Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [672,2,Mod(529,672)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(672, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("672.529");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 672 = 2^{5} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 672.bk (of order \(6\), 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: | \(5.36594701583\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 168) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 529.13 | ||
Character | \(\chi\) | \(=\) | 672.529 |
Dual form | 672.2.bk.a.625.13 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/672\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(421\) | \(449\) | \(577\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | ||||||||
\(3\) | 0.866025 | + | 0.500000i | 0.500000 | + | 0.288675i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.0402223 | + | 0.0232224i | −0.0179880 | + | 0.0103854i | −0.508967 | − | 0.860786i | \(-0.669972\pi\) |
0.490979 | + | 0.871171i | \(0.336639\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.97032 | + | 1.76574i | 0.744711 | + | 0.667387i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.500000 | + | 0.866025i | 0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.11586 | + | 1.79894i | 0.939468 | + | 0.542402i | 0.889793 | − | 0.456364i | \(-0.150848\pi\) |
0.0496743 | + | 0.998765i | \(0.484182\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 6.29415i | − | 1.74568i | −0.488004 | − | 0.872842i | \(-0.662275\pi\) | ||
0.488004 | − | 0.872842i | \(-0.337725\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.0464447 | −0.0119920 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.258110 | − | 0.447060i | 0.0626010 | − | 0.108428i | −0.833026 | − | 0.553233i | \(-0.813394\pi\) |
0.895627 | + | 0.444805i | \(0.146727\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.80834 | + | 1.62140i | −0.644278 | + | 0.371974i | −0.786261 | − | 0.617895i | \(-0.787986\pi\) |
0.141983 | + | 0.989869i | \(0.454652\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.823477 | + | 2.51434i | 0.179697 | + | 0.548673i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.47322 | + | 6.01578i | 0.724215 | + | 1.25438i | 0.959296 | + | 0.282402i | \(0.0911312\pi\) |
−0.235081 | + | 0.971976i | \(0.575535\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.49892 | + | 4.32826i | −0.499784 | + | 0.865652i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.29579i | 0.426317i | 0.977018 | + | 0.213159i | \(0.0683751\pi\) | ||||
−0.977018 | + | 0.213159i | \(0.931625\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.05460 | − | 1.82662i | 0.189411 | − | 0.328070i | −0.755643 | − | 0.654984i | \(-0.772675\pi\) |
0.945054 | + | 0.326914i | \(0.106009\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.79894 | + | 3.11586i | 0.313156 | + | 0.542402i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.120255 | − | 0.0252667i | −0.0203269 | − | 0.00427085i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.12720 | − | 0.650790i | 0.185311 | − | 0.106989i | −0.404475 | − | 0.914549i | \(-0.632546\pi\) |
0.589785 | + | 0.807560i | \(0.299212\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.14708 | − | 5.45089i | 0.503935 | − | 0.872842i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.1883 | 1.59115 | 0.795576 | − | 0.605854i | \(-0.207168\pi\) | ||||
0.795576 | + | 0.605854i | \(0.207168\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 9.12162i | − | 1.39103i | −0.718510 | − | 0.695517i | \(-0.755176\pi\) | ||
0.718510 | − | 0.695517i | \(-0.244824\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.0402223 | − | 0.0232224i | −0.00599599 | − | 0.00346178i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.32465 | + | 4.02641i | 0.339085 | + | 0.587313i | 0.984261 | − | 0.176722i | \(-0.0565492\pi\) |
−0.645176 | + | 0.764034i | \(0.723216\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.764321 | + | 6.95815i | 0.109189 | + | 0.994021i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.447060 | − | 0.258110i | 0.0626010 | − | 0.0361427i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.91727 | − | 2.83899i | −0.675439 | − | 0.389965i | 0.122696 | − | 0.992444i | \(-0.460846\pi\) |
−0.798134 | + | 0.602480i | \(0.794179\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.167103 | −0.0225321 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.24279 | −0.429519 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.42910 | − | 0.825090i | −0.186053 | − | 0.107418i | 0.404081 | − | 0.914723i | \(-0.367591\pi\) |
−0.590133 | + | 0.807306i | \(0.700925\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.10386 | − | 0.637312i | 0.141334 | − | 0.0815995i | −0.427665 | − | 0.903937i | \(-0.640664\pi\) |
0.569000 | + | 0.822338i | \(0.307331\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.544016 | + | 2.58922i | −0.0685396 | + | 0.326211i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.146165 | + | 0.253165i | 0.0181295 | + | 0.0314013i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.72366 | − | 3.88191i | −0.821426 | − | 0.474251i | 0.0294820 | − | 0.999565i | \(-0.490614\pi\) |
−0.850908 | + | 0.525315i | \(0.823948\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.94643i | 0.836252i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.8320 | −1.40420 | −0.702099 | − | 0.712080i | \(-0.747753\pi\) | ||||
−0.702099 | + | 0.712080i | \(0.747753\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.57028 | − | 9.64802i | 0.651953 | − | 1.12921i | −0.330696 | − | 0.943737i | \(-0.607283\pi\) |
0.982649 | − | 0.185478i | \(-0.0593832\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.32826 | + | 2.49892i | −0.499784 | + | 0.288551i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.96278 | + | 9.04630i | 0.337640 | + | 1.03092i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.75086 | + | 4.76463i | 0.309496 | + | 0.536063i | 0.978252 | − | 0.207419i | \(-0.0665063\pi\) |
−0.668756 | + | 0.743482i | \(0.733173\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.25030i | 0.905588i | 0.891615 | + | 0.452794i | \(0.149573\pi\) | ||||
−0.891615 | + | 0.452794i | \(0.850427\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.0239757i | 0.00260053i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.14789 | + | 1.98821i | −0.123067 | + | 0.213159i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.38218 | − | 12.7863i | −0.782510 | − | 1.35535i | −0.930475 | − | 0.366354i | \(-0.880606\pi\) |
0.147966 | − | 0.988993i | \(-0.452727\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 11.1138 | − | 12.4015i | 1.16505 | − | 1.30003i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.82662 | − | 1.05460i | 0.189411 | − | 0.109357i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.0753053 | − | 0.130433i | 0.00772616 | − | 0.0133821i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.16464 | −0.625925 | −0.312962 | − | 0.949766i | \(-0.601321\pi\) | ||||
−0.312962 | + | 0.949766i | \(0.601321\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.59789i | 0.361601i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.93470 | + | 4.00375i | 0.690029 | + | 0.398388i | 0.803623 | − | 0.595139i | \(-0.202903\pi\) |
−0.113594 | + | 0.993527i | \(0.536236\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.43821 | − | 11.1513i | −0.634376 | − | 1.09877i | −0.986647 | − | 0.162873i | \(-0.947924\pi\) |
0.352271 | − | 0.935898i | \(-0.385409\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.0915109 | − | 0.0820093i | −0.00893055 | − | 0.00800329i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.84815 | − | 5.10848i | 0.855383 | − | 0.493856i | −0.00708048 | − | 0.999975i | \(-0.502254\pi\) |
0.862463 | + | 0.506119i | \(0.168920\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.1275 | − | 5.84714i | −0.970043 | − | 0.560054i | −0.0707935 | − | 0.997491i | \(-0.522553\pi\) |
−0.899249 | + | 0.437437i | \(0.855886\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.30158 | 0.123540 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.08476 | −0.854623 | −0.427311 | − | 0.904105i | \(-0.640539\pi\) | ||||
