Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2240,2,Mod(2239,2240)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2240, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2240.2239");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2240 = 2^{6} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2240.e (of order \(2\), degree \(1\), 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: | \(17.8864900528\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Twist minimal: | no (minimal twist has level 1120) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2239.1 | ||
Character | \(\chi\) | \(=\) | 2240.2239 |
Dual form | 2240.2.e.g.2239.2 |
$q$-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 \(\left(\mathbb{Z}/2240\mathbb{Z}\right)^\times\).
\(n\) | \(897\) | \(1471\) | \(1541\) | \(1921\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 2.21376i | − | 1.27811i | −0.769160 | − | 0.639057i | \(-0.779325\pi\) | ||
0.769160 | − | 0.639057i | \(-0.220675\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.81856 | − | 1.30110i | −0.813283 | − | 0.581868i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.09155 | − | 2.41009i | 0.412566 | − | 0.910928i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.90072 | −0.633573 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.661829i | 0.199549i | 0.995010 | + | 0.0997745i | \(0.0318121\pi\) | ||||
−0.995010 | + | 0.0997745i | \(0.968188\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.235163 | 0.0652226 | 0.0326113 | − | 0.999468i | \(-0.489618\pi\) | ||||
0.0326113 | + | 0.999468i | \(0.489618\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.88031 | + | 4.02584i | −0.743693 | + | 1.03947i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.02258 | 1.46069 | 0.730345 | − | 0.683078i | \(-0.239359\pi\) | ||||
0.730345 | + | 0.683078i | \(0.239359\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.98868 | −1.83273 | −0.916365 | − | 0.400344i | \(-0.868891\pi\) | ||||
−0.916365 | + | 0.400344i | \(0.868891\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.33535 | − | 2.41642i | −1.16427 | − | 0.527306i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −8.48129 | −1.76847 | −0.884236 | − | 0.467041i | \(-0.845320\pi\) | ||||
−0.884236 | + | 0.467041i | \(0.845320\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.61430 | + | 4.73223i | 0.322859 | + | 0.946447i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 2.43354i | − | 0.468335i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.86505 | −1.46050 | −0.730251 | − | 0.683179i | \(-0.760597\pi\) | ||||
−0.730251 | + | 0.683179i | \(0.760597\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.36954 | −0.245977 | −0.122988 | − | 0.992408i | \(-0.539248\pi\) | ||||
−0.122988 | + | 0.992408i | \(0.539248\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.46513 | 0.255046 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5.12080 | + | 2.96268i | −0.865572 | + | 0.500784i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 6.09846i | − | 1.00258i | −0.865279 | − | 0.501291i | \(-0.832859\pi\) | ||
0.865279 | − | 0.501291i | \(-0.167141\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 0.520594i | − | 0.0833618i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.79815i | 0.436998i | 0.975837 | + | 0.218499i | \(0.0701161\pi\) | ||||
−0.975837 | + | 0.218499i | \(0.929884\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.54155 | 1.45507 | 0.727536 | − | 0.686069i | \(-0.240665\pi\) | ||||
0.727536 | + | 0.686069i | \(0.240665\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.45657 | + | 2.47302i | 0.515274 | + | 0.368656i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 7.72404i | − | 1.12667i | −0.826229 | − | 0.563334i | \(-0.809519\pi\) | ||
0.826229 | − | 0.563334i | \(-0.190481\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.61705 | − | 5.26145i | −0.659579 | − | 0.751635i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 13.3325i | − | 1.86693i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.45461i | 1.16133i | 0.814143 | + | 0.580665i | \(0.197207\pi\) | ||||
−0.814143 | + | 0.580665i | \(0.802793\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.861103 | − | 1.20357i | 0.116111 | − | 0.162290i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 17.6850i | 2.34244i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.929088 | 0.120957 | 0.0604785 | − | 0.998170i | \(-0.480737\pi\) | ||||
0.0604785 | + | 0.998170i | \(0.480737\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.28972i | 0.293168i | 0.989198 | + | 0.146584i | \(0.0468279\pi\) | ||||
−0.989198 | + | 0.146584i | \(0.953172\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.07472 | + | 4.58090i | −0.261391 | + | 0.577139i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.427658 | − | 0.305970i | −0.0530444 | − | 0.0379509i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.19295 | 0.390082 | 0.195041 | − | 0.980795i | \(-0.437516\pi\) | ||||
0.195041 | + | 0.980795i | \(0.437516\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 18.7755i | 2.26031i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 0.619016i | − | 0.0734637i | −0.999325 | − | 0.0367318i | \(-0.988305\pi\) | ||
0.999325 | − | 0.0367318i | \(-0.0116947\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.9176 | −1.39485 | −0.697423 | − | 0.716660i | \(-0.745670\pi\) | ||||
−0.697423 | + | 0.716660i | \(0.745670\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 10.4760 | − | 3.57366i | 1.20967 | − | 0.412651i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.59507 | + | 0.722417i | 0.181775 | + | 0.0823271i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.01658i | 0.789427i | 0.918804 | + | 0.394713i | \(0.129156\pi\) | ||||
−0.918804 | + | 0.394713i | \(0.870844\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.0894 | −1.23216 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 7.05444i | − | 0.774326i | −0.922011 | − | 0.387163i | \(-0.873455\pi\) | ||
0.922011 | − | 0.387163i | \(-0.126545\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −10.9524 | − | 7.83596i | −1.18796 | − | 0.849929i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 17.4113i | 1.86669i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.97484i | 1.05733i | 0.848830 | + | 0.528665i | \(0.177307\pi\) | ||||
−0.848830 | + | 0.528665i | \(0.822693\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.256692 | − | 0.566764i | 0.0269086 | − | 0.0594130i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.03183i | 0.314386i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 14.5279 | + | 10.3940i | 1.49053 | + | 1.06641i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.02258 | 0.611500 | 0.305750 | − | 0.952112i | \(-0.401093\pi\) | ||||
0.305750 | + | 0.952112i | \(0.401093\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 1.25795i | − | 0.126429i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.4833i | 1.04312i | 0.853213 | + | 0.521562i | \(0.174651\pi\) | ||||
−0.853213 | + | 0.521562i | \(0.825349\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.79144i | 0.472115i | 0.971739 | + | 0.236058i | \(0.0758554\pi\) | ||||
−0.971739 | + | 0.236058i | \(0.924145\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 6.55864 | + | 11.3362i | 0.640058 | + | 1.10630i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.19295 | −0.308675 | −0.154337 | − | 0.988018i | \(-0.549324\pi\) | ||||
