Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3024,2,Mod(2305,3024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3024, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3024.2305");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3024.q (of order \(3\), 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: | \(24.1467615712\) |
Analytic rank: | \(0\) |
Dimension: | \(22\) |
Relative dimension: | \(11\) over \(\Q(\zeta_{3})\) |
Twist minimal: | no (minimal twist has level 504) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 2305.4 | ||
Character | \(\chi\) | \(=\) | 3024.2305 |
Dual form | 3024.2.q.l.2881.4 |
$q$-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 \(\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1135\) | \(2593\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | ||||||||
\(5\) | −0.891774 | − | 1.54460i | −0.398814 | − | 0.690765i | 0.594766 | − | 0.803899i | \(-0.297245\pi\) |
−0.993580 | + | 0.113133i | \(0.963911\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.54386 | − | 0.727153i | 0.961491 | − | 0.274838i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.80706 | − | 4.86196i | 0.846359 | − | 1.46594i | −0.0380759 | − | 0.999275i | \(-0.512123\pi\) |
0.884435 | − | 0.466663i | \(-0.154544\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.14009 | − | 5.43879i | 0.870903 | − | 1.50845i | 0.00983976 | − | 0.999952i | \(-0.496868\pi\) |
0.861064 | − | 0.508497i | \(-0.169799\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.646279 | − | 1.11939i | −0.156746 | − | 0.271491i | 0.776948 | − | 0.629565i | \(-0.216767\pi\) |
−0.933693 | + | 0.358074i | \(0.883434\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.559062 | + | 0.968324i | −0.128258 | + | 0.222149i | −0.923002 | − | 0.384796i | \(-0.874272\pi\) |
0.794744 | + | 0.606945i | \(0.207605\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.80857 | − | 6.59664i | −0.794142 | − | 1.37549i | −0.923382 | − | 0.383882i | \(-0.874587\pi\) |
0.129240 | − | 0.991613i | \(-0.458746\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.909478 | − | 1.57526i | 0.181896 | − | 0.315052i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.57496 | + | 2.72791i | 0.292462 | + | 0.506560i | 0.974391 | − | 0.224859i | \(-0.0721921\pi\) |
−0.681929 | + | 0.731418i | \(0.738859\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.00311 | −0.180163 | −0.0900816 | − | 0.995934i | \(-0.528713\pi\) | ||||
−0.0900816 | + | 0.995934i | \(0.528713\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.39171 | − | 3.28079i | −0.573304 | − | 0.554555i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.96542 | + | 10.3324i | −0.980708 | + | 1.69864i | −0.321067 | + | 0.947057i | \(0.604041\pi\) |
−0.659642 | + | 0.751580i | \(0.729292\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.14160 | + | 7.17347i | −0.646810 | + | 1.12031i | 0.337071 | + | 0.941479i | \(0.390564\pi\) |
−0.983880 | + | 0.178828i | \(0.942769\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.34804 | − | 4.06693i | −0.358073 | − | 0.620200i | 0.629566 | − | 0.776947i | \(-0.283233\pi\) |
−0.987639 | + | 0.156747i | \(0.949899\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.94400 | −0.283562 | −0.141781 | − | 0.989898i | \(-0.545283\pi\) | ||||
−0.141781 | + | 0.989898i | \(0.545283\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.94250 | − | 3.69956i | 0.848928 | − | 0.528508i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.45992 | + | 7.72481i | 0.612617 | + | 1.06108i | 0.990798 | + | 0.135352i | \(0.0432166\pi\) |
−0.378180 | + | 0.925732i | \(0.623450\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −10.0130 | −1.35016 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.38679 | 1.09187 | 0.545933 | − | 0.837829i | \(-0.316175\pi\) | ||||
0.545933 | + | 0.837829i | \(0.316175\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.82576 | 0.617875 | 0.308937 | − | 0.951082i | \(-0.400027\pi\) | ||||
0.308937 | + | 0.951082i | \(0.400027\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −11.2010 | −1.38931 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.55628 | 0.312299 | 0.156150 | − | 0.987733i | \(-0.450092\pi\) | ||||
0.156150 | + | 0.987733i | \(0.450092\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.86178 | −1.05170 | −0.525850 | − | 0.850577i | \(-0.676253\pi\) | ||||
−0.525850 | + | 0.850577i | \(0.676253\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.67598 | + | 9.83109i | 0.664323 | + | 1.15064i | 0.979468 | + | 0.201598i | \(0.0646135\pi\) |
−0.315145 | + | 0.949044i | \(0.602053\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.60538 | − | 14.4093i | 0.410871 | − | 1.64210i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −13.4577 | −1.51410 | −0.757052 | − | 0.653354i | \(-0.773361\pi\) | ||||
−0.757052 | + | 0.653354i | \(0.773361\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.60203 | − | 2.77479i | −0.175845 | − | 0.304573i | 0.764608 | − | 0.644495i | \(-0.222933\pi\) |
−0.940453 | + | 0.339922i | \(0.889599\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.15267 | + | 1.99648i | −0.125025 | + | 0.216549i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.404646 | − | 0.700867i | 0.0428924 | − | 0.0742917i | −0.843782 | − | 0.536686i | \(-0.819676\pi\) |
0.886675 | + | 0.462394i | \(0.153009\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.03312 | − | 16.1189i | 0.422786 | − | 1.68972i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.99423 | 0.204604 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.10781 | + | 1.91879i | 0.112481 | + | 0.194823i | 0.916770 | − | 0.399415i | \(-0.130787\pi\) |
−0.804289 | + | 0.594238i | \(0.797454\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.70134 | − | 8.14296i | 0.467801 | − | 0.810254i | −0.531522 | − | 0.847044i | \(-0.678380\pi\) |
0.999323 | + | 0.0367899i | \(0.0117132\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.76349 | − | 3.05446i | −0.173762 | − | 0.300964i | 0.765970 | − | 0.642876i | \(-0.222259\pi\) |
