Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [672,2,Mod(223,672)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(672, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("672.223");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 672 = 2^{5} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 672.b (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: | \(5.36594701583\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.836829184.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 14x^{6} + 61x^{4} + 84x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{9} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 223.6 | ||
Root | \(-0.222191i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 672.223 |
Dual form | 672.2.b.b.223.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/672\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(421\) | \(449\) | \(577\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.72844i | 0.772982i | 0.922293 | + | 0.386491i | \(0.126313\pi\) | ||||
−0.922293 | + | 0.386491i | \(0.873687\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.63640 | − | 0.222191i | 0.996467 | − | 0.0839804i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 6.17282i | 1.86118i | 0.366068 | + | 0.930588i | \(0.380704\pi\) | ||||
−0.366068 | + | 0.930588i | \(0.619296\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 2.82843i | − | 0.784465i | −0.919866 | − | 0.392232i | \(-0.871703\pi\) | ||
0.919866 | − | 0.392232i | \(-0.128297\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.72844i | 0.446281i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.72844i | 0.419208i | 0.977786 | + | 0.209604i | \(0.0672175\pi\) | ||||
−0.977786 | + | 0.209604i | \(0.932782\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.90126 | −1.35384 | −0.676921 | − | 0.736056i | \(-0.736686\pi\) | ||||
−0.676921 | + | 0.736056i | \(0.736686\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.63640 | − | 0.222191i | 0.575311 | − | 0.0484861i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 1.54437i | − | 0.322023i | −0.986952 | − | 0.161012i | \(-0.948524\pi\) | ||
0.986952 | − | 0.161012i | \(-0.0514757\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.01250 | 0.402499 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.28531 | 1.53854 | 0.769271 | − | 0.638922i | \(-0.220619\pi\) | ||||
0.769271 | + | 0.638922i | \(0.220619\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.62845 | −0.831295 | −0.415647 | − | 0.909526i | \(-0.636445\pi\) | ||||
−0.415647 | + | 0.909526i | \(0.636445\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 6.17282i | 1.07455i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.384044 | + | 4.55687i | 0.0649153 | + | 0.770251i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.24441 | 0.368978 | 0.184489 | − | 0.982835i | \(-0.440937\pi\) | ||||
0.184489 | + | 0.982835i | \(0.440937\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 2.82843i | − | 0.452911i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 3.92841i | − | 0.613515i | −0.951788 | − | 0.306758i | \(-0.900756\pi\) | ||
0.951788 | − | 0.306758i | \(-0.0992441\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.1012i | 1.54042i | 0.637788 | + | 0.770212i | \(0.279850\pi\) | ||||
−0.637788 | + | 0.770212i | \(0.720150\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.72844i | 0.257661i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.88877 | 0.713100 | 0.356550 | − | 0.934276i | \(-0.383953\pi\) | ||||
0.356550 | + | 0.934276i | \(0.383953\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.90126 | − | 1.17157i | 0.985895 | − | 0.167368i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.72844i | 0.242030i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.17407 | −1.26016 | −0.630078 | − | 0.776532i | \(-0.716977\pi\) | ||||
−0.630078 | + | 0.776532i | \(0.716977\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −10.6694 | −1.43865 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.90126 | −0.781641 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.65685 | 1.25722 | 0.628608 | − | 0.777723i | \(-0.283625\pi\) | ||||
0.628608 | + | 0.777723i | \(0.283625\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 14.2853i | − | 1.82905i | −0.404534 | − | 0.914523i | \(-0.632566\pi\) | ||
0.404534 | − | 0.914523i | \(-0.367434\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.63640 | − | 0.222191i | 0.332156 | − | 0.0279935i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.88877 | 0.606377 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.64436i | 0.811737i | 0.913931 | + | 0.405869i | \(0.133031\pi\) | ||||
−0.913931 | + | 0.405869i | \(0.866969\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 1.54437i | − | 0.185920i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 5.00125i | − | 0.593539i | −0.954949 | − | 0.296770i | \(-0.904091\pi\) | ||
0.954949 | − | 0.296770i | \(-0.0959093\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.19998i | 0.257488i | 0.991678 | + | 0.128744i | \(0.0410945\pi\) | ||||
−0.991678 | + | 0.128744i | \(0.958906\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.01250 | 0.232383 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.37155 | + | 16.2741i | 0.156302 | + | 1.85460i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 9.55812i | − | 1.07537i | −0.843145 | − | 0.537686i | \(-0.819299\pi\) | ||
0.843145 | − | 0.537686i | \(-0.180701\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −12.2025 | −1.33940 | −0.669698 | − | 0.742634i | \(-0.733576\pi\) | ||||
−0.669698 | + | 0.742634i | \(0.733576\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.98750 | −0.324040 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 8.28531 | 0.888278 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 9.16282i | − | 0.971257i | −0.874165 | − | 0.485629i | \(-0.838591\pi\) | ||
0.874165 | − | 0.485629i | \(-0.161409\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.628452 | − | 7.45688i | −0.0658797 | − | 0.781693i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.62845 | −0.479948 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 10.2000i | − | 1.04650i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 17.1137i | − | 1.73764i | −0.495131 | − | 0.868818i | \(-0.664880\pi\) | ||
0.495131 | − | 0.868818i | \(-0.335120\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.17282i | 0.620392i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.58527i | 0.953770i | 0.878966 | + | 0.476885i | \(0.158234\pi\) | ||||
−0.878966 | + | 0.476885i | \(0.841766\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.37155 | −0.332208 | −0.166104 | − | 0.986108i | \(-0.553119\pi\) | ||||
−0.166104 | + | 0.986108i | \(0.553119\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.384044 | + | 4.55687i | 0.0374789 | + | 0.444705i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 5.28406i | − | 0.510829i | −0.966832 | − | 0.255415i | \(-0.917788\pi\) | ||
