Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2880,2,Mod(593,2880)]
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, 3, 2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2880.593");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2880 = 2^{6} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2880.bc (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: | \(96\) |
Relative dimension: | \(48\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 720) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1457.15 | ||
Character | \(\chi\) | \(=\) | 2880.1457 |
Dual form | 2880.2.bc.a.593.15 |
$q$-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 \(\left(\mathbb{Z}/2880\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(641\) | \(901\) | \(2431\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
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 | ||||||||
\(5\) | −1.29201 | − | 1.82503i | −0.577803 | − | 0.816176i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.02860 | − | 2.02860i | 0.766738 | − | 0.766738i | −0.210793 | − | 0.977531i | \(-0.567604\pi\) |
0.977531 | + | 0.210793i | \(0.0676045\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.30349 | + | 3.30349i | −0.996041 | + | 0.996041i | −0.999992 | − | 0.00395115i | \(-0.998742\pi\) |
0.00395115 | + | 0.999992i | \(0.498742\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.32263i | 0.366832i | 0.983035 | + | 0.183416i | \(0.0587156\pi\) | ||||
−0.983035 | + | 0.183416i | \(0.941284\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.37324 | + | 1.37324i | −0.333059 | + | 0.333059i | −0.853747 | − | 0.520688i | \(-0.825675\pi\) |
0.520688 | + | 0.853747i | \(0.325675\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.52013 | + | 3.52013i | 0.807573 | + | 0.807573i | 0.984266 | − | 0.176693i | \(-0.0565401\pi\) |
−0.176693 | + | 0.984266i | \(0.556540\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.72908 | − | 2.72908i | 0.569052 | − | 0.569052i | −0.362811 | − | 0.931863i | \(-0.618183\pi\) |
0.931863 | + | 0.362811i | \(0.118183\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.66144 | + | 4.71589i | −0.332288 | + | 0.943178i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.39873 | + | 5.39873i | −1.00252 | + | 1.00252i | −0.00252292 | + | 0.999997i | \(0.500803\pi\) |
−0.999997 | + | 0.00252292i | \(0.999197\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.163297 | −0.0293289 | −0.0146645 | − | 0.999892i | \(-0.504668\pi\) | ||||
−0.0146645 | + | 0.999892i | \(0.504668\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −6.32321 | − | 1.08128i | −1.06882 | − | 0.182770i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 4.06899i | − | 0.668938i | −0.942407 | − | 0.334469i | \(-0.891443\pi\) | ||
0.942407 | − | 0.334469i | \(-0.108557\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.10945 | −1.26648 | −0.633241 | − | 0.773954i | \(-0.718276\pi\) | ||||
−0.633241 | + | 0.773954i | \(0.718276\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.10902 | −0.931617 | −0.465808 | − | 0.884886i | \(-0.654236\pi\) | ||||
−0.465808 | + | 0.884886i | \(0.654236\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.28261 | − | 3.28261i | 0.478819 | − | 0.478819i | −0.425935 | − | 0.904754i | \(-0.640055\pi\) |
0.904754 | + | 0.425935i | \(0.140055\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 1.23042i | − | 0.175775i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 11.5149i | 1.58170i | 0.612012 | + | 0.790849i | \(0.290361\pi\) | ||||
−0.612012 | + | 0.790849i | \(0.709639\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 10.2971 | + | 1.76083i | 1.38846 | + | 0.237430i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.29599 | + | 8.29599i | 1.08005 | + | 1.08005i | 0.996504 | + | 0.0835415i | \(0.0266231\pi\) |
0.0835415 | + | 0.996504i | \(0.473377\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.11708 | + | 5.11708i | −0.655175 | + | 0.655175i | −0.954234 | − | 0.299059i | \(-0.903327\pi\) |
0.299059 | + | 0.954234i | \(0.403327\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.41384 | − | 1.70885i | 0.299400 | − | 0.211957i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.8288 | 1.32295 | 0.661476 | − | 0.749966i | \(-0.269930\pi\) | ||||
0.661476 | + | 0.749966i | \(0.269930\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.20918 | 0.262181 | 0.131090 | − | 0.991370i | \(-0.458152\pi\) | ||||
0.131090 | + | 0.991370i | \(0.458152\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.31187 | + | 3.31187i | 0.387625 | + | 0.387625i | 0.873839 | − | 0.486215i | \(-0.161623\pi\) |
−0.486215 | + | 0.873839i | \(0.661623\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 13.4029i | 1.52741i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 6.43519i | − | 0.724016i | −0.932175 | − | 0.362008i | \(-0.882091\pi\) | ||
0.932175 | − | 0.362008i | \(-0.117909\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.28920 | 0.909858 | 0.454929 | − | 0.890528i | \(-0.349665\pi\) | ||||
0.454929 | + | 0.890528i | \(0.349665\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.28042 | + | 0.731962i | 0.464277 | + | 0.0793924i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.1147i | 1.07215i | 0.844169 | + | 0.536077i | \(0.180094\pi\) | ||||
−0.844169 | + | 0.536077i | \(0.819906\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.68309 | + | 2.68309i | 0.281264 | + | 0.281264i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.87630 | − | 10.9723i | 0.192504 | − | 1.12574i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.10602 | − | 7.10602i | −0.721507 | − | 0.721507i | 0.247405 | − | 0.968912i | \(-0.420422\pi\) |
−0.968912 | + | 0.247405i | \(0.920422\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.74768 | − | 5.74768i | 0.571916 | − | 0.571916i | −0.360748 | − | 0.932663i | \(-0.617478\pi\) |
0.932663 | + | 0.360748i | \(0.117478\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.7463 | + | 11.7463i | 1.15740 | + | 1.15740i | 0.985034 | + | 0.172362i | \(0.0551398\pi\) |