−0.939732 | + | 0.341912i | \(0.888926\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.39276 | + | 5.87644i | −0.327991 | + | 0.568097i | −0.982113 | − | 0.188292i | \(-0.939705\pi\) |
0.654122 | + | 0.756389i | \(0.273038\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.681848 | + | 1.18099i | 0.0653092 | + | 0.113119i | 0.896831 | − | 0.442373i | \(-0.145863\pi\) |
−0.831522 | + | 0.555492i | \(0.812530\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.76458 | − | 4.78840i | 0.260070 | − | 0.450455i | −0.706190 | − | 0.708022i | \(-0.749588\pi\) |
0.966260 | + | 0.257568i | \(0.0829210\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.79277 | + | 11.7654i | −0.633429 | + | 1.09713i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.45801 | − | 2.37763i | −0.225326 | − | 0.217957i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.2591 | − | 17.7693i | −0.932649 | − | 1.61539i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −12.1619 | −1.08780 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.8209 | 1.13767 | 0.568837 | − | 0.822450i | \(-0.307394\pi\) | ||||
0.568837 | + | 0.822450i | \(0.307394\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.90955 | + | 5.03948i | 0.254208 | + | 0.440302i | 0.964680 | − | 0.263424i | \(-0.0848518\pi\) |
−0.710472 | + | 0.703726i | \(0.751518\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.718059 | + | 2.86981i | −0.0622636 | + | 0.248844i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −7.67046 | + | 13.2856i | −0.655332 | + | 1.13507i | 0.326479 | + | 0.945205i | \(0.394138\pi\) |
−0.981810 | + | 0.189864i | \(0.939195\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.05803 | − | 10.4928i | 0.513835 | − | 0.889988i | −0.486036 | − | 0.873939i | \(-0.661558\pi\) |
0.999871 | − | 0.0160496i | \(-0.00510897\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −17.6288 | − | 30.5340i | −1.47419 | − | 2.55338i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.80901 | − | 4.86535i | 0.233276 | − | 0.404046i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.36849 | + | 4.10235i | 0.194035 | + | 0.336078i | 0.946584 | − | 0.322458i | \(-0.104509\pi\) |
−0.752549 | + | 0.658536i | \(0.771176\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.1845 | − | 21.1041i | 0.991559 | − | 1.71743i | 0.383493 | − | 0.923544i | \(-0.374721\pi\) |
0.608066 | − | 0.793887i | \(-0.291946\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.894545 | + | 1.54940i | 0.0718516 | + | 0.124451i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.30458 | −0.503160 | −0.251580 | − | 0.967836i | \(-0.580950\pi\) | ||||
−0.251580 | + | 0.967836i | \(0.580950\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −14.4853 | − | 14.0116i | −1.14160 | − | 1.10426i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.350678 | + | 0.607392i | −0.0274672 | + | 0.0475746i | −0.879432 | − | 0.476024i | \(-0.842078\pi\) |
0.851965 | + | 0.523599i | \(0.175411\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.53822 | − | 6.12839i | 0.273796 | − | 0.474229i | −0.696035 | − | 0.718008i | \(-0.745054\pi\) |
0.969831 | + | 0.243780i | \(0.0783873\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −13.2203 | − | 22.8982i | −1.01695 | − | 1.76140i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.63534 | −0.504476 | −0.252238 | − | 0.967665i | \(-0.581167\pi\) | ||||
−0.252238 | + | 0.967665i | \(0.581167\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.16813 | − | 4.66858i | 0.0883025 | − | 0.352912i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.63527 | + | 9.76057i | 0.421200 | + | 0.729539i | 0.996057 | − | 0.0887145i | \(-0.0282759\pi\) |
−0.574858 | + | 0.818253i | \(0.694943\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 21.1800 | 1.57430 | 0.787149 | − | 0.616762i | \(-0.211556\pi\) | ||||
0.787149 | + | 0.616762i | \(0.211556\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 21.2792 | 1.56448 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.25657 | −0.530653 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.44088 | −0.683118 | −0.341559 | − | 0.939860i | \(-0.610955\pi\) | ||||
−0.341559 | + | 0.939860i | \(0.610955\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.28042 | −0.452074 | −0.226037 | − | 0.974119i | \(-0.572577\pi\) | ||||
−0.226037 | + | 0.974119i | \(0.572577\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −15.4780 | −1.10276 | −0.551382 | − | 0.834253i | \(-0.685899\pi\) | ||||
−0.551382 | + | 0.834253i | \(0.685899\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.19477 | − | 3.80145i | −0.155583 | − | 0.269478i | 0.777688 | − | 0.628650i | \(-0.216392\pi\) |
−0.933271 | + | 0.359173i | \(0.883059\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.99009 | + | 5.79419i | 0.420422 | + | 0.406673i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 14.7735 | 1.03183 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.13864 | + | 5.43628i | 0.217104 | + | 0.376035i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.93101 | + | 13.7369i | −0.545993 | + | 0.945688i | 0.452550 | + | 0.891739i | \(0.350514\pi\) |
−0.998544 | + | 0.0539495i | \(0.982819\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.18784 | + | 7.25356i | −0.285609 | + | 0.494689i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.55177 | + | 0.729412i | −0.173225 | + | 0.0495157i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.11749 | −0.546041 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.99253 | − | 12.1114i | −0.468254 | − | 0.811040i | 0.531088 | − | 0.847317i | \(-0.321784\pi\) |
−0.999342 | + | 0.0362769i | \(0.988450\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.38364 | + | 9.32474i | −0.357325 | + | 0.618905i | −0.987513 | − | 0.157538i | \(-0.949644\pi\) |
0.630188 | + | 0.776443i | \(0.282978\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.805015 | + | 1.39433i | 0.0531969 | + | 0.0921397i | 0.891398 | − | 0.453222i | \(-0.149726\pi\) |