0.966832 | − | 0.255415i | \(-0.0822119\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.54562 | 0.818522 | 0.409261 | − | 0.912417i | \(-0.365787\pi\) | ||||
0.409261 | + | 0.912417i | \(0.365787\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.24441 | 0.213030 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.36814 | −0.222776 | −0.111388 | − | 0.993777i | \(-0.535530\pi\) | ||||
−0.111388 | + | 0.993777i | \(0.535530\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.66935 | 0.248918 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 2.82843i | − | 0.261488i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.384044 | + | 4.55687i | 0.0352053 | + | 0.417727i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −27.1037 | −2.46398 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 3.92841i | − | 0.354213i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.1207i | 1.08411i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 6.24441i | − | 0.554102i | −0.960855 | − | 0.277051i | \(-0.910643\pi\) | ||
0.960855 | − | 0.277051i | \(-0.0893570\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 10.1012i | 0.889364i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.1457 | 0.886431 | 0.443216 | − | 0.896415i | \(-0.353838\pi\) | ||||
0.443216 | + | 0.896415i | \(0.353838\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −15.5581 | + | 1.31121i | −1.34906 | + | 0.113696i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.72844i | 0.148760i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.76809 | −0.578237 | −0.289118 | − | 0.957293i | \(-0.593362\pi\) | ||||
−0.289118 | + | 0.957293i | \(0.593362\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −15.3137 | −1.29889 | −0.649446 | − | 0.760408i | \(-0.724999\pi\) | ||||
−0.649446 | + | 0.760408i | \(0.724999\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.88877 | 0.411708 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 17.4594 | 1.46003 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 14.3207i | 1.18927i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.90126 | − | 1.17157i | 0.569206 | − | 0.0966297i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −8.40598 | −0.688645 | −0.344322 | − | 0.938851i | \(-0.611891\pi\) | ||||
−0.344322 | + | 0.938851i | \(0.611891\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 4.04443i | − | 0.329131i | −0.986366 | − | 0.164566i | \(-0.947378\pi\) | ||
0.986366 | − | 0.164566i | \(-0.0526222\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.72844i | 0.139736i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 8.00000i | − | 0.642575i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 2.97160i | − | 0.237159i | −0.992945 | − | 0.118580i | \(-0.962166\pi\) | ||
0.992945 | − | 0.118580i | \(-0.0378341\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −9.17407 | −0.727551 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.343146 | − | 4.07159i | −0.0270437 | − | 0.320886i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 12.6694i | − | 0.992340i | −0.868225 | − | 0.496170i | \(-0.834739\pi\) | ||
0.868225 | − | 0.496170i | \(-0.165261\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −10.6694 | −0.830608 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −9.28872 | −0.718782 | −0.359391 | − | 0.933187i | \(-0.617016\pi\) | ||||
−0.359391 | + | 0.933187i | \(0.617016\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.00000 | 0.384615 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.90126 | −0.451281 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 12.0716i | − | 0.917786i | −0.888492 | − | 0.458893i | \(-0.848246\pi\) | ||
0.888492 | − | 0.458893i | \(-0.151754\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.30576 | − | 0.447159i | 0.401077 | − | 0.0338021i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 9.65685 | 0.725854 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 8.17532i | − | 0.611052i | −0.952184 | − | 0.305526i | \(-0.901168\pi\) | ||
0.952184 | − | 0.305526i | \(-0.0988323\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 22.8334i | − | 1.69720i | −0.529039 | − | 0.848598i | \(-0.677447\pi\) | ||
0.529039 | − | 0.848598i | \(-0.322553\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 14.2853i | − | 1.05600i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.87932i | 0.285214i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −10.6694 | −0.780220 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.63640 | − | 0.222191i | 0.191770 | − | 0.0161620i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.6331i | 0.914100i | 0.889441 | + | 0.457050i | \(0.151094\pi\) | ||||
−0.889441 | + | 0.457050i | \(0.848906\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.30121 | 0.597534 | 0.298767 | − | 0.954326i | \(-0.403425\pi\) | ||||
0.298767 | + | 0.954326i | \(0.403425\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.88877 | 0.350092 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −14.8309 | −1.05666 | −0.528330 | − | 0.849039i | \(-0.677182\pi\) | ||||
−0.528330 | + | 0.849039i | \(0.677182\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.0159 | 0.851785 | 0.425892 | − | 0.904774i | \(-0.359960\pi\) | ||||
0.425892 | + | 0.904774i | \(0.359960\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.64436i | 0.468657i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 21.8434 | − | 1.84092i | 1.53311 | − | 0.129208i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.79003 | 0.474236 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 1.54437i | − | 0.107341i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 36.4274i | − | 2.51974i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 17.9038i | − | 1.23255i | −0.787533 | − | 0.616273i | \(-0.788642\pi\) | ||
0.787533 | − | 0.616273i | \(-0.211358\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 5.00125i | − | 0.342680i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −17.4594 | −1.19072 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −12.2025 | + | 1.02840i | −0.828358 | + | 0.0698125i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.19998i | 0.148661i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.88877 | 0.328854 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.58652 | −0.574996 | −0.287498 | − | 0.957781i | \(-0.592823\pi\) | ||||
−0.287498 | + | 0.957781i | \(0.592823\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.01250 | 0.134166 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −13.2569 | −0.879892 | −0.439946 | − | 0.898024i | \(-0.645002\pi\) | ||||
−0.439946 | + | 0.898024i | \(0.645002\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 3.91467i | − | 0.258689i | −0.991600 | − | 0.129344i | \(-0.958713\pi\) | ||
0.991600 | − | 0.129344i | \(-0.0412872\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.37155 | + | 16.2741i | 0.0902412 | + | 1.07075i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −0.343146 | −0.0224802 | −0.0112401 | − | 0.999937i | \(-0.503578\pi\) | ||||