−0.154337 | + | 0.988018i | \(0.549324\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.36906 | 0.322698 | 0.161349 | − | 0.986897i | \(-0.448416\pi\) | ||||
0.161349 | + | 0.986897i | \(0.448416\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −13.5005 | −1.28141 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.7455i | 1.01085i | 0.862871 | + | 0.505424i | \(0.168664\pi\) | ||||
−0.862871 | + | 0.505424i | \(0.831336\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 15.4237 | + | 11.0350i | 1.43827 | + | 1.02902i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.446979 | −0.0413233 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.57392 | − | 14.5150i | 0.602631 | − | 1.33058i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.5620 | 0.960180 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.19443 | 0.558533 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.22140 | − | 10.7062i | 0.288131 | − | 0.957591i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.94371 | −0.704891 | −0.352445 | − | 0.935832i | \(-0.614650\pi\) | ||||
−0.352445 | + | 0.935832i | \(0.614650\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 21.1227i | − | 1.85975i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −14.8215 | −1.29496 | −0.647481 | − | 0.762081i | \(-0.724178\pi\) | ||||
−0.647481 | + | 0.762081i | \(0.724178\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.72002 | + | 19.2534i | −0.756121 | + | 1.66948i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.16627 | + | 4.42553i | −0.272509 | + | 0.380889i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 18.9726i | − | 1.62094i | −0.585780 | − | 0.810470i | \(-0.699212\pi\) | ||
0.585780 | − | 0.810470i | \(-0.300788\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.47968 | −0.804056 | −0.402028 | − | 0.915627i | \(-0.631695\pi\) | ||||
−0.402028 | + | 0.915627i | \(0.631695\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −17.0992 | −1.44001 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.155638i | 0.0130151i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 14.3030 | + | 10.2332i | 1.18780 | + | 0.849820i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −11.6476 | + | 10.2210i | −0.960675 | + | 0.843017i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 13.0440 | 1.06860 | 0.534302 | − | 0.845294i | \(-0.320574\pi\) | ||||
0.534302 | + | 0.845294i | \(0.320574\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 15.0683i | − | 1.22624i | −0.789991 | − | 0.613119i | \(-0.789915\pi\) | ||
0.789991 | − | 0.613119i | \(-0.210085\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −11.4472 | −0.925454 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.49058 | + | 1.78190i | 0.200049 | + | 0.143126i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.5780 | 1.00384 | 0.501918 | − | 0.864915i | \(-0.332628\pi\) | ||||
0.501918 | + | 0.864915i | \(0.332628\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 18.7164 | 1.48431 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −9.25772 | + | 20.4407i | −0.729611 | + | 1.61095i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.22660 | 0.0960748 | 0.0480374 | − | 0.998846i | \(-0.484703\pi\) | ||||
0.0480374 | + | 0.998846i | \(0.484703\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.66442 | − | 1.90627i | −0.207425 | − | 0.148403i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 4.41726i | − | 0.341818i | −0.985287 | − | 0.170909i | \(-0.945330\pi\) | ||
0.985287 | − | 0.170909i | \(-0.0546704\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9447 | −0.995746 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 15.1842 | 1.16117 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.47071 | −0.567988 | −0.283994 | − | 0.958826i | \(-0.591660\pi\) | ||||
−0.283994 | + | 0.958826i | \(0.591660\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 13.1672 | + | 1.27485i | 0.995346 | + | 0.0963699i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 2.05677i | − | 0.154597i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.5662i | 0.939242i | 0.882868 | + | 0.469621i | \(0.155609\pi\) | ||||
−0.882868 | + | 0.469621i | \(0.844391\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 18.7214i | − | 1.39155i | −0.718260 | − | 0.695775i | \(-0.755061\pi\) | ||
0.718260 | − | 0.695775i | \(-0.244939\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.06888 | 0.374702 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −7.93469 | + | 11.0904i | −0.583370 | + | 0.815383i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.98592i | 0.291479i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.86505 | − | 2.65632i | −0.426619 | − | 0.193219i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 16.1501i | − | 1.16858i | −0.811545 | − | 0.584290i | \(-0.801373\pi\) | ||
0.811545 | − | 0.584290i | \(-0.198627\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 2.01309i | − | 0.144905i | −0.997372 | − | 0.0724526i | \(-0.976917\pi\) | ||
0.997372 | − | 0.0724526i | \(-0.0230826\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.677343 | + | 0.946730i | −0.0485056 | + | 0.0677968i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 24.3517i | 1.73499i | 0.497448 | + | 0.867494i | \(0.334271\pi\) | ||||
−0.497448 | + | 0.867494i | \(0.665729\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.55060 | 0.606136 | 0.303068 | − | 0.952969i | \(-0.401989\pi\) | ||||
0.303068 | + | 0.952969i | \(0.401989\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 7.06843i | − | 0.498568i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −8.58506 | + | 18.9555i | −0.602553 | + | 1.33041i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.64067 | − | 5.08860i | 0.254275 | − | 0.355403i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 16.1206 | 1.12046 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 5.28714i | − | 0.365719i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 19.0444i | − | 1.31107i | −0.755164 | − | 0.655536i | \(-0.772443\pi\) | ||
0.755164 | − | 0.655536i | \(-0.227557\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.37035 | −0.0938949 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −17.3519 | − | 12.4145i | −1.18339 | − | 0.846660i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.49492 | + | 3.30071i | −0.101481 | + | 0.224067i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 26.3826i | 1.78277i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.41629 | 0.0952700 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 14.9124i | − | 0.998607i | −0.866427 | − | 0.499304i | \(-0.833589\pi\) | ||
0.866427 | − | 0.499304i | \(-0.166411\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.06833 | − | 8.99465i | −0.204555 | − | 0.599643i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 0.365162i | − | 0.0242366i | −0.999927 | − | 0.0121183i | \(-0.996143\pi\) | ||
0.999927 | − | 0.0121183i | \(-0.00385748\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 3.77634i | − | 0.249548i | −0.992185 | − | 0.124774i | \(-0.960179\pi\) | ||
0.992185 | − | 0.124774i | \(-0.0398206\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.59926 | − | 3.53109i | 0.105223 | − | 0.232329i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 3.46456i | − | 0.226971i | −0.993540 | − | 0.113485i | \(-0.963798\pi\) | ||
