47193i | 0.212796i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 9.74208i | 0.319627i | 0.987147 | + | 0.159814i | \(0.0510893\pi\) | ||||
−0.987147 | + | 0.159814i | \(0.948911\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 0.775942i | − | 0.0254305i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.68826 | 0.0552119 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 49.2496i | − | 1.60892i | −0.594010 | − | 0.804458i | \(-0.702456\pi\) | ||
0.594010 | − | 0.804458i | \(-0.297544\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 37.7486 | 1.23057 | 0.615284 | − | 0.788305i | \(-0.289041\pi\) | ||||
0.615284 | + | 0.788305i | \(0.289041\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.75647 | − | 6.85714i | 0.154892 | − | 0.223299i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 38.3991i | 1.24780i | 0.781502 | + | 0.623902i | \(0.214454\pi\) | ||||
−0.781502 | + | 0.623902i | \(0.785546\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 23.9220 | 0.776541 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.57546 | 0.0510342 | 0.0255171 | − | 0.999674i | \(-0.491877\pi\) | ||||
0.0255171 | + | 0.999674i | \(0.491877\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −50.5352 | −1.63528 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 19.8768i | 0.641857i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −12.3415 | −0.398112 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −29.4874 | −0.949232 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 19.0807 | 0.613594 | 0.306797 | − | 0.951775i | \(-0.400743\pi\) | ||||
0.306797 | + | 0.951775i | \(0.400743\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −19.8466 | −0.636909 | −0.318454 | − | 0.947938i | \(-0.603164\pi\) | ||||
−0.318454 | + | 0.947938i | \(0.603164\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 17.6989i | 0.567402i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 19.9970 | 0.639761 | 0.319880 | − | 0.947458i | \(-0.396357\pi\) | ||||
0.319880 | + | 0.947458i | \(0.396357\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.07018 | 0.0342031 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −34.6159 | −1.10408 | −0.552038 | − | 0.833819i | \(-0.686150\pi\) | ||||
−0.552038 | + | 0.833819i | \(0.686150\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 54.3805i | − | 1.73271i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5.16293 | − | 7.44311i | 0.164172 | − | 0.236677i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −29.6550 | −0.942024 | −0.471012 | − | 0.882127i | \(-0.656111\pi\) | ||||
−0.471012 | + | 0.882127i | \(0.656111\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 43.7579i | − | 1.38722i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −8.27099 | −0.261945 | −0.130972 | − | 0.991386i | \(-0.541810\pi\) | ||||
−0.130972 | + | 0.991386i | \(0.541810\pi\) | |||||||
\(998\) | 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 | 5796.2.p.a.3725.11 | ✓ | 48 | |
3.2 | odd | 2 | inner | 5796.2.p.a.3725.37 | yes | 48 | |
23.22 | odd | 2 | inner | 5796.2.p.a.3725.38 | yes | 48 | |
69.68 | even | 2 | inner | 5796.2.p.a.3725.12 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5796.2.p.a.3725.11 | ✓ | 48 | 1.1 | even | 1 | trivial | |
5796.2.p.a.3725.12 | yes | 48 | 69.68 | even | 2 | inner | |
5796.2.p.a.3725.37 | yes | 48 | 3.2 | odd | 2 | inner | |
5796.2.p.a.3725.38 | yes | 48 | 23.22 | odd | 2 | inner |