Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [576,2,Mod(49,576)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(576, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("576.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 576 = 2^{6} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 576.bb (of order \(12\), degree \(4\), 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: | \(4.59938315643\) |
Analytic rank: | \(0\) |
Dimension: | \(72\) |
Relative dimension: | \(18\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 144) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 337.11 | ||
Character | \(\chi\) | \(=\) | 576.337 |
Dual form | 576.2.bb.e.241.11 |
$q$-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 \(\left(\mathbb{Z}/576\mathbb{Z}\right)^\times\).
\(n\) | \(65\) | \(127\) | \(325\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
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 | ||||||||
\(3\) | −0.215523 | + | 1.71859i | −0.124432 | + | 0.992228i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.733432 | − | 2.73721i | −0.328001 | − | 1.22412i | −0.911261 | − | 0.411830i | \(-0.864890\pi\) |
0.583260 | − | 0.812286i | \(-0.301777\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.14487 | + | 0.660988i | −0.432718 | + | 0.249830i | −0.700504 | − | 0.713648i | \(-0.747041\pi\) |
0.267786 | + | 0.963479i | \(0.413708\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.90710 | − | 0.740791i | −0.969033 | − | 0.246930i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.28367 | − | 0.343957i | −0.387040 | − | 0.103707i | 0.0600515 | − | 0.998195i | \(-0.480874\pi\) |
−0.447092 | + | 0.894488i | \(0.647540\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.36696 | − | 0.902174i | 0.933827 | − | 0.250218i | 0.240341 | − | 0.970689i | \(-0.422741\pi\) |
0.693486 | + | 0.720470i | \(0.256074\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.86220 | − | 0.670538i | 1.25542 | − | 0.173132i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −7.60772 | −1.84514 | −0.922572 | − | 0.385825i | \(-0.873917\pi\) | ||||
−0.922572 | + | 0.385825i | \(0.873917\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.32297 | − | 4.32297i | −0.991757 | − | 0.991757i | 0.00820954 | − | 0.999966i | \(-0.497387\pi\) |
−0.999966 | + | 0.00820954i | \(0.997387\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.889223 | − | 2.11001i | −0.194044 | − | 0.460442i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.46087 | − | 1.99814i | −0.721642 | − | 0.416640i | 0.0937148 | − | 0.995599i | \(-0.470126\pi\) |
−0.815357 | + | 0.578959i | \(0.803459\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.62424 | + | 1.51511i | −0.524849 | + | 0.303021i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.89966 | − | 4.83645i | 0.365590 | − | 0.930776i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.950303 | − | 3.54658i | 0.176467 | − | 0.658583i | −0.819830 | − | 0.572606i | \(-0.805932\pi\) |
0.996297 | − | 0.0859765i | \(-0.0274010\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.569129 | + | 0.985760i | −0.102219 | + | 0.177048i | −0.912598 | − | 0.408857i | \(-0.865927\pi\) |
0.810380 | + | 0.585905i | \(0.199261\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.867781 | − | 2.13197i | 0.151061 | − | 0.371128i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.64894 | + | 2.64894i | 0.447753 | + | 0.447753i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.26014 | − | 2.26014i | 0.371565 | − | 0.371565i | −0.496482 | − | 0.868047i | \(-0.665375\pi\) |
0.868047 | + | 0.496482i | \(0.165375\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.824810 | + | 5.98086i | 0.132075 | + | 0.957704i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.42311 | + | 0.821634i | 0.222253 | + | 0.128318i | 0.606993 | − | 0.794707i | \(-0.292376\pi\) |
−0.384740 | + | 0.923025i | \(0.625709\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.17424 | + | 1.65438i | 0.941563 | + | 0.252291i | 0.696778 | − | 0.717287i | \(-0.254616\pi\) |
0.244784 | + | 0.969578i | \(0.421283\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.104463 | + | 8.50065i | 0.0155724 | + | 1.26720i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.58731 | − | 7.94546i | −0.669129 | − | 1.15896i | −0.978148 | − | 0.207909i | \(-0.933334\pi\) |
0.309020 | − | 0.951056i | \(-0.399999\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.62619 | + | 4.54869i | −0.375170 | + | 0.649813i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.63964 | − | 13.0746i | 0.229595 | − | 1.83080i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.72215 | − | 7.72215i | 1.06072 | − | 1.06072i | 0.0626852 | − | 0.998033i | \(-0.480034\pi\) |
0.998033 | − | 0.0626852i | \(-0.0199664\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.76593i | 0.507798i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 8.36111 | − | 6.49771i | 1.10746 | − | 0.860642i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.28879 | − | 4.80982i | −0.167786 | − | 0.626185i | −0.997668 | − | 0.0682473i | \(-0.978259\pi\) |
0.829883 | − | 0.557938i | \(-0.188407\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.66068 | + | 9.92979i | −0.340665 | + | 1.27138i | 0.556931 | + | 0.830559i | \(0.311979\pi\) |
−0.897596 | + | 0.440820i | \(0.854688\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.81789 | − | 1.07345i | 0.481009 | − | 0.135242i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.93887 | − | 8.55438i | −0.612592 | − | 1.06104i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −13.9276 | + | 3.73189i | −1.70153 | + | 0.455923i | −0.973324 | − | 0.229436i | \(-0.926312\pi\) |
−0.728205 | + | 0.685359i | \(0.759645\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.17987 | − | 5.51718i | 0.503198 | − | 0.664190i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.87498i | 0.934588i | 0.884102 | + | 0.467294i | \(0.154771\pi\) | ||||
−0.884102 | + | 0.467294i | \(0.845229\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 0.577222i | − | 0.0675588i | −0.999429 | − | 0.0337794i | \(-0.989246\pi\) | ||
0.999429 | − | 0.0337794i | \(-0.0107544\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.03826 | − | 4.83654i | −0.235358 | − | 0.558475i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.69698 | − | 0.454704i | 0.193389 | − | 0.0518183i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.716890 | − | 1.24169i | −0.0806564 | − | 0.139701i | 0.822876 | − | 0.568221i | \(-0.192368\pi\) |
−0.903532 | + | 0.428521i | \(0.859035\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.90246 | + | 4.30711i | 0.878051 | + | 0.478567i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.885341 | − | 3.30414i | 0.0971788 | − | 0.362676i | −0.900162 | − | 0.435555i | \(-0.856552\pi\) |
0.997341 | + | 0.0728790i | \(0.0232187\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.57975 | + | 20.8239i | 0.605208 | + | 2.25867i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.89030 | + | 2.39755i | 0.631506 | + | 0.257044i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 16.2114i | 1.71841i | 0.511635 | + | 0.859203i | \(0.329040\pi\) | ||||
−0.511635 | + | 0.859203i | \(0.670960\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.25839 | + | 3.25839i | −0.341572 | + | 0.341572i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.57146 | − | 1.19055i | −0.162952 | − | 0.123455i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −8.66225 | + | 15.0035i | −0.888728 | + | 1.53932i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.648931 | − | 1.12398i | −0.0658889 | − | 0.114123i | 0.831199 | − | 0.555975i | \(-0.187655\pi\) |
−0.897088 | + | 0.441852i | \(0.854322\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.47695 | + | 1.95085i | 0.349446 | + | 0.196068i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.73900 | − | 2.60956i | −0.969067 | − | 0.259661i | −0.260633 | − | 0.965438i | \(-0.583931\pi\) |
−0.708434 | + | 0.705777i | \(0.750598\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.04850 | + | 4.64680i | 0.793042 | + | 0.457863i | 0.841033 | − | 0.540985i | \(-0.181948\pi\) |
−0.0479901 | + | 0.998848i | \(0.515282\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −5.12335 | + | 3.98154i | −0.499988 | + | 0.388558i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.89502 | + | 1.89502i | −0.183199 | + | 0.183199i | −0.792748 | − | 0.609549i | \(-0.791350\pi\) |