0.993540 | − | 0.113485i | \(-0.0362015\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.0497 | + | 14.0466i | −0.655572 | + | 0.916300i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 15.5330 | 1.00898 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.89143i | 0.251716i | 0.992048 | + | 0.125858i | \(0.0401683\pi\) | ||||
−0.992048 | + | 0.125858i | \(0.959832\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 4.65633i | − | 0.299941i | −0.988691 | − | 0.149970i | \(-0.952082\pi\) | ||
0.988691 | − | 0.149970i | \(-0.0479178\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 17.2487i | 1.10650i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.55073 | + | 15.5755i | 0.0990723 | + | 0.995080i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.87864 | −0.119535 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −15.6168 | −0.989676 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.73327 | 0.551239 | 0.275620 | − | 0.961267i | \(-0.411117\pi\) | ||||
0.275620 | + | 0.961267i | \(0.411117\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 5.61317i | − | 0.352897i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −17.3469 | + | 24.2460i | −1.08631 | + | 1.51834i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5.70661 | −0.355968 | −0.177984 | − | 0.984033i | \(-0.556958\pi\) | ||||
−0.177984 | + | 0.984033i | \(0.556958\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −14.6978 | − | 6.65675i | −0.913279 | − | 0.413631i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 14.9492 | 0.925335 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.79832 | 0.604190 | 0.302095 | − | 0.953278i | \(-0.402314\pi\) | ||||
0.302095 | + | 0.953278i | \(0.402314\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 11.0003 | − | 15.3752i | 0.675740 | − | 0.944490i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 22.0819 | 1.35139 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 20.8330i | 1.27021i | 0.772426 | + | 0.635104i | \(0.219043\pi\) | ||||
−0.772426 | + | 0.635104i | \(0.780957\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 13.4035 | 0.814202 | 0.407101 | − | 0.913383i | \(-0.366540\pi\) | ||||
0.407101 | + | 0.913383i | \(0.366540\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.25468 | − | 0.568253i | −0.0759366 | − | 0.0343922i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.13193 | + | 1.06839i | −0.188863 | + | 0.0644263i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 7.77892i | − | 0.467390i | −0.972310 | − | 0.233695i | \(-0.924918\pi\) | ||
0.972310 | − | 0.233695i | \(-0.0750818\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.60311 | 0.155844 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −18.0580 | −1.07725 | −0.538624 | − | 0.842546i | \(-0.681056\pi\) | ||||
−0.538624 | + | 0.842546i | \(0.681056\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 17.6208i | − | 1.04745i | −0.851888 | − | 0.523725i | \(-0.824542\pi\) | ||
0.851888 | − | 0.523725i | \(-0.175458\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 23.0099 | − | 32.1612i | 1.36299 | − | 1.90506i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.74380 | + | 3.05431i | 0.398074 | + | 0.180290i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 19.2715 | 1.13362 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 13.3325i | − | 0.781567i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −19.9862 | −1.16761 | −0.583803 | − | 0.811895i | \(-0.698436\pi\) | ||||
−0.583803 | + | 0.811895i | \(0.698436\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.68960 | − | 1.20883i | −0.0983722 | − | 0.0703810i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.61059 | 0.0934558 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.99449 | −0.115344 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.4150 | − | 22.9960i | 0.600313 | − | 1.32547i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 23.2074 | 1.33323 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.97914 | − | 4.16398i | 0.170585 | − | 0.238429i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 21.1613i | − | 1.20774i | −0.797083 | − | 0.603870i | \(-0.793625\pi\) | ||
0.797083 | − | 0.603870i | \(-0.206375\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 10.6071 | 0.603416 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −24.7737 | −1.40479 | −0.702393 | − | 0.711789i | \(-0.747885\pi\) | ||||
−0.702393 | + | 0.711789i | \(0.747885\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.74418 | −0.268157 | −0.134078 | − | 0.990971i | \(-0.542807\pi\) | ||||
−0.134078 | + | 0.990971i | \(0.542807\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 9.73320 | − | 5.63122i | 0.548404 | − | 0.317283i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0.397922i | 0.0223495i | 0.999938 | + | 0.0111748i | \(0.00355711\pi\) | ||||
−0.999938 | + | 0.0111748i | \(0.996443\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 5.20532i | − | 0.291442i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 7.06843i | 0.394521i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −48.1125 | −2.67705 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.379623 | + | 1.11285i | 0.0210577 | + | 0.0617297i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 7.45829i | − | 0.412444i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −18.6156 | − | 8.43115i | −1.02631 | − | 0.464824i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 4.18036i | − | 0.229773i | −0.993379 | − | 0.114887i | \(-0.963350\pi\) | ||
0.993379 | − | 0.114887i | \(-0.0366505\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 11.5915i | 0.635209i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5.80657 | − | 4.15434i | −0.317247 | − | 0.226976i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 26.3737i | − | 1.43667i | −0.695699 | − | 0.718333i | \(-0.744905\pi\) | ||
0.695699 | − | 0.718333i | \(-0.255095\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 23.7878 | 1.29198 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 0.906401i | − | 0.0490844i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.7203 | + | 5.38440i | −0.956805 | + | 0.290730i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 24.4288 | − | 34.1443i | 1.31520 | − | 1.83827i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.38649 | 0.128114 | 0.0640568 | − | 0.997946i | \(-0.479596\pi\) | ||||
0.0640568 | + | 0.997946i | \(0.479596\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 23.1032i | 1.23669i | 0.785908 | + | 0.618344i | \(0.212196\pi\) | ||||
−0.785908 | + | 0.618344i | \(0.787804\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 0.572279i | − | 0.0305460i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −24.6590 | −1.31246 | −0.656232 | − | 0.754559i | \(-0.727851\pi\) | ||||
−0.656232 | + | 0.754559i | \(0.727851\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.805399 | + | 1.12572i | −0.0427461 | + | 0.0597468i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −32.1326 | − | 14.5531i | −1.70064 | − | 0.770230i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 7.34704i | − | 0.387762i | −0.981025 | − | 0.193881i | \(-0.937892\pi\) | ||
0.981025 | − | 0.193881i | \(-0.0621076\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 44.8191 | 2.35890 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 23.3817i | − | 1.22722i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 21.6728 | + | 15.5059i | 1.13440 | + | 0.811616i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 1.57622i | − | 0.0822782i | −0.999153 | − | 0.0411391i | \(-0.986901\pi\) | ||
