Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [980,2,Mod(569,980)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(980, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("980.569");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 980 = 2^{2} \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 980.q (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: | \(7.82533939809\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-19})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 4x^{2} - 5x + 25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 140) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 569.2 | ||
Root | \(2.13746 + 0.656712i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 980.569 |
Dual form | 980.2.q.g.949.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/980\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(197\) | \(491\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.50000 | − | 0.866025i | 0.866025 | − | 0.500000i | − | 1.00000i | \(-0.5\pi\) | |
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.63746 | − | 1.52274i | 0.732294 | − | 0.680989i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.13746 | − | 1.97014i | −0.342957 | − | 0.594018i | 0.642024 | − | 0.766685i | \(-0.278095\pi\) |
−0.984980 | + | 0.172666i | \(0.944762\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 6.09095i | − | 1.68933i | −0.535299 | − | 0.844663i | \(-0.679801\pi\) | ||
0.535299 | − | 0.844663i | \(-0.320199\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.13746 | − | 3.70219i | 0.293691 | − | 0.955901i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.13746 | + | 2.38876i | −1.00348 | + | 0.579360i | −0.909276 | − | 0.416193i | \(-0.863364\pi\) |
−0.0942047 | + | 0.995553i | \(0.530031\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.13746 | − | 3.70219i | 0.490367 | − | 0.849340i | −0.509572 | − | 0.860428i | \(-0.670196\pi\) |
0.999939 | + | 0.0110882i | \(0.00352954\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.774917 | + | 0.447399i | 0.161581 | + | 0.0932891i | 0.578610 | − | 0.815604i | \(-0.303595\pi\) |
−0.417029 | + | 0.908893i | \(0.636929\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.362541 | − | 4.98684i | 0.0725083 | − | 0.997368i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.19615i | 1.00000i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.27492 | 0.608137 | 0.304068 | − | 0.952650i | \(-0.401655\pi\) | ||||
0.304068 | + | 0.952650i | \(0.401655\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.13746 | − | 3.70219i | −0.383899 | − | 0.664932i | 0.607717 | − | 0.794154i | \(-0.292086\pi\) |
−0.991616 | + | 0.129221i | \(0.958752\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.41238 | − | 1.97014i | −0.594018 | − | 0.342957i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.86254 | + | 2.80739i | 0.799397 | + | 0.461532i | 0.843260 | − | 0.537506i | \(-0.180633\pi\) |
−0.0438633 | + | 0.999038i | \(0.513967\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.27492 | − | 9.13642i | −0.844663 | − | 1.46300i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 11.2749 | 1.76085 | 0.880423 | − | 0.474189i | \(-0.157259\pi\) | ||||
0.880423 | + | 0.474189i | \(0.157259\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.50958i | 0.992701i | 0.868122 | + | 0.496351i | \(0.165327\pi\) | ||||
−0.868122 | + | 0.496351i | \(0.834673\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.86254 | + | 1.07534i | 0.271680 | + | 0.156854i | 0.629651 | − | 0.776878i | \(-0.283198\pi\) |
−0.357971 | + | 0.933733i | \(0.616531\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.13746 | + | 7.16629i | −0.579360 | + | 1.00348i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.41238 | + | 3.70219i | −0.880808 | + | 0.508534i | −0.870925 | − | 0.491417i | \(-0.836479\pi\) |
−0.00988297 | + | 0.999951i | \(0.503146\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.86254 | − | 1.49397i | −0.655665 | − | 0.201446i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 7.40437i | − | 0.980733i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.13746 | − | 3.70219i | −0.278273 | − | 0.481984i | 0.692682 | − | 0.721243i | \(-0.256429\pi\) |
−0.970956 | + | 0.239259i | \(0.923095\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.774917 | − | 1.34220i | 0.0992180 | − | 0.171851i | −0.812143 | − | 0.583458i | \(-0.801699\pi\) |
0.911361 | + | 0.411608i | \(0.135033\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −9.27492 | − | 9.97368i | −1.15041 | − | 1.23708i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.0498 | + | 6.95698i | −1.47212 | + | 0.849930i | −0.999509 | − | 0.0313404i | \(-0.990022\pi\) |
−0.472613 | + | 0.881270i | \(0.656689\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.54983 | 0.186578 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.5498 | 1.25204 | 0.626018 | − | 0.779809i | \(-0.284684\pi\) | ||||
0.626018 | + | 0.779809i | \(0.284684\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.86254 | − | 1.07534i | 0.217994 | − | 0.125859i | −0.387027 | − | 0.922068i | \(-0.626498\pi\) |
0.605021 | + | 0.796209i | \(0.293165\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.77492 | − | 7.79423i | −0.435890 | − | 0.900000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.137459 | + | 0.238085i | −0.0154653 | + | 0.0267867i | −0.873654 | − | 0.486547i | \(-0.838256\pi\) |
0.858189 | + | 0.513334i | \(0.171590\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.50000 | + | 7.79423i | 0.500000 | + | 0.866025i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.67232i | 0.622618i | 0.950309 | + | 0.311309i | \(0.100767\pi\) | ||||
−0.950309 | + | 0.311309i | \(0.899233\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.13746 | + | 10.2118i | −0.340305 | + | 1.10762i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.91238 | − | 2.83616i | 0.526662 | − | 0.304068i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.50000 | − | 6.06218i | 0.370999 | − | 0.642590i | −0.618720 | − | 0.785611i | \(-0.712349\pi\) |
0.989720 | + | 0.143022i | \(0.0456819\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −6.41238 | − | 3.70219i | −0.664932 | − | 0.383899i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.13746 | − | 9.31697i | −0.219299 | − | 0.955901i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.92820i | 0.703452i | 0.936103 | + | 0.351726i | \(0.114405\pi\) | ||||
−0.936103 | + | 0.351726i | \(0.885595\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.774917 | + | 1.34220i | 0.0771071 | + | 0.133553i | 0.902001 | − | 0.431735i | \(-0.142098\pi\) |
−0.824894 | + | 0.565288i | \(0.808765\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.22508 | − | 1.28465i | −0.219244 | − | 0.126581i | 0.386356 | − | 0.922350i | \(-0.373734\pi\) |
−0.605600 | + | 0.795769i | \(0.707067\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.0498 | + | 6.95698i | 1.16490 | + | 0.672556i | 0.952474 | − | 0.304621i | \(-0.0985297\pi\) |