0.609549 | + | 0.792748i | \(0.291350\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.63272 | − | 8.63272i | −0.826864 | − | 0.826864i | 0.160217 | − | 0.987082i | \(-0.448780\pi\) |
−0.987082 | + | 0.160217i | \(0.948780\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.39715 | + | 4.37137i | 0.322443 | + | 0.414912i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.70180 | + | 2.94761i | −0.160092 | + | 0.277288i | −0.934902 | − | 0.354907i | \(-0.884512\pi\) |
0.774809 | + | 0.632195i | \(0.217846\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.93099 | + | 10.9386i | −0.273317 | + | 1.02003i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −10.4564 | + | 0.128497i | −0.966695 | + | 0.0118796i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.70982 | − | 5.02862i | 0.798428 | − | 0.460972i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.99679 | − | 4.61695i | −0.726981 | − | 0.419722i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.71877 | + | 2.26866i | −0.154976 | + | 0.204559i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −3.94700 | − | 3.94700i | −0.353031 | − | 0.353031i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.24504 | 0.465422 | 0.232711 | − | 0.972546i | \(-0.425240\pi\) | ||||
0.232711 | + | 0.972546i | \(0.425240\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.17390 | + | 10.2544i | −0.367491 | + | 0.902852i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.27080 | − | 1.68026i | 0.547883 | − | 0.146805i | 0.0257490 | − | 0.999668i | \(-0.491803\pi\) |
0.522134 | + | 0.852864i | \(0.325136\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.80665 | + | 2.09178i | 0.676922 | + | 0.181381i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −14.6316 | − | 1.65256i | −1.25929 | − | 0.142229i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.16622 | − | 3.56007i | 0.526816 | − | 0.304157i | −0.212903 | − | 0.977073i | \(-0.568292\pi\) |
0.739719 | + | 0.672916i | \(0.234958\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.09091 | + | 4.07133i | 0.0925298 | + | 0.345326i | 0.996633 | − | 0.0819876i | \(-0.0261268\pi\) |
−0.904104 | + | 0.427313i | \(0.859460\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 14.6437 | − | 6.17128i | 1.23322 | − | 0.519716i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.63236 | −0.387378 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −10.4047 | −0.864063 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −7.25133 | − | 5.49369i | −0.598080 | − | 0.453112i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.25338 | + | 8.40971i | 0.184604 | + | 0.688950i | 0.994715 | + | 0.102674i | \(0.0327399\pi\) |
−0.810111 | + | 0.586276i | \(0.800593\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.8103 | − | 10.2828i | 1.44938 | − | 0.836803i | 0.450940 | − | 0.892554i | \(-0.351089\pi\) |
0.998445 | + | 0.0557515i | \(0.0177554\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 22.1164 | + | 5.63573i | 1.78801 | + | 0.455622i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.11564 | + | 0.834834i | 0.250255 | + | 0.0670555i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.90879 | − | 2.38710i | 0.710999 | − | 0.190512i | 0.114847 | − | 0.993383i | \(-0.463362\pi\) |
0.596152 | + | 0.802872i | \(0.296696\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 11.6069 | + | 14.9355i | 0.920487 | + | 1.18446i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.28298 | 0.416357 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.4053 | + | 10.4053i | 0.815004 | + | 0.815004i | 0.985379 | − | 0.170375i | \(-0.0544981\pi\) |
−0.170375 | + | 0.985379i | \(0.554498\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −6.47209 | − | 0.811644i | −0.503851 | − | 0.0631864i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −5.95392 | − | 3.43750i | −0.460728 | − | 0.266001i | 0.251622 | − | 0.967826i | \(-0.419036\pi\) |
−0.712350 | + | 0.701824i | \(0.752369\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.735830 | + | 0.424832i | −0.0566023 | + | 0.0326794i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 9.36488 | + | 15.7697i | 0.716150 | + | 1.20594i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.823927 | − | 3.07494i | 0.0626420 | − | 0.233783i | −0.927506 | − | 0.373808i | \(-0.878052\pi\) |
0.990148 | + | 0.140025i | \(0.0447184\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.00294 | − | 3.46919i | 0.151408 | − | 0.262246i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 8.54387 | − | 1.17827i | 0.642197 | − | 0.0885642i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.73648 | + | 3.73648i | 0.279278 | + | 0.279278i | 0.832821 | − | 0.553543i | \(-0.186725\pi\) |
−0.553543 | + | 0.832821i | \(0.686725\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.169132 | − | 0.169132i | 0.0125715 | − | 0.0125715i | −0.700793 | − | 0.713365i | \(-0.747170\pi\) |
0.713365 | + | 0.700793i | \(0.247170\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −16.4918 | − | 6.71271i | −1.21911 | − | 0.496218i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −7.84414 | − | 4.52882i | −0.576713 | − | 0.332965i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.76578 | + | 2.61673i | 0.714145 | + | 0.191354i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.02198 | + | 6.79274i | 0.0743383 | + | 0.494099i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −11.0451 | − | 19.1306i | −0.799194 | − | 1.38424i | −0.920142 | − | 0.391586i | \(-0.871927\pi\) |
0.120947 | − | 0.992659i | \(-0.461407\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.90683 | − | 13.6950i | 0.569146 | − | 0.985790i | −0.427505 | − | 0.904013i | \(-0.640607\pi\) |
0.996651 | − | 0.0817767i | \(-0.0260594\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 15.7659 | − | 6.64423i | 1.12902 | − | 0.475803i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.19611 | − | 1.19611i | 0.0852196 | − | 0.0852196i | −0.663212 | − | 0.748432i | \(-0.730807\pi\) |
0.748432 | + | 0.663212i | \(0.230807\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.39170i | 0.453095i | 0.974000 | + | 0.226548i | \(0.0727439\pi\) | ||||
−0.974000 | + | 0.226548i | \(0.927256\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.41187 | − | 24.7402i | −0.240655 | − | 1.74504i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.25628 | + | 4.68849i | 0.0881734 | + | 0.329068i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.20523 | − | 4.49796i | 0.0841766 | − | 0.314151i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 8.58090 | + | 8.37256i | 0.596414 | + | 0.581933i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.06233 | + | 7.03617i | 0.280997 | + | 0.486702i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.01376 | − | 0.539586i | 0.138633 | − | 0.0371466i | −0.188835 | − | 0.982009i | \(-0.560471\pi\) |
0.327468 | + | 0.944862i | \(0.393805\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −13.5339 | − | 1.69724i | −0.927324 | − | 0.116293i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 18.1135i | − | 1.23533i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 1.50475i | − | 0.102149i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.992008 | + | 0.124405i | 0.0670337 | + | 0.00840649i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −25.6149 | + | 6.86349i | −1.72304 | + | 0.461688i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −13.6496 | − | 23.6417i | −0.914042 | − | 1.58317i | −0.808297 | − | 0.588775i | \(-0.799611\pi\) |
−0.105745 | − | 0.994393i | \(-0.533723\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8.75131 | − | 2.46055i | 0.583421 | − | 0.164037i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.752368 | − | 2.80787i | 0.0499364 | − | 0.186365i | −0.936452 | − | 0.350794i | \(-0.885912\pi\) |
0.986389 | + | 0.164429i | \(0.0525782\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.73787 | + | 6.48583i | 0.114842 | + | 0.428596i | 0.999275 | − | 0.0380710i | \(-0.0121213\pi\) |
−0.884433 | + | 0.466667i | \(0.845455\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.415712 | + | 3.01441i | 0.0273518 | + | 0.198333i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 11.8159i | 0.774086i | 0.922062 | + | 0.387043i | \(0.126503\pi\) | ||||
