Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2880,2,Mod(2177,2880)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2880, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 0, 2, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2880.2177");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2880 = 2^{6} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2880.w (of order \(4\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(22.9969157821\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 27x^{8} + 107x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{9} \) |
Twist minimal: | no (minimal twist has level 1440) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 2177.5 | ||
Root | \(-0.219986 - 0.219986i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2880.2177 |
Dual form | 2880.2.w.p.2753.5 |
$q$-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 \(\left(\mathbb{Z}/2880\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(641\) | \(901\) | \(2431\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(5\) | 1.34577 | + | 1.78575i | 0.601848 | + | 0.798610i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.90321 | − | 2.90321i | −1.09731 | − | 1.09731i | −0.994724 | − | 0.102587i | \(-0.967288\pi\) |
−0.102587 | − | 0.994724i | \(-0.532712\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 2.15728i | − | 0.650444i | −0.945638 | − | 0.325222i | \(-0.894561\pi\) | ||
0.945638 | − | 0.325222i | \(-0.105439\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.90321 | + | 1.90321i | −0.527856 | + | 0.527856i | −0.919933 | − | 0.392077i | \(-0.871757\pi\) |
0.392077 | + | 0.919933i | \(0.371757\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.974241 | − | 0.974241i | 0.236288 | − | 0.236288i | −0.579023 | − | 0.815311i | \(-0.696566\pi\) |
0.815311 | + | 0.579023i | \(0.196566\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.80642i | 0.414422i | 0.978296 | + | 0.207211i | \(0.0664387\pi\) | ||||
−0.978296 | + | 0.207211i | \(0.933561\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.879946 | + | 0.879946i | 0.183481 | + | 0.183481i | 0.792871 | − | 0.609390i | \(-0.208585\pi\) |
−0.609390 | + | 0.792871i | \(0.708585\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.37778 | + | 4.80642i | −0.275557 | + | 0.961285i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.743067 | −0.137984 | −0.0689920 | − | 0.997617i | \(-0.521978\pi\) | ||||
−0.0689920 | + | 0.997617i | \(0.521978\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.05086 | −1.26637 | −0.633185 | − | 0.774000i | \(-0.718253\pi\) | ||||
−0.633185 | + | 0.774000i | \(0.718253\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.27733 | − | 9.09147i | 0.215909 | − | 1.53674i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.33185 | + | 8.33185i | 1.36975 | + | 1.36975i | 0.860793 | + | 0.508955i | \(0.169968\pi\) |
0.508955 | + | 0.860793i | \(0.330032\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.67726i | 1.19899i | 0.800380 | + | 0.599493i | \(0.204631\pi\) | ||||
−0.800380 | + | 0.599493i | \(0.795369\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.05086 | − | 3.05086i | 0.465251 | − | 0.465251i | −0.435121 | − | 0.900372i | \(-0.643294\pi\) |
0.900372 | + | 0.435121i | \(0.143294\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.54038 | + | 7.54038i | −1.09988 | + | 1.09988i | −0.105453 | + | 0.994424i | \(0.533629\pi\) |
−0.994424 | + | 0.105453i | \(0.966371\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 9.85728i | 1.40818i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.08000 | − | 5.08000i | −0.697792 | − | 0.697792i | 0.266142 | − | 0.963934i | \(-0.414251\pi\) |
−0.963934 | + | 0.266142i | \(0.914251\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.85236 | − | 2.90321i | 0.519452 | − | 0.391469i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 14.2658 | 1.85724 | 0.928622 | − | 0.371026i | \(-0.120994\pi\) | ||||
0.928622 | + | 0.371026i | \(0.120994\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.56199 | −0.584103 | −0.292052 | − | 0.956403i | \(-0.594338\pi\) | ||||
−0.292052 | + | 0.956403i | \(0.594338\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.95995 | − | 0.837362i | −0.739241 | − | 0.103862i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.05086 | + | 7.05086i | 0.861399 | + | 0.861399i | 0.991501 | − | 0.130102i | \(-0.0415304\pi\) |
−0.130102 | + | 0.991501i | \(0.541530\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.5261i | 1.48657i | 0.668973 | + | 0.743286i | \(0.266734\pi\) | ||||
−0.668973 | + | 0.743286i | \(0.733266\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.62222 | − | 3.62222i | 0.423948 | − | 0.423948i | −0.462612 | − | 0.886561i | \(-0.653088\pi\) |
0.886561 | + | 0.462612i | \(0.153088\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6.26304 | + | 6.26304i | −0.713740 | + | 0.713740i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 15.0509i | 1.69335i | 0.532108 | + | 0.846677i | \(0.321400\pi\) | ||||
−0.532108 | + | 0.846677i | \(0.678600\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.81413 | − | 7.81413i | −0.857713 | − | 0.857713i | 0.133356 | − | 0.991068i | \(-0.457425\pi\) |
−0.991068 | + | 0.133356i | \(0.957425\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.05086 | + | 0.428639i | 0.330912 | + | 0.0464925i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.40350 | −0.784769 | −0.392385 | − | 0.919801i | \(-0.628350\pi\) | ||||
−0.392385 | + | 0.919801i | \(0.628350\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 11.0509 | 1.15844 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.22582 | + | 2.43104i | −0.330962 | + | 0.249419i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.67307 | + | 6.67307i | 0.677548 | + | 0.677548i | 0.959445 | − | 0.281897i | \(-0.0909636\pi\) |
−0.281897 | + | 0.959445i | \(0.590964\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.27987i | 0.724374i | 0.932105 | + | 0.362187i | \(0.117970\pi\) | ||||