0.212428 | + | 0.977177i | \(0.431863\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.77492 | + | 3.07425i | 0.170006 | + | 0.294459i | 0.938422 | − | 0.345492i | \(-0.112288\pi\) |
−0.768416 | + | 0.639951i | \(0.778955\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.72508 | 0.923064 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 13.0192i | − | 1.22474i | −0.790572 | − | 0.612369i | \(-0.790217\pi\) | ||
0.790572 | − | 0.612369i | \(-0.209783\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.95017 | − | 0.447399i | 0.181854 | − | 0.0417201i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.91238 | − | 5.04438i | 0.264761 | − | 0.458580i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 16.9124 | − | 9.76436i | 1.52494 | − | 0.880423i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −7.00000 | − | 8.71780i | −0.626099 | − | 0.779744i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.78959i | 0.158801i | 0.996843 | + | 0.0794004i | \(0.0253006\pi\) | ||||
−0.996843 | + | 0.0794004i | \(0.974699\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.63746 | + | 9.76436i | 0.496351 | + | 0.859704i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.13746 | + | 15.8265i | −0.798343 | + | 1.38277i | 0.122351 | + | 0.992487i | \(0.460957\pi\) |
−0.920694 | + | 0.390285i | \(0.872377\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 7.91238 | + | 8.50848i | 0.680989 | + | 0.732294i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 7.96221 | − | 4.59698i | 0.680258 | − | 0.392747i | −0.119695 | − | 0.992811i | \(-0.538192\pi\) |
0.799952 | + | 0.600064i | \(0.204858\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −17.0997 | −1.45037 | −0.725187 | − | 0.688551i | \(-0.758247\pi\) | ||||
−0.725187 | + | 0.688551i | \(0.758247\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.72508 | 0.313709 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −12.0000 | + | 6.92820i | −1.00349 | + | 0.579365i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.36254 | − | 4.98684i | 0.445335 | − | 0.414134i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.77492 | − | 6.53835i | 0.309253 | − | 0.535642i | −0.668946 | − | 0.743311i | \(-0.733254\pi\) |
0.978199 | + | 0.207669i | \(0.0665876\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.1375 | + | 17.5586i | 0.824975 | + | 1.42890i | 0.901939 | + | 0.431864i | \(0.142144\pi\) |
−0.0769640 | + | 0.997034i | \(0.524523\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −9.13746 | − | 2.80739i | −0.733938 | − | 0.225495i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.41238 | + | 5.43424i | −0.751189 | + | 0.433699i | −0.826123 | − | 0.563489i | \(-0.809459\pi\) |
0.0749341 | + | 0.997188i | \(0.476125\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −6.41238 | + | 11.1066i | −0.508534 | + | 0.880808i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.41238 | − | 3.70219i | −0.502256 | − | 0.289978i | 0.227389 | − | 0.973804i | \(-0.426981\pi\) |
−0.729645 | + | 0.683826i | \(0.760315\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −8.58762 | + | 1.97014i | −0.668546 | + | 0.153375i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 12.6005i | − | 0.975058i | −0.873107 | − | 0.487529i | \(-0.837898\pi\) | ||
0.873107 | − | 0.487529i | \(-0.162102\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −24.0997 | −1.85382 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 16.2371 | + | 9.37451i | 1.23449 | + | 0.712731i | 0.967962 | − | 0.251097i | \(-0.0807915\pi\) |
0.266524 | + | 0.963828i | \(0.414125\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −6.41238 | − | 3.70219i | −0.481984 | − | 0.278273i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.137459 | + | 0.238085i | 0.0102741 | + | 0.0177953i | 0.871117 | − | 0.491076i | \(-0.163396\pi\) |
−0.860843 | + | 0.508871i | \(0.830063\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.7251 | 1.24317 | 0.621583 | − | 0.783348i | \(-0.286490\pi\) | ||||
0.621583 | + | 0.783348i | \(0.286490\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 2.68439i | − | 0.198436i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 12.2371 | − | 2.80739i | 0.899692 | − | 0.206403i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.41238 | + | 5.43424i | 0.688301 | + | 0.397391i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −11.4124 | + | 19.7668i | −0.825771 | + | 1.43028i | 0.0755585 | + | 0.997141i | \(0.475926\pi\) |
−0.901329 | + | 0.433135i | \(0.857407\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.96221 | − | 4.59698i | 0.573132 | − | 0.330898i | −0.185267 | − | 0.982688i | \(-0.559315\pi\) |
0.758399 | + | 0.651790i | \(0.225982\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −22.5498 | − | 6.92820i | −1.61483 | − | 0.496139i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 26.0383i | 1.85515i | 0.373634 | + | 0.927576i | \(0.378112\pi\) | ||||
−0.373634 | + | 0.927576i | \(0.621888\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.86254 | − | 8.42217i | −0.344696 | − | 0.597032i | 0.640602 | − | 0.767873i | \(-0.278685\pi\) |
−0.985299 | + | 0.170841i | \(0.945351\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −12.0498 | + | 20.8709i | −0.849930 | + | 1.47212i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 18.4622 | − | 17.1687i | 1.28946 | − | 1.19912i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −9.72508 | −0.672698 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −19.6495 | −1.35273 | −0.676364 | − | 0.736568i | \(-0.736445\pi\) | ||||
−0.676364 | + | 0.736568i | \(0.736445\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 15.8248 | − | 9.13642i | 1.08429 | − | 0.626018i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 9.91238 | + | 10.6592i | 0.676018 | + | 0.726949i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.86254 | − | 3.22602i | 0.125859 | − | 0.217994i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 14.5498 | + | 25.2011i | 0.978728 | + | 1.69521i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.71780i | 0.583787i | 0.956451 | + | 0.291893i | \(0.0942853\pi\) | ||||
−0.956451 | + | 0.291893i | \(0.905715\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.58762 | − | 3.22602i | 0.370864 | − | 0.214118i | −0.302972 | − | 0.952999i | \(-0.597979\pi\) |
0.673836 | + | 0.738881i | \(0.264646\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.13746 | − | 3.70219i | 0.141247 | − | 0.244647i | −0.786719 | − | 0.617311i | \(-0.788222\pi\) |
0.927967 | + | 0.372663i | \(0.121555\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 16.1375 | + | 9.31697i | 1.05720 | + | 0.610375i | 0.924656 | − | 0.380802i | \(-0.124352\pi\) |
0.132544 | + | 0.991177i | \(0.457686\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.68729 | − | 1.07534i | 0.305765 | − | 0.0701474i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.476171i | 0.0309306i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 14.5498 | 0.941151 | 0.470575 | − | 0.882360i | \(-0.344046\pi\) | ||||