−0.922062 | + | 0.387043i | \(0.873497\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −18.3839 | + | 18.3839i | −1.19923 | + | 1.19923i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.28846 | − | 0.964426i | 0.148651 | − | 0.0626462i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.75364 | − | 3.03739i | 0.113433 | − | 0.196472i | −0.803719 | − | 0.595009i | \(-0.797148\pi\) |
0.917152 | + | 0.398537i | \(0.130482\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.35635 | − | 7.54543i | −0.280617 | − | 0.486044i | 0.690920 | − | 0.722932i | \(-0.257206\pi\) |
−0.971537 | + | 0.236888i | \(0.923873\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −9.10531 | + | 12.6528i | −0.584106 | + | 0.811678i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 14.3768 | + | 3.85226i | 0.918502 | + | 0.246112i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −18.4553 | − | 10.6552i | −1.17428 | − | 0.677973i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5.48765 | + | 2.23366i | 0.347766 | + | 0.141552i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.70213 | − | 9.70213i | 0.612393 | − | 0.612393i | −0.331176 | − | 0.943569i | \(-0.607445\pi\) |
0.943569 | + | 0.331176i | \(0.107445\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.75533 | + | 3.75533i | 0.236096 | + | 0.236096i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −36.9903 | + | 5.10127i | −2.31642 | + | 0.319454i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −9.26857 | + | 16.0536i | −0.578158 | + | 1.00140i | 0.417533 | + | 0.908662i | \(0.362895\pi\) |
−0.995691 | + | 0.0927366i | \(0.970439\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.09363 | + | 4.08149i | −0.0679550 | + | 0.253611i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.38990 | + | 9.60628i | −0.333626 | + | 0.594614i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.42692 | − | 1.97853i | 0.211313 | − | 0.122002i | −0.390608 | − | 0.920557i | \(-0.627735\pi\) |
0.601922 | + | 0.798555i | \(0.294402\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −26.8008 | − | 15.4734i | −1.64636 | − | 0.950525i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −27.8608 | − | 3.49393i | −1.70505 | − | 0.213825i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 17.6742 | + | 17.6742i | 1.07762 | + | 1.07762i | 0.996723 | + | 0.0808951i | \(0.0257779\pi\) |
0.0808951 | + | 0.996723i | \(0.474222\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 26.9563 | 1.63748 | 0.818738 | − | 0.574167i | \(-0.194674\pi\) | ||||
0.818738 | + | 0.574167i | \(0.194674\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4.89758 | − | 6.30209i | −0.296415 | − | 0.381420i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.88979 | − | 1.04226i | 0.234563 | − | 0.0628509i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9.24514 | − | 2.47723i | −0.555487 | − | 0.148842i | −0.0298548 | − | 0.999554i | \(-0.509504\pi\) |
−0.525632 | + | 0.850712i | \(0.676171\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.38476 | − | 2.44410i | 0.142772 | − | 0.146324i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.51476 | + | 4.91600i | −0.507948 | + | 0.293264i | −0.731990 | − | 0.681316i | \(-0.761408\pi\) |
0.224042 | + | 0.974580i | \(0.428075\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.06496 | − | 30.0988i | −0.479412 | − | 1.78919i | −0.604003 | − | 0.796982i | \(-0.706428\pi\) |
0.124591 | − | 0.992208i | \(-0.460238\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −23.9179 | − | 18.1204i | −1.41677 | − | 1.07336i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.17236 | −0.128231 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 40.8774 | 2.40456 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.07152 | − | 0.873002i | 0.121435 | − | 0.0511763i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −8.20472 | − | 30.6204i | −0.479325 | − | 1.78886i | −0.604360 | − | 0.796711i | \(-0.706571\pi\) |
0.125035 | − | 0.992152i | \(-0.460096\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −12.2202 | + | 7.05535i | −0.711489 | + | 0.410778i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.10207 | + | 5.55499i | −0.238026 | + | 0.322333i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −13.4553 | − | 3.60533i | −0.778139 | − | 0.208502i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.16220 | + | 2.18706i | −0.470462 | + | 0.126060i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 6.58374 | − | 16.1749i | 0.378226 | − | 0.929225i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 29.1313 | 1.66805 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −17.2513 | − | 17.2513i | −0.984581 | − | 0.984581i | 0.0153018 | − | 0.999883i | \(-0.495129\pi\) |
−0.999883 | + | 0.0153018i | \(0.995129\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −9.72059 | + | 12.8306i | −0.552985 | + | 0.729906i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.53625 | − | 4.92841i | −0.484046 | − | 0.279464i | 0.238055 | − | 0.971252i | \(-0.423490\pi\) |
−0.722101 | + | 0.691787i | \(0.756824\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.45774 | − | 4.88308i | 0.478060 | − | 0.276008i | −0.241548 | − | 0.970389i | \(-0.577655\pi\) |
0.719608 | + | 0.694381i | \(0.244322\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −5.73843 | − | 9.66305i | −0.323324 | − | 0.544451i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.43237 | − | 12.8098i | 0.192781 | − | 0.719469i | −0.800049 | − | 0.599935i | \(-0.795193\pi\) |
0.992830 | − | 0.119534i | \(-0.0381401\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.43974 | + | 4.22576i | −0.136599 | + | 0.236597i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.84834 | − | 3.66519i | −0.158979 | − | 0.204571i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 32.8879 | + | 32.8879i | 1.82993 | + | 1.82993i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.46883 | + | 7.46883i | −0.414296 | + | 0.414296i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 16.6966 | − | 12.9756i | 0.923327 | − | 0.717550i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 10.5037 | + | 6.06432i | 0.579089 | + | 0.334337i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.02314 | + | 0.274151i | 0.0562371 | + | 0.0150687i | 0.286828 | − | 0.957982i | \(-0.407399\pi\) |
−0.230591 | + | 0.973051i | \(0.574066\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −8.24476 | + | 4.89617i | −0.451810 | + | 0.268308i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 20.4299 | + | 35.3857i | 1.11621 | + | 1.93332i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.50387 | + | 4.33683i | −0.136395 | + | 0.236242i | −0.926129 | − | 0.377206i | \(-0.876885\pi\) |
0.789735 | + | 0.613448i | \(0.210218\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.69895 | − | 3.55998i | −0.255212 | − | 0.193351i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.06963 | − | 1.06963i | 0.0579238 | − | 0.0579238i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 16.1974i | − | 0.874575i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −18.1673 | − | 7.39470i | −0.978094 | − | 0.398117i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.57745 | + | 5.88711i | 0.0846817 | + | 0.316036i | 0.995254 | − | 0.0973140i | \(-0.0310251\pi\) |
−0.910572 | + | 0.413350i | \(0.864358\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.45289 | − | 5.42227i | 0.0777715 | − | 0.290247i | −0.916076 | − | 0.401005i | \(-0.868661\pi\) |
0.993847 | + | 0.110758i | \(0.0353277\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.03276 | − | 17.9980i | 0.108501 | − | 0.960661i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5.06146 | − | 8.76671i | −0.269395 | − | 0.466605i | 0.699311 | − | 0.714817i | \(-0.253490\pi\) |
−0.968706 | + | 0.248212i | \(0.920157\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 21.5554 | − | 5.77576i | 1.14404 | − | 0.306546i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 6.76496 | + | 16.0524i | 0.358040 | + | 0.849582i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 5.28081i | − | 0.278710i | −0.990242 | − | 0.139355i | \(-0.955497\pi\) | ||
0.990242 | − | 0.139355i | \(-0.0445030\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.3761i | 0.967163i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 9.65813 | − | 12.7481i | 0.506920 | − | 0.669104i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.57998 | + | 0.423353i | −0.0826997 | + | 0.0221593i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.01941 | − | 8.69388i | −0.262011 | − | 0.453817i | 0.704765 | − | 0.709441i | \(-0.251052\pi\) |