0.172362 | + | 0.985034i | \(0.444860\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −11.5402 | −1.11563 | −0.557814 | − | 0.829966i | \(-0.688360\pi\) | ||||
−0.557814 | + | 0.829966i | \(0.688360\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.7772 | + | 11.7772i | 1.12805 | + | 1.12805i | 0.990493 | + | 0.137561i | \(0.0439262\pi\) |
0.137561 | + | 0.990493i | \(0.456074\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −14.3930 | − | 14.3930i | −1.35398 | − | 1.35398i | −0.881163 | − | 0.472812i | \(-0.843239\pi\) |
−0.472812 | − | 0.881163i | \(-0.656761\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.50662 | − | 1.45465i | −0.793246 | − | 0.135647i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.57149i | 0.510737i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 10.8262i | − | 0.984196i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.7532 | − | 3.06079i | 0.961797 | − | 0.273765i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.36365 | + | 4.36365i | 0.387211 | + | 0.387211i | 0.873692 | − | 0.486480i | \(-0.161719\pi\) |
−0.486480 | + | 0.873692i | \(0.661719\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.23684 | − | 9.23684i | −0.807027 | − | 0.807027i | 0.177156 | − | 0.984183i | \(-0.443310\pi\) |
−0.984183 | + | 0.177156i | \(0.943310\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 14.2818 | 1.23839 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.76531 | + | 8.76531i | 0.748871 | + | 0.748871i | 0.974267 | − | 0.225396i | \(-0.0723675\pi\) |
−0.225396 | + | 0.974267i | \(0.572368\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.90118 | − | 6.90118i | 0.585350 | − | 0.585350i | −0.351018 | − | 0.936369i | \(-0.614165\pi\) |
0.936369 | + | 0.351018i | \(0.114165\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.36931 | − | 4.36931i | −0.365380 | − | 0.365380i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 16.8280 | + | 2.87763i | 1.39749 | + | 0.238974i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.07872 | + | 7.07872i | 0.579911 | + | 0.579911i | 0.934879 | − | 0.354968i | \(-0.115508\pi\) |
−0.354968 | + | 0.934879i | \(0.615508\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 20.3002i | 1.65201i | 0.563665 | + | 0.826004i | \(0.309391\pi\) | ||||
−0.563665 | + | 0.826004i | \(0.690609\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.210980 | + | 0.298021i | 0.0169463 | + | 0.0239376i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.9083 | −0.950386 | −0.475193 | − | 0.879882i | \(-0.657622\pi\) | ||||
−0.475193 | + | 0.879882i | \(0.657622\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 11.0724i | − | 0.872627i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 20.0121i | 1.56747i | 0.621094 | + | 0.783736i | \(0.286688\pi\) | ||||
−0.621094 | + | 0.783736i | \(0.713312\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −0.214521 | − | 0.214521i | −0.0166001 | − | 0.0166001i | 0.698758 | − | 0.715358i | \(-0.253736\pi\) |
−0.715358 | + | 0.698758i | \(0.753736\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.2506 | 0.865434 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 20.9078 | 1.58959 | 0.794794 | − | 0.606880i | \(-0.207579\pi\) | ||||
0.794794 | + | 0.606880i | \(0.207579\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.19625 | + | 12.9370i | 0.468393 | + | 0.977948i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −11.0326 | + | 11.0326i | −0.824618 | + | 0.824618i | −0.986766 | − | 0.162148i | \(-0.948158\pi\) |
0.162148 | + | 0.986766i | \(0.448158\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.0226 | − | 12.0226i | −0.893633 | − | 0.893633i | 0.101230 | − | 0.994863i | \(-0.467722\pi\) |
−0.994863 | + | 0.101230i | \(0.967722\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −7.42602 | + | 5.25716i | −0.545972 | + | 0.386514i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 9.07295i | − | 0.663480i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.67589i | 0.627765i | 0.949462 | + | 0.313883i | \(0.101630\pi\) | ||||
−0.949462 | + | 0.313883i | \(0.898370\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.197253 | − | 0.197253i | 0.0141986 | − | 0.0141986i | −0.699972 | − | 0.714170i | \(-0.746804\pi\) |
0.714170 | + | 0.699972i | \(0.246804\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −13.6104 | −0.969700 | −0.484850 | − | 0.874597i | \(-0.661126\pi\) | ||||
−0.484850 | + | 0.874597i | \(0.661126\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.3148 | −0.731196 | −0.365598 | − | 0.930773i | \(-0.619135\pi\) | ||||
−0.365598 | + | 0.930773i | \(0.619135\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 21.9037i | 1.53734i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 10.4775 | + | 14.8000i | 0.731777 | + | 1.03367i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −23.2574 | −1.60875 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.23573 | − | 8.23573i | 0.566971 | − | 0.566971i | −0.364308 | − | 0.931279i | \(-0.618694\pi\) |
0.931279 | + | 0.364308i | \(0.118694\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 7.89289 | + | 11.1491i | 0.538291 | + | 0.760364i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.331263 | + | 0.331263i | −0.0224876 | + | 0.0224876i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.81629 | − | 1.81629i | −0.122177 | − | 0.122177i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.03653 | + | 6.03653i | −0.404236 | + | 0.404236i | −0.879723 | − | 0.475487i | \(-0.842272\pi\) |
0.475487 | + | 0.879723i | \(0.342272\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 9.05713i | 0.601143i | 0.953759 | + | 0.300571i | \(0.0971773\pi\) | ||||
−0.953759 | + | 0.300571i | \(0.902823\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −13.6898 | + | 13.6898i | −0.904649 | + | 0.904649i | −0.995834 | − | 0.0911851i | \(-0.970935\pi\) |