0.470575 | + | 0.882360i | \(0.344046\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.41238 | − | 11.1066i | −0.413057 | − | 0.715436i | 0.582165 | − | 0.813071i | \(-0.302206\pi\) |
−0.995222 | + | 0.0976343i | \(0.968872\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −22.5498 | − | 13.0192i | −1.43481 | − | 0.828389i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.91238 | + | 8.50848i | 0.311309 | + | 0.539203i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.45017 | 0.344011 | 0.172006 | − | 0.985096i | \(-0.444975\pi\) | ||||
0.172006 | + | 0.985096i | \(0.444975\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 2.03559i | − | 0.127976i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.13746 | + | 18.0348i | 0.259098 | + | 1.12938i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −21.4124 | − | 12.3624i | −1.33567 | − | 0.771148i | −0.349506 | − | 0.936934i | \(-0.613650\pi\) |
−0.986162 | + | 0.165786i | \(0.946984\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −23.3248 | + | 13.4666i | −1.43827 | + | 0.830383i | −0.997729 | − | 0.0673516i | \(-0.978545\pi\) |
−0.440536 | + | 0.897735i | \(0.645212\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.86254 | + | 15.8265i | −0.298704 | + | 0.972217i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 12.1244i | − | 0.741999i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 14.7749 | + | 25.5909i | 0.900843 | + | 1.56031i | 0.826403 | + | 0.563080i | \(0.190384\pi\) |
0.0744400 | + | 0.997225i | \(0.476283\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.41238 | + | 11.1066i | −0.389524 | + | 0.674676i | −0.992386 | − | 0.123170i | \(-0.960694\pi\) |
0.602861 | + | 0.797846i | \(0.294027\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −10.2371 | + | 4.95807i | −0.617322 | + | 0.298983i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 16.1375 | − | 9.31697i | 0.969606 | − | 0.559802i | 0.0704898 | − | 0.997512i | \(-0.477544\pi\) |
0.899116 | + | 0.437710i | \(0.144210\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.00000 | 0.357930 | 0.178965 | − | 0.983855i | \(-0.442725\pi\) | ||||
0.178965 | + | 0.983855i | \(0.442725\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −16.9622 | + | 9.79314i | −1.00830 | + | 0.582142i | −0.910693 | − | 0.413084i | \(-0.864452\pi\) |
−0.0976056 | + | 0.995225i | \(0.531118\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −11.2749 | − | 12.1244i | −0.667868 | − | 0.718185i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.91238 | − | 5.04438i | 0.171316 | − | 0.296728i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.00000 | + | 10.3923i | 0.351726 | + | 0.609208i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.92820i | 0.404750i | 0.979308 | + | 0.202375i | \(0.0648660\pi\) | ||||
−0.979308 | + | 0.202375i | \(0.935134\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.13746 | − | 2.80739i | −0.532003 | − | 0.163453i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 10.2371 | − | 5.91041i | 0.594018 | − | 0.342957i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.72508 | − | 4.71998i | 0.157596 | − | 0.272964i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.32475 | + | 1.34220i | 0.133553 | + | 0.0771071i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.774917 | − | 3.37779i | −0.0443716 | − | 0.193411i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.99782i | 0.228167i | 0.993471 | + | 0.114084i | \(0.0363932\pi\) | ||||
−0.993471 | + | 0.114084i | \(0.963607\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.45017 | −0.253161 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.41238 | + | 11.1066i | 0.363612 | + | 0.629795i | 0.988552 | − | 0.150878i | \(-0.0482099\pi\) |
−0.624940 | + | 0.780673i | \(0.714877\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.5120 | − | 7.22383i | −0.707223 | − | 0.408315i | 0.102809 | − | 0.994701i | \(-0.467217\pi\) |
−0.810032 | + | 0.586386i | \(0.800550\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.31271 | − | 1.91259i | −0.186060 | − | 0.107422i | 0.404077 | − | 0.914725i | \(-0.367593\pi\) |
−0.590137 | + | 0.807303i | \(0.700926\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.72508 | − | 6.45203i | −0.208565 | − | 0.361244i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 24.0997 | 1.34511 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 20.4235i | 1.13640i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −30.3746 | − | 2.20822i | −1.68488 | − | 0.122490i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5.32475 | + | 3.07425i | 0.294459 | + | 0.170006i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.41238 | − | 4.17836i | 0.132596 | − | 0.229663i | −0.792080 | − | 0.610417i | \(-0.791002\pi\) |
0.924677 | + | 0.380753i | \(0.124335\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −9.13746 | + | 29.7405i | −0.499233 | + | 1.62490i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 13.0192i | − | 0.709198i | −0.935018 | − | 0.354599i | \(-0.884617\pi\) | ||
0.935018 | − | 0.354599i | \(-0.115383\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −11.2749 | − | 19.5287i | −0.612369 | − | 1.06065i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.86254 | + | 8.42217i | −0.263321 | + | 0.456086i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.53779 | − | 2.35999i | 0.136630 | − | 0.127058i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 10.5000 | − | 6.06218i | 0.563670 | − | 0.325435i | −0.190947 | − | 0.981600i | \(-0.561156\pi\) |
0.754617 | + | 0.656165i | \(0.227823\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11.2749 | −0.603532 | −0.301766 | − | 0.953382i | \(-0.597576\pi\) | ||||
−0.301766 | + | 0.953382i | \(0.597576\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 31.6495 | 1.68933 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 18.4124 | − | 10.6304i | 0.979992 | − | 0.565799i | 0.0777242 | − | 0.996975i | \(-0.475235\pi\) |
0.902268 | + | 0.431176i | \(0.141901\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 17.2749 | − | 16.0646i | 0.916857 | − | 0.852622i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −0.687293 | + | 1.19043i | −0.0362739 | + | 0.0628283i | −0.883592 | − | 0.468257i | \(-0.844882\pi\) |
0.847318 | + | 0.531085i | \(0.178216\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.362541 | + | 0.627940i | 0.0190811 | + | 0.0330495i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 10.0888i | − | 0.529523i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.41238 | − | 4.59698i | 0.0739271 | − | 0.240617i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12.7749 | − | 7.37560i | 0.666845 | − | 0.385003i | −0.128035 | − | 0.991770i | \(-0.540867\pi\) |
0.794880 | + | 0.606766i | \(0.207534\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.86254 | + | 2.80739i | 0.251773 | + | 0.145361i | 0.620576 | − | 0.784146i | \(-0.286899\pi\) |
