Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [756,2,Mod(71,756)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(756, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 5, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("756.71");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 756.ba (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: | \(6.03669039281\) |
Analytic rank: | \(0\) |
Dimension: | \(72\) |
Relative dimension: | \(36\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 252) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 575.11 | ||
Character | \(\chi\) | \(=\) | 756.575 |
Dual form | 756.2.ba.a.71.11 |
$q$-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 \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(325\) | \(379\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.802493 | − | 1.16448i | −0.567448 | − | 0.823409i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.712009 | + | 1.86897i | −0.356005 | + | 0.934484i | ||||
\(5\) | 2.73233 | − | 1.57751i | 1.22193 | − | 0.705484i | 0.256604 | − | 0.966517i | \(-0.417396\pi\) |
0.965330 | + | 0.261033i | \(0.0840630\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.866025 | + | 0.500000i | 0.327327 | + | 0.188982i | ||||
\(8\) | 2.74775 | − | 0.670717i | 0.971477 | − | 0.237134i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −4.02965 | − | 1.91579i | −1.27429 | − | 0.605826i | ||||
\(11\) | 2.55685 | − | 4.42859i | 0.770919 | − | 1.33527i | −0.166141 | − | 0.986102i | \(-0.553131\pi\) |
0.937060 | − | 0.349169i | \(-0.113536\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.38370 | + | 4.12868i | 0.661118 | + | 1.14509i | 0.980322 | + | 0.197404i | \(0.0632511\pi\) |
−0.319204 | + | 0.947686i | \(0.603416\pi\) | |||||||
\(14\) | −0.112741 | − | 1.40971i | −0.0301314 | − | 0.376762i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.98609 | − | 2.66145i | −0.746521 | − | 0.665361i | ||||
\(17\) | 7.22631i | 1.75264i | 0.481731 | + | 0.876319i | \(0.340008\pi\) | ||||
−0.481731 | + | 0.876319i | \(0.659992\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 0.531576i | − | 0.121952i | −0.998139 | − | 0.0609759i | \(-0.980579\pi\) | ||
0.998139 | − | 0.0609759i | \(-0.0194213\pi\) | |||||||
\(20\) | 1.00287 | + | 6.22984i | 0.224249 | + | 1.39303i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −7.20884 | + | 0.576526i | −1.53693 | + | 0.122916i | ||||
\(23\) | −1.59577 | − | 2.76396i | −0.332742 | − | 0.576325i | 0.650307 | − | 0.759672i | \(-0.274640\pi\) |
−0.983048 | + | 0.183346i | \(0.941307\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.47708 | − | 4.29042i | 0.495415 | − | 0.858084i | ||||
\(26\) | 2.89485 | − | 6.08899i | 0.567727 | − | 1.19415i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.55110 | + | 1.26257i | −0.293131 | + | 0.238603i | ||||
\(29\) | 1.50966 | + | 0.871600i | 0.280336 | + | 0.161852i | 0.633575 | − | 0.773681i | \(-0.281587\pi\) |
−0.353240 | + | 0.935533i | \(0.614920\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.47432 | + | 0.851200i | −0.264796 | + | 0.152880i | −0.626520 | − | 0.779405i | \(-0.715521\pi\) |
0.361724 | + | 0.932285i | \(0.382188\pi\) | |||||||
\(32\) | −0.702876 | + | 5.61302i | −0.124252 | + | 0.992251i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 8.41487 | − | 5.79907i | 1.44314 | − | 0.994532i | ||||
\(35\) | 3.15502 | 0.533296 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.11392 | 0.511926 | 0.255963 | − | 0.966687i | \(-0.417608\pi\) | ||||
0.255963 | + | 0.966687i | \(0.417608\pi\) | |||||||
\(38\) | −0.619007 | + | 0.426586i | −0.100416 | + | 0.0692014i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 6.44969 | − | 6.16722i | 1.01979 | − | 0.975124i | ||||
\(41\) | 2.32723 | − | 1.34363i | 0.363452 | − | 0.209839i | −0.307142 | − | 0.951664i | \(-0.599373\pi\) |
0.670594 | + | 0.741825i | \(0.266039\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.39025 | + | 2.53471i | 0.669507 | + | 0.386540i | 0.795890 | − | 0.605441i | \(-0.207003\pi\) |
−0.126383 | + | 0.991982i | \(0.540337\pi\) | |||||||
\(44\) | 6.45640 | + | 7.93187i | 0.973339 | + | 1.19577i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.93797 | + | 4.07630i | −0.285738 | + | 0.601017i | ||||
\(47\) | −1.47750 | + | 2.55911i | −0.215516 | + | 0.373285i | −0.953432 | − | 0.301608i | \(-0.902477\pi\) |
0.737916 | + | 0.674892i | \(0.235810\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.500000 | + | 0.866025i | 0.0714286 | + | 0.123718i | ||||
\(50\) | −6.98393 | + | 0.558538i | −0.987677 | + | 0.0789893i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −9.41359 | + | 1.51539i | −1.30543 | + | 0.210147i | ||||
\(53\) | − | 13.6811i | − | 1.87925i | −0.342209 | − | 0.939624i | \(-0.611175\pi\) | ||
0.342209 | − | 0.939624i | \(-0.388825\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 16.1338i | − | 2.17548i | ||||||
\(56\) | 2.71498 | + | 0.793018i | 0.362805 | + | 0.105971i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.196531 | − | 2.45741i | −0.0258058 | − | 0.322674i | ||||
\(59\) | −3.71140 | − | 6.42833i | −0.483183 | − | 0.836898i | 0.516630 | − | 0.856209i | \(-0.327186\pi\) |
−0.999814 | + | 0.0193107i | \(0.993853\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.23838 | − | 5.60903i | 0.414632 | − | 0.718163i | −0.580758 | − | 0.814076i | \(-0.697244\pi\) |
0.995390 | + | 0.0959130i | \(0.0305771\pi\) | |||||||
\(62\) | 2.17433 | + | 1.03373i | 0.276141 | + | 0.131284i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.10028 | − | 3.68593i | 0.887535 | − | 0.460741i | ||||
\(65\) | 13.0261 | + | 7.52061i | 1.61569 | + | 0.932816i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.72700 | + | 0.997087i | −0.210987 | + | 0.121814i | −0.601770 | − | 0.798669i | \(-0.705538\pi\) |
0.390783 | + | 0.920483i | \(0.372204\pi\) | |||||||
\(68\) | −13.5057 | − | 5.14520i | −1.63781 | − | 0.623947i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.53188 | − | 3.67395i | −0.302618 | − | 0.439120i | ||||
\(71\) | −13.0667 | −1.55074 | −0.775368 | − | 0.631509i | \(-0.782436\pi\) | ||||
−0.775368 | + | 0.631509i | \(0.782436\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.59684 | −0.772101 | −0.386051 | − | 0.922478i | \(-0.626161\pi\) | ||||
−0.386051 | + | 0.922478i | \(0.626161\pi\) | |||||||
\(74\) | −2.49890 | − | 3.62609i | −0.290491 | − | 0.421524i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.993498 | + | 0.378487i | 0.113962 | + | 0.0434154i | ||||
\(77\) | 4.42859 | − | 2.55685i | 0.504685 | − | 0.291380i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.73014 | + | 0.998899i | 0.194656 | + | 0.112385i | 0.594161 | − | 0.804346i | \(-0.297484\pi\) |