0.0911851 | + | 0.995834i | \(0.470935\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.31459 | + | 6.31459i | −0.413683 | + | 0.413683i | −0.883019 | − | 0.469337i | \(-0.844493\pi\) |
0.469337 | + | 0.883019i | \(0.344493\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.2320 | − | 1.74970i | −0.667463 | − | 0.114138i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −10.5908 | −0.685060 | −0.342530 | − | 0.939507i | \(-0.611284\pi\) | ||||
−0.342530 | + | 0.939507i | \(0.611284\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 25.8811 | 1.66715 | 0.833574 | − | 0.552408i | \(-0.186291\pi\) | ||||
0.833574 | + | 0.552408i | \(0.186291\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.24555 | + | 1.58971i | −0.143463 | + | 0.101563i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.65584 | + | 4.65584i | −0.296244 | + | 0.296244i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.3065 | + | 12.3065i | −0.776778 | + | 0.776778i | −0.979281 | − | 0.202504i | \(-0.935092\pi\) |
0.202504 | + | 0.979281i | \(0.435092\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 18.0310i | 1.13360i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 13.8942 | − | 13.8942i | 0.866695 | − | 0.866695i | −0.125410 | − | 0.992105i | \(-0.540025\pi\) |
0.992105 | + | 0.125410i | \(0.0400248\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.25435 | − | 8.25435i | −0.512900 | − | 0.512900i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.57250 | − | 9.57250i | 0.590265 | − | 0.590265i | −0.347438 | − | 0.937703i | \(-0.612948\pi\) |
0.937703 | + | 0.347438i | \(0.112948\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 21.0151 | − | 14.8774i | 1.29094 | − | 0.913909i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5.87070 | − | 5.87070i | 0.357943 | − | 0.357943i | −0.505111 | − | 0.863054i | \(-0.668549\pi\) |
0.863054 | + | 0.505111i | \(0.168549\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 13.6589 | 0.829718 | 0.414859 | − | 0.909886i | \(-0.363831\pi\) | ||||
0.414859 | + | 0.909886i | \(0.363831\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −10.0904 | − | 21.0675i | −0.608471 | − | 1.27042i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.46783i | 0.148278i | 0.997248 | + | 0.0741389i | \(0.0236208\pi\) | ||||
−0.997248 | + | 0.0741389i | \(0.976379\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −22.7084 | −1.35467 | −0.677335 | − | 0.735675i | \(-0.736865\pi\) | ||||
−0.677335 | + | 0.735675i | \(0.736865\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.21667 | −0.191211 | −0.0956056 | − | 0.995419i | \(-0.530479\pi\) | ||||
−0.0956056 | + | 0.995419i | \(0.530479\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −16.4508 | + | 16.4508i | −0.971061 | + | 0.971061i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.2284i | 0.778144i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 18.4166i | 1.07591i | 0.842973 | + | 0.537955i | \(0.180803\pi\) | ||||
−0.842973 | + | 0.537955i | \(0.819197\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.42193 | − | 25.8589i | 0.257455 | − | 1.50556i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.60956 | + | 3.60956i | 0.208746 | + | 0.208746i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −12.3927 | + | 12.3927i | −0.714306 | + | 0.714306i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 15.9501 | + | 2.72751i | 0.913300 | + | 0.156177i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −16.5626 | −0.945277 | −0.472638 | − | 0.881256i | \(-0.656698\pi\) | ||||
−0.472638 | + | 0.881256i | \(0.656698\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 20.6119 | 1.16879 | 0.584397 | − | 0.811468i | \(-0.301331\pi\) | ||||
0.584397 | + | 0.811468i | \(0.301331\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.41531 | − | 4.41531i | −0.249568 | − | 0.249568i | 0.571225 | − | 0.820793i | \(-0.306468\pi\) |
−0.820793 | + | 0.571225i | \(0.806468\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 3.21460i | − | 0.180550i | −0.995917 | − | 0.0902750i | \(-0.971225\pi\) | ||
0.995917 | − | 0.0902750i | \(-0.0287746\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 35.6694i | − | 1.99710i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −9.66793 | −0.537938 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.23739 | − | 2.19748i | −0.345988 | − | 0.121894i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 13.3182i | − | 0.734257i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −23.1909 | − | 23.1909i | −1.27469 | − | 1.27469i | −0.943600 | − | 0.331089i | \(-0.892584\pi\) |
−0.331089 | − | 0.943600i | \(-0.607416\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −13.9909 | − | 19.7629i | −0.764405 | − | 1.07976i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −12.5067 | − | 12.5067i | −0.681285 | − | 0.681285i | 0.279005 | − | 0.960290i | \(-0.409995\pi\) |
−0.960290 | + | 0.279005i | \(0.909995\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.539450 | − | 0.539450i | 0.0292128 | − | 0.0292128i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 11.7042 | + | 11.7042i | 0.631965 | + | 0.631965i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 11.9538 | 0.641716 | 0.320858 | − | 0.947127i | \(-0.396029\pi\) | ||||
0.320858 | + | 0.947127i | \(0.396029\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −17.0082 | − | 17.0082i | −0.910429 | − | 0.910429i | 0.0858769 | − | 0.996306i | \(-0.472631\pi\) |
−0.996306 | + | 0.0858769i | \(0.972631\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 14.0137 | + | 14.0137i | 0.745872 | + | 0.745872i | 0.973701 | − | 0.227829i | \(-0.0731627\pi\) |
−0.227829 | + | 0.973701i | \(0.573163\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.85427 | − | 4.03180i | −0.151489 | − | 0.213986i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 19.4255i | − | 1.02524i | −0.858616 | − | 0.512620i | \(-0.828675\pi\) | ||