−0.368803 | + | 0.929508i | \(0.620232\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −18.0498 | − | 7.01452i | −0.932089 | − | 0.362228i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 19.9474i | − | 1.02734i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −23.6495 | −1.21479 | −0.607397 | − | 0.794399i | \(-0.707786\pi\) | ||||
−0.607397 | + | 0.794399i | \(0.707786\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.54983 | + | 2.68439i | 0.0794004 | + | 0.137526i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −17.3248 | − | 10.0025i | −0.885253 | − | 0.511101i | −0.0128665 | − | 0.999917i | \(-0.504096\pi\) |
−0.872387 | + | 0.488816i | \(0.837429\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.68729 | − | 4.65453i | −0.136251 | − | 0.235994i | 0.789824 | − | 0.613334i | \(-0.210172\pi\) |
−0.926075 | + | 0.377340i | \(0.876839\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.27492 | −0.216192 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 31.6531i | 1.59669i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.137459 | + | 0.599168i | 0.00691629 | + | 0.0301474i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13.1375 | + | 7.58492i | 0.659350 | + | 0.380676i | 0.792029 | − | 0.610483i | \(-0.209025\pi\) |
−0.132679 | + | 0.991159i | \(0.542358\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.50000 | + | 2.59808i | −0.0749064 | + | 0.129742i | −0.901046 | − | 0.433724i | \(-0.857199\pi\) |
0.826139 | + | 0.563466i | \(0.190532\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −22.5498 | + | 13.0192i | −1.12329 | + | 0.648530i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 19.2371 | + | 5.91041i | 0.955901 | + | 0.293691i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 12.7732i | − | 0.633142i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.04983 | − | 8.74657i | −0.249698 | − | 0.432490i | 0.713744 | − | 0.700407i | \(-0.246998\pi\) |
−0.963442 | + | 0.267917i | \(0.913665\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7.96221 | − | 13.7910i | 0.392747 | − | 0.680258i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.63746 | + | 9.28819i | 0.423996 | + | 0.455940i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −25.6495 | + | 14.8087i | −1.25606 | + | 0.725187i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 17.0997 | 0.835373 | 0.417687 | − | 0.908591i | \(-0.362841\pi\) | ||||
0.417687 | + | 0.908591i | \(0.362841\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.27492 | 0.159610 | 0.0798048 | − | 0.996811i | \(-0.474570\pi\) | ||||
0.0798048 | + | 0.996811i | \(0.474570\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 10.4124 | + | 21.4989i | 0.505074 | + | 1.04285i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −12.0000 | + | 20.7846i | −0.579365 | + | 1.00349i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9.68729 | − | 16.7789i | −0.466620 | − | 0.808210i | 0.532653 | − | 0.846334i | \(-0.321195\pi\) |
−0.999273 | + | 0.0381236i | \(0.987862\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 26.8756i | − | 1.29156i | −0.763525 | − | 0.645778i | \(-0.776533\pi\) | ||
0.763525 | − | 0.645778i | \(-0.223467\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.72508 | − | 12.1244i | 0.178604 | − | 0.581318i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.31271 | − | 1.91259i | 0.158468 | − | 0.0914917i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.587624 | + | 1.01779i | −0.0280458 | + | 0.0485767i | −0.879708 | − | 0.475515i | \(-0.842262\pi\) |
0.851662 | + | 0.524092i | \(0.175595\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10.5000 | − | 6.06218i | −0.498870 | − | 0.288023i | 0.229377 | − | 0.973338i | \(-0.426331\pi\) |
−0.728247 | + | 0.685315i | \(0.759665\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.50000 | − | 15.2561i | −0.165916 | − | 0.723211i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 13.0767i | − | 0.618507i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 25.8248 | 1.21875 | 0.609373 | − | 0.792884i | \(-0.291421\pi\) | ||||
0.609373 | + | 0.792884i | \(0.291421\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −12.8248 | − | 22.2131i | −0.603894 | − | 1.04598i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 30.4124 | + | 17.5586i | 1.42890 | + | 0.824975i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17.6873 | − | 10.2118i | −0.827377 | − | 0.477686i | 0.0255769 | − | 0.999673i | \(-0.491858\pi\) |
−0.852954 | + | 0.521987i | \(0.825191\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −12.4124 | − | 21.4989i | −0.579360 | − | 1.00348i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14.0000 | 0.652045 | 0.326023 | − | 0.945362i | \(-0.394291\pi\) | ||||
0.326023 | + | 0.945362i | \(0.394291\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 6.50958i | − | 0.302526i | −0.988494 | − | 0.151263i | \(-0.951666\pi\) | ||
0.988494 | − | 0.151263i | \(-0.0483340\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −16.1375 | + | 3.70219i | −0.748357 | + | 0.171685i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −16.5997 | − | 9.58382i | −0.768141 | − | 0.443486i | 0.0640700 | − | 0.997945i | \(-0.479592\pi\) |
−0.832211 | + | 0.554459i | \(0.812925\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −9.41238 | + | 16.3027i | −0.433699 | + | 0.751189i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 12.8248 | − | 7.40437i | 0.589683 | − | 0.340453i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −17.6873 | − | 12.0014i | −0.811549 | − | 0.550660i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6.41238 | + | 11.1066i | 0.292989 | + | 0.507472i | 0.974515 | − | 0.224322i | \(-0.0720168\pi\) |
−0.681526 | + | 0.731794i | \(0.738683\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 17.0997 | − | 29.6175i | 0.779678 | − | 1.35044i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 10.5498 | + | 11.3446i | 0.479043 | + | 0.515134i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 28.9622 | − | 16.7213i | 1.31240 | − | 0.757716i | 0.329909 | − | 0.944013i | \(-0.392982\pi\) |
0.982494 | + | 0.186296i | \(0.0596485\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −12.8248 | −0.579955 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −13.4502 | −0.606997 | −0.303499 | − | 0.952832i | \(-0.598155\pi\) | ||||
−0.303499 | + | 0.952832i | \(0.598155\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −13.5498 | + | 7.82300i | −0.610254 | + | 0.352330i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 19.6873 | − | 34.0994i | 0.881324 | − | 1.52650i | 0.0314548 | − | 0.999505i | \(-0.489986\pi\) |
0.849869 | − | 0.526993i | \(-0.176681\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −10.9124 | − | 18.9008i | −0.487529 | − | 0.844425i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 16.1797i | − | 0.721418i | −0.932678 | − | 0.360709i | \(-0.882535\pi\) | ||