−0.838201 | + | 0.545362i | \(0.816392\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.510606 | − | 0.884395i | 0.0334509 | − | 0.0579387i | −0.848815 | − | 0.528690i | \(-0.822684\pi\) |
0.882266 | + | 0.470751i | \(0.156017\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.73361 | + | 3.00270i | 0.113088 | + | 0.195875i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.96428 | + | 12.0625i | −0.450482 | + | 0.780258i | −0.998416 | − | 0.0562640i | \(-0.982081\pi\) |
0.547934 | + | 0.836522i | \(0.315414\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.28788 | − | 12.6230i | 0.469454 | − | 0.813118i | −0.529936 | − | 0.848037i | \(-0.677784\pi\) |
0.999390 | + | 0.0349197i | \(0.0111175\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −11.0137 | − | 5.87960i | −0.703639 | − | 0.375634i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.51101 | + | 6.08124i | 0.223400 | + | 0.386940i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 18.0287 | 1.13796 | 0.568981 | − | 0.822350i | \(-0.307338\pi\) | ||||
0.568981 | + | 0.822350i | \(0.307338\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −42.7635 | −2.68852 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 13.4633 | + | 23.3191i | 0.839818 | + | 1.45461i | 0.890047 | + | 0.455869i | \(0.150672\pi\) |
−0.0502291 | + | 0.998738i | \(0.515995\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.66198 | + | 30.6220i | −0.476092 | + | 1.90276i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −0.769419 | + | 1.33267i | −0.0474444 | + | 0.0821761i | −0.888772 | − | 0.458349i | \(-0.848441\pi\) |
0.841328 | + | 0.540525i | \(0.181774\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.95448 | − | 13.7776i | 0.488640 | − | 0.846349i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.26461 | − | 5.65446i | −0.199047 | − | 0.344759i | 0.749173 | − | 0.662374i | \(-0.230451\pi\) |
−0.948220 | + | 0.317616i | \(0.897118\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.64494 | − | 9.77733i | 0.342906 | − | 0.593930i | −0.642065 | − | 0.766650i | \(-0.721922\pi\) |
0.984971 | + | 0.172720i | \(0.0552555\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.10591 | − | 8.84370i | −0.307898 | − | 0.533295i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.905938 | + | 1.56913i | −0.0544325 | + | 0.0942799i | −0.891958 | − | 0.452119i | \(-0.850668\pi\) |
0.837525 | + | 0.546399i | \(0.184002\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.98798 | + | 5.17533i | 0.178248 | + | 0.308734i | 0.941280 | − | 0.337626i | \(-0.109624\pi\) |
−0.763033 | + | 0.646360i | \(0.776290\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 19.9952 | 1.18859 | 0.594295 | − | 0.804247i | \(-0.297431\pi\) | ||||
0.594295 | + | 0.804247i | \(0.297431\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.31947 | + | 21.2599i | −0.313998 | + | 1.25493i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.66465 | − | 13.2756i | 0.450862 | − | 0.780915i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.95166 | − | 8.57652i | 0.289279 | − | 0.501046i | −0.684359 | − | 0.729145i | \(-0.739918\pi\) |
0.973638 | + | 0.228099i | \(0.0732511\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.47912 | − | 12.9542i | −0.435451 | − | 0.754224i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −47.8370 | −2.76649 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.93038 | − | 8.63833i | −0.514738 | − | 0.497905i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.30348 | − | 7.45385i | −0.246417 | − | 0.426806i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 23.7122 | 1.35332 | 0.676662 | − | 0.736293i | \(-0.263426\pi\) | ||||
0.676662 | + | 0.736293i | \(0.263426\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 20.3449 | 1.15365 | 0.576826 | − | 0.816867i | \(-0.304291\pi\) | ||||
0.576826 | + | 0.816867i | \(0.304291\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.71871 | 0.549334 | 0.274667 | − | 0.961539i | \(-0.411432\pi\) | ||||
0.274667 | + | 0.961539i | \(0.411432\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.32838 | 0.186941 | 0.0934703 | − | 0.995622i | \(-0.470204\pi\) | ||||
0.0934703 | + | 0.995622i | \(0.470204\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 17.6840 | 0.990113 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.44524 | 0.0804153 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.71168 | − | 9.89292i | −0.316827 | − | 0.548760i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.94528 | + | 1.41359i | −0.272642 | + | 0.0779335i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.43469 | 0.0788578 | 0.0394289 | − | 0.999222i | \(-0.487446\pi\) | ||||
0.0394289 | + | 0.999222i | \(0.487446\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.27962 | − | 3.94843i | −0.124549 | − | 0.215726i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.00257316 | − | 0.00445685i | 0.000140169 | − | 0.000242780i | −0.865955 | − | 0.500121i | \(-0.833289\pi\) |
0.866095 | + | 0.499879i | \(0.166622\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.81578 | + | 4.87707i | −0.152483 | + | 0.264108i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 12.4268 | − | 13.7323i | 0.670982 | − | 0.741473i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 23.1072 | 1.24046 | 0.620229 | − | 0.784421i | \(-0.287040\pi\) | ||||
0.620229 | + | 0.784421i | \(0.287040\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.09723 | + | 10.5607i | 0.326377 | + | 0.565302i | 0.981790 | − | 0.189969i | \(-0.0608387\pi\) |
−0.655413 | + | 0.755271i | \(0.727505\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12.3536 | − | 21.3970i | 0.657515 | − | 1.13885i | −0.323742 | − | 0.946145i | \(-0.604941\pi\) |
0.981257 | − | 0.192704i | \(-0.0617257\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.90271 | + | 13.6879i | 0.419432 | + | 0.726478i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8.20362 | − | 14.2091i | 0.432970 | − | 0.749927i | −0.564157 | − | 0.825667i | \(-0.690799\pi\) |