−0.399504 | + | 0.916731i | \(0.630818\pi\) | |||||||
\(80\) | −12.3574 | − | 2.56136i | −1.38160 | − | 0.286369i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −3.43221 | − | 1.63175i | −0.379024 | − | 0.180197i | ||||
\(83\) | 3.28016 | − | 5.68140i | 0.360044 | − | 0.623615i | −0.627923 | − | 0.778275i | \(-0.716095\pi\) |
0.987968 | + | 0.154660i | \(0.0494282\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 11.3996 | + | 19.7446i | 1.23646 | + | 2.14161i | ||||
\(86\) | −0.571535 | − | 7.14643i | −0.0616302 | − | 0.770620i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4.05525 | − | 13.8836i | 0.432292 | − | 1.48000i | ||||
\(89\) | − | 9.77920i | − | 1.03659i | −0.855201 | − | 0.518297i | \(-0.826566\pi\) | ||
0.855201 | − | 0.518297i | \(-0.173434\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.76739i | 0.499758i | ||||||||
\(92\) | 6.30196 | − | 1.01448i | 0.657025 | − | 0.105767i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 4.16571 | − | 0.333152i | 0.429660 | − | 0.0343620i | ||||
\(95\) | −0.838566 | − | 1.45244i | −0.0860350 | − | 0.149017i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.15806 | + | 10.6661i | −0.625257 | + | 1.08298i | 0.363234 | + | 0.931698i | \(0.381672\pi\) |
−0.988491 | + | 0.151279i | \(0.951661\pi\) | |||||||
\(98\) | 0.607219 | − | 1.27722i | 0.0613384 | − | 0.129018i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 6.25496 | + | 7.68439i | 0.625496 | + | 0.768439i | ||||
\(101\) | 3.16824 | + | 1.82918i | 0.315251 | + | 0.182010i | 0.649274 | − | 0.760555i | \(-0.275073\pi\) |
−0.334023 | + | 0.942565i | \(0.608406\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.62116 | − | 1.51333i | 0.258270 | − | 0.149112i | −0.365275 | − | 0.930900i | \(-0.619025\pi\) |
0.623545 | + | 0.781787i | \(0.285692\pi\) | |||||||
\(104\) | 9.31898 | + | 9.74581i | 0.913801 | + | 0.955655i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −15.9314 | + | 10.9790i | −1.54739 | + | 1.06638i | ||||
\(107\) | 4.00810 | 0.387478 | 0.193739 | − | 0.981053i | \(-0.437939\pi\) | ||||
0.193739 | + | 0.981053i | \(0.437939\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.58898 | −0.152197 | −0.0760984 | − | 0.997100i | \(-0.524246\pi\) | ||||
−0.0760984 | + | 0.997100i | \(0.524246\pi\) | |||||||
\(110\) | −18.7874 | + | 12.9473i | −1.79131 | + | 1.23447i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.25530 | − | 3.79792i | −0.118615 | − | 0.358870i | ||||
\(113\) | −5.56042 | + | 3.21031i | −0.523080 | + | 0.302001i | −0.738194 | − | 0.674588i | \(-0.764321\pi\) |
0.215114 | + | 0.976589i | \(0.430988\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.72035 | − | 5.03470i | −0.813177 | − | 0.469488i | ||||
\(116\) | −2.70388 | + | 2.20091i | −0.251049 | + | 0.204349i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −4.50727 | + | 9.48053i | −0.414928 | + | 0.872754i | ||||
\(119\) | −3.61316 | + | 6.25817i | −0.331217 | + | 0.573685i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.57496 | − | 13.1202i | −0.688632 | − | 1.19275i | ||||
\(122\) | −9.13036 | + | 0.730199i | −0.826624 | + | 0.0661091i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.541135 | − | 3.36152i | −0.0485954 | − | 0.301874i | ||||
\(125\) | 0.144654i | 0.0129383i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 5.15607i | − | 0.457527i | −0.973482 | − | 0.228764i | \(-0.926532\pi\) | ||
0.973482 | − | 0.228764i | \(-0.0734683\pi\) | |||||||
\(128\) | −9.99010 | − | 5.31017i | −0.883008 | − | 0.469357i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.69577 | − | 21.2038i | −0.148729 | − | 1.85969i | ||||
\(131\) | 7.48154 | + | 12.9584i | 0.653666 | + | 1.13218i | 0.982227 | + | 0.187699i | \(0.0601030\pi\) |
−0.328561 | + | 0.944483i | \(0.606564\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.265788 | − | 0.460358i | 0.0230467 | − | 0.0399181i | ||||
\(134\) | 2.54699 | + | 1.21090i | 0.220027 | + | 0.104606i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.84681 | + | 19.8561i | 0.415610 | + | 1.70265i | ||||
\(137\) | −0.472178 | − | 0.272612i | −0.0403409 | − | 0.0232908i | 0.479694 | − | 0.877436i | \(-0.340748\pi\) |
−0.520035 | + | 0.854145i | \(0.674081\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.99978 | + | 5.19603i | −0.763351 | + | 0.440721i | −0.830498 | − | 0.557022i | \(-0.811944\pi\) |
0.0671463 | + | 0.997743i | \(0.478611\pi\) | |||||||
\(140\) | −2.24640 | + | 5.89663i | −0.189856 | + | 0.498356i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 10.4860 | + | 15.2159i | 0.879963 | + | 1.27689i | ||||
\(143\) | 24.3790 | 2.03867 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.49983 | 0.456736 | ||||||||
\(146\) | 5.29392 | + | 7.68186i | 0.438128 | + | 0.635755i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.21714 | + | 5.81982i | −0.182248 | + | 0.478387i | ||||
\(149\) | −11.1828 | + | 6.45637i | −0.916127 | + | 0.528926i | −0.882398 | − | 0.470505i | \(-0.844072\pi\) |
−0.0337298 | + | 0.999431i | \(0.510739\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.78931 | + | 1.61041i | 0.226991 | + | 0.131053i | 0.609183 | − | 0.793030i | \(-0.291497\pi\) |
−0.382192 | + | 0.924083i | \(0.624831\pi\) | |||||||
\(152\) | −0.356537 | − | 1.46064i | −0.0289189 | − | 0.118473i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −6.53131 | − | 3.10514i | −0.526308 | − | 0.250219i | ||||
\(155\) | −2.68555 | + | 4.65151i | −0.215709 | + | 0.373618i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.13601 | + | 5.43172i | 0.250281 | + | 0.433499i | 0.963603 | − | 0.267337i | \(-0.0861438\pi\) |
−0.713322 | + | 0.700836i | \(0.752810\pi\) | |||||||
\(158\) | −0.225235 | − | 2.81632i | −0.0179187 | − | 0.224054i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 6.93410 | + | 16.4454i | 0.548189 | + | 1.30012i | ||||
\(161\) | − | 3.19155i | − | 0.251529i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 17.5965i | − | 1.37826i | −0.724636 | − | 0.689132i | \(-0.757992\pi\) | ||
0.724636 | − | 0.689132i | \(-0.242008\pi\) | |||||||
\(164\) | 0.854187 | + | 5.30619i | 0.0667008 | + | 0.414344i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −9.24816 | + | 0.739620i | −0.717797 | + | 0.0574057i | ||||
\(167\) | −1.40973 | − | 2.44173i | −0.109088 | − | 0.188946i | 0.806313 | − | 0.591489i | \(-0.201460\pi\) |
−0.915401 | + | 0.402543i | \(0.868126\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.86401 | + | 8.42471i | −0.374154 | + | 0.648054i | ||||