0.932678 | − | 0.360709i | \(-0.117465\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.31271 | + | 1.01779i | 0.147414 | + | 0.0452913i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −36.1495 | + | 20.8709i | −1.60546 | + | 0.926910i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 14.7749 | − | 25.5909i | 0.654887 | − | 1.13430i | −0.327036 | − | 0.945012i | \(-0.606050\pi\) |
0.981922 | − | 0.189285i | \(-0.0606170\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 19.2371 | + | 11.1066i | 0.849340 | + | 0.490367i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5.59967 | + | 1.28465i | −0.246751 | + | 0.0566085i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 4.89261i | − | 0.215177i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 32.4743 | 1.42546 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.41238 | − | 11.1066i | −0.280931 | − | 0.486587i | 0.690683 | − | 0.723158i | \(-0.257310\pi\) |
−0.971614 | + | 0.236570i | \(0.923977\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −10.1375 | − | 5.85286i | −0.443280 | − | 0.255928i | 0.261708 | − | 0.965147i | \(-0.415714\pi\) |
−0.704988 | + | 0.709219i | \(0.749048\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 17.6873 | + | 10.2118i | 0.770471 | + | 0.444831i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.0997 | − | 19.2252i | −0.482594 | − | 0.835878i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 68.6750i | − | 2.97464i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 30.3248 | − | 6.95698i | 1.31105 | − | 0.300776i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.412376 | + | 0.238085i | 0.0177953 | + | 0.0102741i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.22508 | − | 2.12191i | 0.0526704 | − | 0.0912278i | −0.838488 | − | 0.544920i | \(-0.816560\pi\) |
0.891159 | + | 0.453692i | \(0.149893\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 25.0876 | − | 14.4843i | 1.07661 | − | 0.621583i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7.58762 | + | 2.33122i | 0.325018 | + | 0.0998585i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 36.1271i | 1.54468i | 0.635208 | + | 0.772341i | \(0.280914\pi\) | ||||
−0.635208 | + | 0.772341i | \(0.719086\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.00000 | − | 12.1244i | 0.298210 | − | 0.516515i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 15.9244 | − | 14.8087i | 0.675954 | − | 0.628596i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.86254 | − | 2.80739i | 0.206032 | − | 0.118953i | −0.393434 | − | 0.919353i | \(-0.628713\pi\) |
0.599466 | + | 0.800400i | \(0.295380\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 39.6495 | 1.67700 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 18.8248 | 0.794782 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 10.5997 | − | 6.11972i | 0.446723 | − | 0.257916i | −0.259722 | − | 0.965683i | \(-0.583631\pi\) |
0.706445 | + | 0.707768i | \(0.250298\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −19.8248 | − | 21.3183i | −0.834034 | − | 0.896869i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −14.6873 | + | 25.4391i | −0.615723 | + | 1.06646i | 0.374534 | + | 0.927213i | \(0.377803\pi\) |
−0.990257 | + | 0.139251i | \(0.955531\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.137459 | + | 0.238085i | 0.00575246 | + | 0.00996356i | 0.868887 | − | 0.495010i | \(-0.164836\pi\) |
−0.863135 | + | 0.504974i | \(0.831502\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 39.5336i | 1.65154i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.51204 | − | 3.70219i | 0.104760 | − | 0.154392i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.13746 | − | 4.12081i | 0.297136 | − | 0.171552i | −0.344019 | − | 0.938963i | \(-0.611789\pi\) |
0.641156 | + | 0.767411i | \(0.278455\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 7.96221 | − | 13.7910i | 0.330898 | − | 0.573132i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 14.5876 | + | 8.42217i | 0.604158 | + | 0.348811i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 13.9715i | 0.576665i | 0.957530 | + | 0.288333i | \(0.0931009\pi\) | ||||
−0.957530 | + | 0.288333i | \(0.906899\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −18.2749 | −0.753005 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 22.5498 | + | 39.0575i | 0.927576 | + | 1.60661i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −17.5876 | − | 10.1542i | −0.722237 | − | 0.416984i | 0.0933384 | − | 0.995634i | \(-0.470246\pi\) |
−0.815576 | + | 0.578651i | \(0.803579\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −14.5876 | − | 8.42217i | −0.597032 | − | 0.344696i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.13746 | − | 1.97014i | −0.0464753 | − | 0.0804976i | 0.841852 | − | 0.539709i | \(-0.181466\pi\) |
−0.888327 | + | 0.459211i | \(0.848132\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −14.0000 | −0.571072 | −0.285536 | − | 0.958368i | \(-0.592172\pi\) | ||||
−0.285536 | + | 0.958368i | \(0.592172\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.91238 | − | 12.6948i | −0.118405 | − | 0.516115i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −27.8746 | − | 16.0934i | −1.13139 | − | 0.653211i | −0.187109 | − | 0.982339i | \(-0.559912\pi\) |
−0.944285 | + | 0.329128i | \(0.893245\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.54983 | − | 11.3446i | 0.264978 | − | 0.458955i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −32.0619 | + | 18.5109i | −1.29497 | + | 0.747650i | −0.979530 | − | 0.201297i | \(-0.935484\pi\) |
−0.315437 | + | 0.948947i | \(0.602151\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 12.8248 | − | 41.7419i | 0.517144 | − | 1.68319i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.57919i | 0.144093i | 0.997401 | + | 0.0720464i | \(0.0229530\pi\) | ||||
−0.997401 | + | 0.0720464i | \(0.977047\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −21.9622 | − | 38.0397i | −0.882736 | − | 1.52894i | −0.848287 | − | 0.529537i | \(-0.822366\pi\) |
−0.0344487 | − | 0.999406i | \(-0.510968\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.32475 | + | 4.02659i | −0.0932891 | + | 0.161581i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.7371 | − | 3.61587i | −0.989485 | − | 0.144635i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −14.5876 | + | 8.42217i | −0.582574 | + | 0.336349i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −26.8248 | −1.06957 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.90033 | 0.115460 | 0.0577302 | − | 0.998332i | \(-0.481614\pi\) | ||||
0.0577302 | + | 0.998332i | \(0.481614\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −29.4743 | + | 17.0170i | −1.17150 | + | 0.676364i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.72508 | + | 2.93039i | 0.108142 | + | 0.116289i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −14.0498 | − | 24.3350i | −0.554935 | − | 0.961176i | −0.997909 | − | 0.0646411i | \(-0.979410\pi\) |