−0.966776 | + | 0.255624i | \(0.917719\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.52847 | − | 3.44280i | −0.183685 | − | 0.179225i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.73657 | + | 13.9451i | −0.193993 | + | 0.723992i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6.74869 | − | 25.1865i | −0.349434 | − | 1.30411i | −0.887346 | − | 0.461105i | \(-0.847453\pi\) |
0.537912 | − | 0.843001i | \(-0.319213\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 7.63395 | − | 5.93261i | 0.394215 | − | 0.306359i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 12.7985i | − | 0.659157i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.3259 | − | 11.3259i | 0.581771 | − | 0.581771i | −0.353619 | − | 0.935390i | \(-0.615049\pi\) |
0.935390 | + | 0.353619i | \(0.115049\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.13043 | + | 9.01407i | −0.0579135 | + | 0.461805i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.50076 | + | 4.33145i | −0.127783 | + | 0.221327i | −0.922817 | − | 0.385238i | \(-0.874119\pi\) |
0.795034 | + | 0.606564i | \(0.207453\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.48924 | − | 4.31148i | −0.126863 | − | 0.219733i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −16.7236 | − | 9.38328i | −0.850107 | − | 0.476979i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 12.9035 | + | 3.45749i | 0.654235 | + | 0.175302i | 0.570643 | − | 0.821198i | \(-0.306694\pi\) |
0.0835921 | + | 0.996500i | \(0.473361\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 26.3294 | + | 15.2013i | 1.33153 | + | 0.768761i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.53617 | + | 11.1391i | 0.0774895 | + | 0.561892i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.87297 | + | 2.87297i | −0.144555 | + | 0.144555i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −18.7165 | − | 18.7165i | −0.939356 | − | 0.939356i | 0.0589078 | − | 0.998263i | \(-0.481238\pi\) |
−0.998263 | + | 0.0589078i | \(0.981238\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −5.27743 | + | 12.9656i | −0.264202 | + | 0.649092i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.66124 | − | 11.5376i | 0.332647 | − | 0.576161i | −0.650383 | − | 0.759606i | \(-0.725392\pi\) |
0.983030 | + | 0.183445i | \(0.0587250\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.02691 | + | 3.83247i | −0.0511538 | + | 0.190909i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 5.99352 | − | 24.7896i | 0.297820 | − | 1.23181i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.67866 | + | 2.12388i | −0.182345 | + | 0.105277i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10.6037 | + | 6.12206i | 0.524320 | + | 0.302717i | 0.738701 | − | 0.674034i | \(-0.235440\pi\) |
−0.214380 | + | 0.976750i | \(0.568773\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.78934 | + | 11.3645i | 0.236241 | + | 0.560568i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.65472 | + | 4.65472i | 0.229044 | + | 0.229044i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.69344 | −0.475832 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7.23206 | + | 0.997361i | −0.354156 | + | 0.0488410i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −32.0424 | + | 8.58573i | −1.56537 | + | 0.419440i | −0.934360 | − | 0.356332i | \(-0.884027\pi\) |
−0.631013 | + | 0.775772i | \(0.717361\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −24.7035 | − | 6.61930i | −1.20398 | − | 0.322605i | −0.399581 | − | 0.916698i | \(-0.630844\pi\) |
−0.804396 | + | 0.594093i | \(0.797511\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 7.44985 | + | 26.4965i | 0.362224 | + | 1.28830i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 19.9645 | − | 11.5265i | 0.968421 | − | 0.559118i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.51736 | − | 13.1269i | −0.170217 | − | 0.635258i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.998381 | − | 7.96113i | 0.0482023 | − | 0.384367i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10.3041 | 0.496332 | 0.248166 | − | 0.968717i | \(-0.420172\pi\) | ||||
0.248166 | + | 0.968717i | \(0.420172\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11.7692 | −0.565591 | −0.282795 | − | 0.959180i | \(-0.591262\pi\) | ||||
−0.282795 | + | 0.959180i | \(0.591262\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.24245 | − | 17.8814i | 0.107517 | − | 0.857347i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.32337 | + | 23.5991i | 0.302488 | + | 1.12890i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −23.9893 | + | 13.8502i | −1.14494 | + | 0.661034i | −0.947650 | − | 0.319310i | \(-0.896549\pi\) |
−0.197294 | + | 0.980344i | \(0.563215\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 11.0042 | − | 11.2780i | 0.524011 | − | 0.537050i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 24.2836 | + | 6.50677i | 1.15375 | + | 0.309146i | 0.784466 | − | 0.620172i | \(-0.212937\pi\) |
0.369282 | + | 0.929317i | \(0.379604\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 44.3739 | − | 11.8900i | 2.10353 | − | 0.563638i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −14.9385 | + | 2.06014i | −0.706567 | + | 0.0974413i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −20.0988 | −0.948522 | −0.474261 | − | 0.880384i | \(-0.657285\pi\) | ||||
−0.474261 | + | 0.880384i | \(0.657285\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.54419 | − | 1.54419i | −0.0727133 | − | 0.0727133i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 13.8334 | + | 32.8248i | 0.649949 | + | 1.54225i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 11.3087 | + | 6.52907i | 0.530159 | + | 0.306088i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 20.8270 | − | 12.0245i | 0.974244 | − | 0.562480i | 0.0737167 | − | 0.997279i | \(-0.476514\pi\) |
0.900527 | + | 0.434799i | \(0.143181\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −14.4521 | + | 36.7944i | −0.674566 | + | 1.71742i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.04759 | − | 3.90967i | 0.0487913 | − | 0.182092i | −0.937230 | − | 0.348713i | \(-0.886619\pi\) |
0.986021 | + | 0.166621i | \(0.0532856\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.16489 | + | 8.94585i | −0.240033 | + | 0.415749i | −0.960723 | − | 0.277508i | \(-0.910492\pi\) |
0.720691 | + | 0.693257i | \(0.243825\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.10623 | + | 5.17459i | −0.0976741 | + | 0.239966i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −11.8966 | − | 11.8966i | −0.550509 | − | 0.550509i | 0.376079 | − | 0.926588i | \(-0.377272\pi\) |
−0.926588 | + | 0.376079i | \(0.877272\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13.4785 | − | 13.4785i | 0.622380 | − | 0.622380i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.18240 | + | 15.8250i | 0.100560 | + | 0.729179i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7.35663 | − | 4.24735i | −0.338258 | − | 0.195293i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 17.8943 | + | 4.79476i | 0.821046 | + | 0.219999i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −28.1695 | + | 16.7286i | −1.28980 | + | 0.765948i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.47878 | + | 12.9536i | 0.341714 | + | 0.591866i | 0.984751 | − | 0.173969i | \(-0.0556593\pi\) |
−0.643037 | + | 0.765835i | \(0.722326\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.57077 | − | 9.64886i | 0.254005 | − | 0.439950i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.13860 | + | 9.07927i | −0.0518082 | + | 0.413121i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.60062 | + | 2.60062i | −0.118088 | + | 0.118088i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 27.0362i | − | 1.22513i | −0.790420 | − | 0.612565i | \(-0.790138\pi\) | ||
0.790420 | − | 0.612565i | \(-0.209862\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −20.1250 | + | 15.6398i | −0.910082 | + | 0.707257i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.45189 | + | 5.41853i | 0.0655229 | + | 0.244535i | 0.990918 | − | 0.134470i | \(-0.0429331\pi\) |