−0.0112401 | + | 0.999937i | \(0.503578\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.44994i | 0.551213i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 9.55812i | − | 0.620866i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 28.8038i | 1.86316i | 0.363535 | + | 0.931581i | \(0.381570\pi\) | ||||
−0.363535 | + | 0.931581i | \(0.618430\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 24.5481i | 1.58128i | 0.612279 | + | 0.790642i | \(0.290253\pi\) | ||||
−0.612279 | + | 0.790642i | \(0.709747\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.02499 | + | 11.9284i | 0.129372 | + | 0.762078i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 16.6913i | 1.06204i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −12.2025 | −0.773300 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.7681 | −0.805915 | −0.402957 | − | 0.915219i | \(-0.632018\pi\) | ||||
−0.402957 | + | 0.915219i | \(0.632018\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.53312 | 0.599342 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.98750 | −0.187085 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 18.9853i | 1.18427i | 0.805838 | + | 0.592137i | \(0.201715\pi\) | ||||
−0.805838 | + | 0.592137i | \(0.798285\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.91717 | − | 0.498688i | 0.367675 | − | 0.0309870i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.28531 | 0.512848 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 19.9150i | − | 1.22801i | −0.789301 | − | 0.614006i | \(-0.789557\pi\) | ||
0.789301 | − | 0.614006i | \(-0.210443\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 15.8568i | − | 0.974077i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 9.16282i | − | 0.560756i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 12.6197i | 0.769437i | 0.923034 | + | 0.384718i | \(0.125701\pi\) | ||||
−0.923034 | + | 0.384718i | \(0.874299\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.14908 | −0.312784 | −0.156392 | − | 0.987695i | \(-0.549986\pi\) | ||||
−0.156392 | + | 0.987695i | \(0.549986\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.628452 | − | 7.45688i | −0.0380357 | − | 0.451311i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 12.4228i | 0.749122i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.3262 | 0.860778 | 0.430389 | − | 0.902643i | \(-0.358376\pi\) | ||||
0.430389 | + | 0.902643i | \(0.358376\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.62845 | −0.277098 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −12.9456 | −0.772268 | −0.386134 | − | 0.922443i | \(-0.626190\pi\) | ||||
−0.386134 | + | 0.922443i | \(0.626190\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 26.4719 | 1.57359 | 0.786795 | − | 0.617215i | \(-0.211739\pi\) | ||||
0.786795 | + | 0.617215i | \(0.211739\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − | 10.2000i | − | 0.604194i | ||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.872860 | − | 10.3569i | −0.0515233 | − | 0.611348i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 14.0125 | 0.824264 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 17.1137i | − | 1.00322i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 15.5285i | 0.907183i | 0.891210 | + | 0.453591i | \(0.149857\pi\) | ||||
−0.891210 | + | 0.453591i | \(0.850143\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 16.6913i | 0.971804i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 6.17282i | 0.358183i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.36814 | −0.252616 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.24441 | + | 26.6310i | 0.129366 | + | 1.53498i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 9.58527i | 0.550659i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 24.6913 | 1.41382 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 13.1332 | 0.749550 | 0.374775 | − | 0.927116i | \(-0.377720\pi\) | ||||
0.374775 | + | 0.927116i | \(0.377720\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.37155 | −0.191801 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.87932 | 0.219976 | 0.109988 | − | 0.993933i | \(-0.464919\pi\) | ||||
0.109988 | + | 0.993933i | \(0.464919\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 21.1362i | 1.19469i | 0.801984 | + | 0.597345i | \(0.203778\pi\) | ||||
−0.801984 | + | 0.597345i | \(0.796222\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.384044 | + | 4.55687i | 0.0216384 | + | 0.256750i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 13.9422 | 0.783070 | 0.391535 | − | 0.920163i | \(-0.371944\pi\) | ||||
0.391535 | + | 0.920163i | \(0.371944\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 51.1437i | 2.86350i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 5.28406i | − | 0.294927i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 10.2000i | − | 0.567542i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 5.69220i | − | 0.315746i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 8.54562 | 0.472574 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 12.8888 | − | 1.08624i | 0.710581 | − | 0.0598864i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 14.3037i | − | 0.786203i | −0.919495 | − | 0.393102i | \(-0.871402\pi\) | ||
0.919495 | − | 0.393102i | \(-0.128598\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.24441 | 0.122993 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −11.4844 | −0.627458 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 17.1162 | 0.932381 | 0.466190 | − | 0.884684i | \(-0.345626\pi\) | ||||
0.466190 | + | 0.884684i | \(0.345626\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.36814 | −0.128620 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 28.5706i | − | 1.54719i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.9342 | − | 4.62214i | 0.968356 | − | 0.249572i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.66935 | 0.143713 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4.11602i | 0.220959i | 0.993878 | + | 0.110480i | \(0.0352387\pi\) | ||||
−0.993878 | + | 0.110480i | \(0.964761\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 34.5766i | 1.85085i | 0.378936 | + | 0.925423i | \(0.376290\pi\) | ||||
−0.378936 | + | 0.925423i | \(0.623710\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 2.82843i | − | 0.150970i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 14.2991i | − | 0.761062i | −0.924768 | − | 0.380531i | \(-0.875741\pi\) | ||
0.924768 | − | 0.380531i | \(-0.124259\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.64436 | 0.458795 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.384044 | + | 4.55687i | 0.0203258 | + | 0.241175i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 26.8831i | 1.41883i | 0.704789 | + | 0.709417i | \(0.251042\pi\) | ||||
−0.704789 | + | 0.709417i | \(0.748958\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.8249 | 0.832889 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −27.1037 | −1.42258 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.80252 | −0.199033 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −16.3072 | −0.851231 | −0.425616 | − | 0.904904i | \(-0.639942\pi\) | ||||