\(170\) | 13.8441 | − | 29.1195i | 1.06179 | − | 2.23336i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −7.86320 | + | 6.40050i | −0.599563 | + | 0.488034i | ||||
\(173\) | −3.41022 | − | 1.96889i | −0.259274 | − | 0.149692i | 0.364729 | − | 0.931114i | \(-0.381162\pi\) |
−0.624003 | + | 0.781422i | \(0.714495\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.29042 | − | 2.47708i | 0.324325 | − | 0.187249i | ||||
\(176\) | −19.4214 | + | 6.41924i | −1.46395 | + | 0.483869i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −11.3876 | + | 7.84774i | −0.853540 | + | 0.588213i | ||||
\(179\) | −1.19273 | −0.0891491 | −0.0445746 | − | 0.999006i | \(-0.514193\pi\) | ||||
−0.0445746 | + | 0.999006i | \(0.514193\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.516134 | −0.0383639 | −0.0191820 | − | 0.999816i | \(-0.506106\pi\) | ||||
−0.0191820 | + | 0.999816i | \(0.506106\pi\) | |||||||
\(182\) | 5.55151 | − | 3.82580i | 0.411505 | − | 0.283587i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −6.23862 | − | 6.52436i | −0.459917 | − | 0.480982i | ||||
\(185\) | 8.50826 | − | 4.91224i | 0.625540 | − | 0.361155i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 32.0024 | + | 18.4766i | 2.34025 | + | 1.35114i | ||||
\(188\) | −3.73090 | − | 4.58352i | −0.272104 | − | 0.334287i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.01839 | + | 2.14206i | −0.0738815 | + | 0.155402i | ||||
\(191\) | −13.1346 | + | 22.7498i | −0.950385 | + | 1.64611i | −0.205791 | + | 0.978596i | \(0.565977\pi\) |
−0.744593 | + | 0.667518i | \(0.767357\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.21149 | + | 14.2227i | 0.591076 | + | 1.02377i | 0.994088 | + | 0.108579i | \(0.0346300\pi\) |
−0.403012 | + | 0.915195i | \(0.632037\pi\) | |||||||
\(194\) | 17.3622 | − | 1.38854i | 1.24653 | − | 0.0996913i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.97458 | + | 0.317866i | −0.141041 | + | 0.0227047i | ||||
\(197\) | 5.79981i | 0.413219i | 0.978423 | + | 0.206610i | \(0.0662430\pi\) | ||||
−0.978423 | + | 0.206610i | \(0.933757\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 25.1918i | 1.78580i | 0.450253 | + | 0.892901i | \(0.351334\pi\) | ||||
−0.450253 | + | 0.892901i | \(0.648666\pi\) | |||||||
\(200\) | 3.92873 | − | 13.4504i | 0.277803 | − | 0.951089i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −0.412450 | − | 5.15724i | −0.0290198 | − | 0.362862i | ||||
\(203\) | 0.871600 | + | 1.50966i | 0.0611743 | + | 0.105957i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.23917 | − | 7.34245i | 0.296076 | − | 0.512819i | ||||
\(206\) | −3.86569 | − | 1.83784i | −0.269335 | − | 0.128048i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3.87034 | − | 18.6727i | 0.268360 | − | 1.29472i | ||||
\(209\) | −2.35413 | − | 1.35916i | −0.162839 | − | 0.0940150i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.6040 | + | 7.27691i | −0.867694 | + | 0.500963i | −0.866581 | − | 0.499036i | \(-0.833687\pi\) |
−0.00111255 | + | 0.999999i | \(0.500354\pi\) | |||||||
\(212\) | 25.5696 | + | 9.74109i | 1.75613 | + | 0.669021i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3.21647 | − | 4.66734i | −0.219874 | − | 0.319053i | ||||
\(215\) | 15.9941 | 1.09079 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.70240 | −0.115566 | ||||||||
\(218\) | 1.27515 | + | 1.85033i | 0.0863638 | + | 0.125320i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 30.1536 | + | 11.4874i | 2.03296 | + | 0.774482i | ||||
\(221\) | −29.8351 | + | 17.2253i | −2.00693 | + | 1.15870i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.1948 | + | 7.61804i | 0.883591 | + | 0.510141i | 0.871841 | − | 0.489789i | \(-0.162926\pi\) |
0.0117502 | + | 0.999931i | \(0.496260\pi\) | |||||||
\(224\) | −3.41522 | + | 4.50958i | −0.228189 | + | 0.301309i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 8.20053 | + | 3.89872i | 0.545491 | + | 0.259339i | ||||
\(227\) | −2.90472 | + | 5.03112i | −0.192793 | + | 0.333927i | −0.946175 | − | 0.323656i | \(-0.895088\pi\) |
0.753382 | + | 0.657583i | \(0.228421\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.47034 | − | 12.9390i | −0.493654 | − | 0.855034i | 0.506319 | − | 0.862346i | \(-0.331006\pi\) |
−0.999973 | + | 0.00731207i | \(0.997672\pi\) | |||||||
\(230\) | 1.13524 | + | 14.1949i | 0.0748554 | + | 0.935987i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.73275 | + | 1.38239i | 0.310721 | + | 0.0907583i | ||||
\(233\) | 0.536725i | 0.0351620i | 0.999845 | + | 0.0175810i | \(0.00559649\pi\) | ||||
−0.999845 | + | 0.0175810i | \(0.994404\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.32310i | 0.608172i | ||||||||
\(236\) | 14.6569 | − | 2.35946i | 0.954083 | − | 0.153588i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 10.1870 | − | 0.814705i | 0.660327 | − | 0.0528095i | ||||
\(239\) | −10.0017 | − | 17.3234i | −0.646956 | − | 1.12056i | −0.983846 | − | 0.179017i | \(-0.942708\pi\) |
0.336890 | − | 0.941544i | \(-0.390625\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.07407 | − | 13.9847i | 0.520096 | − | 0.900833i | −0.479631 | − | 0.877470i | \(-0.659229\pi\) |
0.999727 | − | 0.0233628i | \(-0.00743728\pi\) | |||||||
\(242\) | −9.19932 | + | 19.3497i | −0.591355 | + | 1.24385i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 8.17735 | + | 10.0461i | 0.523501 | + | 0.643136i | ||||
\(245\) | 2.73233 | + | 1.57751i | 0.174562 | + | 0.100783i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.19471 | − | 1.26711i | 0.139646 | − | 0.0806246i | ||||
\(248\) | −3.48015 | + | 3.32774i | −0.220990 | + | 0.211312i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0.168446 | − | 0.116084i | 0.0106535 | − | 0.00734180i | ||||
\(251\) | −25.4053 | −1.60357 | −0.801785 | − | 0.597613i | \(-0.796116\pi\) | ||||
−0.801785 | + | 0.597613i | \(0.796116\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −16.3206 | −1.02607 | ||||||||
\(254\) | −6.00412 | + | 4.13771i | −0.376732 | + | 0.259623i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.83342 | + | 15.8946i | 0.114589 | + | 0.993413i | ||||
\(257\) | 5.65981 | − | 3.26769i | 0.353049 | − | 0.203833i | −0.312978 | − | 0.949760i | \(-0.601327\pi\) |
0.666027 | + | 0.745927i | \(0.267993\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.69674 | + | 1.55696i | 0.167567 | + | 0.0967449i | ||||
\(260\) | −23.3305 | + | 18.9906i | −1.44689 | + | 1.17775i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 9.08588 | − | 19.1111i | 0.561327 | − | 1.18069i | ||||
\(263\) | 2.54968 | − | 4.41617i | 0.157220 | − | 0.272313i | −0.776645 | − | 0.629938i | \(-0.783080\pi\) |
0.933865 | + | 0.357625i | \(0.116414\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −21.5821 | − | 37.3813i | −1.32578 | − | 2.29632i | ||||