0.999153 | − | 0.0411391i | \(-0.0130987\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 5.31851i | − | 0.276870i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 20.3764 | + | 9.22859i | 1.05789 | + | 0.479125i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 32.5286i | − | 1.68427i | −0.539271 | − | 0.842133i | \(-0.681300\pi\) | ||
0.539271 | − | 0.842133i | \(-0.318700\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −23.7009 | − | 7.13140i | −1.22391 | − | 0.368264i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.84957 | −0.0952577 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 36.0655i | 1.85256i | 0.376839 | + | 0.926279i | \(0.377011\pi\) | ||||
−0.376839 | + | 0.926279i | \(0.622989\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 17.5855i | 0.900930i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 18.6692i | − | 0.953951i | −0.878917 | − | 0.476976i | \(-0.841733\pi\) | ||
0.878917 | − | 0.476976i | \(-0.158267\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.96079 | − | 3.38909i | −0.0999309 | − | 0.172724i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −18.1358 | −0.921895 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 20.9929 | 1.06438 | 0.532192 | − | 0.846624i | \(-0.321368\pi\) | ||||
0.532192 | + | 0.846624i | \(0.321368\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −51.0793 | −2.58319 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 32.8113i | 1.65511i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 9.12924 | − | 12.7600i | 0.459342 | − | 0.642027i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −36.1967 | −1.81666 | −0.908329 | − | 0.418256i | \(-0.862641\pi\) | ||||
−0.908329 | + | 0.418256i | \(0.862641\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 42.6224 | + | 19.3040i | 2.13379 | + | 0.966409i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.76155 | 0.487469 | 0.243734 | − | 0.969842i | \(-0.421628\pi\) | ||||
0.243734 | + | 0.969842i | \(0.421628\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.322065 | −0.0160432 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 20.1667 | + | 14.4284i | 1.00209 | + | 0.716953i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.03614 | 0.200064 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 21.8238i | − | 1.07912i | −0.841949 | − | 0.539558i | \(-0.818591\pi\) | ||
0.841949 | − | 0.539558i | \(-0.181409\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −42.0008 | −2.07175 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.01414 | − | 2.23918i | 0.0499027 | − | 0.110183i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.17851 | + | 12.8289i | −0.450555 | + | 0.629746i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 20.9857i | 1.02767i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −32.2899 | −1.57746 | −0.788732 | − | 0.614737i | \(-0.789262\pi\) | ||||
−0.788732 | + | 0.614737i | \(0.789262\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.26869 | 0.402991 | 0.201496 | − | 0.979489i | \(-0.435420\pi\) | ||||
0.201496 | + | 0.979489i | \(0.435420\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 14.6812i | 0.713826i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 9.72223 | + | 28.5003i | 0.471598 | + | 1.38247i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.51842 | + | 2.49933i | 0.267055 | + | 0.120951i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.344545 | 0.0166348 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 36.0982i | 1.73879i | 0.494120 | + | 0.869394i | \(0.335490\pi\) | ||||
−0.494120 | + | 0.869394i | \(0.664510\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −30.9851 | −1.48905 | −0.744524 | − | 0.667595i | \(-0.767324\pi\) | ||||
−0.744524 | + | 0.667595i | \(0.767324\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 22.6538 | − | 31.6634i | 1.08617 | − | 1.51815i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 67.7544 | 3.24113 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12.9148 | −0.616391 | −0.308195 | − | 0.951323i | \(-0.599725\pi\) | ||||
−0.308195 | + | 0.951323i | \(0.599725\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 8.77573 | + | 10.0005i | 0.417892 | + | 0.476216i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −11.7872 | −0.560028 | −0.280014 | − | 0.959996i | \(-0.590339\pi\) | ||||
−0.280014 | + | 0.959996i | \(0.590339\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 12.9782 | − | 18.1398i | 0.615227 | − | 0.859909i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 28.8762i | − | 1.36580i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −0.434095 | −0.0204862 | −0.0102431 | − | 0.999948i | \(-0.503261\pi\) | ||||
−0.0102431 | + | 0.999948i | \(0.503261\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.85190 | −0.0872026 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −33.3575 | −1.56727 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.20422 | + | 0.696713i | −0.0564549 | + | 0.0326624i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 17.4775i | − | 0.817561i | −0.912633 | − | 0.408781i | \(-0.865954\pi\) | ||
0.912633 | − | 0.408781i | \(-0.134046\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 14.6562i | − | 0.684092i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 6.32441i | − | 0.294557i | −0.989095 | − | 0.147279i | \(-0.952949\pi\) | ||
0.989095 | − | 0.147279i | \(-0.0470514\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 26.5240 | 1.23268 | 0.616338 | − | 0.787482i | \(-0.288615\pi\) | ||||
0.616338 | + | 0.787482i | \(0.288615\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.94470 | − | 5.51355i | 0.182931 | − | 0.255685i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 18.6029i | − | 0.860839i | −0.902629 | − | 0.430419i | \(-0.858366\pi\) | ||
0.902629 | − | 0.430419i | \(-0.141634\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.48526 | − | 7.69530i | 0.160934 | − | 0.355336i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 27.8447i | − | 1.28302i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.31488i | 0.290358i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −12.8961 | − | 37.8043i | −0.591714 | − | 1.73458i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 16.0698i | − | 0.735787i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8.79631 | −0.401914 | −0.200957 | − | 0.979600i | \(-0.564405\pi\) | ||||
−0.200957 | + | 0.979600i | \(0.564405\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 1.43413i | − | 0.0653909i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 45.2507 | + | 20.4943i | 2.05898 | + | 0.932525i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −10.9524 | − | 7.83596i | −0.497323 | − | 0.355813i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −35.2570 | −1.59765 | −0.798824 | − | 0.601564i | \(-0.794544\pi\) | ||||
−0.798824 | + | 0.601564i | \(0.794544\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 2.71540i | − | 0.122794i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 38.4114i | 1.73348i | 0.498759 | + | 0.866741i | \(0.333789\pi\) | ||||