−0.425616 | + | 0.904904i | \(0.639942\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 3.92841i | − | 0.204505i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −24.1866 | + | 2.03840i | −1.25570 | + | 0.105828i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −28.9188 | −1.49736 | −0.748678 | − | 0.662934i | \(-0.769311\pi\) | ||||
−0.748678 | + | 0.662934i | \(0.769311\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 12.1207i | 0.625909i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 23.4344i | − | 1.20693i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 28.6150i | 1.46986i | 0.678145 | + | 0.734928i | \(0.262784\pi\) | ||||
−0.678145 | + | 0.734928i | \(0.737216\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 6.24441i | − | 0.319911i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 25.4594 | 1.30091 | 0.650457 | − | 0.759543i | \(-0.274578\pi\) | ||||
0.650457 | + | 0.759543i | \(0.274578\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −28.1287 | + | 2.37064i | −1.43357 | + | 0.120819i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 10.1012i | 0.513475i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 8.25350 | 0.418469 | 0.209234 | − | 0.977866i | \(-0.432903\pi\) | ||||
0.209234 | + | 0.977866i | \(0.432903\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.66935 | 0.134995 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 10.1457 | 0.511781 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 16.5206 | 0.831243 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 27.9422i | − | 1.40238i | −0.712976 | − | 0.701188i | \(-0.752653\pi\) | ||
0.712976 | − | 0.701188i | \(-0.247347\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −15.5581 | + | 1.31121i | −0.778880 | + | 0.0656426i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 23.8593 | 1.19148 | 0.595739 | − | 0.803178i | \(-0.296859\pi\) | ||||
0.595739 | + | 0.803178i | \(0.296859\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 13.0912i | 0.652121i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.72844i | 0.0858869i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 13.8543i | 0.686734i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10.9363i | 0.540763i | 0.962753 | + | 0.270381i | \(0.0871498\pi\) | ||||
−0.962753 | + | 0.270381i | \(0.912850\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.76809 | −0.333845 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 25.4594 | − | 2.14567i | 1.25277 | − | 0.105582i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 21.0912i | − | 1.03533i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −15.3137 | −0.749916 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.08624 | 0.248479 | 0.124240 | − | 0.992252i | \(-0.460351\pi\) | ||||
0.124240 | + | 0.992252i | \(0.460351\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.8150 | −0.527092 | −0.263546 | − | 0.964647i | \(-0.584892\pi\) | ||||
−0.263546 | + | 0.964647i | \(0.584892\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.88877 | 0.237700 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.47848i | 0.168731i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.17407 | − | 37.6619i | −0.153604 | − | 1.82258i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 17.4594 | 0.842947 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 2.10999i | − | 0.101634i | −0.998708 | − | 0.0508172i | \(-0.983817\pi\) | ||
0.998708 | − | 0.0508172i | \(-0.0161826\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 21.2619i | 1.02178i | 0.859646 | + | 0.510891i | \(0.170684\pi\) | ||||
−0.859646 | + | 0.510891i | \(0.829316\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 14.3207i | 0.686623i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 9.11373i | 0.435969i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 35.6210 | 1.70010 | 0.850048 | − | 0.526706i | \(-0.176573\pi\) | ||||
0.850048 | + | 0.526706i | \(0.176573\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.90126 | − | 1.17157i | 0.328632 | − | 0.0557892i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 2.14101i | − | 0.101723i | −0.998706 | − | 0.0508613i | \(-0.983803\pi\) | ||
0.998706 | − | 0.0508613i | \(-0.0161966\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 15.8374 | 0.750764 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −8.40598 | −0.397589 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.40257 | 0.443735 | 0.221867 | − | 0.975077i | \(-0.428785\pi\) | ||||
0.221867 | + | 0.975077i | \(0.428785\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 24.2494 | 1.14186 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 4.04443i | − | 0.190024i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 12.8888 | − | 1.08624i | 0.604235 | − | 0.0509238i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15.5801 | 0.728804 | 0.364402 | − | 0.931242i | \(-0.381273\pi\) | ||||
0.364402 | + | 0.931242i | \(0.381273\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.72844i | 0.0806767i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 29.8766i | − | 1.39149i | −0.718288 | − | 0.695746i | \(-0.755074\pi\) | ||
0.718288 | − | 0.695746i | \(-0.244926\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 35.3356i | − | 1.64219i | −0.570794 | − | 0.821093i | \(-0.693364\pi\) | ||
0.570794 | − | 0.821093i | \(-0.306636\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 8.00000i | − | 0.370991i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −24.3232 | −1.12554 | −0.562771 | − | 0.826613i | \(-0.690265\pi\) | ||||
−0.562771 | + | 0.826613i | \(0.690265\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.47632 | + | 17.5172i | 0.0681701 | + | 0.808870i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 2.97160i | − | 0.136924i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −62.3531 | −2.86700 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −11.8763 | −0.544921 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −9.17407 | −0.420052 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −19.6000 | −0.895549 | −0.447775 | − | 0.894146i | \(-0.647783\pi\) | ||||
−0.447775 | + | 0.894146i | \(0.647783\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 6.34814i | − | 0.289450i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.343146 | − | 4.07159i | −0.0156137 | − | 0.185264i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 29.5801 | 1.34316 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 21.7331i | 0.984821i | 0.870363 | + | 0.492410i | \(0.163884\pi\) | ||||
−0.870363 | + | 0.492410i | \(0.836116\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 12.6694i | − | 0.572928i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 34.9409i | − | 1.57686i | −0.615124 | − | 0.788431i | \(-0.710894\pi\) | ||