0.997128 | + | 0.0757407i | \(0.0241321\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.87490 | + | 15.3718i | 0.467100 | + | 0.809041i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10.1234 | − | 17.5342i | 0.529882 | − | 0.917783i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.90900 | + | 5.03854i | −0.151849 | + | 0.263010i | −0.931907 | − | 0.362697i | \(-0.881856\pi\) |
0.780058 | + | 0.625707i | \(0.215189\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 16.9626 | + | 16.4078i | 0.880652 | + | 0.851852i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.42483 | − | 7.66403i | −0.229109 | − | 0.396829i | 0.728435 | − | 0.685115i | \(-0.240248\pi\) |
−0.957544 | + | 0.288286i | \(0.906915\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 19.7820 | 1.01883 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −17.3300 | −0.890181 | −0.445091 | − | 0.895486i | \(-0.646829\pi\) | ||||
−0.445091 | + | 0.895486i | \(0.646829\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.54545 | − | 6.14090i | −0.181164 | − | 0.313785i | 0.761113 | − | 0.648619i | \(-0.224653\pi\) |
−0.942277 | + | 0.334834i | \(0.891320\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −25.4718 | + | 7.28101i | −1.29816 | + | 0.371075i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.32120 | − | 5.75249i | 0.168392 | − | 0.291663i | −0.769463 | − | 0.638691i | \(-0.779476\pi\) |
0.937854 | + | 0.347029i | \(0.112809\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.92280 | + | 8.52654i | −0.248957 | + | 0.431206i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 12.0012 | + | 20.7867i | 0.603845 | + | 1.04589i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.86340 | − | 13.6198i | 0.394653 | − | 0.683559i | −0.598404 | − | 0.801195i | \(-0.704198\pi\) |
0.993057 | + | 0.117636i | \(0.0375315\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.98280 | + | 5.16635i | 0.148954 | + | 0.257995i | 0.930841 | − | 0.365424i | \(-0.119076\pi\) |
−0.781887 | + | 0.623420i | \(0.785743\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.14984 | + | 5.45569i | −0.156905 | + | 0.271767i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 33.4905 | + | 58.0073i | 1.66006 | + | 2.87531i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −17.6189 | −0.871197 | −0.435598 | − | 0.900141i | \(-0.643463\pi\) | ||||
−0.435598 | + | 0.900141i | \(0.643463\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 21.3349 | − | 6.09848i | 1.04982 | − | 0.300086i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.85729 | + | 4.94897i | −0.140259 | + | 0.242936i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9.62164 | − | 16.6652i | 0.470048 | − | 0.814147i | −0.529365 | − | 0.848394i | \(-0.677570\pi\) |
0.999413 | + | 0.0342470i | \(0.0109033\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.77999 | + | 13.4753i | 0.379174 | + | 0.656748i | 0.990942 | − | 0.134289i | \(-0.0428750\pi\) |
−0.611769 | + | 0.791037i | \(0.709542\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.35111 | −0.114045 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12.2761 | − | 3.50906i | 0.594081 | − | 0.169815i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −16.9779 | − | 29.4067i | −0.817799 | − | 1.41647i | −0.907301 | − | 0.420482i | \(-0.861861\pi\) |
0.0895020 | − | 0.995987i | \(-0.471472\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −34.8338 | −1.67401 | −0.837004 | − | 0.547197i | \(-0.815695\pi\) | ||||
−0.837004 | + | 0.547197i | \(0.815695\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8.51692 | 0.407419 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −15.5588 | −0.742579 | −0.371290 | − | 0.928517i | \(-0.621084\pi\) | ||||
−0.371290 | + | 0.928517i | \(0.621084\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 18.3242 | 0.870611 | 0.435305 | − | 0.900283i | \(-0.356640\pi\) | ||||
0.435305 | + | 0.900283i | \(0.356640\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.44341 | −0.0684242 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.75072 | 0.129815 | 0.0649073 | − | 0.997891i | \(-0.479325\pi\) | ||||
0.0649073 | + | 0.997891i | \(0.479325\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 23.2514 | + | 40.2727i | 1.09487 | + | 1.89637i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −28.4938 | + | 8.14483i | −1.33581 | + | 0.381836i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 20.6813 | 0.967433 | 0.483716 | − | 0.875225i | \(-0.339287\pi\) | ||||
0.483716 | + | 0.875225i | \(0.339287\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6.40670 | − | 11.0967i | −0.298390 | − | 0.516826i | 0.677378 | − | 0.735635i | \(-0.263116\pi\) |
−0.975768 | + | 0.218809i | \(0.929783\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.54704 | + | 9.60775i | −0.257793 | + | 0.446510i | −0.965650 | − | 0.259845i | \(-0.916328\pi\) |
0.707858 | + | 0.706355i | \(0.249662\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5.36754 | − | 9.29686i | 0.248380 | − | 0.430207i | −0.714696 | − | 0.699435i | \(-0.753435\pi\) |
0.963077 | + | 0.269228i | \(0.0867684\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.50283 | − | 1.85881i | 0.300273 | − | 0.0858317i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −26.3643 | −1.21223 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.01691 | + | 1.76134i | 0.0466590 | + | 0.0808157i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.89754 | − | 6.75074i | 0.178083 | − | 0.308449i | −0.763141 | − | 0.646232i | \(-0.776344\pi\) |
0.941224 | + | 0.337783i | \(0.109677\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 37.4639 | + | 64.8893i | 1.70820 | + | 2.95870i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.97583 | − | 3.42225i | 0.0897180 | − | 0.155396i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −13.9984 | − | 24.2459i | −0.634326 | − | 1.09868i | −0.986657 | − | 0.162810i | \(-0.947944\pi\) |
0.352331 | − | 0.935875i | \(-0.385389\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12.1227 | + | 20.9971i | −0.547089 | + | 0.947586i | 0.451383 | + | 0.892330i | \(0.350931\pi\) |