\(266\) | −0.749369 | + | 0.0599306i | −0.0459468 | + | 0.00367458i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −0.633880 | − | 3.93765i | −0.0387204 | − | 0.240530i | ||||
\(269\) | 23.1813i | 1.41339i | 0.707519 | + | 0.706694i | \(0.249814\pi\) | ||||
−0.707519 | + | 0.706694i | \(0.750186\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 3.33548i | − | 0.202616i | −0.994855 | − | 0.101308i | \(-0.967697\pi\) | ||
0.994855 | − | 0.101308i | \(-0.0323027\pi\) | |||||||
\(272\) | 19.2324 | − | 21.5784i | 1.16614 | − | 1.30838i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.0614694 | + | 0.768609i | 0.00371350 | + | 0.0464334i | ||||
\(275\) | −12.6670 | − | 21.9399i | −0.763850 | − | 1.32303i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.01165 | + | 10.4125i | −0.361205 | + | 0.625625i | −0.988159 | − | 0.153430i | \(-0.950968\pi\) |
0.626954 | + | 0.779056i | \(0.284301\pi\) | |||||||
\(278\) | 13.2729 | + | 6.31025i | 0.796056 | + | 0.378464i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 8.66921 | − | 2.11613i | 0.518084 | − | 0.126463i | ||||
\(281\) | −16.0334 | − | 9.25689i | −0.956472 | − | 0.552220i | −0.0613869 | − | 0.998114i | \(-0.519552\pi\) |
−0.895086 | + | 0.445894i | \(0.852886\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −18.7908 | + | 10.8489i | −1.11700 | + | 0.644899i | −0.940633 | − | 0.339426i | \(-0.889767\pi\) |
−0.176365 | + | 0.984325i | \(0.556434\pi\) | |||||||
\(284\) | 9.30364 | − | 24.4213i | 0.552069 | − | 1.44914i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −19.5640 | − | 28.3888i | −1.15684 | − | 1.67866i | ||||
\(287\) | 2.68725 | 0.158624 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −35.2196 | −2.07174 | ||||||||
\(290\) | −4.41358 | − | 6.40442i | −0.259174 | − | 0.376081i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 4.69701 | − | 12.3293i | 0.274872 | − | 0.721517i | ||||
\(293\) | 11.5943 | − | 6.69399i | 0.677348 | − | 0.391067i | −0.121507 | − | 0.992591i | \(-0.538773\pi\) |
0.798855 | + | 0.601524i | \(0.205439\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −20.2815 | − | 11.7095i | −1.18084 | − | 0.681756i | ||||
\(296\) | 8.55629 | − | 2.08856i | 0.497324 | − | 0.121395i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 16.4924 | + | 7.84086i | 0.955378 | + | 0.454209i | ||||
\(299\) | 7.60767 | − | 13.1769i | 0.439963 | − | 0.762038i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.53471 | + | 4.39025i | 0.146098 | + | 0.253050i | ||||
\(302\) | −0.363120 | − | 4.54043i | −0.0208952 | − | 0.261272i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.41476 | + | 1.58733i | −0.0811420 | + | 0.0910396i | ||||
\(305\) | − | 20.4343i | − | 1.17006i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 14.9315i | − | 0.852187i | −0.904679 | − | 0.426093i | \(-0.859889\pi\) | ||
0.904679 | − | 0.426093i | \(-0.140111\pi\) | |||||||
\(308\) | 1.62547 | + | 10.0974i | 0.0926198 | + | 0.575353i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 7.57171 | − | 0.605546i | 0.430044 | − | 0.0343927i | ||||
\(311\) | 3.83776 | + | 6.64720i | 0.217619 | + | 0.376928i | 0.954080 | − | 0.299553i | \(-0.0968375\pi\) |
−0.736460 | + | 0.676481i | \(0.763504\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.6398 | − | 20.1608i | 0.657923 | − | 1.13956i | −0.323229 | − | 0.946321i | \(-0.604768\pi\) |
0.981152 | − | 0.193236i | \(-0.0618982\pi\) | |||||||
\(314\) | 3.80849 | − | 8.01072i | 0.214925 | − | 0.452071i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.09879 | + | 2.52236i | −0.174320 | + | 0.141894i | ||||
\(317\) | −23.4749 | − | 13.5533i | −1.31848 | − | 0.761226i | −0.334998 | − | 0.942219i | \(-0.608736\pi\) |
−0.983485 | + | 0.180992i | \(0.942069\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.71992 | − | 4.45710i | 0.432233 | − | 0.249550i | ||||
\(320\) | 13.5857 | − | 21.2719i | 0.759464 | − | 1.18914i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −3.71648 | + | 2.56119i | −0.207111 | + | 0.142730i | ||||
\(323\) | 3.84133 | 0.213737 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 23.6184 | 1.31011 | ||||||||
\(326\) | −20.4907 | + | 14.1211i | −1.13488 | + | 0.782094i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 5.49345 | − | 5.25286i | 0.303325 | − | 0.290041i | ||||
\(329\) | −2.55911 | + | 1.47750i | −0.141088 | + | 0.0814574i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −15.5271 | − | 8.96456i | −0.853445 | − | 0.492737i | 0.00836643 | − | 0.999965i | \(-0.497337\pi\) |
−0.861812 | + | 0.507228i | \(0.830670\pi\) | |||||||
\(332\) | 8.28286 | + | 10.1757i | 0.454581 | + | 0.558466i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1.71203 | + | 3.60107i | −0.0936782 | + | 0.197042i | ||||
\(335\) | −3.14583 | + | 5.44873i | −0.171875 | + | 0.297696i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.33464 | − | 5.77577i | −0.181650 | − | 0.314626i | 0.760793 | − | 0.648995i | \(-0.224810\pi\) |
−0.942442 | + | 0.334368i | \(0.891477\pi\) | |||||||
\(338\) | 13.7137 | − | 1.09675i | 0.745927 | − | 0.0596554i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −45.0187 | + | 7.24708i | −2.44148 | + | 0.393028i | ||||
\(341\) | 8.70556i | 0.471432i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 13.7634 | + | 4.02015i | 0.742073 | + | 0.216752i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0.443951 | + | 5.55114i | 0.0238670 | + | 0.298431i | ||||
\(347\) | 15.7139 | + | 27.2173i | 0.843568 | + | 1.46110i | 0.886859 | + | 0.462041i | \(0.152883\pi\) |
−0.0432902 | + | 0.999063i | \(0.513784\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.17117 | + | 5.49263i | −0.169749 | + | 0.294014i | −0.938332 | − | 0.345737i | \(-0.887629\pi\) |
0.768583 | + | 0.639751i | \(0.220962\pi\) | |||||||
\(350\) | −6.32753 | − | 3.00826i | −0.338221 | − | 0.160798i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 23.0606 | + | 17.4644i | 1.22914 | + | 0.930855i | ||||
\(353\) | −22.5568 | − | 13.0232i | −1.20058 | − | 0.693155i | −0.239896 | − | 0.970799i | \(-0.577113\pi\) |
−0.960684 | + | 0.277644i | \(0.910447\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −35.7026 | + | 20.6129i | −1.89490 | + | 1.09402i | ||||
\(356\) | 18.2770 | + | 6.96288i | 0.968680 | + | 0.369032i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0.957161 | + | 1.38891i | 0.0505875 | + | 0.0734062i | ||||
\(359\) | −31.2925 | −1.65156 | −0.825778 | − | 0.563996i | \(-0.809263\pi\) | ||||
−0.825778 | + | 0.563996i | \(0.809263\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.7174 | 0.985128 | ||||||||