−0.925395 | + | 0.379005i | \(0.876266\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.22964 | + | 26.9814i | −0.325607 | + | 1.21518i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.78977 | − | 10.9479i | 0.125391 | − | 0.492073i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −5.20527 | − | 9.01579i | −0.233488 | − | 0.404413i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 21.2035 | − | 5.68146i | 0.949198 | − | 0.254337i | 0.249176 | − | 0.968458i | \(-0.419840\pi\) |
0.700022 | + | 0.714121i | \(0.253174\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 7.19085 | − | 9.49148i | 0.321264 | − | 0.424048i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 23.1955i | 1.03423i | 0.855915 | + | 0.517117i | \(0.172995\pi\) | ||||
−0.855915 | + | 0.517117i | \(0.827005\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 28.5716i | 1.27142i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.571523 | − | 1.35615i | −0.0253822 | − | 0.0602288i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 12.5788 | − | 3.37049i | 0.557547 | − | 0.149394i | 0.0309681 | − | 0.999520i | \(-0.490141\pi\) |
0.526579 | + | 0.850126i | \(0.323474\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.381537 | + | 0.660842i | 0.0168782 | + | 0.0292339i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −29.1200 | + | 12.6957i | −1.28568 | + | 0.560527i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6.81623 | − | 25.4385i | 0.300359 | − | 1.12095i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.15568 | + | 11.7772i | 0.138787 | + | 0.517959i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5.10698 | + | 2.07871i | 0.224171 | + | 0.0912453i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 21.4547i | − | 0.939949i | −0.882680 | − | 0.469974i | \(-0.844263\pi\) | ||
0.882680 | − | 0.469974i | \(-0.155737\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.07495 | + | 2.07495i | −0.0907314 | + | 0.0907314i | −0.751016 | − | 0.660284i | \(-0.770436\pi\) |
0.660284 | + | 0.751016i | \(0.270436\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 5.53043 | + | 4.18992i | 0.241368 | + | 0.182863i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.32977 | − | 7.49939i | 0.188608 | − | 0.326678i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.51490 | − | 6.08799i | −0.152822 | − | 0.264695i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.183562 | + | 14.9374i | 0.00796593 | + | 0.648226i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.53282 | + | 1.48251i | 0.239653 | + | 0.0642148i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.57693 | + | 3.79719i | 0.284346 | + | 0.164167i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −7.22677 | + | 5.61618i | −0.311858 | + | 0.242356i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.93571 | − | 4.93571i | 0.212596 | − | 0.212596i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 22.7947 | + | 22.7947i | 0.980022 | + | 0.980022i | 0.999804 | − | 0.0197819i | \(-0.00629719\pi\) |
−0.0197819 | + | 0.999804i | \(0.506297\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.254217 | + | 0.327121i | 0.0109095 | + | 0.0140381i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −17.2980 | + | 29.9610i | −0.740965 | + | 1.28339i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.58528 | − | 13.3804i | 0.153295 | − | 0.572106i | −0.845950 | − | 0.533262i | \(-0.820966\pi\) |
0.999245 | − | 0.0388438i | \(-0.0123675\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 15.0908 | − | 26.8959i | 0.644058 | − | 1.14789i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −19.4399 | + | 11.2236i | −0.828166 | + | 0.478142i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.64148 | + | 0.947711i | 0.0698030 | + | 0.0403008i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 9.47377 | − | 12.5048i | 0.402139 | − | 0.530799i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −8.62660 | − | 8.62660i | −0.365521 | − | 0.365521i | 0.500320 | − | 0.865841i | \(-0.333216\pi\) |
−0.865841 | + | 0.500320i | \(0.833216\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 22.2810 | 0.942384 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.60184 | + | 16.2194i | −0.278730 | + | 0.684784i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −20.3923 | + | 5.46409i | −0.859432 | + | 0.230284i | −0.661513 | − | 0.749934i | \(-0.730085\pi\) |
−0.197920 | + | 0.980218i | \(0.563418\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9.31636 | + | 2.49631i | 0.391942 | + | 0.105021i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −11.8942 | + | 0.292376i | −0.499509 | + | 0.0122786i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −21.4776 | + | 12.4001i | −0.900389 | + | 0.519840i | −0.877326 | − | 0.479894i | \(-0.840675\pi\) |
−0.0230625 | + | 0.999734i | \(0.507342\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.74438 | + | 17.7063i | 0.198546 | + | 0.740985i | 0.991320 | + | 0.131469i | \(0.0419694\pi\) |
−0.792774 | + | 0.609516i | \(0.791364\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 35.2582 | − | 14.8589i | 1.47293 | − | 0.620738i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 12.1096 | 0.505004 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −23.4462 | −0.976078 | −0.488039 | − | 0.872822i | \(-0.662288\pi\) | ||||
−0.488039 | + | 0.872822i | \(0.662288\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 21.8320 | + | 16.5402i | 0.907308 | + | 0.687387i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.17040 | + | 4.36800i | 0.0485564 | + | 0.181215i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −12.5688 | + | 7.25657i | −0.520545 | + | 0.300537i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 8.02079 | + | 28.5271i | 0.331619 | + | 1.17945i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 16.1657 | + | 4.33159i | 0.667230 | + | 0.178784i | 0.576507 | − | 0.817092i | \(-0.304415\pi\) |
0.0907235 | + | 0.995876i | \(0.471082\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.72173 | − | 1.80108i | 0.276964 | − | 0.0742123i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.79784 | + | 2.31342i | 0.0739532 | + | 0.0951613i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 6.18675 | 0.254059 | 0.127030 | − | 0.991899i | \(-0.459456\pi\) | ||||
0.127030 | + | 0.991899i | \(0.459456\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −20.1524 | − | 20.1524i | −0.826168 | − | 0.826168i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −10.9847 | − | 1.37756i | −0.449574 | − | 0.0563797i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 7.98730 | + | 4.61147i | 0.326352 | + | 0.188420i | 0.654220 | − | 0.756304i | \(-0.272997\pi\) |
−0.327868 | + | 0.944723i | \(0.606330\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15.0097 | − | 8.66586i | 0.612259 | − | 0.353488i | −0.161590 | − | 0.986858i | \(-0.551662\pi\) |
0.773849 | + | 0.633370i | \(0.218329\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 43.2535 | − | 0.531535i | 1.76142 | − | 0.0216458i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −6.77243 | + | 25.2751i | −0.275339 | + | 1.02758i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −11.8418 | + | 20.5106i | −0.480643 | + | 0.832498i | −0.999753 | − | 0.0222090i | \(-0.992930\pi\) |
0.519110 | + | 0.854707i | \(0.326263\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −8.32835 | + | 1.14855i | −0.337482 | + | 0.0465415i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −22.6135 | − | 22.6135i | −0.914844 | − | 0.914844i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 15.4110 | − | 15.4110i | 0.622445 | − | 0.622445i | −0.323711 | − | 0.946156i | \(-0.604930\pi\) |
0.946156 | + | 0.323711i | \(0.104930\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 7.47040 | + | 3.04070i | 0.301236 | + | 0.122613i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11.9979 | + | 6.92700i | 0.483018 | + | 0.278870i | 0.721673 | − | 0.692234i | \(-0.243373\pi\) |
−0.238655 | + | 0.971104i | \(0.576707\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −38.6333 | − | 10.3518i | −1.55280 | − | 0.416072i | −0.622427 | − | 0.782678i | \(-0.713853\pi\) |
−0.930376 | + | 0.366606i | \(0.880520\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −16.2384 | + | 12.9426i | −0.651624 | + | 0.519367i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −10.7156 | − | 18.5599i | −0.429310 | − | 0.743586i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −15.4844 | + | 26.8198i | −0.619377 | + | 1.07279i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −12.9678 | + | 5.46503i | −0.517884 | + | 0.218252i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −17.1945 | + | 17.1945i | −0.685591 | + | 0.685591i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16.7956i | 0.668624i | 0.942462 | + | 0.334312i | \(0.108504\pi\) | ||||