0.858616 | − | 0.512620i | \(-0.171325\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.78259i | 0.304347i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.76529 | − | 10.3232i | 0.0923996 | − | 0.540341i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.99308 | + | 8.99308i | 0.469435 | + | 0.469435i | 0.901732 | − | 0.432296i | \(-0.142297\pi\) |
−0.432296 | + | 0.901732i | \(0.642297\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 23.3592 | + | 23.3592i | 1.21275 | + | 1.21275i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.75511 | 0.194432 | 0.0972160 | − | 0.995263i | \(-0.469006\pi\) | ||||
0.0972160 | + | 0.995263i | \(0.469006\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −7.14054 | − | 7.14054i | −0.367757 | − | 0.367757i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.2095 | − | 11.2095i | 0.575794 | − | 0.575794i | −0.357948 | − | 0.933742i | \(-0.616523\pi\) |
0.933742 | + | 0.357948i | \(0.116523\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7.22015 | + | 7.22015i | 0.368932 | + | 0.368932i | 0.867088 | − | 0.498155i | \(-0.165989\pi\) |
−0.498155 | + | 0.867088i | \(0.665989\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 24.4607 | − | 17.3167i | 1.24663 | − | 0.882539i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −24.5313 | − | 24.5313i | −1.24379 | − | 1.24379i | −0.958418 | − | 0.285369i | \(-0.907884\pi\) |
−0.285369 | − | 0.958418i | \(-0.592116\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.49533i | 0.379055i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −11.7444 | + | 8.31431i | −0.590924 | + | 0.418338i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.77500 | −0.289839 | −0.144919 | − | 0.989443i | \(-0.546292\pi\) | ||||
−0.144919 | + | 0.989443i | \(0.546292\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 19.4666i | − | 0.972116i | −0.873927 | − | 0.486058i | \(-0.838434\pi\) | ||
0.873927 | − | 0.486058i | \(-0.161566\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 0.215982i | − | 0.0107588i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 13.4419 | + | 13.4419i | 0.666290 | + | 0.666290i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −24.6895 | −1.22081 | −0.610407 | − | 0.792088i | \(-0.708994\pi\) | ||||
−0.610407 | + | 0.792088i | \(0.708994\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 33.6585 | 1.65622 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −10.7097 | − | 15.1280i | −0.525718 | − | 0.742605i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −12.5085 | + | 12.5085i | −0.611082 | + | 0.611082i | −0.943228 | − | 0.332146i | \(-0.892227\pi\) |
0.332146 | + | 0.943228i | \(0.392227\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.90394 | − | 3.90394i | −0.190266 | − | 0.190266i | 0.605545 | − | 0.795811i | \(-0.292955\pi\) |
−0.795811 | + | 0.605545i | \(0.792955\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.19448 | − | 8.75758i | −0.203462 | − | 0.424805i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 20.7610i | 1.00470i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 33.5433i | − | 1.61572i | −0.589371 | − | 0.807862i | \(-0.700624\pi\) | ||
0.589371 | − | 0.807862i | \(-0.299376\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −24.0797 | + | 24.0797i | −1.15720 | + | 1.15720i | −0.172121 | + | 0.985076i | \(0.555062\pi\) |
−0.985076 | + | 0.172121i | \(0.944938\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 19.2134 | 0.919101 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.80454 | 0.0861261 | 0.0430630 | − | 0.999072i | \(-0.486288\pi\) | ||||
0.0430630 | + | 0.999072i | \(0.486288\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7.99522i | 0.379865i | 0.981797 | + | 0.189932i | \(0.0608268\pi\) | ||||
−0.981797 | + | 0.189932i | \(0.939173\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 18.4596 | − | 13.0682i | 0.875067 | − | 0.619494i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −23.9985 | −1.13256 | −0.566279 | − | 0.824214i | \(-0.691617\pi\) | ||||
−0.566279 | + | 0.824214i | \(0.691617\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 26.7895 | − | 26.7895i | 1.26147 | − | 1.26147i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.43014 | − | 8.36328i | 0.0670460 | − | 0.392077i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.921521 | − | 0.921521i | 0.0431069 | − | 0.0431069i | −0.685225 | − | 0.728332i | \(-0.740296\pi\) |
0.728332 | + | 0.685225i | \(0.240296\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.71477 | − | 7.71477i | −0.359313 | − | 0.359313i | 0.504247 | − | 0.863560i | \(-0.331770\pi\) |
−0.863560 | + | 0.504247i | \(0.831770\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10.7374 | + | 10.7374i | −0.499009 | + | 0.499009i | −0.911129 | − | 0.412120i | \(-0.864788\pi\) |
0.412120 | + | 0.911129i | \(0.364788\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 11.8647i | 0.549033i | 0.961582 | + | 0.274516i | \(0.0885178\pi\) | ||||
−0.961582 | + | 0.274516i | \(0.911482\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 21.9673 | − | 21.9673i | 1.01436 | − | 1.01436i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 20.1811 | − | 20.1811i | 0.927929 | − | 0.927929i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −22.4490 | + | 10.7521i | −1.03003 | + | 0.493338i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 14.6761 | 0.670568 | 0.335284 | − | 0.942117i | \(-0.391168\pi\) | ||||
0.335284 | + | 0.942117i | \(0.391168\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.38178 | 0.245388 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.78765 | + | 22.1497i | −0.171988 | + | 1.00577i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −15.8046 | + | 15.8046i | −0.716177 | + | 0.716177i | −0.967820 | − | 0.251643i | \(-0.919029\pi\) |
0.251643 | + | 0.967820i | \(0.419029\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.5216 | − | 12.5216i | 0.565091 | − | 0.565091i | −0.365658 | − | 0.930749i | \(-0.619156\pi\) |