0.615124 | − | 0.788431i | \(-0.289106\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 14.3207i | 0.644970i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −10.6694 | −0.479552 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.11123 | − | 13.1853i | −0.0498457 | − | 0.591442i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 19.5288i | 0.874229i | 0.899406 | + | 0.437115i | \(0.144000\pi\) | ||||
−0.899406 | + | 0.437115i | \(0.856000\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −9.28872 | −0.414989 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −30.4249 | −1.35658 | −0.678291 | − | 0.734794i | \(-0.737279\pi\) | ||||
−0.678291 | + | 0.734794i | \(0.737279\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −16.5676 | −0.737247 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5.00000 | 0.222058 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 13.8766i | 0.615070i | 0.951537 | + | 0.307535i | \(0.0995041\pi\) | ||||
−0.951537 | + | 0.307535i | \(0.900496\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.488815 | + | 5.80002i | 0.0216239 | + | 0.256578i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.90126 | −0.260547 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 5.82752i | − | 0.256791i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 30.1775i | 1.32720i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 12.0716i | − | 0.529884i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 11.3628i | 0.497813i | 0.968527 | + | 0.248907i | \(0.0800712\pi\) | ||||
−0.968527 | + | 0.248907i | \(0.919929\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.52063 | −0.197673 | −0.0988366 | − | 0.995104i | \(-0.531512\pi\) | ||||
−0.0988366 | + | 0.995104i | \(0.531512\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 5.30576 | − | 0.447159i | 0.231562 | − | 0.0195156i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 8.00000i | − | 0.348485i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 20.6149 | 0.896301 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 9.65685 | 0.419072 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −11.1112 | −0.481281 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.13317 | 0.394862 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 8.17532i | − | 0.352791i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 7.23191 | + | 42.6003i | 0.311500 | + | 1.83492i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −46.1287 | −1.98323 | −0.991614 | − | 0.129231i | \(-0.958749\pi\) | ||||
−0.991614 | + | 0.129231i | \(0.958749\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 22.8334i | − | 0.979876i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 14.7706i | 0.632702i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.8718i | 0.721387i | 0.932684 | + | 0.360694i | \(0.117460\pi\) | ||||
−0.932684 | + | 0.360694i | \(0.882540\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 14.2853i | − | 0.609682i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −48.8938 | −2.08294 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.12373 | − | 25.1991i | −0.0903102 | − | 1.07157i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.87932i | 0.164668i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −43.7197 | −1.85246 | −0.926231 | − | 0.376955i | \(-0.876971\pi\) | ||||
−0.926231 | + | 0.376955i | \(0.876971\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 28.5706 | 1.20841 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −10.6694 | −0.450460 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −19.4662 | −0.820402 | −0.410201 | − | 0.911995i | \(-0.634542\pi\) | ||||
−0.410201 | + | 0.911995i | \(0.634542\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 4.09318i | − | 0.172202i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.63640 | − | 0.222191i | 0.110719 | − | 0.00933116i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −12.1775 | −0.510507 | −0.255253 | − | 0.966874i | \(-0.582159\pi\) | ||||
−0.255253 | + | 0.966874i | \(0.582159\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 6.04193i | − | 0.252847i | −0.991976 | − | 0.126424i | \(-0.959650\pi\) | ||
0.991976 | − | 0.126424i | \(-0.0403498\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 12.6331i | 0.527756i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 3.10804i | − | 0.129614i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 3.03444i | − | 0.126325i | −0.998003 | − | 0.0631626i | \(-0.979881\pi\) | ||
0.998003 | − | 0.0631626i | \(-0.0201187\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 8.30121 | 0.344987 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −32.1707 | + | 2.71128i | −1.33466 | + | 0.112483i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 56.6299i | − | 2.34537i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.88877 | 0.202126 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 32.2075 | 1.32934 | 0.664672 | − | 0.747135i | \(-0.268571\pi\) | ||||
0.664672 | + | 0.747135i | \(0.268571\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 27.3137 | 1.12544 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −14.8309 | −0.610063 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 35.2196i | 1.44630i | 0.690693 | + | 0.723148i | \(0.257306\pi\) | ||||
−0.690693 | + | 0.723148i | \(0.742694\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.87627 | + | 0.663798i | −0.322896 | + | 0.0272130i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 12.0159 | 0.491778 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 20.7149i | − | 0.846388i | −0.906039 | − | 0.423194i | \(-0.860909\pi\) | ||
0.906039 | − | 0.423194i | \(-0.139091\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 24.8620i | − | 1.01414i | −0.861905 | − | 0.507070i | \(-0.830729\pi\) | ||
0.861905 | − | 0.507070i | \(-0.169271\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.64436i | 0.270579i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 46.8472i | − | 1.90461i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.19101 | 0.0483417 | 0.0241709 | − | 0.999708i | \(-0.492305\pi\) | ||||
0.0241709 | + | 0.999708i | \(0.492305\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 21.8434 | − | 1.84092i | 0.885140 | − | 0.0745980i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 13.8275i | − | 0.559401i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.60242 | 0.105111 | 0.0525555 | − | 0.998618i | \(-0.483263\pi\) | ||||
0.0525555 | + | 0.998618i | \(0.483263\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 6.79003 | 0.273800 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 33.9161 | 1.36541 | 0.682706 | − | 0.730693i | \(-0.260803\pi\) | ||||
0.682706 | + | 0.730693i | \(0.260803\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −18.8688 | −0.758400 | −0.379200 | − | 0.925315i | \(-0.623801\pi\) | ||||
−0.379200 | + | 0.925315i | \(0.623801\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 1.54437i | − | 0.0619734i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.03590 | − | 24.1569i | −0.0815666 | − | 0.967826i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −10.8874 | −0.435495 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 36.4274i | − | 1.45477i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.87932i | 0.154679i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.44688i | 0.0974088i | 0.998813 | + | 0.0487044i | \(0.0155092\pi\) | ||||