−0.998472 | + | 0.0552556i | \(0.982403\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.03572 | − | 3.52598i | 0.0916844 | − | 0.158802i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −22.5432 | + | 6.44387i | −1.01120 | + | 0.289047i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16.8874 | − | 29.2499i | −0.755984 | − | 1.30940i | −0.944883 | − | 0.327407i | \(-0.893825\pi\) |
0.188899 | − | 0.981996i | \(-0.439508\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.09819 | −0.0489661 | −0.0244830 | − | 0.999700i | \(-0.507794\pi\) | ||||
−0.0244830 | + | 0.999700i | \(0.507794\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −16.7701 | −0.746261 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8.10672 | + | 14.0413i | 0.359324 | + | 0.622368i | 0.987848 | − | 0.155423i | \(-0.0496739\pi\) |
−0.628524 | + | 0.777790i | \(0.716341\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 21.5876 | + | 20.8817i | 0.954981 | + | 0.923750i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.14527 | + | 5.44777i | −0.138597 | + | 0.240057i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.45692 | + | 9.45167i | −0.239995 | + | 0.415684i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −19.1738 | − | 33.2099i | −0.840017 | − | 1.45495i | −0.889879 | − | 0.456197i | \(-0.849211\pi\) |
0.0498617 | − | 0.998756i | \(-0.484122\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −20.6021 | + | 35.6838i | −0.900865 | + | 1.56034i | −0.0744911 | + | 0.997222i | \(0.523733\pi\) |
−0.826374 | + | 0.563122i | \(0.809600\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.648287 | + | 1.12287i | 0.0282398 | + | 0.0489128i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.5105 | + | 30.3290i | −0.761324 | + | 1.31865i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 26.0100 | + | 45.0506i | 1.12662 | + | 1.95136i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12.1023 | 0.523229 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.30619 | − | 39.2771i | −0.0562616 | − | 1.69178i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.09371 | + | 15.7508i | −0.390969 | + | 0.677178i | −0.992578 | − | 0.121613i | \(-0.961193\pi\) |
0.601609 | + | 0.798791i | \(0.294527\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.21611 | − | 2.10636i | 0.0520924 | − | 0.0902266i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.338699 | − | 0.586644i | −0.0144817 | − | 0.0250831i | 0.858694 | − | 0.512489i | \(-0.171277\pi\) |
−0.873175 | + | 0.487406i | \(0.837943\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.52200 | −0.150042 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −34.2345 | + | 9.78577i | −1.45580 | + | 0.416133i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −14.8659 | − | 25.7484i | −0.629887 | − | 1.09100i | −0.987574 | − | 0.157155i | \(-0.949768\pi\) |
0.357687 | − | 0.933842i | \(-0.383565\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −29.4922 | −1.24739 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 21.3478 | 0.899705 | 0.449852 | − | 0.893103i | \(-0.351477\pi\) | ||||
0.449852 | + | 0.893103i | \(0.351477\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.86153 | −0.414878 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 15.1242 | 0.634041 | 0.317021 | − | 0.948419i | \(-0.397318\pi\) | ||||
0.317021 | + | 0.948419i | \(0.397318\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19.8863 | −0.832215 | −0.416107 | − | 0.909315i | \(-0.636606\pi\) | ||||
−0.416107 | + | 0.909315i | \(0.636606\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −13.8553 | −0.577804 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 19.8090 | + | 34.3102i | 0.824661 | + | 1.42835i | 0.902178 | + | 0.431363i | \(0.141967\pi\) |
−0.0775179 | + | 0.996991i | \(0.524700\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.09304 | − | 5.89378i | −0.252782 | − | 0.244515i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 50.0770 | 2.07398 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.13275 | + | 1.96199i | 0.0467537 | + | 0.0809798i | 0.888455 | − | 0.458963i | \(-0.151779\pi\) |
−0.841701 | + | 0.539943i | \(0.818446\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.560799 | − | 0.971332i | 0.0231073 | − | 0.0400230i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −5.97295 | + | 10.3454i | −0.245280 | + | 0.424837i | −0.962210 | − | 0.272308i | \(-0.912213\pi\) |
0.716931 | + | 0.697145i | \(0.245546\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.48049 | + | 5.91695i | −0.0606941 | + | 0.242571i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2.95272 | −0.120645 | −0.0603224 | − | 0.998179i | \(-0.519213\pi\) | ||||
−0.0603224 | + | 0.998179i | \(0.519213\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15.9751 | + | 27.6697i | 0.651638 | + | 1.12867i | 0.982725 | + | 0.185071i | \(0.0592514\pi\) |
−0.331087 | + | 0.943600i | \(0.607415\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −18.2977 | + | 31.6925i | −0.743906 | + | 1.28848i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.20069 | + | 9.00786i | 0.211089 | + | 0.365618i | 0.952056 | − | 0.305925i | \(-0.0989655\pi\) |
−0.740966 | + | 0.671542i | \(0.765632\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6.10433 | + | 10.5730i | −0.246955 | + | 0.427739i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.22441 | + | 10.7810i | 0.251402 | + | 0.435441i | 0.963912 | − | 0.266221i | \(-0.0857751\pi\) |
−0.712510 | + | 0.701662i | \(0.752442\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4.70100 | − | 8.14237i | 0.189255 | − | 0.327799i | −0.755747 | − | 0.654864i | \(-0.772726\pi\) |
0.945002 | + | 0.327064i | \(0.106059\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11.0598 | + | 19.1561i | −0.444531 | + | 0.769951i | −0.998019 | − | 0.0629064i | \(-0.979963\pi\) |
0.553488 | + | 0.832857i | \(0.313296\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.519727 | − | 2.07715i | 0.0208224 | − | 0.0832193i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6.29831 | + | 10.9090i | 0.251932 | + | 0.436360i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 15.4213 | 0.614887 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −18.3705 | −0.731316 | −0.365658 | − | 0.930749i | \(-0.619156\pi\) | ||||