0.930749 | + | 0.365658i | \(0.119156\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 14.8275i | − | 0.667796i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.48153 | − | 4.48153i | 0.201024 | − | 0.201024i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16.6276 | − | 16.6276i | −0.744356 | − | 0.744356i | 0.229057 | − | 0.973413i | \(-0.426436\pi\) |
−0.973413 | + | 0.229057i | \(0.926436\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 25.0801 | − | 25.0801i | 1.11827 | − | 1.11827i | 0.126269 | − | 0.991996i | \(-0.459700\pi\) |
0.991996 | − | 0.126269i | \(-0.0403003\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −17.9157 | − | 3.06363i | −0.797239 | − | 0.136330i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.37812 | + | 1.37812i | −0.0610839 | + | 0.0610839i | −0.736989 | − | 0.675905i | \(-0.763753\pi\) |
0.675905 | + | 0.736989i | \(0.263753\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 13.4369 | 0.594414 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6.26100 | − | 36.6135i | 0.275893 | − | 1.61339i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 21.6882i | 0.953846i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 17.2515 | 0.755802 | 0.377901 | − | 0.925846i | \(-0.376646\pi\) | ||||
0.377901 | + | 0.925846i | \(0.376646\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −24.4981 | −1.07123 | −0.535613 | − | 0.844464i | \(-0.679919\pi\) | ||||
−0.535613 | + | 0.844464i | \(0.679919\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.224245 | − | 0.224245i | 0.00976826 | − | 0.00976826i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.10430i | 0.352361i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 10.7258i | − | 0.464587i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 14.9100 | + | 21.0611i | 0.644613 | + | 0.910550i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.06470 | + | 4.06470i | 0.175079 | + | 0.175079i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.53300 | − | 3.53300i | 0.151896 | − | 0.151896i | −0.627068 | − | 0.778964i | \(-0.715745\pi\) |
0.778964 | + | 0.627068i | \(0.215745\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.27750 | − | 36.7100i | 0.268898 | − | 1.57248i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.27786 | −0.353936 | −0.176968 | − | 0.984217i | \(-0.556629\pi\) | ||||
−0.176968 | + | 0.984217i | \(0.556629\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −38.0085 | −1.61921 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −13.0544 | − | 13.0544i | −0.555130 | − | 0.555130i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 41.4835i | 1.75771i | 0.477088 | + | 0.878855i | \(0.341692\pi\) | ||||
−0.477088 | + | 0.878855i | \(0.658308\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 8.07999i | − | 0.341747i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 21.7731 | 0.917628 | 0.458814 | − | 0.888532i | \(-0.348274\pi\) | ||||
0.458814 | + | 0.888532i | \(0.348274\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.67173 | + | 44.8633i | −0.322752 | + | 1.88741i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 10.0468i | 0.421182i | 0.977574 | + | 0.210591i | \(0.0675388\pi\) | ||||
−0.977574 | + | 0.210591i | \(0.932461\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.72264 | + | 9.72264i | 0.406880 | + | 0.406880i | 0.880649 | − | 0.473769i | \(-0.157107\pi\) |
−0.473769 | + | 0.880649i | \(0.657107\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.33582 | + | 17.4042i | 0.347628 | + | 0.725806i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7.38116 | − | 7.38116i | −0.307282 | − | 0.307282i | 0.536572 | − | 0.843854i | \(-0.319719\pi\) |
−0.843854 | + | 0.536572i | \(0.819719\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 16.8155 | − | 16.8155i | 0.697623 | − | 0.697623i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −38.0395 | − | 38.0395i | −1.57544 | − | 1.57544i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −39.8451 | −1.64458 | −0.822292 | − | 0.569066i | \(-0.807305\pi\) | ||||
−0.822292 | + | 0.569066i | \(0.807305\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.574825 | − | 0.574825i | −0.0236853 | − | 0.0236853i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 10.3163 | + | 10.3163i | 0.423641 | + | 0.423641i | 0.886455 | − | 0.462814i | \(-0.153160\pi\) |
−0.462814 | + | 0.886455i | \(0.653160\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 10.1681 | − | 7.19840i | 0.416852 | − | 0.295105i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 4.32724i | − | 0.176806i | −0.996085 | − | 0.0884030i | \(-0.971824\pi\) | ||
0.996085 | − | 0.0884030i | \(-0.0281763\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 35.7850i | 1.45970i | 0.683607 | + | 0.729851i | \(0.260410\pi\) | ||||
−0.683607 | + | 0.729851i | \(0.739590\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −19.7580 | + | 13.9875i | −0.803277 | + | 0.568671i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −10.5879 | − | 10.5879i | −0.429748 | − | 0.429748i | 0.458794 | − | 0.888543i | \(-0.348282\pi\) |
−0.888543 | + | 0.458794i | \(0.848282\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.34169 | + | 4.34169i | 0.175646 | + | 0.175646i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9.05654 | −0.365790 | −0.182895 | − | 0.983132i | \(-0.558547\pi\) | ||||
−0.182895 | + | 0.983132i | \(0.558547\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8.00692 | + | 8.00692i | 0.322346 | + | 0.322346i | 0.849667 | − | 0.527320i | \(-0.176803\pi\) |
−0.527320 | + | 0.849667i | \(0.676803\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −16.5160 | + | 16.5160i | −0.663834 | + | 0.663834i | −0.956281 | − | 0.292448i | \(-0.905530\pi\) |
0.292448 | + | 0.956281i | \(0.405530\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 20.5186 | + | 20.5186i | 0.822061 | + | 0.822061i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19.4792 | − | 15.6703i | −0.779169 | − | 0.626813i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.58768 | + | 5.58768i | 0.222796 | + | 0.222796i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 1.83078i | − | 0.0728822i | −0.999336 | − | 0.0364411i | \(-0.988398\pi\) | ||