0.442973 | − | 0.896535i | \(-0.353924\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 38.3353i | 1.51180i | 0.654689 | + | 0.755898i | \(0.272800\pi\) | ||||
−0.654689 | + | 0.755898i | \(0.727200\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 24.0997 | + | 7.40437i | 0.948924 | + | 0.291547i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −0.675248 | + | 0.389855i | −0.0265468 | + | 0.0153268i | −0.513215 | − | 0.858260i | \(-0.671546\pi\) |
0.486668 | + | 0.873587i | \(0.338212\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.86254 | + | 8.42217i | −0.190871 | + | 0.330599i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −32.0619 | − | 18.5109i | −1.25468 | − | 0.724389i | −0.282643 | − | 0.959225i | \(-0.591211\pi\) |
−0.972035 | + | 0.234836i | \(0.924545\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9.13746 | + | 39.8293i | 0.357030 | + | 1.55626i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 25.4502 | 0.991398 | 0.495699 | − | 0.868494i | \(-0.334912\pi\) | ||||
0.495699 | + | 0.868494i | \(0.334912\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.77492 | − | 13.4666i | −0.302409 | − | 0.523788i | 0.674272 | − | 0.738483i | \(-0.264458\pi\) |
−0.976681 | + | 0.214695i | \(0.931124\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 43.6495 | + | 25.2011i | 1.69521 | + | 0.978728i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.53779 | + | 1.46519i | 0.0982636 | + | 0.0567325i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 7.54983 | + | 13.0767i | 0.291893 | + | 0.505574i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.52575 | −0.136110 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 3.57919i | − | 0.137968i | −0.997618 | − | 0.0689838i | \(-0.978024\pi\) | ||
0.997618 | − | 0.0689838i | \(-0.0219757\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 25.9124 | + | 1.88382i | 0.997368 | + | 0.0725083i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 21.3127 | + | 12.3049i | 0.819114 | + | 0.472916i | 0.850111 | − | 0.526604i | \(-0.176535\pi\) |
−0.0309969 | + | 0.999519i | \(0.509868\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.58762 | − | 9.67805i | 0.214118 | − | 0.370864i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 13.5997 | − | 7.85177i | 0.520377 | − | 0.300440i | −0.216712 | − | 0.976236i | \(-0.569533\pi\) |
0.737089 | + | 0.675796i | \(0.236200\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.03779 | − | 19.6517i | 0.230692 | − | 0.750854i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 7.40437i | − | 0.282494i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 22.5498 | + | 39.0575i | 0.859080 | + | 1.48797i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.68729 | + | 6.38658i | −0.140271 | + | 0.242957i | −0.927599 | − | 0.373578i | \(-0.878131\pi\) |
0.787327 | + | 0.616535i | \(0.211464\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −28.0000 | + | 26.0383i | −1.06210 | + | 0.987689i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −46.6495 | + | 26.9331i | −1.76698 | + | 1.02016i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 32.2749 | 1.22075 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −13.8248 | −0.522154 | −0.261077 | − | 0.965318i | \(-0.584078\pi\) | ||||
−0.261077 | + | 0.965318i | \(0.584078\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 20.7870 | − | 12.0014i | 0.783995 | − | 0.452640i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 6.09967 | − | 5.67232i | 0.229727 | − | 0.213632i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −12.7749 | + | 22.1268i | −0.479772 | + | 0.830990i | −0.999731 | − | 0.0232018i | \(-0.992614\pi\) |
0.519959 | + | 0.854191i | \(0.325947\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 3.82518i | − | 0.143254i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9.09967 | + | 29.6175i | −0.340308 | + | 1.10763i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 21.8248 | − | 12.6005i | 0.815060 | − | 0.470575i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −3.68729 | + | 6.38658i | −0.137513 | + | 0.238179i | −0.926555 | − | 0.376160i | \(-0.877244\pi\) |
0.789042 | + | 0.614340i | \(0.210577\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −19.2371 | − | 11.1066i | −0.715436 | − | 0.413057i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.18729 | − | 16.3315i | 0.0440950 | − | 0.606536i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 18.6915i | 0.693228i | 0.938008 | + | 0.346614i | \(0.112669\pi\) | ||||
−0.938008 | + | 0.346614i | \(0.887331\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −15.5498 | − | 26.9331i | −0.575131 | − | 0.996157i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −28.8625 | − | 16.6638i | −1.06606 | − | 0.615491i | −0.138959 | − | 0.990298i | \(-0.544376\pi\) |
−0.927103 | + | 0.374807i | \(0.877709\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 27.4124 | + | 15.8265i | 1.00975 | + | 0.582978i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15.9622 | + | 27.6474i | 0.587179 | + | 1.01702i | 0.994600 | + | 0.103784i | \(0.0330950\pi\) |
−0.407420 | + | 0.913241i | \(0.633572\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −45.0997 | −1.65678 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 19.5287i | 0.716440i | 0.933637 | + | 0.358220i | \(0.116616\pi\) | ||||
−0.933637 | + | 0.358220i | \(0.883384\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.77492 | − | 16.4545i | −0.138302 | − | 0.602846i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11.1375 | − | 19.2906i | 0.406412 | − | 0.703926i | −0.588073 | − | 0.808808i | \(-0.700113\pi\) |
0.994485 | + | 0.104882i | \(0.0334466\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 8.17525 | − | 4.71998i | 0.297923 | − | 0.172006i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 43.3368 | + | 13.3148i | 1.57719 | + | 0.484575i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.43996i | 0.343101i | 0.985175 | + | 0.171551i | \(0.0548777\pi\) | ||||
−0.985175 | + | 0.171551i | \(0.945122\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.76287 | − | 3.05338i | −0.0639882 | − | 0.110831i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −14.9622 | + | 25.9153i | −0.542380 | + | 0.939429i | 0.456387 | + | 0.889781i | \(0.349143\pi\) |
−0.998767 | + | 0.0496479i | \(0.984190\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −22.5498 | + | 13.0192i | −0.814227 | + | 0.470094i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −14.0000 | −0.504853 | −0.252426 | − | 0.967616i | \(-0.581229\pi\) | ||||
−0.252426 | + | 0.967616i | \(0.581229\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −42.8248 | −1.54230 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −23.5876 | + | 13.6183i | −0.848388 | + | 0.489817i | −0.860107 | − | 0.510114i | \(-0.829603\pi\) |