−0.365658 | + | 0.930749i | \(0.619156\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −11.4334 | − | 19.8032i | −0.453720 | − | 0.785866i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.46116 | − | 43.9369i | −0.0578932 | − | 1.74084i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −16.8617 | + | 29.2052i | −0.665995 | + | 1.15354i | 0.313019 | + | 0.949747i | \(0.398660\pi\) |
−0.979014 | + | 0.203791i | \(0.934674\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10.0635 | + | 17.4306i | −0.396867 | + | 0.687394i | −0.993338 | − | 0.115241i | \(-0.963236\pi\) |
0.596470 | + | 0.802635i | \(0.296569\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −11.1891 | − | 19.3800i | −0.439887 | − | 0.761907i | 0.557793 | − | 0.829980i | \(-0.311648\pi\) |
−0.997680 | + | 0.0680731i | \(0.978315\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 23.5422 | − | 40.7763i | 0.924112 | − | 1.60061i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −20.3377 | − | 35.2259i | −0.795875 | − | 1.37850i | −0.922282 | − | 0.386518i | \(-0.873678\pi\) |
0.126406 | − | 0.991979i | \(-0.459656\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.18932 | − | 8.98816i | 0.202763 | − | 0.351197i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7.69321 | + | 13.3250i | 0.299685 | + | 0.519070i | 0.976064 | − | 0.217484i | \(-0.0697851\pi\) |
−0.676379 | + | 0.736554i | \(0.736452\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 49.1473 | 1.91161 | 0.955804 | − | 0.294006i | \(-0.0949885\pi\) | ||||
0.955804 | + | 0.294006i | \(0.0949885\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5.07305 | − | 1.45011i | 0.196724 | − | 0.0562328i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 11.9967 | − | 20.7789i | 0.464513 | − | 0.804561i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 13.5462 | − | 23.4627i | 0.522944 | − | 0.905766i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.99961 | − | 12.1237i | −0.269815 | − | 0.467334i | 0.698999 | − | 0.715123i | \(-0.253629\pi\) |
−0.968814 | + | 0.247789i | \(0.920296\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 46.7740 | 1.79767 | 0.898836 | − | 0.438285i | \(-0.144414\pi\) | ||||
0.898836 | + | 0.438285i | \(0.144414\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.21337 | + | 4.07558i | 0.161694 | + | 0.156406i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 21.6222 | + | 37.4508i | 0.827352 | + | 1.43302i | 0.900109 | + | 0.435665i | \(0.143487\pi\) |
−0.0727571 | + | 0.997350i | \(0.523180\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 27.3613 | 1.04542 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 56.0181 | 2.13412 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11.7214 | 0.445905 | 0.222952 | − | 0.974829i | \(-0.428431\pi\) | ||||
0.222952 | + | 0.974829i | \(0.428431\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −21.6096 | −0.819697 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 10.7065 | 0.405538 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −0.0120975 | −0.000456915 | −0.000228458 | − | 1.00000i | \(-0.500073\pi\) | ||||
−0.000228458 | 1.00000i | \(0.500073\pi\) | ||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.67008 | − | 11.5529i | −0.251567 | − | 0.435726i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.03839 | − | 24.1332i | 0.227097 | − | 0.907621i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.07478 | 0.0403640 | 0.0201820 | − | 0.999796i | \(-0.493575\pi\) | ||||
0.0201820 | + | 0.999796i | \(0.493575\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.82041 | + | 6.61714i | 0.143075 | + | 0.247814i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −31.4418 | + | 54.4588i | −1.17586 | + | 2.03664i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 12.7777 | − | 22.1317i | 0.476529 | − | 0.825372i | −0.523109 | − | 0.852266i | \(-0.675228\pi\) |
0.999638 | + | 0.0268932i | \(0.00856140\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.70714 | − | 6.48779i | −0.249787 | − | 0.241618i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5.72956 | 0.212790 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6.20522 | − | 10.7478i | −0.230139 | − | 0.398612i | 0.727710 | − | 0.685885i | \(-0.240585\pi\) |
−0.957849 | + | 0.287273i | \(0.907251\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.03498 | + | 5.25674i | −0.112253 | + | 0.194427i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14.7095 | − | 25.4775i | −0.543307 | − | 0.941035i | −0.998711 | − | 0.0507502i | \(-0.983839\pi\) |
0.455405 | − | 0.890285i | \(-0.349495\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 7.17562 | − | 12.4285i | 0.264317 | − | 0.457811i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7.75910 | − | 13.4392i | −0.285423 | − | 0.494368i | 0.687288 | − | 0.726385i | \(-0.258801\pi\) |
−0.972712 | + | 0.232017i | \(0.925468\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −13.6333 | + | 23.6136i | −0.500159 | + | 0.866301i | 0.499841 | + | 0.866117i | \(0.333392\pi\) |
−1.00000 | 0.000183414i | \(0.999942\pi\) | ||||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.22432 | − | 7.31674i | 0.154767 | − | 0.268065i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.35766 | + | 17.4159i | −0.159226 | + | 0.636364i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.57176 | − | 7.91853i | −0.166826 | − | 0.288951i | 0.770476 | − | 0.637469i | \(-0.220018\pi\) |
−0.937302 | + | 0.348518i | \(0.886685\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −43.4632 | −1.58179 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −20.6307 | −0.749834 | −0.374917 | − | 0.927058i | \(-0.622329\pi\) | ||||
−0.374917 | + | 0.927058i | \(0.622329\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −0.239208 | − | 0.414321i | −0.00867130 | − | 0.0150191i | 0.861657 | − | 0.507491i | \(-0.169427\pi\) |