−0.498759 | + | 0.866741i | \(0.666211\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −47.3679 | −2.13334 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.63672 | + | 2.28766i | −0.0735649 | + | 0.102823i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.49188 | − | 0.675684i | −0.0669201 | − | 0.0303086i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 20.1510i | − | 0.902084i | −0.892503 | − | 0.451042i | \(-0.851052\pi\) | ||
0.892503 | − | 0.451042i | \(-0.148948\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −9.77875 | −0.436882 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 25.4467i | − | 1.13461i | −0.823507 | − | 0.567306i | \(-0.807986\pi\) | ||
0.823507 | − | 0.567306i | \(-0.192014\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13.6397 | − | 19.0644i | 0.606961 | − | 0.848356i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 28.6564i | 1.27268i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 2.87999i | − | 0.127654i | −0.997961 | − | 0.0638268i | \(-0.979669\pi\) | ||
0.997961 | − | 0.0638268i | \(-0.0203305\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −13.0086 | + | 28.7224i | −0.575465 | + | 1.27060i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 19.4408i | 0.858331i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6.23413 | − | 8.71351i | 0.274709 | − | 0.383963i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.11200 | 0.224825 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 16.5383i | 0.725952i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 33.1526i | − | 1.45244i | −0.687462 | − | 0.726220i | \(-0.741275\pi\) | ||
0.687462 | − | 0.726220i | \(-0.258725\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 3.73506i | − | 0.163323i | −0.996660 | − | 0.0816615i | \(-0.973977\pi\) | ||
0.996660 | − | 0.0816615i | \(-0.0260226\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.82222 | − | 29.1489i | 0.123172 | − | 1.27216i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −8.24816 | −0.359296 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 48.9323 | 2.12749 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.76594 | −0.0766351 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.658023i | 0.0285021i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.80657 | + | 4.15434i | 0.251040 | + | 0.179608i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 27.8185 | 1.20046 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.48218 | − | 3.05570i | 0.149988 | − | 0.131618i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.0946 | 0.476996 | 0.238498 | − | 0.971143i | \(-0.423345\pi\) | ||||
0.238498 | + | 0.971143i | \(0.423345\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −41.4446 | −1.77856 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −6.12683 | − | 4.38347i | −0.262445 | − | 0.187767i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −23.4626 | −1.00319 | −0.501595 | − | 0.865103i | \(-0.667253\pi\) | ||||
−0.501595 | + | 0.865103i | \(0.667253\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 4.35211i | − | 0.185744i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 62.8314 | 2.67671 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 16.9106 | + | 7.65892i | 0.719111 | + | 0.325690i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 24.5515 | + | 17.5655i | 1.04215 | + | 0.745613i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 13.7120i | − | 0.580996i | −0.956876 | − | 0.290498i | \(-0.906179\pi\) | ||
0.956876 | − | 0.290498i | \(-0.0938209\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.24382 | 0.0949036 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.82386 | 0.372544 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 19.4840i | 0.821155i | 0.911826 | + | 0.410577i | \(0.134673\pi\) | ||||
−0.911826 | + | 0.410577i | \(0.865327\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 13.9809 | − | 19.5412i | 0.588180 | − | 0.822105i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −12.1046 | + | 26.7265i | −0.508346 | + | 1.12241i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.64067 | −0.0687804 | −0.0343902 | − | 0.999408i | \(-0.510949\pi\) | ||||
−0.0343902 | + | 0.999408i | \(0.510949\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 11.3282i | − | 0.474069i | −0.971501 | − | 0.237034i | \(-0.923825\pi\) | ||
0.971501 | − | 0.237034i | \(-0.0761754\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −35.7524 | −1.49358 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −13.6913 | − | 40.1355i | −0.570968 | − | 1.67376i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 23.6001 | 0.982483 | 0.491242 | − | 0.871023i | \(-0.336543\pi\) | ||||
0.491242 | + | 0.871023i | \(0.336543\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −4.45648 | −0.185205 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −17.0018 | − | 7.70025i | −0.705355 | − | 0.319460i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.59551 | −0.231742 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.812857 | + | 0.581563i | 0.0336075 | + | 0.0240447i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 4.16287i | − | 0.171820i | −0.996303 | − | 0.0859099i | \(-0.972620\pi\) | ||
0.996303 | − | 0.0859099i | \(-0.0273797\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10.9408 | 0.450808 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 53.9088 | 2.21751 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −11.5914 | −0.476003 | −0.238002 | − | 0.971265i | \(-0.576492\pi\) | ||||
−0.238002 | + | 0.971265i | \(0.576492\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −30.8404 | + | 17.8430i | −1.26433 | + | 0.731490i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 18.9289i | − | 0.774710i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 27.8564i | − | 1.13818i | −0.822275 | − | 0.569090i | \(-0.807296\pi\) | ||
0.822275 | − | 0.569090i | \(-0.192704\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.8809i | 0.484632i | 0.970197 | + | 0.242316i | \(0.0779070\pi\) | ||||
−0.970197 | + | 0.242316i | \(0.922093\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6.06891 | −0.247145 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −19.2076 | − | 13.7422i | −0.780898 | − | 0.558698i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.44568i | 0.180445i | 0.995922 | + | 0.0902224i | \(0.0287578\pi\) | ||||
−0.995922 | + | 0.0902224i | \(0.971242\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 41.9628 | + | 19.0052i | 1.70042 | + | 0.770131i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 1.81641i | − | 0.0734841i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 24.4542i | − | 0.987697i | −0.869548 | − | 0.493848i | \(-0.835590\pi\) | ||
0.869548 | − | 0.493848i | \(-0.164410\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −11.2649 | − | 8.05955i | −0.454246 | − | 0.324993i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 45.9516i | − | 1.84994i | −0.380037 | − | 0.924971i | \(-0.624089\pi\) | ||
0.380037 | − | 0.924971i | \(-0.375911\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.63803 | 0.347192 | 0.173596 | − | 0.984817i | \(-0.444461\pi\) | ||||
0.173596 | + | 0.984817i | \(0.444461\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 20.6396i | 0.828237i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 24.0402 | + | 10.8880i | 0.963152 | + | 0.436218i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19.7881 | + | 15.2785i | −0.791524 | + | 0.611138i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −11.7045 | −0.467431 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 36.7285i | − | 1.46446i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 23.5730i | 0.938426i | 0.883085 | + | 0.469213i | \(0.155462\pi\) | ||||