−0.932105 | + | 0.362187i | \(0.882030\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.70964 | − | 8.70964i | 0.858186 | − | 0.858186i | −0.132938 | − | 0.991124i | \(-0.542441\pi\) |
0.991124 | + | 0.132938i | \(0.0424412\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.49957 | + | 3.49957i | −0.338317 | + | 0.338317i | −0.855733 | − | 0.517417i | \(-0.826894\pi\) |
0.517417 | + | 0.855733i | \(0.326894\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.9081i | 1.52372i | 0.647740 | + | 0.761861i | \(0.275714\pi\) | ||||
−0.647740 | + | 0.761861i | \(0.724286\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10.6000 | − | 10.6000i | −0.997162 | − | 0.997162i | 0.00283397 | − | 0.999996i | \(-0.499098\pi\) |
−0.999996 | + | 0.00283397i | \(0.999098\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.387152 | + | 2.75557i | −0.0361021 | + | 0.256958i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.65685 | −0.518563 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.34614 | 0.576922 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.4372 | + | 4.00799i | −0.933535 | + | 0.358485i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.9032 | − | 10.9032i | −0.967504 | − | 0.967504i | 0.0319847 | − | 0.999488i | \(-0.489817\pi\) |
−0.999488 | + | 0.0319847i | \(0.989817\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.7111i | 1.02320i | 0.859223 | + | 0.511602i | \(0.170948\pi\) | ||||
−0.859223 | + | 0.511602i | \(0.829052\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.24443 | − | 5.24443i | 0.454750 | − | 0.454750i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −5.82307 | + | 5.82307i | −0.497498 | + | 0.497498i | −0.910658 | − | 0.413160i | \(-0.864425\pi\) |
0.413160 | + | 0.910658i | \(0.364425\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 3.14272i | − | 0.266562i | −0.991078 | − | 0.133281i | \(-0.957449\pi\) | ||
0.991078 | − | 0.133281i | \(-0.0425513\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.10576 | + | 4.10576i | 0.343341 | + | 0.343341i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.00000 | − | 1.32693i | −0.0830455 | − | 0.110195i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.31475 | −0.517325 | −0.258662 | − | 0.965968i | \(-0.583282\pi\) | ||||
−0.258662 | + | 0.965968i | \(0.583282\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −18.3684 | −1.49480 | −0.747400 | − | 0.664374i | \(-0.768698\pi\) | ||||
−0.747400 | + | 0.664374i | \(0.768698\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −9.48886 | − | 12.5910i | −0.762163 | − | 1.01134i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.0365650 | − | 0.0365650i | −0.00291821 | − | 0.00291821i | 0.705646 | − | 0.708564i | \(-0.250657\pi\) |
−0.708564 | + | 0.705646i | \(0.750657\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 5.10934i | − | 0.402672i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.05086 | + | 7.05086i | −0.552266 | + | 0.552266i | −0.927094 | − | 0.374829i | \(-0.877702\pi\) |
0.374829 | + | 0.927094i | \(0.377702\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.09147 | − | 9.09147i | 0.703519 | − | 0.703519i | −0.261645 | − | 0.965164i | \(-0.584265\pi\) |
0.965164 | + | 0.261645i | \(0.0842650\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.75557i | 0.442736i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −12.3599 | − | 12.3599i | −0.939703 | − | 0.939703i | 0.0585793 | − | 0.998283i | \(-0.481343\pi\) |
−0.998283 | + | 0.0585793i | \(0.981343\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 17.9541 | − | 9.95407i | 1.35720 | − | 0.752457i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 10.9163 | 0.815924 | 0.407962 | − | 0.912999i | \(-0.366240\pi\) | ||||
0.407962 | + | 0.912999i | \(0.366240\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 19.5210 | 1.45098 | 0.725492 | − | 0.688231i | \(-0.241612\pi\) | ||||
0.725492 | + | 0.688231i | \(0.241612\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.66579 | + | 26.0914i | −0.269514 | + | 1.91828i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.10171 | − | 2.10171i | −0.153692 | − | 0.153692i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 23.8398i | − | 1.72499i | −0.506068 | − | 0.862493i | \(-0.668902\pi\) | ||
0.506068 | − | 0.862493i | \(-0.331098\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.66370 | + | 9.66370i | −0.695609 | + | 0.695609i | −0.963460 | − | 0.267852i | \(-0.913686\pi\) |
0.267852 | + | 0.963460i | \(0.413686\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.99379 | − | 9.99379i | 0.712028 | − | 0.712028i | −0.254931 | − | 0.966959i | \(-0.582053\pi\) |
0.966959 | + | 0.254931i | \(0.0820528\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.7556i | 1.04599i | 0.852334 | + | 0.522997i | \(0.175186\pi\) | ||||
−0.852334 | + | 0.522997i | \(0.824814\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.15728 | + | 2.15728i | 0.151411 | + | 0.151411i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −13.7096 | + | 10.3319i | −0.957522 | + | 0.721608i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.89696 | 0.269559 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.47013 | −0.583108 | −0.291554 | − | 0.956554i | \(-0.594172\pi\) | ||||
−0.291554 | + | 0.956554i | \(0.594172\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 9.55382 | + | 1.34229i | 0.651565 | + | 0.0915437i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 20.4701 | + | 20.4701i | 1.38960 | + | 1.38960i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.70837i | 0.249452i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.56691 | + | 5.56691i | −0.372788 | + | 0.372788i | −0.868492 | − | 0.495704i | \(-0.834910\pi\) |
0.495704 | + | 0.868492i | \(0.334910\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −9.97141 | + | 9.97141i | −0.661826 | + | 0.661826i | −0.955810 | − | 0.293984i | \(-0.905019\pi\) |