\(362\) | 0.414194 | + | 0.601025i | 0.0217695 | + | 0.0315892i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −8.91010 | − | 3.39443i | −0.467016 | − | 0.177916i | ||||
\(365\) | −18.0247 | + | 10.4066i | −0.943457 | + | 0.544705i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 19.3046 | + | 11.1455i | 1.00769 | + | 0.581792i | 0.910515 | − | 0.413475i | \(-0.135685\pi\) |
0.0971776 | + | 0.995267i | \(0.469019\pi\) | |||||||
\(368\) | −2.59101 | + | 12.5005i | −0.135066 | + | 0.651633i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −12.5480 | − | 5.96562i | −0.652340 | − | 0.310138i | ||||
\(371\) | 6.84057 | − | 11.8482i | 0.355144 | − | 0.615128i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.29840 | + | 16.1053i | 0.481453 | + | 0.833901i | 0.999773 | − | 0.0212856i | \(-0.00677594\pi\) |
−0.518321 | + | 0.855186i | \(0.673443\pi\) | |||||||
\(374\) | −4.16616 | − | 52.0934i | −0.215427 | − | 2.69368i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.34337 | + | 8.02279i | −0.120850 | + | 0.413744i | ||||
\(377\) | 8.31051i | 0.428013i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 21.2022i | − | 1.08908i | −0.838733 | − | 0.544542i | \(-0.816703\pi\) | ||
0.838733 | − | 0.544542i | \(-0.183297\pi\) | |||||||
\(380\) | 3.31163 | − | 0.533103i | 0.169883 | − | 0.0273476i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 37.0320 | − | 2.96162i | 1.89472 | − | 0.151530i | ||||
\(383\) | 5.85031 | + | 10.1330i | 0.298937 | + | 0.517774i | 0.975893 | − | 0.218250i | \(-0.0700347\pi\) |
−0.676956 | + | 0.736023i | \(0.736701\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8.06691 | − | 13.9723i | 0.411128 | − | 0.712094i | ||||
\(386\) | 9.97235 | − | 20.9757i | 0.507579 | − | 1.06764i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −15.5500 | − | 19.1036i | −0.789430 | − | 0.969837i | ||||
\(389\) | 20.6139 | + | 11.9014i | 1.04517 | + | 0.603427i | 0.921292 | − | 0.388871i | \(-0.127135\pi\) |
0.123874 | + | 0.992298i | \(0.460468\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 19.9732 | − | 11.5316i | 1.01009 | − | 0.583176i | ||||
\(392\) | 1.95473 | + | 2.04426i | 0.0987290 | + | 0.103251i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 6.75374 | − | 4.65431i | 0.340249 | − | 0.234481i | ||||
\(395\) | 6.30309 | 0.317143 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.08225 | −0.455825 | −0.227912 | − | 0.973682i | \(-0.573190\pi\) | ||||
−0.227912 | + | 0.973682i | \(0.573190\pi\) | |||||||
\(398\) | 29.3353 | − | 20.2163i | 1.47045 | − | 1.01335i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −18.8155 | + | 6.21896i | −0.940774 | + | 0.310948i | ||||
\(401\) | 22.6865 | − | 13.0981i | 1.13291 | − | 0.654087i | 0.188246 | − | 0.982122i | \(-0.439720\pi\) |
0.944666 | + | 0.328035i | \(0.106386\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.02866 | − | 4.05800i | −0.350123 | − | 0.202143i | ||||
\(404\) | −5.67450 | + | 4.61894i | −0.282317 | + | 0.229801i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.05850 | − | 2.22645i | 0.0525327 | − | 0.110497i | ||||
\(407\) | 7.96183 | − | 13.7903i | 0.394653 | − | 0.683560i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.62676 | − | 8.01379i | −0.228779 | − | 0.396256i | 0.728668 | − | 0.684867i | \(-0.240140\pi\) |
−0.957446 | + | 0.288611i | \(0.906807\pi\) | |||||||
\(410\) | −11.9520 | + | 0.955860i | −0.590268 | + | 0.0472066i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0.962070 | + | 5.97636i | 0.0473978 | + | 0.294434i | ||||
\(413\) | − | 7.42280i | − | 0.365252i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 20.6979i | − | 1.01602i | ||||||
\(416\) | −24.8498 | + | 10.4778i | −1.21836 | + | 0.513715i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0.306467 | + | 3.83205i | 0.0149898 | + | 0.187432i | ||||
\(419\) | 14.3147 | + | 24.7937i | 0.699317 | + | 1.21125i | 0.968704 | + | 0.248220i | \(0.0798457\pi\) |
−0.269387 | + | 0.963032i | \(0.586821\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.82164 | + | 11.8154i | −0.332466 | + | 0.575849i | −0.982995 | − | 0.183633i | \(-0.941214\pi\) |
0.650528 | + | 0.759482i | \(0.274547\pi\) | |||||||
\(422\) | 18.5884 | + | 8.83736i | 0.904869 | + | 0.430196i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −9.17617 | − | 37.5924i | −0.445634 | − | 1.82565i | ||||
\(425\) | 31.0039 | + | 17.9001i | 1.50391 | + | 0.868283i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.60903 | − | 3.23838i | 0.271440 | − | 0.156716i | ||||
\(428\) | −2.85380 | + | 7.49101i | −0.137944 | + | 0.362092i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −12.8352 | − | 18.6248i | −0.618968 | − | 0.898167i | ||||
\(431\) | −11.9995 | −0.577994 | −0.288997 | − | 0.957330i | \(-0.593322\pi\) | ||||
−0.288997 | + | 0.957330i | \(0.593322\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 18.6726 | 0.897349 | 0.448674 | − | 0.893695i | \(-0.351896\pi\) | ||||
0.448674 | + | 0.893695i | \(0.351896\pi\) | |||||||
\(434\) | 1.36616 | + | 1.98240i | 0.0655780 | + | 0.0951584i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.13137 | − | 2.96975i | 0.0541827 | − | 0.142225i | ||||
\(437\) | −1.46925 | + | 0.848274i | −0.0702839 | + | 0.0405784i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −22.6620 | − | 13.0839i | −1.08160 | − | 0.624461i | −0.150271 | − | 0.988645i | \(-0.548015\pi\) |
−0.931327 | + | 0.364184i | \(0.881348\pi\) | |||||||
\(440\) | −10.8212 | − | 44.3317i | −0.515882 | − | 2.11343i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 44.0010 | + | 20.9191i | 2.09291 | + | 0.995020i | ||||
\(443\) | 17.3363 | − | 30.0273i | 0.823671 | − | 1.42664i | −0.0792601 | − | 0.996854i | \(-0.525256\pi\) |
0.902931 | − | 0.429786i | \(-0.141411\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −15.4268 | − | 26.7200i | −0.731300 | − | 1.26665i | ||||
\(446\) | −1.71774 | − | 21.4785i | −0.0813372 | − | 1.01704i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 7.99198 | + | 0.358033i | 0.377586 | + | 0.0169155i | ||||
\(449\) | 14.5939i | 0.688731i | 0.938836 | + | 0.344365i | \(0.111906\pi\) | ||||
−0.938836 | + | 0.344365i | \(0.888094\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 13.7418i | − | 0.647076i | ||||||
\(452\) | −2.04090 | − | 12.6780i | −0.0959958 | − | 0.596324i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 8.18963 | − | 0.654964i | 0.384358 | − | 0.0307390i | ||||
\(455\) | 7.52061 | + | 13.0261i | 0.352571 | + | 0.610672i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.0109808 | − | 0.0190193i | 0.000513661 | − | 0.000889687i | −0.865768 | − | 0.500445i | \(-0.833170\pi\) |