−0.870328 | + | 0.492472i | \(0.836094\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.59329 | + | 2.50848i | 0.0938835 | + | 0.0908132i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 26.3352 | − | 45.6140i | 0.950910 | − | 1.64702i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −13.3518 | + | 23.1261i | −0.481480 | + | 0.833948i | −0.999774 | − | 0.0212548i | \(-0.993234\pi\) |
0.518294 | + | 0.855202i | \(0.326567\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 13.5143 | + | 23.4074i | 0.486074 | + | 0.841905i | 0.999872 | − | 0.0160062i | \(-0.00509514\pi\) |
−0.513798 | + | 0.857911i | \(0.671762\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.912303 | + | 1.58016i | −0.0327709 | + | 0.0567609i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4.63083 | − | 8.02083i | −0.165917 | − | 0.287376i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −24.8755 | + | 43.0857i | −0.890116 | + | 1.54173i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.62226 | + | 9.73804i | 0.200667 | + | 0.347566i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −49.1830 | −1.75319 | −0.876593 | − | 0.481233i | \(-0.840189\pi\) | ||||
−0.876593 | + | 0.481233i | \(0.840189\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.55083 | − | 14.1913i | 0.126253 | − | 0.504585i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 15.1533 | − | 26.2463i | 0.538109 | − | 0.932032i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −22.1538 | + | 38.3715i | −0.784728 | + | 1.35919i | 0.144434 | + | 0.989514i | \(0.453864\pi\) |
−0.929162 | + | 0.369674i | \(0.879469\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.25637 | + | 2.17609i | 0.0444471 | + | 0.0769846i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 63.7312 | 2.24903 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.72463 | + | 34.8690i | −0.307503 | + | 1.22897i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 16.7359 | + | 28.9874i | 0.588402 | + | 1.01914i | 0.994442 | + | 0.105286i | \(0.0335759\pi\) |
−0.406040 | + | 0.913855i | \(0.633091\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 43.7383 | 1.53586 | 0.767929 | − | 0.640535i | \(-0.221287\pi\) | ||||
0.767929 | + | 0.640535i | \(0.221287\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.25090 | 0.0438172 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.25080 | 0.183702 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 22.5132 | 0.785714 | 0.392857 | − | 0.919599i | \(-0.371487\pi\) | ||||
0.392857 | + | 0.919599i | \(0.371487\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −14.6735 | −0.511485 | −0.255743 | − | 0.966745i | \(-0.582320\pi\) | ||||
−0.255743 | + | 0.966745i | \(0.582320\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 45.0520 | 1.56661 | 0.783306 | − | 0.621636i | \(-0.213532\pi\) | ||||
0.783306 | + | 0.621636i | \(0.213532\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 20.6688 | + | 35.7993i | 0.717856 | + | 1.24336i | 0.961848 | + | 0.273585i | \(0.0882095\pi\) |
−0.243992 | + | 0.969777i | \(0.578457\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −7.98175 | − | 4.26101i | −0.276551 | − | 0.147635i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −12.6212 | −0.436774 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.04477 | + | 3.54164i | 0.0705932 | + | 0.122271i | 0.899161 | − | 0.437617i | \(-0.144177\pi\) |
−0.828568 | + | 0.559888i | \(0.810844\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.53902 | − | 16.5221i | 0.328932 | − | 0.569726i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −23.5790 | + | 40.8401i | −0.811143 | + | 1.40494i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −39.0189 | − | 37.7428i | −1.34070 | − | 1.29686i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 90.8789 | 3.11529 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −21.1012 | − | 36.5484i | −0.722491 | − | 1.25139i | −0.959998 | − | 0.280006i | \(-0.909664\pi\) |
0.237507 | − | 0.971386i | \(-0.423670\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −27.5623 | + | 47.7393i | −0.941509 | + | 1.63074i | −0.178915 | + | 0.983864i | \(0.557259\pi\) |
−0.762594 | + | 0.646877i | \(0.776075\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −18.9767 | − | 32.8686i | −0.647476 | − | 1.12146i | −0.983724 | − | 0.179688i | \(-0.942491\pi\) |
0.336247 | − | 0.941774i | \(-0.390842\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 6.27205 | − | 10.8635i | 0.213503 | − | 0.369798i | −0.739305 | − | 0.673370i | \(-0.764846\pi\) |
0.952809 | + | 0.303572i | \(0.0981793\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.91723 | + | 10.2489i | 0.201192 | + | 0.348474i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −37.7764 | + | 65.4306i | −1.28148 | + | 2.21958i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.02694 | − | 13.9031i | 0.271983 | − | 0.471088i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −30.9383 | + | 8.84359i | −1.04591 | + | 0.298968i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4.85337 | − | 8.40628i | −0.163887 | − | 0.283860i | 0.772373 | − | 0.635169i | \(-0.219070\pi\) |
−0.936259 | + | 0.351310i | \(0.885736\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 11.6652 | 0.393012 | 0.196506 | − | 0.980503i | \(-0.437041\pi\) | ||||
0.196506 | + | 0.980503i | \(0.437041\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 13.1758 | 0.443401 | 0.221701 | − | 0.975115i | \(-0.428839\pi\) | ||||
0.221701 | + | 0.975115i | \(0.428839\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0.415361 | + | 0.719426i | 0.0139464 | + | 0.0241560i | 0.872914 | − | 0.487873i | \(-0.162227\pi\) |