−0.883085 | + | 0.469213i | \(0.844538\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −42.1597 | −1.67570 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 14.4461 | + | 10.3355i | 0.573276 | + | 0.410153i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.08576 | − | 1.23730i | −0.0430194 | − | 0.0490236i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.17658i | 0.0465446i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −27.3036 | −1.07843 | −0.539214 | − | 0.842169i | \(-0.681279\pi\) | ||||
−0.539214 | + | 0.842169i | \(0.681279\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 17.5703i | − | 0.692904i | −0.938068 | − | 0.346452i | \(-0.887386\pi\) | ||
0.938068 | − | 0.346452i | \(-0.112614\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −27.4826 | + | 38.4128i | −1.08213 | + | 1.51250i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 36.3691i | 1.42982i | 0.699218 | + | 0.714908i | \(0.253532\pi\) | ||||
−0.699218 | + | 0.714908i | \(0.746468\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.614897i | 0.0241368i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.30697 | + | 3.30938i | 0.286383 | + | 0.129705i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 31.1711i | 1.21982i | 0.792471 | + | 0.609910i | \(0.208794\pi\) | ||||
−0.792471 | + | 0.609910i | \(0.791206\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 26.9538 | + | 19.2842i | 1.05317 | + | 0.753497i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 22.6519 | 0.883737 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 28.3559i | − | 1.10459i | −0.833649 | − | 0.552295i | \(-0.813752\pi\) | ||
0.833649 | − | 0.552295i | \(-0.186248\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 22.4537i | − | 0.873346i | −0.899620 | − | 0.436673i | \(-0.856157\pi\) | ||
0.899620 | − | 0.436673i | \(-0.143843\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 3.13532i | − | 0.121766i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 40.9084 | − | 23.6679i | 1.58636 | − | 0.917801i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 66.7058 | 2.58286 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −33.0124 | −1.27633 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.51540 | −0.0585015 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.02934i | 0.348056i | 0.984741 | + | 0.174028i | \(0.0556783\pi\) | ||||
−0.984741 | + | 0.174028i | \(0.944322\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 11.5161 | − | 3.92845i | 0.443254 | − | 0.151206i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.14690 | 0.0825120 | 0.0412560 | − | 0.999149i | \(-0.486864\pi\) | ||||
0.0412560 | + | 0.999149i | \(0.486864\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.57392 | − | 14.5150i | 0.252284 | − | 0.557033i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.808380 | −0.0309772 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 35.6440 | 1.36388 | 0.681939 | − | 0.731409i | \(-0.261137\pi\) | ||||
0.681939 | + | 0.731409i | \(0.261137\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −24.6852 | + | 34.5028i | −0.943174 | + | 1.31828i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −8.35991 | −0.318950 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.98821i | 0.0757449i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.87253 | 0.185360 | 0.0926800 | − | 0.995696i | \(-0.470457\pi\) | ||||
0.0926800 | + | 0.995696i | \(0.470457\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3.03178 | − | 1.37311i | −0.115168 | − | 0.0521602i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 17.2393 | + | 12.3340i | 0.653925 | + | 0.467855i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 16.8521i | 0.638319i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −7.66969 | −0.290094 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 29.9296 | 1.13043 | 0.565213 | − | 0.824945i | \(-0.308794\pi\) | ||||
0.565213 | + | 0.824945i | \(0.308794\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 48.7187i | 1.83746i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 31.0958 | + | 22.2476i | 1.17113 | + | 0.837895i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 25.2656 | + | 11.4430i | 0.950211 | + | 0.430357i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 26.7899 | 1.00611 | 0.503057 | − | 0.864253i | \(-0.332208\pi\) | ||||
0.503057 | + | 0.864253i | \(0.332208\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 13.3365i | − | 0.500160i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 11.6155 | 0.435003 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.202500 | − | 0.283036i | 0.00757307 | − | 0.0105850i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 8.61468 | 0.321721 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −39.7507 | −1.48245 | −0.741225 | − | 0.671256i | \(-0.765755\pi\) | ||||
−0.741225 | + | 0.671256i | \(0.765755\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11.5478 | + | 5.23008i | 0.430063 | + | 0.194778i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −10.3080 | −0.383358 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −12.6965 | − | 37.2192i | −0.471537 | − | 1.38229i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16.8141i | 0.623599i | 0.950148 | + | 0.311799i | \(0.100932\pi\) | ||||
−0.950148 | + | 0.311799i | \(0.899068\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 4.91609 | 0.182077 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 57.4648 | 2.12541 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 13.5587 | 0.500803 | 0.250401 | − | 0.968142i | \(-0.419437\pi\) | ||||
0.250401 | + | 0.968142i | \(0.419437\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 34.4803 | − | 3.43293i | 1.27183 | − | 0.126626i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.11319i | 0.0778404i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 29.5016i | − | 1.08523i | −0.839980 | − | 0.542617i | \(-0.817433\pi\) | ||
0.839980 | − | 0.542617i | \(-0.182567\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.15886i | 0.152780i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 31.3403 | 1.14976 | 0.574882 | − | 0.818237i | \(-0.305048\pi\) | ||||
0.574882 | + | 0.818237i | \(0.305048\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −23.7212 | − | 16.9715i | −0.869078 | − | 0.621787i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 13.4085i | 0.490592i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.48526 | + | 7.69530i | −0.127349 | + | 0.281180i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 49.3249i | 1.79989i | 0.436002 | + | 0.899946i | \(0.356394\pi\) | ||||
−0.436002 | + | 0.899946i | \(0.643606\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 19.3333i | − | 0.704546i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −19.6053 | + | 27.4025i | −0.713508 | + | 0.997279i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 25.4706i | − | 0.925743i | −0.886425 | − | 0.462872i | \(-0.846819\pi\) | ||
0.886425 | − | 0.462872i | \(-0.153181\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −12.4262 | −0.451042 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 39.7349i | − | 1.44039i | −0.693772 | − | 0.720194i | \(-0.744053\pi\) | ||