0.293984 | + | 0.955810i | \(0.405019\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 15.1240i | 0.999421i | 0.866192 | + | 0.499711i | \(0.166560\pi\) | ||||
−0.866192 | + | 0.499711i | \(0.833440\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −4.07643 | − | 4.07643i | −0.267056 | − | 0.267056i | 0.560857 | − | 0.827913i | \(-0.310472\pi\) |
−0.827913 | + | 0.560857i | \(0.810472\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −23.6128 | − | 3.31756i | −1.54033 | − | 0.216414i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −0.547516 | −0.0354159 | −0.0177079 | − | 0.999843i | \(-0.505637\pi\) | ||||
−0.0177079 | + | 0.999843i | \(0.505637\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −22.4701 | −1.44743 | −0.723714 | − | 0.690100i | \(-0.757567\pi\) | ||||
−0.723714 | + | 0.690100i | \(0.757567\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −17.6026 | + | 13.2657i | −1.12459 | + | 0.847513i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.43801 | − | 3.43801i | −0.218755 | − | 0.218755i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.23173i | 0.519582i | 0.965665 | + | 0.259791i | \(0.0836537\pi\) | ||||
−0.965665 | + | 0.259791i | \(0.916346\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.89829 | − | 1.89829i | 0.119344 | − | 0.119344i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.61069 | − | 4.61069i | 0.287607 | − | 0.287607i | −0.548526 | − | 0.836133i | \(-0.684811\pi\) |
0.836133 | + | 0.548526i | \(0.184811\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 48.3783i | − | 3.00608i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −7.74918 | − | 7.74918i | −0.477835 | − | 0.477835i | 0.426604 | − | 0.904439i | \(-0.359710\pi\) |
−0.904439 | + | 0.426604i | \(0.859710\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.23506 | − | 15.9081i | 0.137299 | − | 0.977229i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 13.3139 | 0.811763 | 0.405881 | − | 0.913926i | \(-0.366965\pi\) | ||||
0.405881 | + | 0.913926i | \(0.366965\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.0830 | 1.21995 | 0.609977 | − | 0.792419i | \(-0.291179\pi\) | ||||
0.609977 | + | 0.792419i | \(0.291179\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 10.3688 | + | 2.97227i | 0.625262 | + | 0.179234i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.90321 | + | 3.90321i | 0.234521 | + | 0.234521i | 0.814577 | − | 0.580056i | \(-0.196969\pi\) |
−0.580056 | + | 0.814577i | \(0.696969\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 1.60280i | − | 0.0956152i | −0.998857 | − | 0.0478076i | \(-0.984777\pi\) | ||
0.998857 | − | 0.0478076i | \(-0.0152234\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −18.1017 | + | 18.1017i | −1.07603 | + | 1.07603i | −0.0791742 | + | 0.996861i | \(0.525228\pi\) |
−0.996861 | + | 0.0791742i | \(0.974772\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 22.2887 | − | 22.2887i | 1.31566 | − | 1.31566i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15.1017i | 0.888336i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 18.9553 | + | 18.9553i | 1.10738 | + | 1.10738i | 0.993493 | + | 0.113889i | \(0.0363310\pi\) |
0.113889 | + | 0.993493i | \(0.463669\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 19.1985 | + | 25.4750i | 1.11778 | + | 1.48321i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.34945 | −0.193704 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −17.7146 | −1.02105 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6.13941 | − | 8.14656i | −0.351542 | − | 0.466471i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.19358 | + | 6.19358i | 0.353486 | + | 0.353486i | 0.861405 | − | 0.507919i | \(-0.169585\pi\) |
−0.507919 | + | 0.861405i | \(0.669585\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 17.3882i | − | 0.985992i | −0.870032 | − | 0.492996i | \(-0.835902\pi\) | ||
0.870032 | − | 0.492996i | \(-0.164098\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.2953 | − | 15.2953i | 0.864541 | − | 0.864541i | −0.127321 | − | 0.991862i | \(-0.540638\pi\) |
0.991862 | + | 0.127321i | \(0.0406378\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 11.3430 | − | 11.3430i | 0.637089 | − | 0.637089i | −0.312747 | − | 0.949836i | \(-0.601249\pi\) |
0.949836 | + | 0.312747i | \(0.101249\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.60300i | 0.0897510i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.75989 | + | 1.75989i | 0.0979230 | + | 0.0979230i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.52543 | − | 11.7699i | −0.361966 | − | 0.652874i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 43.7826 | 2.41381 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 18.9304 | 1.04051 | 0.520255 | − | 0.854011i | \(-0.325837\pi\) | ||||
0.520255 | + | 0.854011i | \(0.325837\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.10219 | + | 22.0799i | −0.169490 | + | 1.20635i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.09234 | − | 4.09234i | −0.222924 | − | 0.222924i | 0.586805 | − | 0.809729i | \(-0.300386\pi\) |
−0.809729 | + | 0.586805i | \(0.800386\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 15.2107i | 0.823704i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8.29529 | − | 8.29529i | 0.447903 | − | 0.447903i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −16.4230 | + | 16.4230i | −0.881635 | + | 0.881635i | −0.993701 | − | 0.112065i | \(-0.964253\pi\) |
0.112065 | + | 0.993701i | \(0.464253\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.4380i | 0.612262i | 0.951989 | + | 0.306131i | \(0.0990346\pi\) | ||||
−0.951989 | + | 0.306131i | \(0.900965\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −12.7055 | − | 12.7055i | −0.676248 | − | 0.676248i | 0.282901 | − | 0.959149i | \(-0.408703\pi\) |
−0.959149 | + | 0.282901i | \(0.908703\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −22.3684 | + | 16.8573i | −1.18719 | + | 0.894691i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −30.8389 | −1.62762 | −0.813809 | − | 0.581133i | \(-0.802610\pi\) | ||||