0.866282 | + | 0.499555i | \(0.166503\pi\) | |||||||
\(458\) | −9.07227 | + | 19.0825i | −0.423919 | + | 0.891667i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 15.6187 | − | 12.7133i | 0.728224 | − | 0.592761i | ||||
\(461\) | −7.01426 | − | 4.04969i | −0.326687 | − | 0.188613i | 0.327682 | − | 0.944788i | \(-0.393732\pi\) |
−0.654369 | + | 0.756175i | \(0.727066\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −27.8853 | + | 16.0996i | −1.29594 | + | 0.748211i | −0.979700 | − | 0.200469i | \(-0.935753\pi\) |
−0.316239 | + | 0.948680i | \(0.602420\pi\) | |||||||
\(464\) | −2.18824 | − | 6.62054i | −0.101587 | − | 0.307351i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0.625003 | − | 0.430718i | 0.0289527 | − | 0.0199526i | ||||
\(467\) | 11.6187 | 0.537648 | 0.268824 | − | 0.963189i | \(-0.413365\pi\) | ||||
0.268824 | + | 0.963189i | \(0.413365\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.99417 | −0.0920824 | ||||||||
\(470\) | 10.8565 | − | 7.48173i | 0.500774 | − | 0.345106i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −14.5096 | − | 15.1742i | −0.667858 | − | 0.698448i | ||||
\(473\) | 22.4504 | − | 12.9618i | 1.03227 | − | 0.595982i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.28068 | − | 1.31675i | −0.104645 | − | 0.0604168i | ||||
\(476\) | −9.12372 | − | 11.2087i | −0.418185 | − | 0.513752i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −12.1464 | + | 25.5487i | −0.555566 | + | 1.16857i | ||||
\(479\) | −3.05275 | + | 5.28752i | −0.139484 | + | 0.241593i | −0.927301 | − | 0.374316i | \(-0.877878\pi\) |
0.787818 | + | 0.615909i | \(0.211211\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.42264 | + | 12.8564i | 0.338443 | + | 0.586201i | ||||
\(482\) | −22.7642 | + | 1.82056i | −1.03688 | + | 0.0829244i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 29.9147 | − | 4.81564i | 1.35976 | − | 0.218893i | ||||
\(485\) | 38.8576i | 1.76443i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 18.6740i | 0.846201i | 0.906083 | + | 0.423100i | \(0.139058\pi\) | ||||
−0.906083 | + | 0.423100i | \(0.860942\pi\) | |||||||
\(488\) | 5.13618 | − | 17.5843i | 0.232504 | − | 0.796002i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −0.355702 | − | 4.44767i | −0.0160690 | − | 0.200925i | ||||
\(491\) | −1.67975 | − | 2.90941i | −0.0758060 | − | 0.131300i | 0.825630 | − | 0.564211i | \(-0.190820\pi\) |
−0.901437 | + | 0.432911i | \(0.857486\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.29845 | + | 10.9092i | −0.283668 | + | 0.491327i | ||||
\(494\) | −3.23676 | − | 1.53883i | −0.145629 | − | 0.0692353i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.66787 | + | 1.38207i | 0.299396 | + | 0.0620568i | ||||
\(497\) | −11.3161 | − | 6.53337i | −0.507598 | − | 0.293062i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 37.5927 | − | 21.7041i | 1.68288 | − | 0.971610i | 0.723146 | − | 0.690696i | \(-0.242696\pi\) |
0.959733 | − | 0.280915i | \(-0.0906378\pi\) | |||||||
\(500\) | −0.270354 | − | 0.102995i | −0.0120906 | − | 0.00460608i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 20.3876 | + | 29.5839i | 0.909943 | + | 1.32039i | ||||
\(503\) | 7.34385 | 0.327446 | 0.163723 | − | 0.986506i | \(-0.447650\pi\) | ||||
0.163723 | + | 0.986506i | \(0.447650\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 11.5422 | 0.513622 | ||||||||
\(506\) | 13.0972 | + | 19.0050i | 0.582240 | + | 0.844873i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 9.63653 | + | 3.67117i | 0.427552 | + | 0.162882i | ||||
\(509\) | −7.79196 | + | 4.49869i | −0.345372 | + | 0.199401i | −0.662645 | − | 0.748933i | \(-0.730566\pi\) |
0.317273 | + | 0.948334i | \(0.397233\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.71303 | − | 3.29842i | −0.252730 | − | 0.145913i | ||||
\(512\) | 17.0376 | − | 14.8903i | 0.752962 | − | 0.658064i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −8.34710 | − | 3.96841i | −0.368175 | − | 0.175039i | ||||
\(515\) | 4.77457 | − | 8.26980i | 0.210393 | − | 0.364411i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.55551 | + | 13.0865i | 0.332291 | + | 0.575544i | ||||
\(518\) | −0.351068 | − | 4.38974i | −0.0154251 | − | 0.192874i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 40.8366 | + | 11.9280i | 1.79080 | + | 0.523075i | ||||
\(521\) | − | 9.29655i | − | 0.407289i | −0.979045 | − | 0.203645i | \(-0.934721\pi\) | ||
0.979045 | − | 0.203645i | \(-0.0652787\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.26367i | 0.405072i | 0.979275 | + | 0.202536i | \(0.0649183\pi\) | ||||
−0.979275 | + | 0.202536i | \(0.935082\pi\) | |||||||
\(524\) | −29.5458 | + | 4.75626i | −1.29071 | + | 0.207778i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7.18863 | + | 0.574909i | −0.313439 | + | 0.0250672i | ||||
\(527\) | −6.15103 | − | 10.6539i | −0.267943 | − | 0.464091i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.40702 | − | 11.0973i | 0.278566 | − | 0.482490i | ||||
\(530\) | −26.2102 | + | 55.1301i | −1.13850 | + | 2.39470i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0.671151 | + | 0.824528i | 0.0290981 | + | 0.0357478i | ||||
\(533\) | 11.0948 | + | 6.40559i | 0.480570 | + | 0.277457i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 10.9514 | − | 6.32282i | 0.473472 | − | 0.273359i | ||||
\(536\) | −4.07662 | + | 3.89808i | −0.176083 | + | 0.168371i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 26.9940 | − | 18.6028i | 1.16380 | − | 0.802025i | ||||
\(539\) | 5.11370 | 0.220263 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −39.0275 | −1.67792 | −0.838962 | − | 0.544189i | \(-0.816837\pi\) | ||||
−0.838962 | + | 0.544189i | \(0.816837\pi\) | |||||||
\(542\) | −3.88409 | + | 2.67670i | −0.166836 | + | 0.114974i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −40.5614 | − | 5.07920i | −1.73906 | − | 0.217769i | ||||
\(545\) | −4.34162 | + | 2.50663i | −0.185974 | + | 0.107372i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15.6709 | + | 9.04762i | 0.670041 | + | 0.386848i | 0.796092 | − | 0.605175i | \(-0.206897\pi\) |
−0.126051 | + | 0.992024i | \(0.540230\pi\) | |||||||
\(548\) | 0.845698 | − | 0.688383i | 0.0361264 | − | 0.0294063i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −15.3833 | + | 32.3571i | −0.655947 | + | 1.37971i | ||||
\(551\) | 0.463321 | − | 0.802496i | 0.0197381 | − | 0.0341875i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.998899 | + | 1.73014i | 0.0424775 | + | 0.0735732i | ||||
\(554\) | 16.9494 | − | 1.35552i | 0.720111 | − | 0.0575907i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.30328 | − | 20.5199i | −0.140090 | − | 0.870239i | ||||