0.693772 | − | 0.720194i | \(-0.255947\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.67749 | − | 8.11974i | 0.133134 | − | 0.293954i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 20.8175 | + | 14.8940i | 0.752657 | + | 0.538492i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.218487 | 0.00788912 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 48.0580i | − | 1.73302i | −0.499163 | − | 0.866508i | \(-0.666359\pi\) | ||
0.499163 | − | 0.866508i | \(-0.333641\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 12.6330i | 0.454968i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2.33155 | −0.0838599 | −0.0419300 | − | 0.999121i | \(-0.513351\pi\) | ||||
−0.0419300 | + | 0.999121i | \(0.513351\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.21084 | − | 6.48098i | −0.0794158 | − | 0.232804i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −14.7364 | + | 32.5374i | −0.528667 | + | 1.16727i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 22.3536i | − | 0.800900i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.409683 | 0.0146596 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 19.1399i | 0.684004i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −22.8739 | − | 16.3652i | −0.816403 | − | 0.584100i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 17.9954i | − | 0.641467i | −0.947170 | − | 0.320733i | \(-0.896071\pi\) | ||
0.947170 | − | 0.320733i | \(-0.103929\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 21.6911i | − | 0.772224i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 25.8975 | + | 11.7292i | 0.920809 | + | 0.417041i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.538458i | 0.0191212i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −34.0369 | − | 24.3519i | −1.20716 | − | 0.863673i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 25.2255 | 0.893533 | 0.446767 | − | 0.894650i | \(-0.352575\pi\) | ||||
0.446767 | + | 0.894650i | \(0.352575\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 46.5187i | − | 1.64571i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 18.9594i | − | 0.669896i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 7.88739i | − | 0.278340i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 43.4310 | − | 25.1273i | 1.53074 | − | 0.885622i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 46.1191 | 1.62347 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −32.3648 | −1.13789 | −0.568943 | − | 0.822377i | \(-0.692648\pi\) | ||||
−0.568943 | + | 0.822377i | \(0.692648\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 22.1516 | 0.777847 | 0.388924 | − | 0.921270i | \(-0.372847\pi\) | ||||
0.388924 | + | 0.921270i | \(0.372847\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 29.6720i | − | 1.04064i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.23064 | − | 1.59593i | −0.0781360 | − | 0.0559028i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −76.2244 | −2.66676 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.487899 | + | 1.07726i | −0.0170486 | + | 0.0376425i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −32.6307 | −1.13882 | −0.569409 | − | 0.822054i | \(-0.692828\pi\) | ||||
−0.569409 | + | 0.822054i | \(0.692828\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −45.3224 | −1.57984 | −0.789920 | − | 0.613210i | \(-0.789878\pi\) | ||||
−0.789920 | + | 0.613210i | \(0.789878\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.36515 | + | 6.93333i | 0.0823441 | + | 0.241388i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −5.55080 | −0.193020 | −0.0965102 | − | 0.995332i | \(-0.530768\pi\) | ||||
−0.0965102 | + | 0.995332i | \(0.530768\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 28.0542i | 0.974363i | 0.873301 | + | 0.487182i | \(0.161975\pi\) | ||||
−0.873301 | + | 0.487182i | \(0.838025\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −17.2206 | −0.597378 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −27.8066 | − | 31.6875i | −0.963441 | − | 1.09791i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.74728 | + | 8.03304i | −0.198893 | + | 0.277995i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.33283i | 0.115199i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −20.1929 | −0.697138 | −0.348569 | − | 0.937283i | \(-0.613332\pi\) | ||||
−0.348569 | + | 0.937283i | \(0.613332\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 32.8589 | 1.13307 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 39.9759i | 1.37684i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 23.5407 | + | 16.8423i | 0.809824 | + | 0.579393i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 11.5289 | − | 25.4553i | 0.396137 | − | 0.874655i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −39.0082 | −1.33876 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 51.7229i | 1.77304i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 41.4211 | 1.41823 | 0.709116 | − | 0.705092i | \(-0.249094\pi\) | ||||
0.709116 | + | 0.705092i | \(0.249094\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −27.6134 | − | 19.7562i | −0.944359 | − | 0.675647i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 51.7709 | 1.76846 | 0.884229 | − | 0.467053i | \(-0.154684\pi\) | ||||
0.884229 | + | 0.467053i | \(0.154684\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 15.6976 | 0.535596 | 0.267798 | − | 0.963475i | \(-0.413704\pi\) | ||||
0.267798 | + | 0.963475i | \(0.413704\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6.76151 | − | 14.9291i | 0.230432 | − | 0.508783i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 5.91090 | 0.201210 | 0.100605 | − | 0.994926i | \(-0.467922\pi\) | ||||
0.100605 | + | 0.994926i | \(0.467922\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 13.5859 | + | 9.72011i | 0.461935 | + | 0.330494i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 42.6624i | − | 1.44889i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.64378 | −0.157529 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.750866 | 0.0254421 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −11.4472 | −0.387430 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −22.2866 | − | 19.4502i | −0.753423 | − | 0.657536i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 37.5650i | 1.26848i | 0.773136 | + | 0.634240i | \(0.218687\pi\) | ||||
−0.773136 | + | 0.634240i | \(0.781313\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 44.2446i | 1.49233i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 41.3815i | 1.39418i | 0.716984 | + | 0.697089i | \(0.245522\pi\) | ||||
−0.716984 | + | 0.697089i | \(0.754478\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −13.8550 | −0.466258 | −0.233129 | − | 0.972446i | \(-0.574897\pi\) | ||||
−0.233129 | + | 0.972446i | \(0.574897\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.67606 | + | 3.74036i | −0.0899548 | + | 0.125731i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 1.16763i | − | 0.0392053i | −0.999808 | − | 0.0196027i | \(-0.993760\pi\) | ||