−0.427311 | + | 0.904105i | \(0.640539\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.279401 | − | 0.161312i | −0.0260543 | − | 0.0150425i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.45089 | − | 3.14708i | 0.503935 | − | 0.290947i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.29795 | − | 0.425096i | 0.118983 | − | 0.0389685i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.972397 | + | 1.68424i | 0.0883997 | + | 0.153113i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 8.82337 | + | 5.09417i | 0.795576 | + | 0.459326i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 0.464347i | − | 0.0415324i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −14.1059 | −1.25170 | −0.625849 | − | 0.779944i | \(-0.715247\pi\) | ||||
−0.625849 | + | 0.779944i | \(0.715247\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.56081 | − | 7.89955i | 0.401557 | − | 0.695517i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −14.8183 | + | 8.55535i | −1.29468 | + | 0.747484i | −0.979480 | − | 0.201541i | \(-0.935405\pi\) |
−0.315200 | + | 0.949025i | \(0.602072\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.39630 | − | 1.76413i | −0.728052 | − | 0.152970i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.0232224 | − | 0.0402223i | −0.00199866 | − | 0.00346178i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.48594 | − | 4.30578i | 0.212388 | − | 0.367867i | −0.740073 | − | 0.672526i | \(-0.765209\pi\) |
0.952462 | + | 0.304659i | \(0.0985425\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 5.20468i | − | 0.441455i | −0.975335 | − | 0.220728i | \(-0.929157\pi\) | ||
0.975335 | − | 0.220728i | \(-0.0708432\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.64930i | 0.391542i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 11.3228 | − | 19.6117i | 0.946862 | − | 1.64001i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.0533136 | − | 0.0923419i | −0.00442746 | − | 0.00766858i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.81715 | + | 6.40809i | −0.232355 | + | 0.528531i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.725874 | − | 0.419084i | 0.0594659 | − | 0.0343327i | −0.469972 | − | 0.882681i | \(-0.655736\pi\) |
0.529438 | + | 0.848349i | \(0.322403\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.21803 | − | 5.57379i | 0.261879 | − | 0.453588i | −0.704862 | − | 0.709345i | \(-0.748991\pi\) |
0.966741 | + | 0.255756i | \(0.0823244\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.516221 | 0.0417340 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.0979610i | 0.00786842i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.73349 | + | 2.73288i | 0.377774 | + | 0.218108i | 0.676849 | − | 0.736122i | \(-0.263345\pi\) |
−0.299075 | + | 0.954229i | \(0.596678\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.83899 | − | 4.91727i | −0.225146 | − | 0.389965i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.77897 | + | 17.9858i | −0.297825 | + | 1.41748i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −13.2105 | + | 7.62708i | −1.03473 | + | 0.597399i | −0.918335 | − | 0.395805i | \(-0.870466\pi\) |
−0.116390 | + | 0.993204i | \(0.537132\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.144715 | − | 0.0835514i | −0.0112661 | − | 0.00650447i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.77463 | 0.137325 | 0.0686625 | − | 0.997640i | \(-0.478127\pi\) | ||||
0.0686625 | + | 0.997640i | \(0.478127\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −26.6163 | −2.04741 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.80834 | − | 1.62140i | −0.214759 | − | 0.123991i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.23631 | − | 1.29114i | 0.170024 | − | 0.0981633i | −0.412573 | − | 0.910924i | \(-0.635370\pi\) |
0.582597 | + | 0.812761i | \(0.302037\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −12.5663 | + | 4.11561i | −0.949920 | + | 0.311111i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.825090 | − | 1.42910i | −0.0620175 | − | 0.107418i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 17.0438 | + | 9.84027i | 1.27392 | + | 0.735496i | 0.975723 | − | 0.219009i | \(-0.0702824\pi\) |
0.298194 | + | 0.954505i | \(0.403616\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 25.5613i | − | 1.89996i | −0.312315 | − | 0.949979i | \(-0.601104\pi\) | ||
0.312315 | − | 0.949979i | \(-0.398896\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.27462 | 0.0942230 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.0302257 | + | 0.0523525i | −0.00222224 | + | 0.00384903i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.60847 | − | 0.928652i | 0.117623 | − | 0.0679098i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.76574 | + | 1.97032i | −0.128439 | + | 0.143320i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.98804 | − | 12.1036i | −0.505637 | − | 0.875788i | −0.999979 | − | 0.00652098i | \(-0.997924\pi\) |
0.494342 | − | 0.869267i | \(-0.335409\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.00706 | − | 15.6007i | 0.648342 | − | 1.12296i | −0.335176 | − | 0.942155i | \(-0.608796\pi\) |
0.983519 | − | 0.180806i | \(-0.0578707\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.292330i | 0.0209342i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 3.70082i | − | 0.263672i | −0.991272 | − | 0.131836i | \(-0.957913\pi\) | ||
0.991272 | − | 0.131836i | \(-0.0420873\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.882192 | + | 1.52800i | −0.0625369 | + | 0.108317i | −0.895599 | − | 0.444863i | \(-0.853252\pi\) |
0.833062 | + | 0.553180i | \(0.186586\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.88191 | − | 6.72366i | −0.273809 | − | 0.474251i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.05377 | + | 4.52344i | −0.284519 | + | 0.317483i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.409799 | + | 0.236597i | −0.0286216 | + | 0.0165247i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −3.47322 | + | 6.01578i | −0.241405 | + | 0.418126i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −11.6672 | −0.807038 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.6757i | 0.734945i | 0.930034 | + | 0.367473i | \(0.119777\pi\) | ||||
−0.930034 | + | 0.367473i | \(0.880223\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −10.2468 | − | 5.91599i | −0.702099 | − | 0.405357i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.211825 | + | 0.366892i | 0.0144464 | + | 0.0250218i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.30323 | − | 1.73688i | 0.360007 | − | 0.117907i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 9.64802 | − | 5.57028i | 0.651953 | − | 0.376405i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.81386 | − | 1.62459i | −0.189281 | − | 0.109281i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 22.2212 | 1.48804 | 0.744020 | − | 0.668158i | \(-0.232917\pi\) | ||||
0.744020 | + | 0.668158i | \(0.232917\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.99784 | −0.333190 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −17.0728 | − | 9.85697i | −1.13316 | − | 0.654230i | −0.188432 | − | 0.982086i | \(-0.560340\pi\) |
−0.944728 | + | 0.327856i | \(0.893674\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.06806 | + | 3.50340i | −0.400989 | + | 0.231511i | −0.686911 | − | 0.726742i | \(-0.741034\pi\) |
0.285922 | + | 0.958253i | \(0.407700\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.95731 | + | 9.31571i | −0.128781 | + | 0.612929i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 12.3717 | + | 21.4284i | 0.810495 | + | 1.40382i | 0.912518 | + | 0.409036i | \(0.134135\pi\) |
−0.102023 | + | 0.994782i | \(0.532532\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.187006 | − | 0.107968i | −0.0121989 | − | 0.00704303i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 5.50172i | 0.357375i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −21.9503 | −1.41985 | −0.709924 | − | 0.704278i | \(-0.751271\pi\) | ||||
−0.709924 | + | 0.704278i | \(0.751271\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.39162 | − | 12.8027i | 0.476136 | − | 0.824692i | −0.523490 | − | 0.852032i | \(-0.675370\pi\) |