−0.813809 | + | 0.581133i | \(0.802610\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.7368 | 0.828254 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 11.3430 | + | 1.59368i | 0.593722 | + | 0.0834169i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.2494 | + | 10.2494i | 0.535012 | + | 0.535012i | 0.922060 | − | 0.387048i | \(-0.126505\pi\) |
−0.387048 | + | 0.922060i | \(0.626505\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 29.4966i | 1.53139i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 16.4336 | − | 16.4336i | 0.850898 | − | 0.850898i | −0.139346 | − | 0.990244i | \(-0.544500\pi\) |
0.990244 | + | 0.139346i | \(0.0445001\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.41421 | − | 1.41421i | 0.0728357 | − | 0.0728357i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 3.14272i | − | 0.161431i | −0.996737 | − | 0.0807154i | \(-0.974280\pi\) | ||
0.996737 | − | 0.0807154i | \(-0.0257205\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 12.7796 | + | 12.7796i | 0.653009 | + | 0.653009i | 0.953716 | − | 0.300708i | \(-0.0972228\pi\) |
−0.300708 | + | 0.953716i | \(0.597223\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −19.6128 | − | 2.75557i | −0.999563 | − | 0.140437i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 25.0452 | 1.26984 | 0.634921 | − | 0.772577i | \(-0.281033\pi\) | ||||
0.634921 | + | 0.772577i | \(0.281033\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.71456 | 0.0867089 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −26.8770 | + | 20.2551i | −1.35233 | + | 1.01914i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.57628 | − | 1.57628i | −0.0791114 | − | 0.0791114i | 0.666444 | − | 0.745555i | \(-0.267816\pi\) |
−0.745555 | + | 0.666444i | \(0.767816\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 32.7742i | 1.63666i | 0.574746 | + | 0.818332i | \(0.305101\pi\) | ||||
−0.574746 | + | 0.818332i | \(0.694899\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 13.4193 | − | 13.4193i | 0.668462 | − | 0.668462i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 17.9741 | − | 17.9741i | 0.890945 | − | 0.890945i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.75557i | 0.136254i | 0.997677 | + | 0.0681271i | \(0.0217023\pi\) | ||||
−0.997677 | + | 0.0681271i | \(0.978298\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −41.4165 | − | 41.4165i | −2.03797 | − | 2.03797i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.43801 | − | 24.4701i | 0.168765 | − | 1.20119i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −16.8204 | −0.821732 | −0.410866 | − | 0.911696i | \(-0.634774\pi\) | ||||
−0.410866 | + | 0.911696i | \(0.634774\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.38715 | −0.116343 | −0.0581713 | − | 0.998307i | \(-0.518527\pi\) | ||||
−0.0581713 | + | 0.998307i | \(0.518527\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.34032 | + | 6.02491i | 0.162029 | + | 0.292251i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 13.2444 | + | 13.2444i | 0.640943 | + | 0.640943i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 21.5324i | − | 1.03718i | −0.855024 | − | 0.518589i | \(-0.826457\pi\) | ||
0.855024 | − | 0.518589i | \(-0.173543\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.31756 | − | 6.31756i | 0.303603 | − | 0.303603i | −0.538819 | − | 0.842422i | \(-0.681129\pi\) |
0.842422 | + | 0.538819i | \(0.181129\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.58956 | + | 1.58956i | −0.0760387 | + | 0.0760387i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 17.8350i | 0.851218i | 0.904907 | + | 0.425609i | \(0.139940\pi\) | ||||
−0.904907 | + | 0.425609i | \(0.860060\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.55467 | + | 2.55467i | 0.121376 | + | 0.121376i | 0.765186 | − | 0.643810i | \(-0.222647\pi\) |
−0.643810 | + | 0.765186i | \(0.722647\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.96343 | − | 13.2208i | −0.472312 | − | 0.626725i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −4.66024 | −0.219930 | −0.109965 | − | 0.993935i | \(-0.535074\pi\) | ||||
−0.109965 | + | 0.993935i | \(0.535074\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 16.5620 | 0.779874 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 14.8720 | + | 19.7340i | 0.697208 | + | 0.925146i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −22.7748 | − | 22.7748i | −1.06536 | − | 1.06536i | −0.997709 | − | 0.0676502i | \(-0.978450\pi\) |
−0.0676502 | − | 0.997709i | \(-0.521550\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 28.0175i | − | 1.30490i | −0.757830 | − | 0.652452i | \(-0.773740\pi\) | ||
0.757830 | − | 0.652452i | \(-0.226260\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.5669 | − | 13.5669i | 0.630508 | − | 0.630508i | −0.317687 | − | 0.948195i | \(-0.602906\pi\) |
0.948195 | + | 0.317687i | \(0.102906\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4.71195 | − | 4.71195i | 0.218043 | − | 0.218043i | −0.589630 | − | 0.807673i | \(-0.700727\pi\) |
0.807673 | + | 0.589630i | \(0.200727\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 40.9403i | − | 1.89045i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6.58155 | − | 6.58155i | −0.302620 | − | 0.302620i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8.68244 | − | 2.48886i | −0.398378 | − | 0.114197i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.89696 | −0.178057 | −0.0890284 | − | 0.996029i | \(-0.528376\pi\) | ||||
−0.0890284 | + | 0.996029i | \(0.528376\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −31.7146 | −1.44606 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.93597 | + | 20.8969i | −0.133316 | + | 0.948878i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.39207 | − | 5.39207i | −0.244338 | − | 0.244338i | 0.574304 | − | 0.818642i | \(-0.305273\pi\) |
−0.818642 | + | 0.574304i | \(0.805273\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 23.6897i | − | 1.06910i | −0.845137 | − | 0.534550i | \(-0.820481\pi\) | ||