\(557\) | 11.4867i | 0.486705i | 0.969938 | + | 0.243353i | \(0.0782472\pi\) | ||||
−0.969938 | + | 0.243353i | \(0.921753\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 24.1679i | 1.02219i | ||||||||
\(560\) | −9.42116 | − | 8.39691i | −0.398117 | − | 0.354834i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 2.08727 | + | 26.0991i | 0.0880462 | + | 1.10092i | ||||
\(563\) | 1.41954 | + | 2.45871i | 0.0598263 | + | 0.103622i | 0.894387 | − | 0.447293i | \(-0.147612\pi\) |
−0.834561 | + | 0.550915i | \(0.814279\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10.1286 | + | 17.5432i | −0.426113 | + | 0.738050i | ||||
\(566\) | 27.7128 | + | 13.1753i | 1.16485 | + | 0.553799i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −35.9041 | + | 8.76408i | −1.50650 | + | 0.367733i | ||||
\(569\) | −5.82245 | − | 3.36159i | −0.244090 | − | 0.140925i | 0.372965 | − | 0.927845i | \(-0.378341\pi\) |
−0.617055 | + | 0.786920i | \(0.711674\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14.0370 | + | 8.10429i | −0.587432 | + | 0.339154i | −0.764081 | − | 0.645120i | \(-0.776807\pi\) |
0.176650 | + | 0.984274i | \(0.443474\pi\) | |||||||
\(572\) | −17.3581 | + | 45.5636i | −0.725777 | + | 1.90511i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −2.15650 | − | 3.12924i | −0.0900107 | − | 0.130612i | ||||
\(575\) | −15.8114 | −0.659381 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.47679 | −0.228002 | −0.114001 | − | 0.993481i | \(-0.536367\pi\) | ||||
−0.114001 | + | 0.993481i | \(0.536367\pi\) | |||||||
\(578\) | 28.2635 | + | 41.0124i | 1.17561 | + | 1.70589i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −3.91593 | + | 10.2790i | −0.162600 | + | 0.426813i | ||||
\(581\) | 5.68140 | − | 3.28016i | 0.235704 | − | 0.136084i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −60.5882 | − | 34.9806i | −2.50931 | − | 1.44875i | ||||
\(584\) | −18.1265 | + | 4.42461i | −0.750079 | + | 0.183092i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −17.0994 | − | 8.12944i | −0.706368 | − | 0.335824i | ||||
\(587\) | −18.7598 | + | 32.4930i | −0.774301 | + | 1.34113i | 0.160886 | + | 0.986973i | \(0.448565\pi\) |
−0.935187 | + | 0.354155i | \(0.884769\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.452477 | + | 0.783713i | 0.0186440 | + | 0.0322923i | ||||
\(590\) | 2.64030 | + | 33.0142i | 0.108700 | + | 1.35917i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −9.29844 | − | 8.28754i | −0.382164 | − | 0.340616i | ||||
\(593\) | − | 47.4039i | − | 1.94665i | −0.229438 | − | 0.973323i | \(-0.573689\pi\) | ||
0.229438 | − | 0.973323i | \(-0.426311\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 22.7992i | 0.934674i | ||||||||
\(596\) | −4.10452 | − | 25.4972i | −0.168128 | − | 1.04441i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −21.4493 | + | 1.71540i | −0.877126 | + | 0.0701479i | ||||
\(599\) | 15.9337 | + | 27.5979i | 0.651032 | + | 1.12762i | 0.982873 | + | 0.184285i | \(0.0589970\pi\) |
−0.331841 | + | 0.943335i | \(0.607670\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.7566 | − | 22.0950i | 0.520351 | − | 0.901274i | −0.479369 | − | 0.877613i | \(-0.659135\pi\) |
0.999720 | − | 0.0236606i | \(-0.00753212\pi\) | |||||||
\(602\) | 3.07825 | − | 6.47476i | 0.125460 | − | 0.263892i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −4.99582 | + | 4.06650i | −0.203277 | + | 0.165464i | ||||
\(605\) | −41.3945 | − | 23.8991i | −1.68293 | − | 0.971638i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13.9168 | − | 8.03488i | 0.564866 | − | 0.326126i | −0.190230 | − | 0.981740i | \(-0.560923\pi\) |
0.755096 | + | 0.655614i | \(0.227590\pi\) | |||||||
\(608\) | 2.98374 | + | 0.373632i | 0.121007 | + | 0.0151528i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −23.7952 | + | 16.3984i | −0.963441 | + | 0.663951i | ||||
\(611\) | −14.0877 | −0.569926 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 10.1572 | 0.410246 | 0.205123 | − | 0.978736i | \(-0.434240\pi\) | ||||
0.205123 | + | 0.978736i | \(0.434240\pi\) | |||||||
\(614\) | −17.3874 | + | 11.9824i | −0.701698 | + | 0.483572i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 10.4538 | − | 9.99592i | 0.421194 | − | 0.402747i | ||||
\(617\) | 3.85193 | − | 2.22391i | 0.155073 | − | 0.0895312i | −0.420456 | − | 0.907313i | \(-0.638130\pi\) |
0.575528 | + | 0.817782i | \(0.304796\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 32.5736 | + | 18.8064i | 1.30924 | + | 0.755892i | 0.981970 | − | 0.189038i | \(-0.0605369\pi\) |
0.327273 | + | 0.944930i | \(0.393870\pi\) | |||||||
\(620\) | −6.78139 | − | 8.33113i | −0.272347 | − | 0.334586i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 4.66072 | − | 9.80331i | 0.186878 | − | 0.393077i | ||||
\(623\) | 4.88960 | − | 8.46904i | 0.195898 | − | 0.339305i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 12.6136 | + | 21.8473i | 0.504543 | + | 0.873894i | ||||
\(626\) | −32.8177 | + | 2.62459i | −1.31166 | + | 0.104900i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −12.3846 | + | 1.99366i | −0.494199 | + | 0.0795557i | ||||
\(629\) | 22.5022i | 0.897221i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 21.9573i | 0.874106i | 0.899436 | + | 0.437053i | \(0.143978\pi\) | ||||
−0.899436 | + | 0.437053i | \(0.856022\pi\) | |||||||
\(632\) | 5.42398 | + | 1.58429i | 0.215754 | + | 0.0630196i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 3.05603 | + | 38.2124i | 0.121370 | + | 1.51761i | ||||
\(635\) | −8.13375 | − | 14.0881i | −0.322778 | − | 0.559068i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.38370 | + | 4.12868i | −0.0944454 | + | 0.163584i | ||||
\(638\) | −11.3854 | − | 5.41287i | −0.450751 | − | 0.214298i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −35.6731 | + | 1.25035i | −1.41010 | + | 0.0494244i | ||||
\(641\) | 23.3369 | + | 13.4735i | 0.921750 | + | 0.532173i | 0.884193 | − | 0.467122i | \(-0.154709\pi\) |
0.0375573 | + | 0.999294i | \(0.488042\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −22.9917 | + | 13.2743i | −0.906704 | + | 0.523486i | −0.879369 | − | 0.476141i | \(-0.842035\pi\) |
−0.0273346 | + | 0.999626i | \(0.508702\pi\) | |||||||
\(644\) | 5.96490 | + | 2.27241i | 0.235050 | + | 0.0895455i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.08264 | − | 4.47314i | −0.121285 | − | 0.175993i | ||||
\(647\) | 23.8568 | 0.937906 | 0.468953 | − | 0.883223i | \(-0.344631\pi\) | ||||
0.468953 | + | 0.883223i | \(0.344631\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −37.9580 | −1.48998 | ||||||||
\(650\) | −18.9536 | − | 27.5030i | −0.743421 | − | 1.07876i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 32.8873 | + | 12.5289i | 1.28797 | + | 0.490668i | ||||