0.999626 | + | 0.0273397i | \(0.00870359\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.866025 | + | 0.500000i | −0.0555556 | + | 0.0320750i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.192327 | − | 0.262123i | −0.0122873 | − | 0.0167464i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 10.2053 | + | 17.6761i | 0.649349 | + | 1.12471i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.12515 | + | 7.14497i | −0.261421 | + | 0.452794i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 14.4785i | − | 0.913876i | −0.889499 | − | 0.456938i | \(-0.848946\pi\) | ||
0.889499 | − | 0.456938i | \(-0.151054\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 24.9925i | 1.57126i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.0119879 | + | 0.0207636i | −0.000750709 | + | 0.00130027i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −7.93731 | − | 13.7478i | −0.495116 | − | 0.857566i | 0.504868 | − | 0.863196i | \(-0.331541\pi\) |
−0.999984 | + | 0.00563049i | \(0.998208\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.37007 | + | 0.708080i | 0.209406 | + | 0.0439980i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.98821 | + | 1.14789i | −0.123067 | + | 0.0710529i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.162710 | − | 0.281822i | 0.0100331 | − | 0.0173779i | −0.860965 | − | 0.508664i | \(-0.830140\pi\) |
0.870998 | + | 0.491286i | \(0.163473\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.263712 | 0.0161997 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 14.7644i | − | 0.903565i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −20.3761 | − | 11.7642i | −1.24235 | − | 0.717273i | −0.272780 | − | 0.962076i | \(-0.587943\pi\) |
−0.969573 | + | 0.244803i | \(0.921277\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.751567 | + | 1.30175i | 0.0456544 | + | 0.0790758i | 0.887950 | − | 0.459941i | \(-0.152129\pi\) |
−0.842295 | + | 0.539017i | \(0.818796\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 15.8256 | − | 5.18309i | 0.957809 | − | 0.313695i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −15.5726 | + | 8.99084i | −0.939062 | + | 0.542168i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 12.6685 | + | 7.31418i | 0.761178 | + | 0.439466i | 0.829719 | − | 0.558182i | \(-0.188501\pi\) |
−0.0685405 | + | 0.997648i | \(0.521834\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.10920 | 0.126274 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 21.3285 | 1.27235 | 0.636175 | − | 0.771545i | \(-0.280516\pi\) | ||||
0.636175 | + | 0.771545i | \(0.280516\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.0068 | + | 8.66416i | 0.892059 | + | 0.515031i | 0.874616 | − | 0.484817i | \(-0.161114\pi\) |
0.0174438 | + | 0.999848i | \(0.494447\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.130433 | − | 0.0753053i | 0.00772616 | − | 0.00446070i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 20.0743 | + | 17.9900i | 1.18495 | + | 1.06191i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.36676 | + | 14.4917i | 0.492162 | + | 0.852450i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5.33874 | − | 3.08232i | −0.312962 | − | 0.180689i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 29.6927i | 1.73466i | 0.497730 | + | 0.867332i | \(0.334167\pi\) | ||||
−0.497730 | + | 0.867332i | \(0.665833\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.0766421 | 0.00446228 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.79894 | + | 3.11586i | −0.104385 | + | 0.180801i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 37.8643 | − | 21.8609i | 2.18975 | − | 1.26425i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 16.1064 | − | 17.9725i | 0.928358 | − | 1.03592i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4.00375 | + | 6.93470i | 0.230010 | + | 0.398388i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.0295998 | + | 0.0512683i | −0.00169488 | + | 0.00293562i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.88243i | 0.278655i | 0.990246 | + | 0.139327i | \(0.0444940\pi\) | ||||
−0.990246 | + | 0.139327i | \(0.955506\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 12.8764i | − | 0.732514i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.08277 | − | 15.7318i | 0.515036 | − | 0.892069i | −0.484811 | − | 0.874619i | \(-0.661112\pi\) |
0.999848 | − | 0.0174504i | \(-0.00555493\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.80533 | + | 11.7872i | 0.384660 | + | 0.666251i | 0.991722 | − | 0.128404i | \(-0.0409853\pi\) |
−0.607062 | + | 0.794655i | \(0.707652\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.0382461 | − | 0.116778i | −0.00215493 | − | 0.00657967i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 21.6407 | − | 12.4943i | 1.21546 | − | 0.701749i | 0.251520 | − | 0.967852i | \(-0.419070\pi\) |
0.963944 | + | 0.266103i | \(0.0857363\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.13000 | + | 7.15336i | −0.231235 | + | 0.400511i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 10.2170 | 0.570255 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.67400i | 0.0931437i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 27.2427 | + | 15.7286i | 1.51115 | + | 0.872465i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −5.84714 | − | 10.1275i | −0.323348 | − | 0.560054i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.52929 | + | 12.0380i | −0.139445 | + | 0.663679i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.34783 | + | 3.66492i | −0.348908 | + | 0.201442i | −0.664204 | − | 0.747551i | \(-0.731229\pi\) |
0.315296 | + | 0.948993i | \(0.397896\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.12720 | + | 0.650790i | 0.0617702 | + | 0.0356631i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.360588 | 0.0197010 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.49107 | 0.0812237 | 0.0406118 | − | 0.999175i | \(-0.487069\pi\) | ||||
0.0406118 | + | 0.999175i | \(0.487069\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −7.86764 | − | 4.54238i | −0.427311 | − | 0.246708i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.57197 | − | 3.79433i | 0.355892 | − | 0.205474i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10.7803 | + | 15.0594i | −0.582083 | + | 0.813129i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.161312 | − | 0.279401i | −0.00868477 | − | 0.0150425i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −20.6494 | − | 11.9219i | −1.10852 | − | 0.640003i | −0.170073 | − | 0.985431i | \(-0.554400\pi\) |
−0.938445 | + | 0.345428i | \(0.887734\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.5733i | 0.619504i | 0.950817 | + | 0.309752i | \(0.100246\pi\) | ||||
−0.950817 | + | 0.309752i | \(0.899754\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.29415 | 0.335957 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5.01488 | + | 8.68603i | −0.266915 | + | 0.462311i | −0.968064 | − | 0.250705i | \(-0.919338\pi\) |
0.701148 | + | 0.713015i | \(0.252671\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.475909 | − | 0.274766i | 0.0252586 | − | 0.0145831i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.33661 | + | 0.280832i | 0.0707408 | + | 0.0148632i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.80639 | + | 3.12876i | 0.0953375 | + | 0.165129i | 0.909749 | − | 0.415158i | \(-0.136274\pi\) |
−0.814412 | + | 0.580287i | \(0.802940\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.24214 | + | 7.34760i | −0.223271 | + | 0.386716i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.94479i | 0.102075i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.517420i | 0.0270830i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.0055 | − | 19.0620i | 0.574480 | − | 0.995029i | −0.421617 | − | 0.906774i | \(-0.638537\pi\) |
0.996098 | − | 0.0882554i | \(-0.0281292\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.09417 | + | 8.82337i | 0.265192 | + | 0.459326i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.67568 | − | 14.2763i | −0.242749 | − | 0.741190i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −27.9915 | + | 16.1609i | −1.44934 | + | 0.836780i | −0.998442 | − | 0.0557935i | \(-0.982231\pi\) |