0.999808 | − | 0.0196027i | \(-0.00624012\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.67093 | + | 19.1451i | −0.290814 | + | 0.642105i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 7.33930i | − | 0.245876i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 61.7049i | 2.06488i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 16.3498 | − | 22.8523i | 0.546515 | − | 0.763870i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.41531i | 0.147423i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 10.7715 | 0.359249 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 50.9186i | 1.69634i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −50.9075 | − | 23.0564i | −1.69410 | − | 0.767268i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −24.3583 | + | 34.0459i | −0.809698 | + | 1.13172i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −39.8376 | −1.32278 | −0.661392 | − | 0.750040i | \(-0.730034\pi\) | ||||
−0.661392 | + | 0.750040i | \(0.730034\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 19.9258i | − | 0.660896i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 5.38823i | − | 0.178520i | −0.996008 | − | 0.0892600i | \(-0.971550\pi\) | ||
0.996008 | − | 0.0892600i | \(-0.0284502\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.66884 | 0.154516 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −9.21804 | − | 6.59510i | −0.304739 | − | 0.218027i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −16.1784 | + | 35.7212i | −0.534257 | + | 1.17962i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 12.9544i | 0.427326i | 0.976907 | + | 0.213663i | \(0.0685395\pi\) | ||||
−0.976907 | + | 0.213663i | \(0.931461\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −46.8460 | −1.54363 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 0.145570i | − | 0.00479149i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 28.8594 | − | 9.84473i | 0.948890 | − | 0.323693i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 9.10719i | − | 0.299119i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 40.1582i | 1.31755i | 0.752341 | + | 0.658774i | \(0.228924\pi\) | ||||
−0.752341 | + | 0.658774i | \(0.771076\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 36.8842 | + | 42.0320i | 1.20883 | + | 1.37754i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 54.8429i | 1.79548i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5.18607 | − | 7.24862i | 0.169602 | − | 0.237055i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −6.49291 | −0.212114 | −0.106057 | − | 0.994360i | \(-0.533823\pi\) | ||||
−0.106057 | + | 0.994360i | \(0.533823\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 10.5025i | 0.342735i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 37.3828i | 1.21864i | 0.792923 | + | 0.609322i | \(0.208558\pi\) | ||||
−0.792923 | + | 0.609322i | \(0.791442\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 23.7320i | − | 0.772819i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 7.20979 | + | 12.4617i | 0.234534 | + | 0.405378i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −14.7989 | −0.480901 | −0.240450 | − | 0.970661i | \(-0.577295\pi\) | ||||
−0.240450 | + | 0.970661i | \(0.577295\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.80257 | −0.0909754 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0.880903 | 0.0285653 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 18.4435i | 0.597443i | 0.954340 | + | 0.298722i | \(0.0965602\pi\) | ||||
−0.954340 | + | 0.298722i | \(0.903440\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −21.0128 | + | 29.3699i | −0.679960 | + | 0.950387i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −11.5233 | −0.372496 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −45.7257 | − | 20.7095i | −1.47656 | − | 0.668745i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.1244 | −0.939496 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.06891 | 0.195568 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.61922 | + | 3.66091i | −0.0843157 | + | 0.117849i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 16.7295 | 0.537983 | 0.268991 | − | 0.963143i | \(-0.413310\pi\) | ||||
0.268991 | + | 0.963143i | \(0.413310\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 106.509i | 3.42157i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −42.8284 | −1.37443 | −0.687214 | − | 0.726455i | \(-0.741166\pi\) | ||||
−0.687214 | + | 0.726455i | \(0.741166\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −10.3475 | + | 22.8469i | −0.331726 | + | 0.732437i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.46357 | − | 0.840394i | 0.0788975 | − | 0.0269141i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 11.9457i | 0.382177i | 0.981573 | + | 0.191088i | \(0.0612017\pi\) | ||||
−0.981573 | + | 0.191088i | \(0.938798\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.60164 | −0.210989 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.40364 | −0.204453 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 19.4014i | 0.618809i | 0.950930 | + | 0.309405i | \(0.100130\pi\) | ||||
−0.950930 | + | 0.309405i | \(0.899870\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 31.6839 | − | 44.2850i | 1.00953 | − | 1.41104i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −18.6645 | + | 41.2105i | −0.594098 | + | 1.31174i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −80.9247 | −2.57326 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 26.6231i | − | 0.845712i | −0.906197 | − | 0.422856i | \(-0.861028\pi\) | ||
0.906197 | − | 0.422856i | \(-0.138972\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −9.25430 | −0.293676 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −15.5497 | − | 11.1251i | −0.492960 | − | 0.352691i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 22.6223 | 0.716454 | 0.358227 | − | 0.933635i | \(-0.383381\pi\) | ||||
0.358227 | + | 0.933635i | \(0.383381\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −14.8409 | −0.469544 |
(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 | 2240.2.e.g.2239.1 | 48 | ||
4.3 | odd | 2 | inner | 2240.2.e.g.2239.26 | 48 | ||
5.4 | even | 2 | inner | 2240.2.e.g.2239.28 | 48 | ||
7.6 | odd | 2 | inner | 2240.2.e.g.2239.46 | 48 | ||
8.3 | odd | 2 | 1120.2.e.a.1119.45 | yes | 48 | ||
8.5 | even | 2 | 1120.2.e.a.1119.28 | yes | 48 | ||
20.19 | odd | 2 | inner | 2240.2.e.g.2239.45 | 48 | ||
28.27 | even | 2 | inner | 2240.2.e.g.2239.27 | 48 | ||
35.34 | odd | 2 | inner | 2240.2.e.g.2239.25 | 48 | ||
40.19 | odd | 2 | 1120.2.e.a.1119.26 | yes | 48 | ||
40.29 | even | 2 | 1120.2.e.a.1119.1 | ✓ | 48 | ||
56.13 | odd | 2 | 1120.2.e.a.1119.25 | yes | 48 | ||
56.27 | even | 2 | 1120.2.e.a.1119.2 | yes | 48 | ||
140.139 | even | 2 | inner | 2240.2.e.g.2239.2 | 48 | ||
280.69 | odd | 2 | 1120.2.e.a.1119.46 | yes | 48 | ||
280.139 | even | 2 | 1120.2.e.a.1119.27 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1120.2.e.a.1119.1 | ✓ | 48 | 40.29 | even | 2 | ||
1120.2.e.a.1119.2 | yes | 48 | 56.27 | even | 2 | ||
1120.2.e.a.1119.25 | yes | 48 | 56.13 | odd | 2 | ||
1120.2.e.a.1119.26 | yes | 48 | 40.19 | odd | 2 | ||
1120.2.e.a.1119.27 | yes | 48 | 280.139 | even | 2 | ||
1120.2.e.a.1119.28 | yes | 48 | 8.5 | even | 2 | ||
1120.2.e.a.1119.45 | yes | 48 | 8.3 | odd | 2 | ||
1120.2.e.a.1119.46 | yes | 48 | 280.69 | odd | 2 | ||
2240.2.e.g.2239.1 | 48 | 1.1 | even | 1 | trivial | ||
2240.2.e.g.2239.2 | 48 | 140.139 | even | 2 | inner | ||
2240.2.e.g.2239.25 | 48 | 35.34 | odd | 2 | inner | ||
2240.2.e.g.2239.26 | 48 | 4.3 | odd | 2 | inner | ||
2240.2.e.g.2239.27 | 48 | 28.27 | even | 2 | inner | ||
2240.2.e.g.2239.28 | 48 | 5.4 | even | 2 | inner | ||
2240.2.e.g.2239.45 | 48 | 20.19 | odd | 2 | inner | ||
2240.2.e.g.2239.46 | 48 | 7.6 | odd | 2 | inner |