0.0117187 | + | 0.999931i | \(0.496270\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −19.2371 | + | 9.31697i | −0.691018 | + | 0.334675i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 24.0997 | − | 41.7419i | 0.863460 | − | 1.49556i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12.0000 | − | 20.7846i | −0.429394 | − | 0.743732i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 17.0170i | 0.608137i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7.13746 | + | 23.2309i | −0.254747 | + | 0.829147i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.50000 | − | 0.866025i | 0.0534692 | − | 0.0308705i | −0.473027 | − | 0.881048i | \(-0.656839\pi\) |
0.526496 | + | 0.850177i | \(0.323505\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −23.3248 | + | 40.3997i | −0.830383 | + | 1.43827i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.17525 | − | 4.71998i | −0.290312 | − | 0.167611i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 6.41238 | + | 27.9509i | 0.227424 | + | 0.991316i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 29.3873i | 1.04095i | 0.853876 | + | 0.520476i | \(0.174246\pi\) | ||||
−0.853876 | + | 0.520476i | \(0.825754\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −10.2749 | −0.363500 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4.23713 | − | 2.44631i | −0.149525 | − | 0.0863283i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 44.3248 | + | 25.5909i | 1.56031 | + | 0.900843i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 21.5997 | + | 37.4117i | 0.759404 | + | 1.31533i | 0.943155 | + | 0.332353i | \(0.107843\pi\) |
−0.183751 | + | 0.982973i | \(0.558824\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −22.5498 | −0.791832 | −0.395916 | − | 0.918287i | \(-0.629573\pi\) | ||||
−0.395916 | + | 0.918287i | \(0.629573\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 22.2131i | 0.779048i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −16.1375 | + | 3.70219i | −0.565271 | + | 0.129682i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 24.0997 | + | 13.9140i | 0.843141 | + | 0.486788i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −8.68729 | + | 15.0468i | −0.303189 | + | 0.525138i | −0.976856 | − | 0.213896i | \(-0.931385\pi\) |
0.673668 | + | 0.739034i | \(0.264718\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 27.9743 | − | 16.1509i | 0.975121 | − | 0.562987i | 0.0743276 | − | 0.997234i | \(-0.476319\pi\) |
0.900794 | + | 0.434247i | \(0.142986\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −11.0619 | + | 16.3027i | −0.385125 | + | 0.567588i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 45.5670i | − | 1.58452i | −0.610183 | − | 0.792261i | \(-0.708904\pi\) | ||
0.610183 | − | 0.792261i | \(-0.291096\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −0.962210 | − | 1.66660i | −0.0334189 | − | 0.0578833i | 0.848832 | − | 0.528662i | \(-0.177306\pi\) |
−0.882251 | + | 0.470779i | \(0.843973\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 16.1375 | − | 27.9509i | 0.559802 | − | 0.969606i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −19.1873 | − | 20.6328i | −0.664004 | − | 0.714029i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 19.2371 | − | 11.1066i | 0.664932 | − | 0.383899i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 10.9003 | 0.376321 | 0.188161 | − | 0.982138i | \(-0.439747\pi\) | ||||
0.188161 | + | 0.982138i | \(0.439747\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18.2749 | −0.630170 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 9.00000 | − | 5.19615i | 0.309976 | − | 0.178965i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −39.4622 | + | 36.6975i | −1.35754 | + | 1.26243i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −16.9622 | + | 29.3794i | −0.582142 | + | 1.00830i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.51204 | + | 4.35099i | 0.0861118 | + | 0.149150i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 30.4547i | − | 1.04275i | −0.853327 | − | 0.521375i | \(-0.825419\pi\) | ||
0.853327 | − | 0.521375i | \(-0.174581\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −28.8625 | + | 16.6638i | −0.985926 | + | 0.569224i | −0.904054 | − | 0.427418i | \(-0.859423\pi\) |
−0.0818717 | + | 0.996643i | \(0.526090\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −17.6873 | + | 30.6353i | −0.603483 | + | 1.04526i | 0.388807 | + | 0.921319i | \(0.372887\pi\) |
−0.992289 | + | 0.123943i | \(0.960446\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −21.7749 | − | 12.5718i | −0.741227 | − | 0.427947i | 0.0812884 | − | 0.996691i | \(-0.474097\pi\) |
−0.822515 | + | 0.568743i | \(0.807430\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 40.8625 | − | 9.37451i | 1.38937 | − | 0.318743i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 10.0888i | − | 0.342632i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.625414 | 0.0212157 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 42.3746 | + | 73.3949i | 1.43581 | + | 2.48689i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 38.6873 | + | 22.3361i | 1.30638 | + | 0.754237i | 0.981490 | − | 0.191516i | \(-0.0613402\pi\) |
0.324887 | + | 0.945753i | \(0.394674\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 6.00000 | + | 10.3923i | 0.202375 | + | 0.350524i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −40.0241 | −1.34845 | −0.674223 | − | 0.738528i | \(-0.735521\pi\) | ||||
−0.674223 | + | 0.738528i | \(0.735521\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 20.6695i | − | 0.695585i | −0.937572 | − | 0.347792i | \(-0.886931\pi\) | ||
0.937572 | − | 0.347792i | \(-0.113069\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −16.1375 | + | 3.70219i | −0.542455 | + | 0.124448i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 33.9743 | + | 19.6150i | 1.14074 | + | 0.658609i | 0.946615 | − | 0.322367i | \(-0.104479\pi\) |
0.194129 | + | 0.980976i | \(0.437812\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 10.2371 | − | 17.7312i | 0.342957 | − | 0.594018i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7.96221 | − | 4.59698i | 0.266445 | − | 0.153832i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.587624 | + | 0.180541i | 0.0196421 | + | 0.00603483i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 9.43996i | − | 0.315191i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −7.00000 | − | 12.1244i | −0.233463 | − | 0.404370i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 17.6873 | − | 30.6353i | 0.589249 | − | 1.02061i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 27.3866 | − | 25.4679i | 0.910362 | − | 0.846582i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 39.2492 | − | 22.6605i | 1.30325 | − | 0.752430i | 0.322288 | − | 0.946642i | \(-0.395548\pi\) |
0.980960 | + | 0.194212i | \(0.0622148\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.09967 | 0.168960 | 0.0844798 | − | 0.996425i | \(-0.473077\pi\) | ||||