−0.450903 | + | 0.892573i | \(0.648898\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.232173 | − | 0.402136i | 0.0119894 | − | 0.0207662i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 14.4500 | 0.744215 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 16.6668i | 0.856115i | 0.903751 | + | 0.428058i | \(0.140802\pi\) | ||||
−0.903751 | + | 0.428058i | \(0.859198\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −12.2161 | − | 7.05296i | −0.625849 | − | 0.361334i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 12.1998 | + | 21.1307i | 0.623383 | + | 1.07973i | 0.988851 | + | 0.148907i | \(0.0475755\pi\) |
−0.365468 | + | 0.930824i | \(0.619091\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.329246 | − | 0.295060i | −0.0167799 | − | 0.0150377i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 7.89955 | − | 4.56081i | 0.401557 | − | 0.231839i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7.38356 | + | 4.26290i | 0.374362 | + | 0.216138i | 0.675362 | − | 0.737486i | \(-0.263987\pi\) |
−0.301001 | + | 0.953624i | \(0.597321\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.58589 | 0.181346 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −17.1107 | −0.863120 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.221292 | − | 0.127763i | −0.0111344 | − | 0.00642845i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.91805 | + | 3.41679i | −0.297019 | + | 0.171484i | −0.641103 | − | 0.767455i | \(-0.721523\pi\) |
0.344084 | + | 0.938939i | \(0.388189\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −6.38934 | − | 5.72593i | −0.319867 | − | 0.286655i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.24408 | + | 9.08301i | 0.261877 | + | 0.453584i | 0.966741 | − | 0.255759i | \(-0.0823253\pi\) |
−0.704864 | + | 0.709343i | \(0.748992\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −11.4970 | − | 6.63780i | −0.572707 | − | 0.330652i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 0.0464447i | − | 0.00230786i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.68294 | 0.232125 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.01466 | + | 6.95360i | −0.198512 | + | 0.343833i | −0.948046 | − | 0.318133i | \(-0.896944\pi\) |
0.749534 | + | 0.661966i | \(0.230278\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.30578 | − | 2.48594i | 0.212388 | − | 0.122622i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.35888 | − | 4.14911i | −0.0668663 | − | 0.204164i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.191591 | − | 0.331846i | −0.00940485 | − | 0.0162897i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.60234 | − | 4.50739i | 0.127437 | − | 0.220728i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 16.7264i | 0.817139i | 0.912727 | + | 0.408570i | \(0.133972\pi\) | ||||
−0.912727 | + | 0.408570i | \(0.866028\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.7157i | 0.717199i | 0.933492 | + | 0.358599i | \(0.116746\pi\) | ||||
−0.933492 | + | 0.358599i | \(0.883254\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.32465 | + | 4.02641i | −0.113028 | + | 0.195771i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.28999 | + | 2.23434i | 0.0625739 | + | 0.108381i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.30028 | + | 0.693416i | 0.159712 | + | 0.0335568i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 19.6117 | − | 11.3228i | 0.946862 | − | 0.546671i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.57036 | + | 2.71995i | −0.0756416 | + | 0.131015i | −0.901365 | − | 0.433060i | \(-0.857434\pi\) |
0.825723 | + | 0.564075i | \(0.190767\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 33.6748 | 1.61831 | 0.809155 | − | 0.587595i | \(-0.199925\pi\) | ||||
0.809155 | + | 0.587595i | \(0.199925\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 0.106627i | − | 0.00511239i | ||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −19.5080 | − | 11.2629i | −0.933192 | − | 0.538779i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.68016 | − | 6.37423i | −0.175645 | − | 0.304225i | 0.764740 | − | 0.644340i | \(-0.222868\pi\) |
−0.940384 | + | 0.340114i | \(0.889534\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.64377 | + | 4.14100i | −0.268751 | + | 0.197190i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 22.3955 | − | 12.9300i | 1.06404 | − | 0.614325i | 0.137494 | − | 0.990503i | \(-0.456095\pi\) |
0.926547 | + | 0.376178i | \(0.122762\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.593857 | + | 0.342863i | 0.0281515 | + | 0.0162533i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0.838167 | 0.0396439 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −19.7508 | −0.932096 | −0.466048 | − | 0.884759i | \(-0.654323\pi\) | ||||
−0.466048 | + | 0.884759i | \(0.654323\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 31.7455 | + | 18.3283i | 1.49484 | + | 0.863044i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.57379 | − | 3.21803i | 0.261879 | − | 0.151196i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.159032 | + | 0.756906i | −0.00745555 | + | 0.0354843i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.28552 | − | 2.22658i | −0.0601339 | − | 0.104155i | 0.834391 | − | 0.551173i | \(-0.185819\pi\) |
−0.894525 | + | 0.447018i | \(0.852486\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.447060 | + | 0.258110i | 0.0208670 | + | 0.0120476i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 30.2081i | − | 1.40693i | −0.710728 | − | 0.703467i | \(-0.751634\pi\) | ||
0.710728 | − | 0.703467i | \(-0.248366\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 20.1707 | 0.937412 | 0.468706 | − | 0.883354i | \(-0.344720\pi\) | ||||
0.468706 | + | 0.883354i | \(0.344720\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.0489805 | + | 0.0848367i | −0.00227142 | + | 0.00393421i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −7.99333 | + | 4.61495i | −0.369887 | + | 0.213554i | −0.673409 | − | 0.739270i | \(-0.735171\pi\) |
0.303522 | + | 0.952824i | \(0.401837\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.39332 | − | 19.5208i | −0.295216 | − | 0.901389i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.73288 | + | 4.73349i | 0.125925 | + | 0.218108i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 16.4093 | − | 28.4217i | 0.754499 | − | 1.30683i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 16.2070i | − | 0.743627i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 5.67797i | − | 0.259976i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −19.6055 | + | 33.9577i | −0.895797 | + | 1.55157i | −0.0629820 | + | 0.998015i | \(0.520061\pi\) |
−0.832815 | + | 0.553551i | \(0.813272\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.09617 | − | 7.09477i | −0.186769 | − | 0.323494i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −12.2656 | + | 13.6867i | −0.558104 | + | 0.622766i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.247956 | − | 0.143157i | 0.0112591 | − | 0.00650045i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.06454 | − | 5.30794i | 0.138868 | − | 0.240526i | −0.788201 | − | 0.615418i | \(-0.788987\pi\) |
0.927068 | + | 0.374893i | \(0.122320\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −15.2542 | −0.689817 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 20.5291i | 0.926463i | 0.886237 | + | 0.463232i | \(0.153310\pi\) | ||||
−0.886237 | + | 0.463232i | \(0.846690\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.02636 | + | 0.592567i | 0.0462248 | + | 0.0266879i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.0835514 | − | 0.144715i | −0.00375536 | − | 0.00650447i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −23.3128 | − | 20.8922i | −1.04572 | − | 0.937143i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9.57940 | + | 5.53067i | −0.428833 | + | 0.247587i | −0.698849 | − | 0.715269i | \(-0.746304\pi\) |
0.270016 | + | 0.962856i | \(0.412971\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.53688 | + | 0.887315i | 0.0686625 | + | 0.0396423i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2.64242 | −0.117820 | −0.0589099 | − | 0.998263i | \(-0.518762\pi\) | ||||