0.999336 | − | 0.0364411i | \(-0.0116021\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.32591 | − | 13.6016i | 0.0923010 | − | 0.539765i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.62740 | 0.0644799 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 14.7618i | 0.583058i | 0.956562 | + | 0.291529i | \(0.0941640\pi\) | ||||
−0.956562 | + | 0.291529i | \(0.905836\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 17.1777i | 0.677421i | 0.940891 | + | 0.338710i | \(0.109991\pi\) | ||||
−0.940891 | + | 0.338710i | \(0.890009\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 15.7483 | + | 15.7483i | 0.619130 | + | 0.619130i | 0.945308 | − | 0.326178i | \(-0.105761\pi\) |
−0.326178 | + | 0.945308i | \(0.605761\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −54.8115 | −2.15154 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 34.1501 | 1.33640 | 0.668199 | − | 0.743983i | \(-0.267065\pi\) | ||||
0.668199 | + | 0.743983i | \(0.267065\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.92342 | + | 28.7915i | −0.192374 | + | 1.12498i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.91488 | − | 3.91488i | 0.152502 | − | 0.152502i | −0.626732 | − | 0.779234i | \(-0.715608\pi\) |
0.779234 | + | 0.626732i | \(0.215608\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −33.0265 | − | 33.0265i | −1.28458 | − | 1.28458i | −0.938032 | − | 0.346548i | \(-0.887354\pi\) |
−0.346548 | − | 0.938032i | \(-0.612646\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −18.4522 | − | 26.0647i | −0.715547 | − | 1.01075i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 29.4671i | 1.14097i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 33.8085i | − | 1.30516i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 13.0734 | − | 13.0734i | 0.503942 | − | 0.503942i | −0.408719 | − | 0.912660i | \(-0.634024\pi\) |
0.912660 | + | 0.408719i | \(0.134024\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.97260 | 0.152679 | 0.0763397 | − | 0.997082i | \(-0.475677\pi\) | ||||
0.0763397 | + | 0.997082i | \(0.475677\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −28.8305 | −1.10641 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 18.7686i | − | 0.718161i | −0.933307 | − | 0.359081i | \(-0.883090\pi\) | ||
0.933307 | − | 0.359081i | \(-0.116910\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.67209 | − | 27.3218i | 0.178511 | − | 1.04391i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −15.2300 | −0.580218 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13.2261 | − | 13.2261i | 0.503144 | − | 0.503144i | −0.409270 | − | 0.912413i | \(-0.634216\pi\) |
0.912413 | + | 0.409270i | \(0.134216\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −21.5112 | − | 3.67846i | −0.815966 | − | 0.139532i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 11.1362 | − | 11.1362i | 0.421813 | − | 0.421813i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.85188 | + | 5.85188i | 0.221022 | + | 0.221022i | 0.808929 | − | 0.587906i | \(-0.200048\pi\) |
−0.587906 | + | 0.808929i | \(0.700048\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 14.3234 | − | 14.3234i | 0.540216 | − | 0.540216i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 23.3195i | − | 0.877019i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11.1418 | − | 11.1418i | 0.418438 | − | 0.418438i | −0.466227 | − | 0.884665i | \(-0.654387\pi\) |
0.884665 | + | 0.466227i | \(0.154387\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.445649 | + | 0.445649i | −0.0166897 | + | 0.0166897i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.32893 | + | 13.6193i | −0.0870970 | + | 0.509332i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −8.83653 | −0.329547 | −0.164773 | − | 0.986331i | \(-0.552689\pi\) | ||||
−0.164773 | + | 0.986331i | \(0.552689\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 47.6570 | 1.77484 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −16.4902 | − | 34.4295i | −0.612429 | − | 1.27868i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 21.8860 | − | 21.8860i | 0.811708 | − | 0.811708i | −0.173182 | − | 0.984890i | \(-0.555405\pi\) |
0.984890 | + | 0.173182i | \(0.0554048\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.38912 | − | 8.38912i | 0.310283 | − | 0.310283i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9.81906i | 0.362675i | 0.983421 | + | 0.181338i | \(0.0580427\pi\) | ||||
−0.983421 | + | 0.181338i | \(0.941957\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −35.7730 | + | 35.7730i | −1.31771 | + | 1.31771i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 28.7826 | + | 28.7826i | 1.05879 | + | 1.05879i | 0.998161 | + | 0.0606259i | \(0.0193097\pi\) |
0.0606259 | + | 0.998161i | \(0.480690\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 33.6714 | − | 33.6714i | 1.23528 | − | 1.23528i | 0.273376 | − | 0.961907i | \(-0.411860\pi\) |
0.961907 | − | 0.273376i | \(-0.0881404\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.77310 | − | 22.0646i | 0.138236 | − | 0.808384i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −23.4103 | + | 23.4103i | −0.855395 | + | 0.855395i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.304020 | 0.0110939 | 0.00554693 | − | 0.999985i | \(-0.498234\pi\) | ||||
0.00554693 | + | 0.999985i | \(0.498234\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 37.0484 | − | 26.2280i | 1.34833 | − | 0.954534i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 33.6193i | − | 1.22191i | −0.791664 | − | 0.610956i | \(-0.790785\pi\) | ||
0.791664 | − | 0.610956i | \(-0.209215\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 26.6846 | 0.967317 | 0.483659 | − | 0.875257i | \(-0.339308\pi\) | ||||