−0.998813 | + | 0.0487044i | \(0.984491\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 17.9038i | − | 0.711611i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 10.7931 | 0.428310 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.31371 | − | 19.5197i | −0.131294 | − | 0.773399i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 5.00125i | − | 0.197846i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −23.6619 | −0.934587 | −0.467293 | − | 0.884102i | \(-0.654771\pi\) | ||||
−0.467293 | + | 0.884102i | \(0.654771\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 20.1237 | 0.793602 | 0.396801 | − | 0.917905i | \(-0.370120\pi\) | ||||
0.396801 | + | 0.917905i | \(0.370120\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −17.4594 | −0.687462 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5.94320 | 0.233651 | 0.116826 | − | 0.993152i | \(-0.462728\pi\) | ||||
0.116826 | + | 0.993152i | \(0.462728\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 59.6100i | 2.33990i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −12.2025 | + | 1.02840i | −0.478253 | + | 0.0403063i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −5.33974 | −0.208960 | −0.104480 | − | 0.994527i | \(-0.533318\pi\) | ||||
−0.104480 | + | 0.994527i | \(0.533318\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 17.5362i | 0.685195i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.19998i | 0.0858292i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 25.5754i | − | 0.996276i | −0.867098 | − | 0.498138i | \(-0.834017\pi\) | ||
0.867098 | − | 0.498138i | \(-0.165983\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 21.7197i | 0.844798i | 0.906410 | + | 0.422399i | \(0.138812\pi\) | ||||
−0.906410 | + | 0.422399i | \(0.861188\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4.88877 | 0.189864 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.26635 | − | 26.8913i | −0.0878851 | − | 1.04280i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 12.7956i | − | 0.495447i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −8.58652 | −0.331974 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 88.1807 | 3.40418 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −42.6175 | −1.64279 | −0.821393 | − | 0.570363i | \(-0.806803\pi\) | ||||
−0.821393 | + | 0.570363i | \(0.806803\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.01250 | 0.0774610 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 33.7559i | − | 1.29735i | −0.761067 | − | 0.648673i | \(-0.775324\pi\) | ||
0.761067 | − | 0.648673i | \(-0.224676\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.80252 | − | 45.1187i | −0.145927 | − | 1.73150i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −13.2569 | −0.508006 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 38.1553i | 1.45997i | 0.683462 | + | 0.729986i | \(0.260474\pi\) | ||||
−0.683462 | + | 0.729986i | \(0.739526\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 11.6982i | − | 0.446966i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 3.91467i | − | 0.149354i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 25.9482i | 0.988547i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 32.8120 | 1.24823 | 0.624113 | − | 0.781334i | \(-0.285460\pi\) | ||||
0.624113 | + | 0.781334i | \(0.285460\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.37155 | + | 16.2741i | 0.0521008 | + | 0.618200i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 26.4688i | − | 1.00402i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.79003 | 0.257191 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −0.343146 | −0.0129790 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −14.9077 | −0.563057 | −0.281529 | − | 0.959553i | \(-0.590841\pi\) | ||||
−0.281529 | + | 0.959553i | \(0.590841\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −13.2448 | −0.499539 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 8.44994i | 0.318243i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.12976 | + | 25.2707i | 0.0800980 | + | 0.950401i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.47937 | 0.205782 | 0.102891 | − | 0.994693i | \(-0.467191\pi\) | ||||
0.102891 | + | 0.994693i | \(0.467191\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 9.55812i | − | 0.358457i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 7.14804i | 0.267696i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 30.1775i | 1.12857i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 28.8038i | 1.07570i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −3.60005 | −0.134259 | −0.0671296 | − | 0.997744i | \(-0.521384\pi\) | ||||
−0.0671296 | + | 0.997744i | \(0.521384\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.88877 | + | 0.749129i | −0.331035 | + | 0.0278990i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 24.5481i | 0.912954i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 16.6741 | 0.619262 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −17.3147 | −0.642168 | −0.321084 | − | 0.947051i | \(-0.604047\pi\) | ||||
−0.321084 | + | 0.947051i | \(0.604047\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −17.4594 | −0.645758 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 15.7490i | 0.581703i | 0.956768 | + | 0.290851i | \(0.0939385\pi\) | ||||
−0.956768 | + | 0.290851i | \(0.906061\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.02499 | + | 11.9284i | 0.0746930 | + | 0.439986i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −41.0144 | −1.51079 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.87182i | 0.326355i | 0.986597 | + | 0.163178i | \(0.0521744\pi\) | ||||
−0.986597 | + | 0.163178i | \(0.947826\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 16.6913i | 0.613170i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.90057i | 0.106412i | 0.998584 | + | 0.0532058i | \(0.0169439\pi\) | ||||
−0.998584 | + | 0.0532058i | \(0.983056\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 14.5292i | − | 0.532310i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −12.2025 | −0.446465 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.17407 | − | 13.9309i | −0.0428997 | − | 0.509025i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 9.98056i | − | 0.364196i | −0.983280 | − | 0.182098i | \(-0.941711\pi\) | ||
0.983280 | − | 0.182098i | \(-0.0582888\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −12.7681 | −0.465295 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 6.99056 | 0.254412 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.34814 | 0.158036 | 0.0790180 | − | 0.996873i | \(-0.474822\pi\) | ||||
0.0790180 | + | 0.996873i | \(0.474822\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 9.53312 | 0.346030 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 46.8197i | 1.69721i | 0.529025 | + | 0.848606i | \(0.322558\pi\) | ||||