−0.0589099 | + | 0.998263i | \(0.518762\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.371906 | −0.0165496 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −23.0504 | − | 13.3082i | −1.02371 | − | 0.591036i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −28.9903 | + | 16.7376i | −1.28497 | + | 0.741880i | −0.977753 | − | 0.209758i | \(-0.932732\pi\) |
−0.307220 | + | 0.951638i | \(0.599399\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 28.0111 | − | 9.17400i | 1.23914 | − | 0.405834i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.62140 | − | 2.80834i | −0.0715864 | − | 0.123991i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.517919 | + | 0.299021i | 0.0228222 | + | 0.0131764i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 16.7277i | 0.735682i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.58227 | 0.113349 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.4133 | − | 21.5005i | 0.543837 | − | 0.941954i | −0.454842 | − | 0.890572i | \(-0.650304\pi\) |
0.998679 | − | 0.0513815i | \(-0.0163625\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.00205 | + | 2.31058i | −0.174997 | + | 0.101035i | −0.584940 | − | 0.811076i | \(-0.698882\pi\) |
0.409943 | + | 0.912111i | \(0.365549\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −12.9405 | − | 2.71891i | −0.564770 | − | 0.118663i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −0.544406 | − | 0.942938i | −0.0237147 | − | 0.0410750i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12.6264 | + | 21.8696i | −0.548976 | + | 0.950854i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 1.65018i | − | 0.0716117i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 64.1270i | − | 2.77765i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.237262 | + | 0.410950i | −0.0102577 | + | 0.0177669i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 9.84027 | + | 17.0438i | 0.424639 | + | 0.735496i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −10.1358 | + | 23.0556i | −0.436580 | + | 0.993075i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −21.7241 | + | 12.5424i | −0.933992 | + | 0.539241i | −0.888072 | − | 0.459704i | \(-0.847955\pi\) |
−0.0459203 | + | 0.998945i | \(0.514622\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 12.7807 | − | 22.1367i | 0.548470 | − | 0.949979i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.543137 | 0.0232654 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 38.8014i | 1.65903i | 0.558487 | + | 0.829514i | \(0.311382\pi\) | ||||
−0.558487 | + | 0.829514i | \(0.688618\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.10386 | + | 0.637312i | 0.0471115 | + | 0.0271998i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.72239 | − | 6.44736i | −0.158579 | − | 0.274667i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.99303 | + | 14.2452i | −0.127276 | + | 0.605766i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.0523525 | + | 0.0302257i | −0.00222224 | + | 0.00128301i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 27.2335 | + | 15.7233i | 1.15392 | + | 0.666217i | 0.949840 | − | 0.312737i | \(-0.101246\pi\) |
0.204082 | + | 0.978954i | \(0.434579\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −57.4128 | −2.42830 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.85730 | 0.0784154 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −9.22107 | − | 5.32379i | −0.388622 | − | 0.224371i | 0.292941 | − | 0.956131i | \(-0.405366\pi\) |
−0.681563 | + | 0.731760i | \(0.738699\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.365410 | − | 0.210970i | 0.0153729 | − | 0.00887556i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.51434 | + | 0.823477i | −0.105592 | + | 0.0345828i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −13.1394 | − | 22.7581i | −0.550832 | − | 0.954069i | −0.998215 | − | 0.0597265i | \(-0.980977\pi\) |
0.447383 | − | 0.894343i | \(-0.352356\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.37133 | + | 3.67849i | 0.266632 | + | 0.153940i | 0.627356 | − | 0.778733i | \(-0.284137\pi\) |
−0.360724 | + | 0.932673i | \(0.617470\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 13.9761i | − | 0.583859i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −34.7172 | −1.44781 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.42935 | − | 11.1360i | 0.267658 | − | 0.463596i | −0.700599 | − | 0.713555i | \(-0.747084\pi\) |
0.968256 | + | 0.249959i | \(0.0804171\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 15.6007 | − | 9.00706i | 0.648342 | − | 0.374321i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −14.5679 | + | 16.2557i | −0.604378 | + | 0.674402i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −10.2144 | − | 17.6918i | −0.423035 | − | 0.732719i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.146165 | + | 0.253165i | −0.00604318 | + | 0.0104671i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 7.51402i | − | 0.310137i | −0.987904 | − | 0.155068i | \(-0.950440\pi\) | ||
0.987904 | − | 0.155068i | \(-0.0495598\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.83969i | 0.281825i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.85041 | − | 3.20500i | 0.0761157 | − | 0.131836i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −9.63761 | − | 16.6928i | −0.395769 | − | 0.685492i | 0.597430 | − | 0.801921i | \(-0.296189\pi\) |
−0.993199 | + | 0.116429i | \(0.962855\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.0423349 | + | 0.0472398i | −0.00173556 | + | 0.00193664i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.52800 | + | 0.882192i | −0.0625369 | + | 0.0361057i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.76773 | + | 13.4541i | −0.317381 | + | 0.549720i | −0.979941 | − | 0.199289i | \(-0.936137\pi\) |
0.662560 | + | 0.749009i | \(0.269470\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −44.5011 | −1.81524 | −0.907620 | − | 0.419793i | \(-0.862103\pi\) | ||||
−0.907620 | + | 0.419793i | \(0.862103\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 7.76382i | − | 0.316167i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.0782241 | − | 0.0451627i | −0.00318026 | − | 0.00183612i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −11.9183 | − | 20.6432i | −0.483751 | − | 0.837881i | 0.516075 | − | 0.856543i | \(-0.327393\pi\) |
−0.999826 | + | 0.0186624i | \(0.994059\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5.77239 | + | 1.89053i | −0.233909 | + | 0.0766081i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 25.3428 | − | 14.6317i | 1.02526 | − | 0.591935i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 17.7261 | + | 10.2342i | 0.715950 | + | 0.413354i | 0.813260 | − | 0.581900i | \(-0.197690\pi\) |
−0.0973099 | + | 0.995254i | \(0.531024\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.473195 | −0.0190811 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 19.3039 | 0.777146 | 0.388573 | − | 0.921418i | \(-0.372968\pi\) | ||||
0.388573 | + | 0.921418i | \(0.372968\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 21.1475 | + | 12.2095i | 0.849990 | + | 0.490742i | 0.860647 | − | 0.509201i | \(-0.170059\pi\) |
−0.0106577 | + | 0.999943i | \(0.503393\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6.01578 | + | 3.47322i | −0.241405 | + | 0.139375i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8.03205 | − | 38.2282i | 0.321797 | − | 1.53158i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12.4838 | − | 21.6226i | −0.499353 | − | 0.864905i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −10.1041 | − | 5.83361i | −0.403519 | − | 0.232972i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 0.671902i | − | 0.0267905i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20.7613 | 0.826494 | 0.413247 | − | 0.910619i | \(-0.364395\pi\) | ||||