0.483659 | + | 0.875257i | \(0.339308\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 47.7825 | 1.72984 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −10.9725 | + | 10.9725i | −0.396196 | + | 0.396196i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.66538i | 0.0961159i | 0.998845 | + | 0.0480580i | \(0.0153032\pi\) | ||||
−0.998845 | + | 0.0480580i | \(0.984697\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0.126666i | 0.00455587i | 0.999997 | + | 0.00227793i | \(0.000725089\pi\) | ||||
−0.999997 | + | 0.00227793i | \(0.999275\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.271308 | − | 0.770089i | 0.00974566 | − | 0.0276624i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −28.5463 | − | 28.5463i | −1.02278 | − | 1.02278i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.29800 | + | 7.29800i | −0.261143 | + | 0.261143i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 15.3856 | + | 21.7330i | 0.549136 | + | 0.775683i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −43.9684 | −1.56731 | −0.783653 | − | 0.621199i | \(-0.786646\pi\) | ||||
−0.783653 | + | 0.621199i | \(0.786646\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −58.3950 | −2.07629 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6.76802 | − | 6.76802i | −0.240339 | − | 0.240339i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 40.6870i | − | 1.44121i | −0.693347 | − | 0.720604i | \(-0.743865\pi\) | ||
0.693347 | − | 0.720604i | \(-0.256135\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.01561i | 0.318949i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −21.8815 | −0.772181 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −20.2074 | + | 14.3056i | −0.712218 | + | 0.504206i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 9.49678i | 0.333889i | 0.985966 | + | 0.166944i | \(0.0533900\pi\) | ||||
−0.985966 | + | 0.166944i | \(0.946610\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.57198 | + | 6.57198i | 0.230773 | + | 0.230773i | 0.813015 | − | 0.582242i | \(-0.197824\pi\) |
−0.582242 | + | 0.813015i | \(0.697824\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 36.5227 | − | 25.8558i | 1.27933 | − | 0.905689i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −21.5045 | − | 21.5045i | −0.752348 | − | 0.752348i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6.14199 | + | 6.14199i | −0.214357 | + | 0.214357i | −0.806115 | − | 0.591758i | \(-0.798434\pi\) |
0.591758 | + | 0.806115i | \(0.298434\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −31.1801 | − | 31.1801i | −1.08687 | − | 1.08687i | −0.995849 | − | 0.0910195i | \(-0.970987\pi\) |
−0.0910195 | − | 0.995849i | \(-0.529013\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −0.501217 | −0.0174290 | −0.00871451 | − | 0.999962i | \(-0.502774\pi\) | ||||
−0.00871451 | + | 0.999962i | \(0.502774\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −19.4306 | − | 19.4306i | −0.674851 | − | 0.674851i | 0.283979 | − | 0.958830i | \(-0.408345\pi\) |
−0.958830 | + | 0.283979i | \(0.908345\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.68966 | + | 1.68966i | 0.0585433 | + | 0.0585433i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.114344 | + | 0.668668i | −0.00395703 | + | 0.0231402i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 14.2054i | − | 0.490424i | −0.969469 | − | 0.245212i | \(-0.921142\pi\) | ||
0.969469 | − | 0.245212i | \(-0.0788576\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 29.2927i | − | 1.01009i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −14.5359 | − | 20.5327i | −0.500050 | − | 0.706347i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −21.9619 | − | 21.9619i | −0.754620 | − | 0.754620i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −11.1046 | − | 11.1046i | −0.380660 | − | 0.380660i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0.980294 | 0.0335646 | 0.0167823 | − | 0.999859i | \(-0.494658\pi\) | ||||
0.0167823 | + | 0.999859i | \(0.494658\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.66573 | − | 1.66573i | −0.0569003 | − | 0.0569003i | 0.678084 | − | 0.734984i | \(-0.262811\pi\) |
−0.734984 | + | 0.678084i | \(0.762811\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 35.4006 | − | 35.4006i | 1.20785 | − | 1.20785i | 0.236133 | − | 0.971721i | \(-0.424120\pi\) |
0.971721 | − | 0.236133i | \(-0.0758801\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 32.0987 | + | 32.0987i | 1.09265 | + | 1.09265i | 0.995244 | + | 0.0974086i | \(0.0310554\pi\) |
0.0974086 | + | 0.995244i | \(0.468945\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −27.0129 | − | 38.1572i | −0.918468 | − | 1.29738i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 21.2586 | + | 21.2586i | 0.721149 | + | 0.721149i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 14.3226i | 0.485301i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 15.6048 | − | 28.0231i | 0.527540 | − | 0.947352i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −10.3966 | −0.351069 | −0.175534 | − | 0.984473i | \(-0.556165\pi\) | ||||
−0.175534 | + | 0.984473i | \(0.556165\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 41.2431i | 1.38951i | 0.719245 | + | 0.694757i | \(0.244488\pi\) | ||||
−0.719245 | + | 0.694757i | \(0.755512\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 22.8134i | 0.767732i | 0.923389 | + | 0.383866i | \(0.125407\pi\) | ||||
−0.923389 | + | 0.383866i | \(0.874593\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 15.9633 | + | 15.9633i | 0.535996 | + | 0.535996i | 0.922350 | − | 0.386354i | \(-0.126266\pi\) |
−0.386354 | + | 0.922350i | \(0.626266\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 17.7042 | 0.593779 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 23.1104 | 0.773361 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 34.3891 | + | 5.88062i | 1.14950 | + | 0.196567i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.881595 | − | 0.881595i | 0.0294028 | − | 0.0294028i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −15.8127 | − | 15.8127i | −0.526798 | − | 0.526798i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −6.40829 | + | 37.4748i | −0.213019 | + | 1.24571i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 33.6267i | − | 1.11656i | −0.829654 | − | 0.558278i | \(-0.811462\pi\) | ||