−0.942462 | + | 0.334312i | \(0.891496\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.493315 | + | 3.57712i | 0.0196075 | + | 0.142178i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3.84688 | − | 14.3567i | −0.152659 | − | 0.569730i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.73856 | + | 17.6845i | −0.187749 | + | 0.700687i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.83371 | − | 22.8933i | 0.230778 | − | 0.905647i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 20.0246 | + | 34.6837i | 0.790925 | + | 1.36992i | 0.925395 | + | 0.379005i | \(0.123734\pi\) |
−0.134470 | + | 0.990918i | \(0.542933\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.07859 | + | 0.289008i | −0.0425356 | + | 0.0113974i | −0.280024 | − | 0.959993i | \(-0.590342\pi\) |
0.237489 | + | 0.971390i | \(0.423676\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 31.1297 | + | 3.90388i | 1.22573 | + | 0.153715i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 31.9272i | 1.25519i | 0.778541 | + | 0.627594i | \(0.215960\pi\) | ||||
−0.778541 | + | 0.627594i | \(0.784040\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.61750i | 0.259759i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.58605 | + | 0.324308i | 0.101355 | + | 0.0127106i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 12.5651 | − | 3.36682i | 0.491712 | − | 0.131754i | −0.00443888 | − | 0.999990i | \(-0.501413\pi\) |
0.496151 | + | 0.868236i | \(0.334746\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9.19841 | − | 15.9321i | −0.359412 | − | 0.622519i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −0.427601 | + | 1.67804i | −0.0166823 | + | 0.0654667i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.15007 | − | 15.4883i | 0.161664 | − | 0.603337i | −0.836779 | − | 0.547541i | \(-0.815564\pi\) |
0.998442 | − | 0.0557954i | \(-0.0177695\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.89283 | − | 21.9923i | −0.229204 | − | 0.855403i | −0.980676 | − | 0.195637i | \(-0.937322\pi\) |
0.751472 | − | 0.659765i | \(-0.229344\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −6.27493 | − | 45.5007i | −0.243698 | − | 1.76710i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 22.9026i | − | 0.888124i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −10.3754 | + | 10.3754i | −0.401738 | + | 0.401738i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 43.5722 | − | 18.3627i | 1.68460 | − | 0.709941i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.83085 | − | 11.8314i | 0.263702 | − | 0.456745i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16.3212 | + | 28.2692i | 0.629136 | + | 1.08970i | 0.987725 | + | 0.156201i | \(0.0499246\pi\) |
−0.358589 | + | 0.933496i | \(0.616742\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.34257 | + | 15.5702i | 0.0901656 | + | 0.599298i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −14.3681 | − | 3.84993i | −0.552212 | − | 0.147965i | −0.0280861 | − | 0.999606i | \(-0.508941\pi\) |
−0.524126 | + | 0.851641i | \(0.675608\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.48588 | + | 0.857871i | 0.0570227 | + | 0.0329221i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.66343 | + | 1.89817i | 0.178703 | + | 0.0727381i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −21.4912 | + | 21.4912i | −0.822338 | + | 0.822338i | −0.986443 | − | 0.164105i | \(-0.947526\pi\) |
0.164105 | + | 0.986443i | \(0.447526\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −14.2671 | − | 14.2671i | −0.545120 | − | 0.545120i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −11.5210 | + | 1.58885i | −0.439555 | + | 0.0606183i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 19.0334 | − | 32.9669i | 0.725116 | − | 1.25594i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.36807 | + | 8.83775i | −0.0900855 | + | 0.336204i | −0.996229 | − | 0.0867676i | \(-0.972346\pi\) |
0.906143 | + | 0.422971i | \(0.139013\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −5.27012 | + | 0.0647636i | −0.200195 | + | 0.00246017i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 10.3440 | − | 5.97209i | 0.392369 | − | 0.226534i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −10.8266 | − | 6.25077i | −0.410088 | − | 0.236765i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −20.3067 | − | 2.54660i | −0.768070 | − | 0.0963212i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.05144 | − | 4.05144i | −0.153021 | − | 0.153021i | 0.626445 | − | 0.779466i | \(-0.284509\pi\) |
−0.779466 | + | 0.626445i | \(0.784509\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −19.5411 | −0.737005 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −27.6322 | − | 35.5565i | −1.04069 | − | 1.33913i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 12.8747 | − | 3.44978i | 0.484204 | − | 0.129742i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.76098 | + | 1.00775i | 0.141247 | + | 0.0378469i | 0.328750 | − | 0.944417i | \(-0.393373\pi\) |
−0.187503 | + | 0.982264i | \(0.560039\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.16424 | + | 4.14078i | 0.0436623 | + | 0.155291i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.93936 | − | 2.27439i | 0.147530 | − | 0.0851767i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.39752 | + | 12.6797i | 0.127060 | + | 0.474195i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 4.84208 | + | 3.66841i | 0.180831 | + | 0.136999i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 37.0063 | 1.38010 | 0.690050 | − | 0.723761i | \(-0.257588\pi\) | ||||
0.690050 | + | 0.723761i | \(0.257588\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12.2859 | −0.457552 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 13.9064 | − | 5.86057i | 0.517184 | − | 0.217957i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.87962 | + | 10.7469i | 0.106946 | + | 0.399129i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 28.4066 | − | 16.4006i | 1.05354 | − | 0.608264i | 0.129905 | − | 0.991526i | \(-0.458533\pi\) |
0.923640 | + | 0.383262i | \(0.125199\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −19.7826 | − | 18.3753i | −0.732688 | − | 0.680565i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −46.9719 | − | 12.5861i | −1.73732 | − | 0.465513i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −40.9566 | + | 10.9743i | −1.51277 | + | 0.405345i | −0.917353 | − | 0.398075i | \(-0.869678\pi\) |
−0.595413 | + | 0.803419i | \(0.703012\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −9.71899 | + | 23.8776i | −0.358490 | + | 0.880740i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 19.1620 | 0.705842 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15.3761 | + | 15.3761i | 0.565620 | + | 0.565620i | 0.930898 | − | 0.365278i | \(-0.119026\pi\) |
−0.365278 | + | 0.930898i | \(0.619026\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 22.2894 | − | 29.4207i | 0.818823 | − | 1.08080i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 40.4824 | + | 23.3725i | 1.48516 | + | 0.857456i | 0.999857 | − | 0.0168926i | \(-0.00537734\pi\) |
0.485299 | + | 0.874348i | \(0.338711\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 21.3664 | − | 12.3359i | 0.782805 | − | 0.451952i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −5.02145 | + | 8.94961i | −0.183725 | + | 0.327449i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.916958 | − | 3.42213i | 0.0335049 | − | 0.125042i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −25.7074 | + | 44.5265i | −0.938077 | + | 1.62480i | −0.169023 | + | 0.985612i | \(0.554061\pi\) |
−0.769054 | + | 0.639184i | \(0.779272\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 14.5829 | + | 18.7650i | 0.531432 | + | 0.683835i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −41.2088 | − | 41.2088i | −1.49974 | − | 1.49974i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 25.4143 | − | 25.4143i | 0.923698 | − | 0.923698i | −0.0735910 | − | 0.997289i | \(-0.523446\pi\) |