0.845137 | − | 0.534550i | \(-0.179519\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.723926 | + | 0.723926i | −0.0326040 | + | 0.0326040i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 36.3659 | − | 36.3659i | 1.63123 | − | 1.63123i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 9.21585i | − | 0.412558i | −0.978493 | − | 0.206279i | \(-0.933865\pi\) | ||
0.978493 | − | 0.206279i | \(-0.0661355\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2.01344 | − | 2.01344i | −0.0897749 | − | 0.0897749i | 0.660793 | − | 0.750568i | \(-0.270220\pi\) |
−0.750568 | + | 0.660793i | \(0.770220\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −13.0000 | + | 9.79706i | −0.578492 | + | 0.435963i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 15.5766 | 0.690419 | 0.345209 | − | 0.938526i | \(-0.387808\pi\) | ||||
0.345209 | + | 0.938526i | \(0.387808\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −21.0321 | −0.930406 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 27.2744 | + | 3.83200i | 1.20185 | + | 0.168858i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 16.2667 | + | 16.2667i | 0.715409 | + | 0.715409i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 6.42013i | − | 0.281271i | −0.990061 | − | 0.140636i | \(-0.955085\pi\) | ||
0.990061 | − | 0.140636i | \(-0.0449146\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −25.9813 | + | 25.9813i | −1.13608 | + | 1.13608i | −0.146935 | + | 0.989146i | \(0.546941\pi\) |
−0.989146 | + | 0.146935i | \(0.953059\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6.86923 | + | 6.86923i | −0.299228 | + | 0.299228i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 21.4514i | − | 0.932669i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −14.6114 | − | 14.6114i | −0.632892 | − | 0.632892i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −10.9590 | − | 1.53972i | −0.473798 | − | 0.0665678i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 21.2649 | 0.915945 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −30.0098 | −1.29022 | −0.645112 | − | 0.764088i | \(-0.723189\pi\) | ||||
−0.645112 | + | 0.764088i | \(0.723189\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −28.4079 | + | 21.4088i | −1.21686 | + | 0.917050i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.12399 | + | 9.12399i | 0.390113 | + | 0.390113i | 0.874728 | − | 0.484614i | \(-0.161040\pi\) |
−0.484614 | + | 0.874728i | \(0.661040\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 1.34229i | − | 0.0571836i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 43.6958 | − | 43.6958i | 1.85814 | − | 1.85814i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 14.5039 | − | 14.5039i | 0.614550 | − | 0.614550i | −0.329578 | − | 0.944128i | \(-0.606907\pi\) |
0.944128 | + | 0.329578i | \(0.106907\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 11.6128i | 0.491171i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −18.1829 | − | 18.1829i | −0.766319 | − | 0.766319i | 0.211137 | − | 0.977456i | \(-0.432283\pi\) |
−0.977456 | + | 0.211137i | \(0.932283\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.66370 | − | 33.1941i | 0.196203 | − | 1.39648i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.42137 | −0.143431 | −0.0717156 | − | 0.997425i | \(-0.522847\pi\) | ||||
−0.0717156 | + | 0.997425i | \(0.522847\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.17130 | 0.132715 | 0.0663574 | − | 0.997796i | \(-0.478862\pi\) | ||||
0.0663574 | + | 0.997796i | \(0.478862\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5.44177 | + | 3.01702i | −0.226937 | + | 0.125818i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8.22570 | − | 8.22570i | −0.342440 | − | 0.342440i | 0.514844 | − | 0.857284i | \(-0.327850\pi\) |
−0.857284 | + | 0.514844i | \(0.827850\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 45.3722i | 1.88236i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −10.9590 | + | 10.9590i | −0.453875 | + | 0.453875i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 22.4773 | − | 22.4773i | 0.927737 | − | 0.927737i | −0.0698224 | − | 0.997559i | \(-0.522243\pi\) |
0.997559 | + | 0.0698224i | \(0.0222433\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 12.7368i | − | 0.524812i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −10.2228 | − | 10.2228i | −0.419800 | − | 0.419800i | 0.465335 | − | 0.885135i | \(-0.345934\pi\) |
−0.885135 | + | 0.465335i | \(0.845934\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.61285 | − | 10.1017i | −0.312096 | − | 0.414130i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −30.1615 | −1.23237 | −0.616183 | − | 0.787603i | \(-0.711322\pi\) | ||||
−0.616183 | + | 0.787603i | \(0.711322\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 40.0830 | 1.63502 | 0.817509 | − | 0.575915i | \(-0.195354\pi\) | ||||
0.817509 | + | 0.575915i | \(0.195354\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 8.54047 | + | 11.3326i | 0.347220 | + | 0.460736i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −13.3921 | − | 13.3921i | −0.543568 | − | 0.543568i | 0.381005 | − | 0.924573i | \(-0.375578\pi\) |
−0.924573 | + | 0.381005i | \(0.875578\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 28.7019i | − | 1.16115i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 17.1891 | − | 17.1891i | 0.694262 | − | 0.694262i | −0.268904 | − | 0.963167i | \(-0.586662\pi\) |
0.963167 | + | 0.268904i | \(0.0866616\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 23.2831 | − | 23.2831i | 0.937344 | − | 0.937344i | −0.0608053 | − | 0.998150i | \(-0.519367\pi\) |
0.998150 | + | 0.0608053i | \(0.0193669\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 44.6735i | − | 1.79558i | −0.440422 | − | 0.897791i | \(-0.645171\pi\) | ||