0.829654 | − | 0.558278i | \(-0.188538\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 16.3069i | 0.540272i | 0.962822 | + | 0.270136i | \(0.0870687\pi\) | ||||
−0.962822 | + | 0.270136i | \(0.912931\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −27.3833 | + | 27.3833i | −0.906256 | + | 0.906256i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −37.4757 | −1.23756 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −25.5350 | −0.842323 | −0.421162 | − | 0.906986i | \(-0.638377\pi\) | ||||
−0.421162 | + | 0.906986i | \(0.638377\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.92193i | 0.0961765i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 19.1889 | + | 6.76039i | 0.630928 | + | 0.222280i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −14.3973 | −0.472360 | −0.236180 | − | 0.971709i | \(-0.575895\pi\) | ||||
−0.236180 | + | 0.971709i | \(0.575895\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.33125 | − | 4.33125i | 0.141951 | − | 0.141951i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −16.5584 | + | 11.7223i | −0.541517 | + | 0.383361i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −41.3301 | + | 41.3301i | −1.35020 | + | 1.35020i | −0.464757 | + | 0.885438i | \(0.653858\pi\) |
−0.885438 | + | 0.464757i | \(0.846142\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −32.9564 | − | 32.9564i | −1.07435 | − | 1.07435i | −0.997005 | − | 0.0773431i | \(-0.975356\pi\) |
−0.0773431 | − | 0.997005i | \(-0.524644\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −22.1313 | + | 22.1313i | −0.720694 | + | 0.720694i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 5.80564i | 0.188658i | 0.995541 | + | 0.0943290i | \(0.0300706\pi\) | ||||
−0.995541 | + | 0.0943290i | \(0.969929\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.38039 | + | 4.38039i | −0.142193 | + | 0.142193i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 31.6012 | − | 31.6012i | 1.02366 | − | 1.02366i | 0.0239501 | − | 0.999713i | \(-0.492376\pi\) |
0.999713 | − | 0.0239501i | \(-0.00762429\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 15.8337 | − | 11.2093i | 0.512367 | − | 0.362725i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 35.5626 | 1.14838 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.9733 | −0.999140 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −0.614843 | − | 0.105140i | −0.0197925 | − | 0.00338456i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 30.6886 | − | 30.6886i | 0.986878 | − | 0.986878i | −0.0130369 | − | 0.999915i | \(-0.504150\pi\) |
0.999915 | + | 0.0130369i | \(0.00414988\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.02162 | − | 5.02162i | 0.161151 | − | 0.161151i | −0.621925 | − | 0.783077i | \(-0.713649\pi\) |
0.783077 | + | 0.621925i | \(0.213649\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 27.9994i | − | 0.897620i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 21.2983 | − | 21.2983i | 0.681392 | − | 0.681392i | −0.278922 | − | 0.960314i | \(-0.589977\pi\) |
0.960314 | + | 0.278922i | \(0.0899770\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −33.4138 | − | 33.4138i | −1.06791 | − | 1.06791i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −33.5737 | + | 33.5737i | −1.07084 | + | 1.07084i | −0.0735434 | + | 0.997292i | \(0.523431\pi\) |
−0.997292 | + | 0.0735434i | \(0.976569\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 17.5847 | + | 24.8393i | 0.560295 | + | 0.791446i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −16.6720 | + | 16.6720i | −0.530138 | + | 0.530138i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −29.9874 | −0.952580 | −0.476290 | − | 0.879288i | \(-0.658019\pi\) | ||||
−0.476290 | + | 0.879288i | \(0.658019\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 13.3268 | + | 18.8248i | 0.422487 | + | 0.596785i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 34.1815i | 1.08254i | 0.840849 | + | 0.541270i | \(0.182056\pi\) | ||||
−0.840849 | + | 0.541270i | \(0.817944\pi\) | |||||||
\(998\) | 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.bc.a.1457.15 | 96 | ||
3.2 | odd | 2 | inner | 2880.2.bc.a.1457.34 | 96 | ||
4.3 | odd | 2 | 720.2.bc.a.197.3 | ✓ | 96 | ||
5.3 | odd | 4 | 2880.2.bg.a.2033.39 | 96 | |||
12.11 | even | 2 | 720.2.bc.a.197.46 | yes | 96 | ||
15.8 | even | 4 | 2880.2.bg.a.2033.10 | 96 | |||
16.3 | odd | 4 | 720.2.bg.a.557.27 | yes | 96 | ||
16.13 | even | 4 | 2880.2.bg.a.17.10 | 96 | |||
20.3 | even | 4 | 720.2.bg.a.53.22 | yes | 96 | ||
48.29 | odd | 4 | 2880.2.bg.a.17.39 | 96 | |||
48.35 | even | 4 | 720.2.bg.a.557.22 | yes | 96 | ||
60.23 | odd | 4 | 720.2.bg.a.53.27 | yes | 96 | ||
80.3 | even | 4 | 720.2.bc.a.413.46 | yes | 96 | ||
80.13 | odd | 4 | inner | 2880.2.bc.a.593.34 | 96 | ||
240.83 | odd | 4 | 720.2.bc.a.413.3 | yes | 96 | ||
240.173 | even | 4 | inner | 2880.2.bc.a.593.15 | 96 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
720.2.bc.a.197.3 | ✓ | 96 | 4.3 | odd | 2 | ||
720.2.bc.a.197.46 | yes | 96 | 12.11 | even | 2 | ||
720.2.bc.a.413.3 | yes | 96 | 240.83 | odd | 4 | ||
720.2.bc.a.413.46 | yes | 96 | 80.3 | even | 4 | ||
720.2.bg.a.53.22 | yes | 96 | 20.3 | even | 4 | ||
720.2.bg.a.53.27 | yes | 96 | 60.23 | odd | 4 | ||
720.2.bg.a.557.22 | yes | 96 | 48.35 | even | 4 | ||
720.2.bg.a.557.27 | yes | 96 | 16.3 | odd | 4 | ||
2880.2.bc.a.593.15 | 96 | 240.173 | even | 4 | inner | ||
2880.2.bc.a.593.34 | 96 | 80.13 | odd | 4 | inner | ||
2880.2.bc.a.1457.15 | 96 | 1.1 | even | 1 | trivial | ||
2880.2.bc.a.1457.34 | 96 | 3.2 | odd | 2 | inner | ||
2880.2.bg.a.17.10 | 96 | 16.13 | even | 4 | |||
2880.2.bg.a.17.39 | 96 | 48.29 | odd | 4 | |||
2880.2.bg.a.2033.10 | 96 | 15.8 | even | 4 | |||
2880.2.bg.a.2033.39 | 96 | 5.3 | odd | 4 |