0.997289 | + | 0.0735910i | \(0.0234459\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −7.26324 | + | 5.64452i | −0.263639 | + | 0.204883i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −20.2336 | − | 11.6819i | −0.733467 | − | 0.423467i | 0.0862220 | − | 0.996276i | \(-0.472521\pi\) |
−0.819689 | + | 0.572808i | \(0.805854\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 15.5894 | + | 4.17717i | 0.564375 | + | 0.151224i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.794725 | − | 64.6706i | −0.0287334 | − | 2.33817i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −8.67859 | − | 15.0318i | −0.313366 | − | 0.542765i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −12.7645 | + | 22.1087i | −0.460299 | + | 0.797261i | −0.998976 | − | 0.0452513i | \(-0.985591\pi\) |
0.538677 | + | 0.842513i | \(0.318924\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −25.5920 | − | 19.3888i | −0.921674 | − | 0.698270i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −19.2256 | + | 19.2256i | −0.691496 | + | 0.691496i | −0.962561 | − | 0.271065i | \(-0.912624\pi\) |
0.271065 | + | 0.962561i | \(0.412624\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 3.44916i | − | 0.123898i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −6.77870 | − | 2.75916i | −0.243185 | − | 0.0989843i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.60017 | − | 9.70397i | −0.0931608 | − | 0.347681i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.70866 | − | 10.1088i | 0.0969234 | − | 0.361723i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −15.3476 | − | 11.3334i | −0.548479 | − | 0.405022i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −13.0680 | − | 22.6344i | −0.466416 | − | 0.807857i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 19.2671 | − | 5.16260i | 0.686797 | − | 0.184027i | 0.101488 | − | 0.994837i | \(-0.467640\pi\) |
0.585309 | + | 0.810810i | \(0.300973\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.66171 | + | 6.31589i | 0.0947593 | + | 0.224852i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 4.49949i | − | 0.159983i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 35.8336i | 1.27249i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 32.3687 | − | 42.7246i | 1.14800 | − | 1.51529i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 11.2772 | − | 3.02171i | 0.399458 | − | 0.107035i | −0.0534965 | − | 0.998568i | \(-0.517037\pi\) |
0.452955 | + | 0.891534i | \(0.350370\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 34.8990 | + | 60.4469i | 1.23464 | + | 2.13846i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 12.0093 | − | 47.1282i | 0.424326 | − | 1.66519i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.198540 | + | 0.740961i | −0.00700632 | + | 0.0261479i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.87471 | − | 14.4606i | −0.136565 | − | 0.509669i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −34.1840 | + | 26.5656i | −1.20333 | + | 0.935152i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 13.1110i | 0.460958i | 0.973077 | + | 0.230479i | \(0.0740292\pi\) | ||||
−0.973077 | + | 0.230479i | \(0.925971\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 34.1945 | − | 34.1945i | 1.20073 | − | 1.20073i | 0.226789 | − | 0.973944i | \(-0.427177\pi\) |
0.973944 | − | 0.226789i | \(-0.0728227\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −5.80969 | + | 46.3267i | −0.203755 | + | 1.62475i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 20.8498 | − | 36.1129i | 0.730337 | − | 1.26498i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −19.5392 | − | 33.8429i | −0.683590 | − | 1.18401i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 11.8862 | − | 7.05868i | 0.415339 | − | 0.246650i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −23.8714 | − | 6.39631i | −0.833116 | − | 0.223233i | −0.183044 | − | 0.983105i | \(-0.558595\pi\) |
−0.650073 | + | 0.759872i | \(0.725262\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −16.2152 | − | 9.36184i | −0.565226 | − | 0.326333i | 0.190014 | − | 0.981781i | \(-0.439147\pi\) |
−0.755240 | + | 0.655448i | \(0.772480\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.952888 | + | 6.90958i | 0.0331753 | + | 0.240561i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 24.1212 | − | 24.1212i | 0.838775 | − | 0.838775i | −0.149923 | − | 0.988698i | \(-0.547902\pi\) |
0.988698 | + | 0.149923i | \(0.0479025\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −20.8683 | − | 20.8683i | −0.724787 | − | 0.724787i | 0.244789 | − | 0.969576i | \(-0.421281\pi\) |
−0.969576 | + | 0.244789i | \(0.921281\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6.24988 | − | 15.3547i | 0.216806 | − | 0.532649i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 19.9793 | − | 34.6052i | 0.692242 | − | 1.19900i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.04234 | + | 18.8183i | −0.174497 | + | 0.651233i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.68643 | + | 4.62517i | 0.127422 | + | 0.159869i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −5.01977 | + | 2.89816i | −0.173302 | + | 0.100056i | −0.584142 | − | 0.811652i | \(-0.698569\pi\) |
0.410840 | + | 0.911707i | \(0.365235\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.4396 | + | 7.75936i | 0.463435 | + | 0.267564i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −6.61346 | − | 15.6929i | −0.227780 | − | 0.540492i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.70253 | + | 1.70253i | 0.0585689 | + | 0.0585689i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 12.2070 | 0.419437 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 53.4657 | − | 7.37337i | 1.83494 | − | 0.253053i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −12.3381 | + | 3.30600i | −0.422946 | + | 0.113328i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.72171 | + | 0.461332i | 0.0589504 | + | 0.0157957i | 0.288174 | − | 0.957578i | \(-0.406952\pi\) |
−0.229223 | + | 0.973374i | \(0.573619\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 36.2964 | − | 37.1996i | 1.24131 | − | 1.27220i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −12.6918 | + | 7.32760i | −0.433543 | + | 0.250306i | −0.700855 | − | 0.713304i | \(-0.747198\pi\) |
0.267312 | + | 0.963610i | \(0.413865\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −13.7688 | − | 51.3859i | −0.469786 | − | 1.75327i | −0.640513 | − | 0.767947i | \(-0.721278\pi\) |
0.170727 | − | 0.985318i | \(-0.445388\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.468194 | − | 3.73340i | 0.0159560 | − | 0.127234i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −23.9467 | −0.815157 | −0.407578 | − | 0.913170i | \(-0.633627\pi\) | ||||
−0.407578 | + | 0.913170i | \(0.633627\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9.02103 | −0.306724 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −8.81003 | + | 70.2515i | −0.299204 | + | 2.38587i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.493159 | + | 1.84049i | 0.0167293 | + | 0.0624345i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −43.5269 | + | 25.1303i | −1.47485 | + | 0.851507i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.05387 | + | 3.74825i | 0.0356681 | + | 0.126859i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 7.12771 | + | 1.90986i | 0.240961 | + | 0.0645652i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −39.7266 | + | 10.6447i | −1.34147 | + | 0.359446i | −0.856980 | − | 0.515349i | \(-0.827662\pi\) |
−0.484492 | + | 0.874796i | \(0.660996\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 54.3922 | − | 7.50114i | 1.83460 | − | 0.253007i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −41.2335 | −1.38919 | −0.694597 | − | 0.719399i | \(-0.744417\pi\) | ||||
−0.694597 | + | 0.719399i | \(0.744417\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 11.9719 | + | 11.9719i | 0.402885 | + | 0.402885i | 0.879248 | − | 0.476364i | \(-0.158045\pi\) |
−0.476364 | + | 0.879248i | \(0.658045\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −9.49151 | − | 22.5221i | −0.319054 | − | 0.757074i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −26.7452 | − | 15.4413i | −0.898016 | − | 0.518470i | −0.0214599 | − | 0.999770i | \(-0.506831\pi\) |