−0.529025 | + | 0.848606i | \(0.677442\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 22.5297 | − | 1.89876i | 0.815630 | − | 0.0687398i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.98750 | −0.108013 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 27.3137i | − | 0.986241i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 2.86377i | − | 0.103270i | −0.998666 | − | 0.0516351i | \(-0.983557\pi\) | ||
0.998666 | − | 0.0516351i | \(-0.0164433\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 18.9853i | 0.683740i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 52.5040i | − | 1.88844i | −0.329317 | − | 0.944219i | \(-0.606819\pi\) | ||
0.329317 | − | 0.944219i | \(-0.393181\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9.31474 | −0.334595 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 5.91717 | − | 0.498688i | 0.212277 | − | 0.0178903i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 23.1826i | 0.830603i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 30.8718 | 1.10468 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 8.28531 | 0.296093 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.13623 | 0.183320 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −46.3981 | −1.65391 | −0.826957 | − | 0.562265i | \(-0.809930\pi\) | ||||
−0.826957 | + | 0.562265i | \(0.809930\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 19.9150i | − | 0.708993i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6.24337 | + | 0.526180i | −0.221989 | + | 0.0187088i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −40.4049 | −1.43482 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − | 15.8568i | − | 0.562384i | ||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 28.5215i | 1.01028i | 0.863036 | + | 0.505142i | \(0.168560\pi\) | ||||
−0.863036 | + | 0.505142i | \(0.831440\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.44994i | 0.298937i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 9.16282i | − | 0.323752i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −13.5801 | −0.479230 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7.03749 | − | 0.593107i | 0.248039 | − | 0.0209043i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 12.6197i | 0.444235i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 53.6100 | 1.88483 | 0.942414 | − | 0.334447i | \(-0.108550\pi\) | ||||
0.942414 | + | 0.334447i | \(0.108550\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −27.7207 | −0.973406 | −0.486703 | − | 0.873567i | \(-0.661801\pi\) | ||||
−0.486703 | + | 0.873567i | \(0.661801\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −5.14908 | −0.180586 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 21.8982 | 0.767061 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 59.6100i | − | 2.08549i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.628452 | − | 7.45688i | −0.0219599 | − | 0.260564i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.56902 | −0.0547593 | −0.0273797 | − | 0.999625i | \(-0.508716\pi\) | ||||
−0.0273797 | + | 0.999625i | \(0.508716\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 24.7132i | − | 0.861449i | −0.902483 | − | 0.430724i | \(-0.858258\pi\) | ||
0.902483 | − | 0.430724i | \(-0.141742\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 12.4228i | 0.432506i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 31.4840i | − | 1.09481i | −0.836869 | − | 0.547404i | \(-0.815616\pi\) | ||
0.836869 | − | 0.547404i | \(-0.184384\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 40.4403i | − | 1.40455i | −0.711906 | − | 0.702275i | \(-0.752168\pi\) | ||
0.711906 | − | 0.702275i | \(-0.247832\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 14.3262 | 0.496971 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.02499 | + | 11.9284i | 0.0701618 | + | 0.413295i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 16.0550i | − | 0.555606i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.62845 | −0.159983 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −39.5732 | −1.36622 | −0.683110 | − | 0.730316i | \(-0.739373\pi\) | ||||
−0.683110 | + | 0.730316i | \(0.739373\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 39.6463 | 1.36711 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −12.9456 | −0.445869 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 8.64220i | 0.297301i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −71.4564 | + | 6.02222i | −2.45527 | + | 0.206926i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 26.4719 | 0.908512 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 3.46620i | − | 0.118820i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 33.5540i | 1.14887i | 0.818551 | + | 0.574434i | \(0.194778\pi\) | ||||
−0.818551 | + | 0.574434i | \(0.805222\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 10.2000i | − | 0.348832i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 19.5060i | 0.666311i | 0.942872 | + | 0.333156i | \(0.108113\pi\) | ||||
−0.942872 | + | 0.333156i | \(0.891887\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.72616 | 0.297733 | 0.148866 | − | 0.988857i | \(-0.452438\pi\) | ||||
0.148866 | + | 0.988857i | \(0.452438\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.872860 | − | 10.3569i | −0.0297470 | − | 0.352962i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 3.08055i | − | 0.104863i | −0.998625 | − | 0.0524315i | \(-0.983303\pi\) | ||
0.998625 | − | 0.0524315i | \(-0.0166971\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 20.8650 | 0.709432 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 14.0125 | 0.475889 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 59.0006 | 2.00146 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 18.7931 | 0.636779 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 17.1137i | − | 0.579212i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.69311 | + | 31.9550i | 0.0910437 | + | 1.08028i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −45.4712 | −1.53545 | −0.767727 | − | 0.640778i | \(-0.778612\pi\) | ||||
−0.767727 | + | 0.640778i | \(0.778612\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 15.5285i | 0.523762i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 38.6765i | 1.30304i | 0.758629 | + | 0.651522i | \(0.225869\pi\) | ||||
−0.758629 | + | 0.651522i | \(0.774131\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 15.5874i | 0.524559i | 0.964992 | + | 0.262279i | \(0.0844742\pi\) | ||||
−0.964992 | + | 0.262279i | \(0.915526\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 16.6913i | 0.561072i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 31.8525 | 1.06950 | 0.534751 | − | 0.845009i | \(-0.320405\pi\) | ||||