0.440422 | − | 0.897791i | \(-0.354829\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 21.4939 | + | 21.4939i | 0.861136 | + | 0.861136i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −21.2034 | − | 13.2444i | −0.848137 | − | 0.529777i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 16.2345 | 0.647310 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.64143 | −0.304200 | −0.152100 | − | 0.988365i | \(-0.548604\pi\) | ||||
−0.152100 | + | 0.988365i | \(0.548604\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.79712 | − | 34.1436i | 0.190368 | − | 1.35495i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −18.7605 | − | 18.7605i | −0.743318 | − | 0.743318i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 12.9304i | − | 0.510721i | −0.966846 | − | 0.255361i | \(-0.917806\pi\) | ||
0.966846 | − | 0.255361i | \(-0.0821942\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.51114 | + | 1.51114i | −0.0595934 | + | 0.0595934i | −0.736275 | − | 0.676682i | \(-0.763417\pi\) |
0.676682 | + | 0.736275i | \(0.263417\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −5.78049 | + | 5.78049i | −0.227254 | + | 0.227254i | −0.811545 | − | 0.584290i | \(-0.801373\pi\) |
0.584290 | + | 0.811545i | \(0.301373\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 30.7753i | − | 1.20803i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4.34390 | + | 4.34390i | 0.169990 | + | 0.169990i | 0.786975 | − | 0.616985i | \(-0.211646\pi\) |
−0.616985 | + | 0.786975i | \(0.711646\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −20.9131 | + | 15.7605i | −0.817141 | + | 0.615813i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.74684 | 0.145956 | 0.0729780 | − | 0.997334i | \(-0.476750\pi\) | ||||
0.0729780 | + | 0.997334i | \(0.476750\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −34.6637 | −1.34826 | −0.674131 | − | 0.738612i | \(-0.735482\pi\) | ||||
−0.674131 | + | 0.738612i | \(0.735482\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 16.4230 | + | 2.30741i | 0.636858 | + | 0.0894774i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.653858 | − | 0.653858i | −0.0253175 | − | 0.0253175i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 9.84150i | 0.379927i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.15257 | + | 4.15257i | −0.160070 | + | 0.160070i | −0.782598 | − | 0.622528i | \(-0.786106\pi\) |
0.622528 | + | 0.782598i | \(0.286106\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 19.4959 | − | 19.4959i | 0.749288 | − | 0.749288i | −0.225057 | − | 0.974346i | \(-0.572257\pi\) |
0.974346 | + | 0.225057i | \(0.0722570\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 38.7467i | − | 1.48696i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 25.0320 | + | 25.0320i | 0.957821 | + | 0.957821i | 0.999146 | − | 0.0413245i | \(-0.0131577\pi\) |
−0.0413245 | + | 0.999146i | \(0.513158\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −18.2351 | − | 2.56199i | −0.696726 | − | 0.0978887i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 19.3366 | 0.736667 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.70471 | −0.140934 | −0.0704670 | − | 0.997514i | \(-0.522449\pi\) | ||||
−0.0704670 | + | 0.997514i | \(0.522449\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 5.61210 | − | 4.22939i | 0.212879 | − | 0.160430i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.47949 | + | 7.47949i | 0.283306 | + | 0.283306i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 36.8352i | − | 1.39125i | −0.718407 | − | 0.695623i | \(-0.755128\pi\) | ||
0.718407 | − | 0.695623i | \(-0.244872\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −15.0509 | + | 15.0509i | −0.567654 | + | 0.567654i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 21.1350 | − | 21.1350i | 0.794863 | − | 0.794863i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.40943i | 0.0529322i | 0.999650 | + | 0.0264661i | \(0.00842540\pi\) | ||||
−0.999650 | + | 0.0264661i | \(0.991575\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6.20437 | − | 6.20437i | −0.232355 | − | 0.232355i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.80642 | + | 12.8573i | −0.0675564 | + | 0.480835i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −18.1829 | −0.678109 | −0.339055 | − | 0.940767i | \(-0.610107\pi\) | ||||
−0.339055 | + | 0.940767i | \(0.610107\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −50.5718 | −1.88339 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.02379 | − | 3.57149i | 0.0380224 | − | 0.132642i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −0.119063 | − | 0.119063i | −0.00441580 | − | 0.00441580i | 0.704895 | − | 0.709311i | \(-0.250994\pi\) |
−0.709311 | + | 0.704895i | \(0.750994\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 5.94453i | − | 0.219867i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 13.4143 | − | 13.4143i | 0.495470 | − | 0.495470i | −0.414554 | − | 0.910025i | \(-0.636063\pi\) |
0.910025 | + | 0.414554i | \(0.136063\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 15.2107 | − | 15.2107i | 0.560292 | − | 0.560292i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 48.8484i | 1.79692i | 0.439058 | + | 0.898458i | \(0.355312\pi\) | ||||
−0.439058 | + | 0.898458i | \(0.644688\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6.74560 | + | 6.74560i | 0.247472 | + | 0.247472i | 0.819932 | − | 0.572460i | \(-0.194011\pi\) |
−0.572460 | + | 0.819932i | \(0.694011\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8.49823 | − | 11.2766i | −0.311351 | − | 0.413141i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 20.3200 | 0.742477 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13.1526 | −0.479944 | −0.239972 | − | 0.970780i | \(-0.577138\pi\) | ||||
−0.239972 | + | 0.970780i | \(0.577138\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −24.7197 | − | 32.8013i | −0.899643 | − | 1.19376i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.85236 | + | 6.85236i | 0.249053 | + | 0.249053i | 0.820582 | − | 0.571529i | \(-0.193649\pi\) |
−0.571529 | + | 0.820582i | \(0.693649\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 52.3133i | 1.89636i | 0.317739 | + | 0.948178i | \(0.397077\pi\) | ||||