−0.858968 | + | 0.512029i | \(0.828894\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 32.6147 | − | 9.32278i | 1.09386 | − | 0.312676i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.08682 | − | 1.88242i | 0.0363690 | − | 0.0629929i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 10.0508 | − | 17.4084i | 0.335960 | − | 0.581900i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.57985 | − | 2.73638i | −0.0526910 | − | 0.0912634i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.76470 | − | 9.98476i | 0.192050 | − | 0.332641i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −18.8878 | − | 32.7146i | −0.627852 | − | 1.08747i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 16.6588 | − | 28.8539i | 0.553146 | − | 0.958077i | −0.444899 | − | 0.895581i | \(-0.646761\pi\) |
0.998045 | − | 0.0624962i | \(-0.0199061\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −11.1353 | − | 19.2870i | −0.368930 | − | 0.639006i | 0.620469 | − | 0.784231i | \(-0.286942\pi\) |
−0.989399 | + | 0.145226i | \(0.953609\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −17.9879 | −0.595313 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 11.0660 | + | 10.7041i | 0.365431 | + | 0.353480i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −10.7906 | + | 18.6899i | −0.355949 | + | 0.616522i | −0.987280 | − | 0.158992i | \(-0.949176\pi\) |
0.631331 | + | 0.775514i | \(0.282509\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −27.8268 | + | 48.1974i | −0.915929 | + | 1.58644i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10.8508 | + | 18.7942i | 0.356773 | + | 0.617949i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 37.1559 | 1.21905 | 0.609523 | − | 0.792768i | \(-0.291361\pi\) | ||||
0.609523 | + | 0.792768i | \(0.291361\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.260145 | + | 7.82255i | 0.00852591 | + | 0.256374i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 6.47122 | + | 11.2085i | 0.211631 | + | 0.366556i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 21.5238 | 0.703152 | 0.351576 | − | 0.936159i | \(-0.385646\pi\) | ||||
0.351576 | + | 0.936159i | \(0.385646\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 47.4064 | 1.54540 | 0.772702 | − | 0.634769i | \(-0.218905\pi\) | ||||
0.772702 | + | 0.634769i | \(0.218905\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 63.0944 | 2.05464 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.50117 | −0.0812771 | −0.0406386 | − | 0.999174i | \(-0.512939\pi\) | ||||
−0.0406386 | + | 0.999174i | \(0.512939\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 71.2923 | 2.31425 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 7.89914 | 0.255878 | 0.127939 | − | 0.991782i | \(-0.459164\pi\) | ||||
0.127939 | + | 0.991782i | \(0.459164\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.41913 | + | 14.5824i | 0.272437 | + | 0.471874i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −9.85194 | + | 39.3745i | −0.318136 | + | 1.27147i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.9938 | −0.967541 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5.60071 | + | 9.70072i | 0.180293 | + | 0.312277i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5.76591 | + | 9.98684i | −0.185419 | + | 0.321155i | −0.943718 | − | 0.330752i | \(-0.892698\pi\) |
0.758299 | + | 0.651907i | \(0.226031\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −9.14669 | + | 15.8425i | −0.293531 | + | 0.508411i | −0.974642 | − | 0.223769i | \(-0.928164\pi\) |
0.681111 | + | 0.732180i | \(0.261497\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7.78092 | − | 31.0974i | 0.249445 | − | 0.996937i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 29.9083 | 0.956850 | 0.478425 | − | 0.878128i | \(-0.341208\pi\) | ||||
0.478425 | + | 0.878128i | \(0.341208\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.27173 | − | 3.93475i | −0.0726047 | − | 0.125755i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −7.27224 | + | 12.5959i | −0.231948 | + | 0.401746i | −0.958381 | − | 0.285491i | \(-0.907843\pi\) |
0.726433 | + | 0.687237i | \(0.241177\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 13.8029 | + | 23.9073i | 0.439797 | + | 0.761751i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −17.8854 | + | 30.9784i | −0.568722 | + | 0.985055i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 14.3753 | + | 24.8987i | 0.456646 | + | 0.790935i | 0.998781 | − | 0.0493567i | \(-0.0157171\pi\) |
−0.542135 | + | 0.840292i | \(0.682384\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.91447 | + | 6.78007i | −0.124097 | + | 0.214943i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −17.9469 | + | 31.0850i | −0.568384 | + | 0.984471i | 0.428341 | + | 0.903617i | \(0.359098\pi\) |
−0.996726 | + | 0.0808539i | \(0.974235\pi\) | |||||||
\(998\) | 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 | 3024.2.q.l.2305.4 | 22 | ||
3.2 | odd | 2 | 1008.2.q.l.625.8 | 22 | |||
4.3 | odd | 2 | 1512.2.q.d.793.4 | 22 | |||
7.4 | even | 3 | 3024.2.t.k.1873.8 | 22 | |||
9.2 | odd | 6 | 1008.2.t.l.961.7 | 22 | |||
9.7 | even | 3 | 3024.2.t.k.289.8 | 22 | |||
12.11 | even | 2 | 504.2.q.c.121.4 | yes | 22 | ||
21.11 | odd | 6 | 1008.2.t.l.193.7 | 22 | |||
28.11 | odd | 6 | 1512.2.t.c.361.8 | 22 | |||
36.7 | odd | 6 | 1512.2.t.c.289.8 | 22 | |||
36.11 | even | 6 | 504.2.t.c.457.5 | yes | 22 | ||
63.11 | odd | 6 | 1008.2.q.l.529.8 | 22 | |||
63.25 | even | 3 | inner | 3024.2.q.l.2881.4 | 22 | ||
84.11 | even | 6 | 504.2.t.c.193.5 | yes | 22 | ||
252.11 | even | 6 | 504.2.q.c.25.4 | ✓ | 22 | ||
252.151 | odd | 6 | 1512.2.q.d.1369.4 | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.q.c.25.4 | ✓ | 22 | 252.11 | even | 6 | ||
504.2.q.c.121.4 | yes | 22 | 12.11 | even | 2 | ||
504.2.t.c.193.5 | yes | 22 | 84.11 | even | 6 | ||
504.2.t.c.457.5 | yes | 22 | 36.11 | even | 6 | ||
1008.2.q.l.529.8 | 22 | 63.11 | odd | 6 | |||
1008.2.q.l.625.8 | 22 | 3.2 | odd | 2 | |||
1008.2.t.l.193.7 | 22 | 21.11 | odd | 6 | |||
1008.2.t.l.961.7 | 22 | 9.2 | odd | 6 | |||
1512.2.q.d.793.4 | 22 | 4.3 | odd | 2 | |||
1512.2.q.d.1369.4 | 22 | 252.151 | odd | 6 | |||
1512.2.t.c.289.8 | 22 | 36.7 | odd | 6 | |||
1512.2.t.c.361.8 | 22 | 28.11 | odd | 6 | |||
3024.2.q.l.2305.4 | 22 | 1.1 | even | 1 | trivial | ||
3024.2.q.l.2881.4 | 22 | 63.25 | even | 3 | inner | ||
3024.2.t.k.289.8 | 22 | 9.7 | even | 3 | |||
3024.2.t.k.1873.8 | 22 | 7.4 | even | 3 |