0.534751 | + | 0.845009i | \(0.320405\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.38745 | − | 16.4628i | −0.0465337 | − | 0.552144i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6.17282i | 0.206797i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −28.8499 | −0.965425 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 14.1305 | 0.472332 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4.36814 | −0.145848 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −38.3481 | −1.27898 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 15.8568i | − | 0.528268i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.24441 | + | 26.6310i | 0.0746892 | + | 0.886223i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 39.4662 | 1.31190 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 5.05387i | − | 0.167811i | −0.996474 | − | 0.0839056i | \(-0.973261\pi\) | ||
0.996474 | − | 0.0839056i | \(-0.0267394\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 9.58527i | 0.317923i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 32.0900i | 1.06319i | 0.846999 | + | 0.531594i | \(0.178407\pi\) | ||||
−0.846999 | + | 0.531594i | \(0.821593\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 75.3237i | − | 2.49285i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 24.6913 | 0.816269 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 26.7481 | − | 2.25428i | 0.883300 | − | 0.0744429i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 20.9332i | 0.690522i | 0.938507 | + | 0.345261i | \(0.112210\pi\) | ||||
−0.938507 | + | 0.345261i | \(0.887790\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 13.1332 | 0.432753 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −14.1457 | −0.465610 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.51686 | 0.148514 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3.37155 | −0.110736 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 21.7059i | − | 0.712149i | −0.934458 | − | 0.356074i | \(-0.884115\pi\) | ||
0.934458 | − | 0.356074i | \(-0.115885\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −40.7262 | + | 6.91376i | −1.33475 | + | 0.226589i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3.87932 | 0.127003 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 18.4413i | − | 0.603096i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 18.1825i | 0.593996i | 0.954878 | + | 0.296998i | \(0.0959854\pi\) | ||||
−0.954878 | + | 0.296998i | \(0.904015\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 21.1362i | 0.689755i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 12.8079i | 0.417524i | 0.977966 | + | 0.208762i | \(0.0669435\pi\) | ||||
−0.977966 | + | 0.208762i | \(0.933057\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.06693 | −0.197566 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.384044 | + | 4.55687i | 0.0124930 | + | 0.148235i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 23.8797i | 0.775985i | 0.921663 | + | 0.387992i | \(0.126831\pi\) | ||||
−0.921663 | + | 0.387992i | \(0.873169\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.22247 | 0.201990 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 13.9422 | 0.452106 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −37.0006 | −1.19857 | −0.599283 | − | 0.800537i | \(-0.704547\pi\) | ||||
−0.599283 | + | 0.800537i | \(0.704547\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −21.8356 | −0.706582 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 51.1437i | 1.65324i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −17.8434 | + | 1.50381i | −0.576194 | + | 0.0485606i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.57743 | −0.308949 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 5.28406i | − | 0.170276i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 14.3481i | 0.461883i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7.93307i | 0.255110i | 0.991831 | + | 0.127555i | \(0.0407130\pi\) | ||||
−0.991831 | + | 0.127555i | \(0.959287\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 10.2000i | − | 0.327670i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 49.2169 | 1.57945 | 0.789723 | − | 0.613464i | \(-0.210224\pi\) | ||||
0.789723 | + | 0.613464i | \(0.210224\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −40.3731 | + | 3.40257i | −1.29430 | + | 0.109082i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 5.69220i | − | 0.182296i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −21.8075 | −0.697684 | −0.348842 | − | 0.937181i | \(-0.613425\pi\) | ||||
−0.348842 | + | 0.937181i | \(0.613425\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 56.5605 | 1.80768 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.54562 | 0.272841 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −45.7436 | −1.45900 | −0.729498 | − | 0.683983i | \(-0.760246\pi\) | ||||
−0.729498 | + | 0.683983i | \(0.760246\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 25.6344i | − | 0.816779i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 12.8888 | − | 1.08624i | 0.410254 | − | 0.0345754i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 15.6000 | 0.496053 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 41.0468i | 1.30389i | 0.758264 | + | 0.651947i | \(0.226048\pi\) | ||||
−0.758264 | + | 0.651947i | \(0.773952\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 14.3037i | − | 0.453915i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 20.7688i | 0.658414i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 23.3009i | − | 0.737946i | −0.929440 | − | 0.368973i | \(-0.879710\pi\) | ||
0.929440 | − | 0.368973i | \(-0.120290\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.24441 | 0.0710099 |
(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 | 672.2.b.b.223.6 | yes | 8 | |
3.2 | odd | 2 | 2016.2.b.c.1567.3 | 8 | |||
4.3 | odd | 2 | 672.2.b.a.223.6 | yes | 8 | ||
7.6 | odd | 2 | 672.2.b.a.223.3 | ✓ | 8 | ||
8.3 | odd | 2 | 1344.2.b.h.895.3 | 8 | |||
8.5 | even | 2 | 1344.2.b.g.895.3 | 8 | |||
12.11 | even | 2 | 2016.2.b.a.1567.3 | 8 | |||
21.20 | even | 2 | 2016.2.b.a.1567.6 | 8 | |||
24.5 | odd | 2 | 4032.2.b.q.3583.6 | 8 | |||
24.11 | even | 2 | 4032.2.b.o.3583.6 | 8 | |||
28.27 | even | 2 | inner | 672.2.b.b.223.3 | yes | 8 | |
56.13 | odd | 2 | 1344.2.b.h.895.6 | 8 | |||
56.27 | even | 2 | 1344.2.b.g.895.6 | 8 | |||
84.83 | odd | 2 | 2016.2.b.c.1567.6 | 8 | |||
168.83 | odd | 2 | 4032.2.b.q.3583.3 | 8 | |||
168.125 | even | 2 | 4032.2.b.o.3583.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
672.2.b.a.223.3 | ✓ | 8 | 7.6 | odd | 2 | ||
672.2.b.a.223.6 | yes | 8 | 4.3 | odd | 2 | ||
672.2.b.b.223.3 | yes | 8 | 28.27 | even | 2 | inner | |
672.2.b.b.223.6 | yes | 8 | 1.1 | even | 1 | trivial | |
1344.2.b.g.895.3 | 8 | 8.5 | even | 2 | |||
1344.2.b.g.895.6 | 8 | 56.27 | even | 2 | |||
1344.2.b.h.895.3 | 8 | 8.3 | odd | 2 | |||
1344.2.b.h.895.6 | 8 | 56.13 | odd | 2 | |||
2016.2.b.a.1567.3 | 8 | 12.11 | even | 2 | |||
2016.2.b.a.1567.6 | 8 | 21.20 | even | 2 | |||
2016.2.b.c.1567.3 | 8 | 3.2 | odd | 2 | |||
2016.2.b.c.1567.6 | 8 | 84.83 | odd | 2 | |||
4032.2.b.o.3583.3 | 8 | 168.125 | even | 2 | |||
4032.2.b.o.3583.6 | 8 | 24.11 | even | 2 | |||
4032.2.b.q.3583.3 | 8 | 168.83 | odd | 2 | |||
4032.2.b.q.3583.6 | 8 | 24.5 | odd | 2 |