−0.317739 | + | 0.948178i | \(0.602923\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 46.1847 | − | 46.1847i | 1.67200 | − | 1.67200i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −27.1508 | + | 27.1508i | −0.980358 | + | 0.980358i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 20.4701i | 0.738172i | 0.929395 | + | 0.369086i | \(0.120329\pi\) | ||||
−0.929395 | + | 0.369086i | \(0.879671\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −8.59979 | − | 8.59979i | −0.309313 | − | 0.309313i | 0.535330 | − | 0.844643i | \(-0.320187\pi\) |
−0.844643 | + | 0.535330i | \(0.820187\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9.71456 | − | 33.8894i | 0.348957 | − | 1.21734i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −13.8684 | −0.496886 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 27.0223 | 0.966933 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.0160876 | − | 0.114504i | 0.000574192 | − | 0.00408683i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15.5210 | + | 15.5210i | 0.553263 | + | 0.553263i | 0.927381 | − | 0.374118i | \(-0.122054\pi\) |
−0.374118 | + | 0.927381i | \(0.622054\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 61.5480i | 2.18839i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.68244 | − | 8.68244i | 0.308322 | − | 0.308322i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.04616 | + | 1.04616i | −0.0370569 | + | 0.0370569i | −0.725392 | − | 0.688336i | \(-0.758342\pi\) |
0.688336 | + | 0.725392i | \(0.258342\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 14.6923i | 0.519776i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −7.81413 | − | 7.81413i | −0.275755 | − | 0.275755i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9.12399 | − | 6.87601i | 0.321578 | − | 0.242348i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 50.2210 | 1.76568 | 0.882838 | − | 0.469677i | \(-0.155630\pi\) | ||||
0.882838 | + | 0.469677i | \(0.155630\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 29.9813 | 1.05278 | 0.526392 | − | 0.850242i | \(-0.323544\pi\) | ||||
0.526392 | + | 0.850242i | \(0.323544\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −22.0799 | − | 3.10219i | −0.773425 | − | 0.108665i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.51114 | + | 5.51114i | 0.192810 | + | 0.192810i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 28.7536i | 1.00351i | 0.865011 | + | 0.501753i | \(0.167312\pi\) | ||||
−0.865011 | + | 0.501753i | \(0.832688\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 21.8622 | − | 21.8622i | 0.762068 | − | 0.762068i | −0.214628 | − | 0.976696i | \(-0.568854\pi\) |
0.976696 | + | 0.214628i | \(0.0688538\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −23.4222 | + | 23.4222i | −0.814470 | + | 0.814470i | −0.985300 | − | 0.170831i | \(-0.945355\pi\) |
0.170831 | + | 0.985300i | \(0.445355\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 39.3176i | 1.36556i | 0.730626 | + | 0.682778i | \(0.239228\pi\) | ||||
−0.730626 | + | 0.682778i | \(0.760772\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 9.60336 | + | 9.60336i | 0.332737 | + | 0.332737i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 28.4701 | + | 4.00000i | 0.985249 | + | 0.138426i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 39.4681 | 1.36259 | 0.681294 | − | 0.732010i | \(-0.261417\pi\) | ||||
0.681294 | + | 0.732010i | \(0.261417\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.4479 | −0.980960 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −10.2780 | + | 7.74570i | −0.353574 | + | 0.266460i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −18.4242 | − | 18.4242i | −0.633063 | − | 0.633063i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 14.6632i | 0.502646i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22.8938 | − | 22.8938i | 0.783870 | − | 0.783870i | −0.196611 | − | 0.980482i | \(-0.562994\pi\) |
0.980482 | + | 0.196611i | \(0.0629937\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −31.4947 | + | 31.4947i | −1.07584 | + | 1.07584i | −0.0789597 | + | 0.996878i | \(0.525160\pi\) |
−0.996878 | + | 0.0789597i | \(0.974840\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 55.6958i | 1.90032i | 0.311767 | + | 0.950158i | \(0.399079\pi\) | ||||
−0.311767 | + | 0.950158i | \(0.600921\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −28.1991 | − | 28.1991i | −0.959909 | − | 0.959909i | 0.0393181 | − | 0.999227i | \(-0.487481\pi\) |
−0.999227 | + | 0.0393181i | \(0.987481\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.43801 | − | 38.7052i | 0.184898 | − | 1.31602i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 32.4689 | 1.10143 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −26.8385 | −0.909389 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 41.9376 | + | 18.6655i | 1.41775 | + | 0.631009i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −20.7003 | − | 20.7003i | −0.698998 | − | 0.698998i | 0.265196 | − | 0.964194i | \(-0.414563\pi\) |
−0.964194 | + | 0.265196i | \(0.914563\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 37.4212i | − | 1.26075i | −0.776290 | − | 0.630376i | \(-0.782901\pi\) | ||
0.776290 | − | 0.630376i | \(-0.217099\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −12.5620 | + | 12.5620i | −0.422745 | + | 0.422745i | −0.886148 | − | 0.463403i | \(-0.846628\pi\) |
0.463403 | + | 0.886148i | \(0.346628\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −23.3774 | + | 23.3774i | −0.784938 | + | 0.784938i | −0.980659 | − | 0.195722i | \(-0.937295\pi\) |
0.195722 | + | 0.980659i | \(0.437295\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 63.3087i | 2.12330i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −13.6211 | − | 13.6211i | −0.455813 | − | 0.455813i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 14.6909 | + | 19.4938i | 0.491063 | + | 0.651605i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.23926 | 0.174739 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −9.89829 | −0.329760 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 26.2708 | + | 34.8595i | 0.873272 | + | 1.15877i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 13.4193 | + | 13.4193i | 0.445580 | + | 0.445580i | 0.893882 | − | 0.448302i | \(-0.147971\pi\) |