0.413247 | + | 0.910619i | \(0.364395\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −5.33785 | + | 9.24542i | −0.212160 | + | 0.367473i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0.567372 | − | 0.327573i | 0.0225155 | − | 0.0129993i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 43.7956 | − | 4.81075i | 1.73525 | − | 0.190609i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5.91599 | − | 10.2468i | −0.234033 | − | 0.405357i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −11.0483 | + | 19.1363i | −0.436383 | + | 0.755838i | −0.997407 | − | 0.0719616i | \(-0.977074\pi\) |
0.561024 | + | 0.827799i | \(0.310407\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 31.9358i | − | 1.25943i | −0.776828 | − | 0.629713i | \(-0.783173\pi\) | ||
0.776828 | − | 0.629713i | \(-0.216827\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.423651i | 0.0166812i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.48741 | − | 2.57626i | 0.0584760 | − | 0.101283i | −0.835305 | − | 0.549786i | \(-0.814709\pi\) |
0.893781 | + | 0.448503i | \(0.148043\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.96858 | − | 5.14173i | −0.116527 | − | 0.201831i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.46117 | + | 1.14744i | 0.214040 | + | 0.0449716i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −14.9217 | + | 8.61507i | −0.583933 | + | 0.337134i | −0.762695 | − | 0.646758i | \(-0.776124\pi\) |
0.178762 | + | 0.983892i | \(0.442791\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.397351 | − | 0.688231i | 0.0155258 | − | 0.0268914i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 11.1406 | 0.434635 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 27.7588i | − | 1.08133i | −0.841238 | − | 0.540665i | \(-0.818173\pi\) | ||
0.841238 | − | 0.540665i | \(-0.181827\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 28.3232 | + | 16.3524i | 1.10164 | + | 0.636034i | 0.936652 | − | 0.350261i | \(-0.113907\pi\) |
0.164991 | + | 0.986295i | \(0.447241\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.62459 | − | 2.81386i | −0.0630937 | − | 0.109281i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.378686 | − | 0.124024i | 0.0146848 | − | 0.00480946i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −13.8110 | + | 7.97377i | −0.534763 | + | 0.308746i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 19.2441 | + | 11.1106i | 0.744020 | + | 0.429560i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.58596 | 0.177039 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12.9387 | 0.498752 | 0.249376 | − | 0.968407i | \(-0.419775\pi\) | ||||
0.249376 | + | 0.968407i | \(0.419775\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.32826 | − | 2.49892i | −0.166595 | − | 0.0961835i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.12548 | − | 0.649798i | 0.0432558 | − | 0.0249738i | −0.478216 | − | 0.878242i | \(-0.658716\pi\) |
0.521472 | + | 0.853268i | \(0.325383\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −12.1463 | − | 10.8852i | −0.466133 | − | 0.417734i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −9.85697 | − | 17.0728i | −0.377720 | − | 0.654230i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −16.8225 | − | 9.71249i | −0.643696 | − | 0.371638i | 0.142341 | − | 0.989818i | \(-0.454537\pi\) |
−0.786037 | + | 0.618179i | \(0.787870\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.230918i | 0.00882291i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7.00679 | −0.267326 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −17.8690 | + | 30.9500i | −0.680755 | + | 1.17910i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.1725 | + | 6.45042i | −0.425020 | + | 0.245386i | −0.697223 | − | 0.716854i | \(-0.745581\pi\) |
0.272203 | + | 0.962240i | \(0.412248\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −6.35294 | + | 7.08899i | −0.241328 | + | 0.269288i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0.120865 | + | 0.209344i | 0.00458467 | + | 0.00794088i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.62972 | − | 4.55480i | 0.0996076 | − | 0.172526i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 24.7433i | 0.935879i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 34.3868i | 1.29877i | 0.760460 | + | 0.649385i | \(0.224974\pi\) | ||||
−0.760460 | + | 0.649385i | \(0.775026\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.11038 | + | 3.65528i | −0.0795944 | + | 0.137862i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.107968 | − | 0.187006i | −0.00406630 | − | 0.00704303i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.59400 | + | 20.1336i | 0.247993 | + | 0.757201i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −19.7915 | + | 11.4266i | −0.743284 | + | 0.429135i | −0.823262 | − | 0.567661i | \(-0.807848\pi\) |
0.0799779 | + | 0.996797i | \(0.474515\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.75086 | + | 4.76463i | −0.103165 | + | 0.178688i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 14.6514 | 0.548699 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.05177i | 0.0393340i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −19.0095 | − | 10.9752i | −0.709924 | − | 0.409875i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −5.21620 | − | 9.03472i | −0.194531 | − | 0.336938i | 0.752215 | − | 0.658917i | \(-0.228985\pi\) |
−0.946747 | + | 0.321979i | \(0.895652\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.00498 | − | 33.3399i | 0.260879 | − | 1.24164i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 12.8027 | − | 7.39162i | 0.476136 | − | 0.274897i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −9.93677 | − | 5.73700i | −0.369042 | − | 0.213067i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.48753 | 0.0922572 | 0.0461286 | − | 0.998936i | \(-0.485312\pi\) | ||||
0.0461286 | + | 0.998936i | \(0.485312\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.07791 | − | 2.35438i | −0.150827 | − | 0.0870800i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −0.674033 | + | 0.389153i | −0.0248960 | + | 0.0143737i | −0.512396 | − | 0.858749i | \(-0.671242\pi\) |
0.487500 | + | 0.873123i | \(0.337909\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.0354987 | − | 0.323169i | −0.00130939 | − | 0.0119203i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −13.9667 | − | 24.1910i | −0.514469 | − | 0.891086i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −22.4331 | − | 12.9518i | −0.825215 | − | 0.476438i | 0.0269963 | − | 0.999636i | \(-0.491406\pi\) |
−0.852212 | + | 0.523197i | \(0.824739\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 20.4106i | 0.749804i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 27.7729 | 1.01889 | 0.509445 | − | 0.860503i | \(-0.329851\pi\) | ||||
0.509445 | + | 0.860503i | \(0.329851\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.0194642 | + | 0.0337130i | −0.000713113 | + | 0.00123515i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −7.14497 | + | 4.12515i | −0.261421 | + | 0.150931i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 26.4539 | + | 5.55819i | 0.966606 | + | 0.203092i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10.5549 | + | 18.2816i | 0.385153 | + | 0.667105i | 0.991790 | − | 0.127874i | \(-0.0408153\pi\) |
−0.606637 | + | 0.794979i | \(0.707482\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 7.23926 | − | 12.5388i | 0.263813 | − | 0.456938i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.298921i | 0.0108788i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 46.6419i | − | 1.69523i | −0.530612 | − | 0.847615i | \(-0.678038\pi\) | ||
0.530612 | − | 0.847615i | \(-0.321962\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −12.4962 | + | 21.6441i | −0.453585 | + | 0.785632i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 12.5114 | + | 21.6703i | 0.453537 | + | 0.785550i | 0.998603 | − | 0.0528439i | \(-0.0168286\pi\) |
−0.545066 | + | 0.838393i | \(0.683495\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.62997 | − | 29.4034i | −0.348628 | − | 1.06447i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.0207636 | + | 0.0119879i | −0.000750709 | + | 0.000433422i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −5.19324 | + | 8.99495i | −0.187517 | + | 0.324789i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.32800 | 0.0478891 | 0.0239445 | − | 0.999713i | \(-0.492377\pi\) | ||||