−0.876556 | + | 0.481300i | \(0.840165\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.00486 | + | 3.46691i | −0.201397 | + | 0.116276i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −8.66266 | − | 8.24700i | −0.290210 | − | 0.276285i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −14.5172 | + | 54.1788i | −0.485798 | + | 1.81302i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.48706 | − | 12.9680i | 0.250265 | − | 0.433471i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 9.09601 | − | 22.3471i | 0.303707 | − | 0.746147i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.95523 | + | 2.95523i | 0.0985624 | + | 0.0985624i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −58.7480 | + | 58.7480i | −1.95718 | + | 1.95718i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.99951 | − | 14.4988i | −0.0665395 | − | 0.482491i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −0.586997 | − | 0.338903i | −0.0195125 | − | 0.0112655i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 26.7351 | + | 7.16365i | 0.887725 | + | 0.237865i | 0.673737 | − | 0.738971i | \(-0.264688\pi\) |
0.213988 | + | 0.976836i | \(0.431355\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 26.3791 | + | 14.8008i | 0.874940 | + | 0.490912i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.83009 | + | 8.36596i | 0.160028 | + | 0.277177i | 0.934878 | − | 0.354968i | \(-0.115508\pi\) |
−0.774850 | + | 0.632145i | \(0.782175\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.27297 | + | 3.93689i | −0.0752242 | + | 0.130292i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −6.27846 | + | 50.0647i | −0.207560 | + | 1.65509i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −6.06859 | + | 6.06859i | −0.200403 | + | 0.200403i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 12.5574i | 0.414229i | 0.978317 | + | 0.207115i | \(0.0664073\pi\) | ||||
−0.978317 | + | 0.207115i | \(0.933593\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 33.3659 | − | 25.9298i | 1.09944 | − | 0.854415i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 7.10460 | + | 26.5147i | 0.233851 | + | 0.872743i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.50681 | + | 9.35553i | −0.0824233 | + | 0.307608i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −19.9555 | − | 19.4710i | −0.655424 | − | 0.639511i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4.50031 | + | 7.79477i | 0.147650 | + | 0.255738i | 0.930359 | − | 0.366651i | \(-0.119496\pi\) |
−0.782708 | + | 0.622389i | \(0.786162\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 31.0168 | − | 8.31092i | 1.01653 | − | 0.272379i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 10.3097 | − | 13.6081i | 0.337523 | − | 0.445510i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 28.6501i | − | 0.936960i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 59.2265i | − | 1.93485i | −0.253166 | − | 0.967423i | \(-0.581472\pi\) | ||
0.253166 | − | 0.967423i | \(-0.418528\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 6.56917 | + | 15.5878i | 0.214377 | + | 0.508689i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 11.0262 | − | 2.95446i | 0.359443 | − | 0.0963126i | −0.0745778 | − | 0.997215i | \(-0.523761\pi\) |
0.434021 | + | 0.900903i | \(0.357094\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.28347 | − | 5.68714i | −0.106925 | − | 0.185199i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 17.8436 | − | 7.77939i | 0.580452 | − | 0.253064i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.22949 | − | 8.32058i | 0.0724488 | − | 0.270382i | −0.920194 | − | 0.391463i | \(-0.871969\pi\) |
0.992643 | + | 0.121080i | \(0.0386359\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.520755 | − | 1.94348i | −0.0169044 | − | 0.0630882i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 21.2750 | + | 8.65964i | 0.689889 | + | 0.280808i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 43.5260i | − | 1.40995i | −0.709234 | − | 0.704973i | \(-0.750959\pi\) | ||
0.709234 | − | 0.704973i | \(-0.249041\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −44.2637 | + | 44.2637i | −1.43234 | + | 1.43234i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −6.73653 | − | 5.10367i | −0.217761 | − | 0.164978i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.70633 | + | 8.15160i | −0.151975 | + | 0.263229i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14.8522 | + | 25.7247i | 0.479103 | + | 0.829830i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.91283 | − | 4.10520i | 0.222763 | − | 0.132288i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −43.2852 | − | 11.5982i | −1.39340 | − | 0.373361i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −26.2267 | − | 15.1420i | −0.843393 | − | 0.486933i | 0.0150229 | − | 0.999887i | \(-0.495218\pi\) |
−0.858416 | + | 0.512954i | \(0.828551\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −63.6090 | + | 49.4328i | −2.04341 | + | 1.58801i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −9.06755 | + | 9.06755i | −0.290992 | + | 0.290992i | −0.837472 | − | 0.546480i | \(-0.815967\pi\) |
0.546480 | + | 0.837472i | \(0.315967\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.94005 | − | 3.94005i | −0.126312 | − | 0.126312i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −11.2261 | − | 14.4456i | −0.359524 | − | 0.462628i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 10.4475 | − | 18.0956i | 0.334246 | − | 0.578931i | −0.649094 | − | 0.760708i | \(-0.724852\pi\) |
0.983340 | + | 0.181778i | \(0.0581851\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.57603 | − | 20.8100i | 0.178211 | − | 0.665092i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 18.7011 | + | 31.4912i | 0.597081 | + | 1.00544i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.14158 | + | 0.659092i | −0.0364108 | + | 0.0210218i | −0.518095 | − | 0.855323i | \(-0.673359\pi\) |
0.481684 | + | 0.876345i | \(0.340025\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.15128 | − | 2.39674i | −0.132271 | − | 0.0763665i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −12.6859 | + | 16.7446i | −0.403796 | + | 0.532986i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −18.0626 | − | 18.0626i | −0.574357 | − | 0.574357i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.51185 | −0.0797914 | −0.0398957 | − | 0.999204i | \(-0.512703\pi\) | ||||
−0.0398957 | + | 0.999204i | \(0.512703\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −0.691664 | + | 1.69928i | −0.0219493 | + | 0.0539250i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 17.4954 | − | 4.68788i | 0.554641 | − | 0.148616i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −44.4227 | − | 11.9030i | −1.40688 | − | 0.376973i | −0.526071 | − | 0.850441i | \(-0.676335\pi\) |
−0.880811 | + | 0.473468i | \(0.843002\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −6.63757 | − | 15.2246i | −0.210003 | − | 0.481685i |
(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 | 576.2.bb.e.337.11 | 72 | ||
3.2 | odd | 2 | 1728.2.bc.e.145.14 | 72 | |||
4.3 | odd | 2 | 144.2.x.e.13.7 | ✓ | 72 | ||
9.2 | odd | 6 | 1728.2.bc.e.721.5 | 72 | |||
9.7 | even | 3 | inner | 576.2.bb.e.529.18 | 72 | ||
12.11 | even | 2 | 432.2.y.e.253.12 | 72 | |||
16.5 | even | 4 | inner | 576.2.bb.e.49.18 | 72 | ||
16.11 | odd | 4 | 144.2.x.e.85.17 | yes | 72 | ||
36.7 | odd | 6 | 144.2.x.e.61.17 | yes | 72 | ||
36.11 | even | 6 | 432.2.y.e.397.2 | 72 | |||
48.5 | odd | 4 | 1728.2.bc.e.1009.5 | 72 | |||
48.11 | even | 4 | 432.2.y.e.37.2 | 72 | |||
144.11 | even | 12 | 432.2.y.e.181.12 | 72 | |||
144.43 | odd | 12 | 144.2.x.e.133.7 | yes | 72 | ||
144.101 | odd | 12 | 1728.2.bc.e.1585.14 | 72 | |||
144.133 | even | 12 | inner | 576.2.bb.e.241.11 | 72 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
144.2.x.e.13.7 | ✓ | 72 | 4.3 | odd | 2 | ||
144.2.x.e.61.17 | yes | 72 | 36.7 | odd | 6 | ||
144.2.x.e.85.17 | yes | 72 | 16.11 | odd | 4 | ||
144.2.x.e.133.7 | yes | 72 | 144.43 | odd | 12 | ||
432.2.y.e.37.2 | 72 | 48.11 | even | 4 | |||
432.2.y.e.181.12 | 72 | 144.11 | even | 12 | |||
432.2.y.e.253.12 | 72 | 12.11 | even | 2 | |||
432.2.y.e.397.2 | 72 | 36.11 | even | 6 | |||
576.2.bb.e.49.18 | 72 | 16.5 | even | 4 | inner | ||
576.2.bb.e.241.11 | 72 | 144.133 | even | 12 | inner | ||
576.2.bb.e.337.11 | 72 | 1.1 | even | 1 | trivial | ||
576.2.bb.e.529.18 | 72 | 9.7 | even | 3 | inner | ||
1728.2.bc.e.145.14 | 72 | 3.2 | odd | 2 | |||
1728.2.bc.e.721.5 | 72 | 9.2 | odd | 6 | |||
1728.2.bc.e.1009.5 | 72 | 48.5 | odd | 4 | |||
1728.2.bc.e.1585.14 | 72 | 144.101 | odd | 12 |