−0.448302 | + | 0.893882i | \(0.647971\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 11.5610i | 0.383032i | 0.981489 | + | 0.191516i | \(0.0613404\pi\) | ||||
−0.981489 | + | 0.191516i | \(0.938660\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −16.8573 | + | 16.8573i | −0.557895 | + | 0.557895i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 33.9998 | − | 33.9998i | 1.12277 | − | 1.12277i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.07313i | 0.0683862i | 0.999415 | + | 0.0341931i | \(0.0108861\pi\) | ||||
−0.999415 | + | 0.0341931i | \(0.989114\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −23.8398 | − | 23.8398i | −0.784696 | − | 0.784696i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −51.5259 | + | 28.5669i | −1.69416 | + | 0.939274i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 24.2889 | 0.796893 | 0.398446 | − | 0.917192i | \(-0.369550\pi\) | ||||
0.398446 | + | 0.917192i | \(0.369550\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −17.8064 | −0.583582 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.924696 | − | 6.58155i | 0.0302408 | − | 0.215240i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −12.4479 | − | 12.4479i | −0.406654 | − | 0.406654i | 0.473916 | − | 0.880570i | \(-0.342840\pi\) |
−0.880570 | + | 0.473916i | \(0.842840\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 20.6007i | 0.671565i | 0.941940 | + | 0.335782i | \(0.109001\pi\) | ||||
−0.941940 | + | 0.335782i | \(0.890999\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.75557 | + | 6.75557i | −0.219992 | + | 0.219992i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −11.5610 | + | 11.5610i | −0.375681 | + | 0.375681i | −0.869541 | − | 0.493860i | \(-0.835585\pi\) |
0.493860 | + | 0.869541i | \(0.335585\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 13.7877i | 0.447567i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −42.1889 | − | 42.1889i | −1.36663 | − | 1.36663i | −0.865190 | − | 0.501444i | \(-0.832802\pi\) |
−0.501444 | − | 0.865190i | \(-0.667198\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 42.5718 | − | 32.0830i | 1.37759 | − | 1.03818i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 33.8112 | 1.09182 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 18.7146 | 0.603695 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −30.2621 | − | 4.25177i | −0.974171 | − | 0.136869i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.23951 | + | 8.23951i | 0.264965 | + | 0.264965i | 0.827067 | − | 0.562103i | \(-0.190007\pi\) |
−0.562103 | + | 0.827067i | \(0.690007\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 29.2292i | − | 0.938009i | −0.883196 | − | 0.469004i | \(-0.844613\pi\) | ||
0.883196 | − | 0.469004i | \(-0.155387\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −9.12399 | + | 9.12399i | −0.292502 | + | 0.292502i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 7.17861 | − | 7.17861i | 0.229664 | − | 0.229664i | −0.582888 | − | 0.812552i | \(-0.698077\pi\) |
0.812552 | + | 0.582888i | \(0.198077\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 15.9714i | 0.510449i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 22.7510 | + | 22.7510i | 0.725646 | + | 0.725646i | 0.969749 | − | 0.244103i | \(-0.0784937\pi\) |
−0.244103 | + | 0.969749i | \(0.578494\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 31.2958 | + | 4.39700i | 0.997166 | + | 0.140100i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5.36917 | 0.170730 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 45.7975 | 1.45481 | 0.727403 | − | 0.686210i | \(-0.240727\pi\) | ||||
0.727403 | + | 0.686210i | \(0.240727\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −26.3497 | + | 19.8577i | −0.835342 | + | 0.629530i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.08742 | − | 5.08742i | −0.161120 | − | 0.161120i | 0.621943 | − | 0.783063i | \(-0.286344\pi\) |
−0.783063 | + | 0.621943i | \(0.786344\pi\) | |||||||
\(998\) | 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 | 2880.2.w.p.2177.5 | 12 | ||
3.2 | odd | 2 | inner | 2880.2.w.p.2177.2 | 12 | ||
4.3 | odd | 2 | 2880.2.w.q.2177.5 | 12 | |||
5.3 | odd | 4 | inner | 2880.2.w.p.2753.2 | 12 | ||
8.3 | odd | 2 | 1440.2.w.g.737.2 | yes | 12 | ||
8.5 | even | 2 | 1440.2.w.f.737.2 | ✓ | 12 | ||
12.11 | even | 2 | 2880.2.w.q.2177.2 | 12 | |||
15.8 | even | 4 | inner | 2880.2.w.p.2753.5 | 12 | ||
20.3 | even | 4 | 2880.2.w.q.2753.2 | 12 | |||
24.5 | odd | 2 | 1440.2.w.f.737.5 | yes | 12 | ||
24.11 | even | 2 | 1440.2.w.g.737.5 | yes | 12 | ||
40.3 | even | 4 | 1440.2.w.g.1313.5 | yes | 12 | ||
40.13 | odd | 4 | 1440.2.w.f.1313.5 | yes | 12 | ||
60.23 | odd | 4 | 2880.2.w.q.2753.5 | 12 | |||
120.53 | even | 4 | 1440.2.w.f.1313.2 | yes | 12 | ||
120.83 | odd | 4 | 1440.2.w.g.1313.2 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1440.2.w.f.737.2 | ✓ | 12 | 8.5 | even | 2 | ||
1440.2.w.f.737.5 | yes | 12 | 24.5 | odd | 2 | ||
1440.2.w.f.1313.2 | yes | 12 | 120.53 | even | 4 | ||
1440.2.w.f.1313.5 | yes | 12 | 40.13 | odd | 4 | ||
1440.2.w.g.737.2 | yes | 12 | 8.3 | odd | 2 | ||
1440.2.w.g.737.5 | yes | 12 | 24.11 | even | 2 | ||
1440.2.w.g.1313.2 | yes | 12 | 120.83 | odd | 4 | ||
1440.2.w.g.1313.5 | yes | 12 | 40.3 | even | 4 | ||
2880.2.w.p.2177.2 | 12 | 3.2 | odd | 2 | inner | ||
2880.2.w.p.2177.5 | 12 | 1.1 | even | 1 | trivial | ||
2880.2.w.p.2753.2 | 12 | 5.3 | odd | 4 | inner | ||
2880.2.w.p.2753.5 | 12 | 15.8 | even | 4 | inner | ||
2880.2.w.q.2177.2 | 12 | 12.11 | even | 2 | |||
2880.2.w.q.2177.5 | 12 | 4.3 | odd | 2 | |||
2880.2.w.q.2753.2 | 12 | 20.3 | even | 4 | |||
2880.2.w.q.2753.5 | 12 | 60.23 | odd | 4 |