0.0239445 | + | 0.999713i | \(0.492377\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 15.8746i | − | 0.571711i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 19.2488 | + | 11.1133i | 0.692332 | + | 0.399718i | 0.804485 | − | 0.593973i | \(-0.202441\pi\) |
−0.112153 | + | 0.993691i | \(0.535775\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.27072 | + | 9.12915i | 0.189330 | + | 0.327929i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.56453 | + | 2.29825i | 0.0920020 | + | 0.0824493i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −28.6124 | + | 16.5194i | −1.02514 | + | 0.591867i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −36.8668 | − | 21.2851i | −1.31920 | − | 0.761639i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.29579 | −0.0820448 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.253856 | −0.00906050 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 16.5930 | + | 9.57996i | 0.591476 | + | 0.341489i | 0.765681 | − | 0.643221i | \(-0.222402\pi\) |
−0.174205 | + | 0.984709i | \(0.555736\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0.281822 | − | 0.162710i | 0.0100331 | − | 0.00579263i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −17.8999 | − | 16.0413i | −0.636447 | − | 0.570364i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.01134 | − | 6.94784i | −0.142447 | − | 0.246725i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.228381 | + | 0.131856i | 0.00809984 | + | 0.00467645i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 35.9779i | 1.27440i | 0.770697 | + | 0.637201i | \(0.219908\pi\) | ||||
−0.770697 | + | 0.637201i | \(0.780092\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.40006 | 0.0849082 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7.38218 | − | 12.7863i | 0.260837 | − | 0.451782i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 34.7125 | − | 20.0413i | 1.22498 | − | 0.707241i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.265674 | − | 0.811187i | −0.00936378 | − | 0.0285906i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −11.7642 | − | 20.3761i | −0.414118 | − | 0.717273i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 4.56264 | − | 7.90272i | 0.160414 | − | 0.277845i | −0.774603 | − | 0.632447i | \(-0.782050\pi\) |
0.935017 | + | 0.354603i | \(0.115384\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 9.64051i | − | 0.338524i | −0.985571 | − | 0.169262i | \(-0.945862\pi\) | ||
0.985571 | − | 0.169262i | \(-0.0541384\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.50313i | 0.0527172i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.354237 | − | 0.613557i | 0.0124084 | − | 0.0214920i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 14.7898 | + | 25.6166i | 0.517428 | + | 0.896212i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 16.2969 | + | 3.42412i | 0.569461 | + | 0.119648i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 16.6309 | − | 9.60187i | 0.580423 | − | 0.335107i | −0.180878 | − | 0.983505i | \(-0.557894\pi\) |
0.761301 | + | 0.648398i | \(0.224561\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −0.820157 | + | 1.42055i | −0.0285889 | + | 0.0495174i | −0.879966 | − | 0.475037i | \(-0.842435\pi\) |
0.851377 | + | 0.524554i | \(0.175768\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −17.9817 | −0.626042 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 27.3891i | − | 0.952412i | −0.879334 | − | 0.476206i | \(-0.842012\pi\) | ||
0.879334 | − | 0.476206i | \(-0.157988\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −15.4922 | − | 8.94441i | −0.538065 | − | 0.310652i | 0.206229 | − | 0.978504i | \(-0.433881\pi\) |
−0.744294 | + | 0.667852i | \(0.767214\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7.31418 | + | 12.6685i | 0.253726 | + | 0.439466i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.30799 | + | 1.45427i | 0.114615 | + | 0.0503875i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.0713797 | + | 0.0412111i | −0.00247020 | + | 0.00142617i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.82662 | + | 1.05460i | 0.0631372 | + | 0.0364523i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −11.0644 | −0.381986 | −0.190993 | − | 0.981591i | \(-0.561171\pi\) | ||||
−0.190993 | + | 0.981591i | \(0.561171\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 23.7294 | 0.818253 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 18.4710 | + | 10.6642i | 0.636175 | + | 0.367296i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.07057 | − | 0.618094i | 0.0368287 | − | 0.0212631i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.05800 | + | 5.03550i | −0.0363533 | + | 0.173022i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 8.66416 | + | 15.0068i | 0.297353 | + | 0.515031i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 7.83002 | + | 4.52067i | 0.268410 | + | 0.154966i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 29.4621i | − | 1.00876i | −0.863480 | − | 0.504382i | \(-0.831720\pi\) | ||
0.863480 | − | 0.504382i | \(-0.168280\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.150611 | 0.00515078 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −8.88103 | + | 15.3824i | −0.303370 | + | 0.525453i | −0.976897 | − | 0.213710i | \(-0.931445\pi\) |
0.673527 | + | 0.739163i | \(0.264779\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −31.7456 | + | 18.3283i | −1.08314 | + | 0.625354i | −0.931743 | − | 0.363118i | \(-0.881712\pi\) |
−0.151402 | + | 0.988472i | \(0.548379\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 8.38987 | + | 25.6169i | 0.285926 | + | 0.873022i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.57129 | − | 2.72156i | −0.0534874 | − | 0.0926429i | 0.838042 | − | 0.545606i | \(-0.183700\pi\) |
−0.891529 | + | 0.452963i | \(0.850367\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.0599664 | + | 0.103865i | −0.00203892 | + | 0.00353151i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 16.7335i | 0.568300i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 19.7946i | 0.671485i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −24.4333 | + | 42.3197i | −0.827891 | + | 1.43395i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.08232 | − | 5.33874i | −0.104321 | − | 0.180689i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.819916 | − | 0.914912i | 0.0277182 | − | 0.0309297i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 12.4428 | − | 7.18384i | 0.420162 | − | 0.242581i | −0.274984 | − | 0.961449i | \(-0.588673\pi\) |
0.695147 | + | 0.718868i | \(0.255339\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −14.8463 | + | 25.7146i | −0.500754 | + | 0.867332i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −21.4314 | −0.722043 | −0.361022 | − | 0.932557i | \(-0.617572\pi\) | ||||
−0.361022 | + | 0.932557i | \(0.617572\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 29.5761i | − | 0.995316i | −0.867373 | − | 0.497658i | \(-0.834194\pi\) | ||
0.867373 | − | 0.497658i | \(-0.165806\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.0663740 | + | 0.0383210i | 0.00223114 | + | 0.00128815i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.90744 | − | 3.30379i | −0.0640456 | − | 0.110930i | 0.832225 | − | 0.554439i | \(-0.187067\pi\) |
−0.896270 | + | 0.443508i | \(0.853734\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −27.7932 | − | 24.9074i | −0.932153 | − | 0.835367i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.11586 | + | 1.79894i | −0.104385 | + | 0.0602669i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −13.0568 | − | 7.53836i | −0.436930 | − | 0.252262i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −0.914057 | −0.0305536 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 43.7219 | 1.45983 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.19353 | + | 2.42114i | 0.139862 | + | 0.0807494i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.53840 | + | 1.46554i | −0.0845662 | + | 0.0488243i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 22.9348 | − | 7.51144i | 0.763223 | − | 0.249965i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.593594 | + | 1.02813i | 0.0197317 | + | 0.0341763i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.23020 | + | 2.44231i | 0.140462 | + | 0.0810955i | 0.568584 | − | 0.822625i | \(-0.307491\pi\) |