0.0844798 | + | 0.996425i | \(0.473077\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 11.1752 | − | 6.45203i | 0.369847 | − | 0.213531i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −4.08762 | − | 4.39558i | −0.135133 | − | 0.145313i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.96221 | − | 5.13070i | 0.0977143 | − | 0.169246i | −0.813024 | − | 0.582230i | \(-0.802180\pi\) |
0.910738 | + | 0.412984i | \(0.135514\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.46221 | + | 5.99672i | 0.114084 | + | 0.197599i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 64.2585i | − | 2.11509i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 15.7629 | − | 23.2309i | 0.518280 | − | 0.763828i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 8.95017 | − | 15.5021i | 0.293645 | − | 0.508609i | −0.681023 | − | 0.732262i | \(-0.738465\pi\) |
0.974669 | + | 0.223653i | \(0.0717982\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 19.2371 | + | 11.1066i | 0.629795 | + | 0.363612i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 23.6873 | − | 5.43424i | 0.774657 | − | 0.177719i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 10.5074i | 0.343262i | 0.985161 | + | 0.171631i | \(0.0549036\pi\) | ||||
−0.985161 | + | 0.171631i | \(0.945096\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −25.0241 | −0.816630 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.13746 | + | 3.70219i | 0.0696792 | + | 0.120688i | 0.898760 | − | 0.438441i | \(-0.144469\pi\) |
−0.829081 | + | 0.559129i | \(0.811136\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.73713 | + | 5.04438i | 0.284520 | + | 0.164268i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −36.1495 | − | 20.8709i | −1.17470 | − | 0.678214i | −0.219918 | − | 0.975518i | \(-0.570579\pi\) |
−0.954783 | + | 0.297304i | \(0.903912\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.54983 | − | 11.3446i | −0.212617 | − | 0.368263i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −6.62541 | −0.214844 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 29.6175i | 0.959405i | 0.877431 | + | 0.479702i | \(0.159255\pi\) | ||||
−0.877431 | + | 0.479702i | \(0.840745\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 11.4124 | + | 49.7454i | 0.369296 | + | 1.60972i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −11.1752 | − | 6.45203i | −0.361244 | − | 0.208565i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.36254 | − | 11.0202i | 0.205243 | − | 0.355492i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6.03779 | − | 19.6517i | 0.194363 | − | 0.632611i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 6.50958i | − | 0.209334i | −0.994507 | − | 0.104667i | \(-0.966622\pi\) | ||
0.994507 | − | 0.104667i | \(-0.0333777\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 17.6873 | + | 30.6353i | 0.568198 | + | 0.984147i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 7.96221 | − | 13.7910i | 0.255519 | − | 0.442573i | −0.709517 | − | 0.704688i | \(-0.751087\pi\) |
0.965036 | + | 0.262116i | \(0.0844202\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −47.4743 | + | 22.9928i | −1.52039 | + | 0.736360i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −14.5876 | + | 8.42217i | −0.466699 | + | 0.269449i | −0.714857 | − | 0.699271i | \(-0.753508\pi\) |
0.248158 | + | 0.968720i | \(0.420175\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −15.9244 | −0.508947 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 32.2251 | − | 18.6052i | 1.02782 | − | 0.593412i | 0.111461 | − | 0.993769i | \(-0.464447\pi\) |
0.916360 | + | 0.400356i | \(0.131114\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 39.6495 | + | 42.6366i | 1.26334 | + | 1.35852i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.91238 | + | 5.04438i | −0.0926082 | + | 0.160402i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 17.2371 | + | 29.8556i | 0.547555 | + | 0.948394i | 0.998441 | + | 0.0558122i | \(0.0177748\pi\) |
−0.450886 | + | 0.892582i | \(0.648892\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 8.35671i | − | 0.265192i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −20.7870 | − | 6.38658i | −0.658991 | − | 0.202468i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.13746 | + | 2.38876i | −0.131035 | + | 0.0756529i | −0.564084 | − | 0.825717i | \(-0.690771\pi\) |
0.433050 | + | 0.901370i | \(0.357437\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −14.5876 | + | 25.2665i | −0.461532 | + | 0.799397i |
(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 | 980.2.q.g.569.2 | 4 | ||
5.4 | even | 2 | 980.2.q.b.569.1 | 4 | |||
7.2 | even | 3 | 980.2.e.c.589.3 | 4 | |||
7.3 | odd | 6 | 140.2.q.b.109.1 | yes | 4 | ||
7.4 | even | 3 | 980.2.q.b.949.2 | 4 | |||
7.5 | odd | 6 | 980.2.e.f.589.2 | 4 | |||
7.6 | odd | 2 | 140.2.q.a.9.1 | ✓ | 4 | ||
21.17 | even | 6 | 1260.2.bm.b.109.2 | 4 | |||
21.20 | even | 2 | 1260.2.bm.a.289.2 | 4 | |||
28.3 | even | 6 | 560.2.bw.a.529.1 | 4 | |||
28.27 | even | 2 | 560.2.bw.e.289.1 | 4 | |||
35.2 | odd | 12 | 4900.2.a.bf.1.4 | 4 | |||
35.3 | even | 12 | 700.2.i.f.501.1 | 8 | |||
35.4 | even | 6 | inner | 980.2.q.g.949.2 | 4 | ||
35.9 | even | 6 | 980.2.e.c.589.1 | 4 | |||
35.12 | even | 12 | 4900.2.a.be.1.2 | 4 | |||
35.13 | even | 4 | 700.2.i.f.401.1 | 8 | |||
35.17 | even | 12 | 700.2.i.f.501.4 | 8 | |||
35.19 | odd | 6 | 980.2.e.f.589.4 | 4 | |||
35.23 | odd | 12 | 4900.2.a.bf.1.2 | 4 | |||
35.24 | odd | 6 | 140.2.q.a.109.1 | yes | 4 | ||
35.27 | even | 4 | 700.2.i.f.401.4 | 8 | |||
35.33 | even | 12 | 4900.2.a.be.1.4 | 4 | |||
35.34 | odd | 2 | 140.2.q.b.9.2 | yes | 4 | ||
105.59 | even | 6 | 1260.2.bm.a.109.2 | 4 | |||
105.104 | even | 2 | 1260.2.bm.b.289.1 | 4 | |||
140.59 | even | 6 | 560.2.bw.e.529.1 | 4 | |||
140.139 | even | 2 | 560.2.bw.a.289.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
140.2.q.a.9.1 | ✓ | 4 | 7.6 | odd | 2 | ||
140.2.q.a.109.1 | yes | 4 | 35.24 | odd | 6 | ||
140.2.q.b.9.2 | yes | 4 | 35.34 | odd | 2 | ||
140.2.q.b.109.1 | yes | 4 | 7.3 | odd | 6 | ||
560.2.bw.a.289.2 | 4 | 140.139 | even | 2 | |||
560.2.bw.a.529.1 | 4 | 28.3 | even | 6 | |||
560.2.bw.e.289.1 | 4 | 28.27 | even | 2 | |||
560.2.bw.e.529.1 | 4 | 140.59 | even | 6 | |||
700.2.i.f.401.1 | 8 | 35.13 | even | 4 | |||
700.2.i.f.401.4 | 8 | 35.27 | even | 4 | |||
700.2.i.f.501.1 | 8 | 35.3 | even | 12 | |||
700.2.i.f.501.4 | 8 | 35.17 | even | 12 | |||
980.2.e.c.589.1 | 4 | 35.9 | even | 6 | |||
980.2.e.c.589.3 | 4 | 7.2 | even | 3 | |||
980.2.e.f.589.2 | 4 | 7.5 | odd | 6 | |||
980.2.e.f.589.4 | 4 | 35.19 | odd | 6 | |||
980.2.q.b.569.1 | 4 | 5.4 | even | 2 | |||
980.2.q.b.949.2 | 4 | 7.4 | even | 3 | |||
980.2.q.g.569.2 | 4 | 1.1 | even | 1 | trivial | ||
980.2.q.g.949.2 | 4 | 35.4 | even | 6 | inner | ||
1260.2.bm.a.109.2 | 4 | 105.59 | even | 6 | |||
1260.2.bm.a.289.2 | 4 | 21.20 | even | 2 | |||
1260.2.bm.b.109.2 | 4 | 21.17 | even | 6 | |||
1260.2.bm.b.289.1 | 4 | 105.104 | even | 2 | |||
4900.2.a.be.1.2 | 4 | 35.12 | even | 12 | |||
4900.2.a.be.1.4 | 4 | 35.33 | even | 12 | |||
4900.2.a.bf.1.2 | 4 | 35.23 | odd | 12 | |||
4900.2.a.bf.1.4 | 4 | 35.2 | odd | 12 |