−0.428122 | + | 0.903721i | \(0.640825\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 8.00751i | 0.265592i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 47.3325 | 1.56820 | 0.784098 | − | 0.620637i | \(-0.213126\pi\) | ||||
0.784098 | + | 0.620637i | \(0.213126\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −14.8418 | + | 25.7068i | −0.491193 | + | 0.850771i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.0512683 | + | 0.0295998i | −0.00169488 | + | 0.000978539i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −44.3033 | − | 9.30849i | −1.46302 | − | 0.307394i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −15.5826 | − | 26.9898i | −0.514022 | − | 0.890312i | −0.999868 | − | 0.0162672i | \(-0.994822\pi\) |
0.485846 | − | 0.874044i | \(-0.338512\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.44121 | + | 4.22831i | −0.0804407 | + | 0.139327i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 74.4722i | 2.45128i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.50509i | 0.213886i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 6.43821 | − | 11.1513i | 0.211459 | − | 0.366257i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 14.3019 | + | 24.7717i | 0.469231 | + | 0.812733i | 0.999381 | − | 0.0351712i | \(-0.0111977\pi\) |
−0.530150 | + | 0.847904i | \(0.677864\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −13.4284 | − | 18.3016i | −0.440098 | − | 0.599811i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 15.7318 | − | 9.08277i | 0.515036 | − | 0.297356i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.0431310 | + | 0.0747050i | −0.00141053 | + | 0.00244312i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.62816 | 0.183864 | 0.0919320 | − | 0.995765i | \(-0.470696\pi\) | ||||
0.0919320 | + | 0.995765i | \(0.470696\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 13.6107i | 0.444167i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −29.2442 | − | 16.8842i | −0.953334 | − | 0.550408i | −0.0592190 | − | 0.998245i | \(-0.518861\pi\) |
−0.894115 | + | 0.447837i | \(0.852194\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 35.3863 | + | 61.2909i | 1.15234 | + | 1.99591i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.0252667 | − | 0.120255i | 0.000821925 | − | 0.00391191i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 10.1554 | − | 5.86321i | 0.330005 | − | 0.190529i | −0.325838 | − | 0.945426i | \(-0.605646\pi\) |
0.655843 | + | 0.754897i | \(0.272313\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −60.7261 | − | 35.0602i | −1.97125 | − | 1.13810i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 24.9886 | 0.810310 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 37.7047 | 1.22137 | 0.610687 | − | 0.791872i | \(-0.290893\pi\) | ||||
0.610687 | + | 0.791872i | \(0.290893\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.562150 | + | 0.324557i | 0.0181907 | + | 0.0105024i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −7.15336 | + | 4.13000i | −0.231235 | + | 0.133504i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 12.5010 | − | 4.09423i | 0.403678 | − | 0.132210i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.2756 | + | 22.9941i | 0.428247 | + | 0.741745i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 8.84815 | + | 5.10848i | 0.285128 | + | 0.164619i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0.836660i | 0.0269330i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.89648 | 0.286092 | 0.143046 | − | 0.989716i | \(-0.454310\pi\) | ||||
0.143046 | + | 0.989716i | \(0.454310\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.836999 | + | 1.44972i | −0.0268883 | + | 0.0465719i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −52.8744 | + | 30.5270i | −1.69682 | + | 0.979659i | −0.748074 | + | 0.663615i | \(0.769021\pi\) |
−0.948745 | + | 0.316044i | \(0.897645\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9.19012 | − | 10.2549i | 0.294622 | − | 0.328757i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 15.7286 | + | 27.2427i | 0.503718 | + | 0.872465i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −23.8132 | + | 41.2456i | −0.761851 | + | 1.31956i | 0.180045 | + | 0.983658i | \(0.442376\pi\) |
−0.941896 | + | 0.335906i | \(0.890958\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 53.1205i | − | 1.69774i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 11.6943i | − | 0.373370i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 6.89129 | − | 11.9361i | 0.219798 | − | 0.380701i | −0.734948 | − | 0.678123i | \(-0.762793\pi\) |
0.954746 | + | 0.297422i | \(0.0961268\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.0859417 | + | 0.148855i | 0.00273833 | + | 0.00474293i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −8.20946 | + | 9.16061i | −0.261310 | + | 0.291585i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 54.8737 | − | 31.6813i | 1.74488 | − | 1.00741i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.32034 | − | 7.48305i | 0.137240 | − | 0.237707i | −0.789211 | − | 0.614122i | \(-0.789510\pi\) |
0.926451 | + | 0.376415i | \(0.122843\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −7.32984 | −0.232605 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 0.0819463i | − | 0.00259787i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 38.0017 | + | 21.9403i | 1.20353 | + | 0.694856i | 0.961337 | − | 0.275374i | \(-0.0888016\pi\) |
0.242188 | + | 0.970229i | \(0.422135\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.650790 | + | 1.12720i | 0.0205901 | + | 0.0356631i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 672.2.bk.a.529.13 | 32 | ||
3.2 | odd | 2 | 2016.2.cr.e.1873.9 | 32 | |||
4.3 | odd | 2 | 168.2.bc.a.109.3 | yes | 32 | ||
7.2 | even | 3 | inner | 672.2.bk.a.625.4 | 32 | ||
7.3 | odd | 6 | 4704.2.c.f.2353.12 | 16 | |||
7.4 | even | 3 | 4704.2.c.e.2353.5 | 16 | |||
8.3 | odd | 2 | 168.2.bc.a.109.14 | yes | 32 | ||
8.5 | even | 2 | inner | 672.2.bk.a.529.4 | 32 | ||
12.11 | even | 2 | 504.2.cj.e.109.14 | 32 | |||
21.2 | odd | 6 | 2016.2.cr.e.1297.8 | 32 | |||
24.5 | odd | 2 | 2016.2.cr.e.1873.8 | 32 | |||
24.11 | even | 2 | 504.2.cj.e.109.3 | 32 | |||
28.3 | even | 6 | 1176.2.c.f.589.9 | 16 | |||
28.11 | odd | 6 | 1176.2.c.e.589.9 | 16 | |||
28.23 | odd | 6 | 168.2.bc.a.37.14 | yes | 32 | ||
56.3 | even | 6 | 1176.2.c.f.589.10 | 16 | |||
56.11 | odd | 6 | 1176.2.c.e.589.10 | 16 | |||
56.37 | even | 6 | inner | 672.2.bk.a.625.13 | 32 | ||
56.45 | odd | 6 | 4704.2.c.f.2353.5 | 16 | |||
56.51 | odd | 6 | 168.2.bc.a.37.3 | ✓ | 32 | ||
56.53 | even | 6 | 4704.2.c.e.2353.12 | 16 | |||
84.23 | even | 6 | 504.2.cj.e.37.3 | 32 | |||
168.107 | even | 6 | 504.2.cj.e.37.14 | 32 | |||
168.149 | odd | 6 | 2016.2.cr.e.1297.9 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
168.2.bc.a.37.3 | ✓ | 32 | 56.51 | odd | 6 | ||
168.2.bc.a.37.14 | yes | 32 | 28.23 | odd | 6 | ||
168.2.bc.a.109.3 | yes | 32 | 4.3 | odd | 2 | ||
168.2.bc.a.109.14 | yes | 32 | 8.3 | odd | 2 | ||
504.2.cj.e.37.3 | 32 | 84.23 | even | 6 | |||
504.2.cj.e.37.14 | 32 | 168.107 | even | 6 | |||
504.2.cj.e.109.3 | 32 | 24.11 | even | 2 | |||
504.2.cj.e.109.14 | 32 | 12.11 | even | 2 | |||
672.2.bk.a.529.4 | 32 | 8.5 | even | 2 | inner | ||
672.2.bk.a.529.13 | 32 | 1.1 | even | 1 | trivial | ||
672.2.bk.a.625.4 | 32 | 7.2 | even | 3 | inner | ||
672.2.bk.a.625.13 | 32 | 56.37 | even | 6 | inner | ||
1176.2.c.e.589.9 | 16 | 28.11 | odd | 6 | |||
1176.2.c.e.589.10 | 16 | 56.11 | odd | 6 | |||
1176.2.c.f.589.9 | 16 | 28.3 | even | 6 | |||
1176.2.c.f.589.10 | 16 | 56.3 | even | 6 | |||
2016.2.cr.e.1297.8 | 32 | 21.2 | odd | 6 | |||
2016.2.cr.e.1297.9 | 32 | 168.149 | odd | 6 | |||
2016.2.cr.e.1873.8 | 32 | 24.5 | odd | 2 | |||
2016.2.cr.e.1873.9 | 32 | 3.2 | odd | 2 | |||
4704.2.c.e.2353.5 | 16 | 7.4 | even | 3 | |||
4704.2.c.e.2353.12 | 16 | 56.53 | even | 6 | |||
4704.2.c.f.2353.5 | 16 | 56.45 | odd | 6 | |||
4704.2.c.f.2353.12 | 16 | 7.3 | odd | 6 |