\(653\) | −23.4749 | + | 13.5532i | −0.918642 | + | 0.530378i | −0.883202 | − | 0.468993i | \(-0.844617\pi\) |
−0.0354406 | + | 0.999372i | \(0.511283\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 40.8841 | + | 23.6044i | 1.59747 | + | 0.922301i | ||||
\(656\) | −10.5253 | − | 2.18161i | −0.410944 | − | 0.0851775i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 3.77419 | + | 1.79434i | 0.147133 | + | 0.0699505i | ||||
\(659\) | 14.6668 | − | 25.4036i | 0.571338 | − | 0.989586i | −0.425091 | − | 0.905150i | \(-0.639758\pi\) |
0.996429 | − | 0.0844352i | \(-0.0269086\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.65945 | + | 16.7307i | 0.375709 | + | 0.650747i | 0.990433 | − | 0.137995i | \(-0.0440659\pi\) |
−0.614724 | + | 0.788742i | \(0.710733\pi\) | |||||||
\(662\) | 2.02136 | + | 25.2749i | 0.0785622 | + | 0.982337i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 5.20245 | − | 17.8111i | 0.201894 | − | 0.691206i | ||||
\(665\) | − | 1.67713i | − | 0.0650364i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 5.56350i | − | 0.215420i | ||||||
\(668\) | 5.56725 | − | 0.896212i | 0.215403 | − | 0.0346755i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 8.86943 | − | 0.709331i | 0.342656 | − | 0.0274038i | ||||
\(671\) | −16.5601 | − | 28.6829i | −0.639295 | − | 1.10729i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 24.8176 | − | 42.9853i | 0.956648 | − | 1.65696i | 0.226096 | − | 0.974105i | \(-0.427404\pi\) |
0.730552 | − | 0.682857i | \(-0.239263\pi\) | |||||||
\(674\) | −4.04972 | + | 8.51813i | −0.155989 | + | 0.328106i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.2823 | − | 15.0891i | −0.472396 | − | 0.580352i | ||||
\(677\) | −27.9037 | − | 16.1102i | −1.07243 | − | 0.619166i | −0.143584 | − | 0.989638i | \(-0.545863\pi\) |
−0.928844 | + | 0.370472i | \(0.879196\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.6661 | + | 6.15806i | −0.409327 | + | 0.236325i | ||||
\(680\) | 44.5663 | + | 46.6075i | 1.70904 | + | 1.78732i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 10.1374 | − | 6.98615i | 0.388182 | − | 0.267513i | ||||
\(683\) | −48.7831 | −1.86663 | −0.933316 | − | 0.359055i | \(-0.883099\pi\) | ||||
−0.933316 | + | 0.359055i | \(0.883099\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.72019 | −0.0657252 | ||||||||
\(686\) | 1.16448 | − | 0.802493i | 0.0444599 | − | 0.0306393i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −6.36367 | − | 19.2533i | −0.242613 | − | 0.734025i | ||||
\(689\) | 56.4850 | − | 32.6116i | 2.15191 | − | 1.24240i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 33.1524 | + | 19.1405i | 1.26118 | + | 0.728140i | 0.973302 | − | 0.229528i | \(-0.0737182\pi\) |
0.287874 | + | 0.957668i | \(0.407052\pi\) | |||||||
\(692\) | 6.10790 | − | 4.97172i | 0.232188 | − | 0.188997i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 19.0836 | − | 40.1402i | 0.724404 | − | 1.52370i | ||||
\(695\) | −16.3936 | + | 28.3945i | −0.621843 | + | 1.07706i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.70946 | + | 16.8173i | 0.367772 | + | 0.637000i | ||||
\(698\) | 8.94088 | − | 0.715045i | 0.338417 | − | 0.0270649i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.57476 | + | 9.78236i | 0.0595202 | + | 0.369739i | ||||
\(701\) | − | 16.4250i | − | 0.620365i | −0.950677 | − | 0.310183i | \(-0.899610\pi\) | ||
0.950677 | − | 0.310183i | \(-0.100390\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 1.65529i | − | 0.0624303i | ||||||
\(704\) | 1.83087 | − | 40.8686i | 0.0690036 | − | 1.54029i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2.93651 | + | 36.7179i | 0.110517 | + | 1.38190i | ||||
\(707\) | 1.82918 | + | 3.16824i | 0.0687935 | + | 0.119154i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.30143 | − | 3.98619i | 0.0864320 | − | 0.149705i | −0.819569 | − | 0.572981i | \(-0.805787\pi\) |
0.906001 | + | 0.423277i | \(0.139120\pi\) | |||||||
\(710\) | 52.6543 | + | 25.0331i | 1.97608 | + | 0.939476i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −6.55907 | − | 26.8708i | −0.245812 | − | 1.00703i | ||||
\(713\) | 4.70536 | + | 2.71664i | 0.176217 | + | 0.101739i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 66.6114 | − | 38.4581i | 2.49113 | − | 1.43825i | ||||
\(716\) | 0.849237 | − | 2.22918i | 0.0317375 | − | 0.0833084i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 25.1120 | + | 36.4394i | 0.937173 | + | 1.35991i | ||||
\(719\) | 27.4630 | 1.02420 | 0.512099 | − | 0.858927i | \(-0.328868\pi\) | ||||
0.512099 | + | 0.858927i | \(0.328868\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.02665 | 0.112718 | ||||||||
\(722\) | −15.0206 | − | 21.7960i | −0.559009 | − | 0.811163i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0.367492 | − | 0.964637i | 0.0136577 | − | 0.0358505i | ||||
\(725\) | 7.47906 | − | 4.31804i | 0.277765 | − | 0.160368i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12.1777 | + | 7.03079i | 0.451645 | + | 0.260758i | 0.708525 | − | 0.705686i | \(-0.249361\pi\) |
−0.256879 | + | 0.966443i | \(0.582694\pi\) | |||||||
\(728\) | 3.19757 | + | 13.0996i | 0.118510 | + | 0.485504i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 26.5829 | + | 12.6381i | 0.983878 | + | 0.467759i | ||||
\(731\) | −18.3166 | + | 31.7253i | −0.677465 | + | 1.17340i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 18.2356 | + | 31.5851i | 0.673549 | + | 1.16662i | 0.976891 | + | 0.213739i | \(0.0685642\pi\) |
−0.303342 | + | 0.952882i | \(0.598102\pi\) | |||||||
\(734\) | −2.51313 | − | 31.4240i | −0.0927612 | − | 1.15988i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 16.6358 | − | 7.01438i | 0.613203 | − | 0.258554i | ||||
\(737\) | 10.1976i | 0.375633i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 0.413262i | − | 0.0152021i | −0.999971 | − | 0.00760104i | \(-0.997580\pi\) | ||
0.999971 | − | 0.00760104i | \(-0.00241951\pi\) | |||||||
\(740\) | 3.12287 | + | 19.3992i | 0.114799 | + | 0.713130i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −19.2865 | + | 1.54243i | −0.708028 | + | 0.0566244i | ||||
\(743\) | 8.68868 | + | 15.0492i | 0.318757 | + | 0.552103i | 0.980229 | − | 0.197867i | \(-0.0634013\pi\) |
−0.661472 | + | 0.749970i | \(0.730068\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −20.3700 | + | 35.2818i | −0.746298 | + | 1.29263i | ||||
\(746\) | 11.2923 | − | 23.7522i | 0.413442 | − | 0.869628i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −57.3182 | + | 46.6560i | −2.09576 | + | 1.70591i | ||||
\(749\) | 3.47112 | + | 2.00405i | 0.126832 | + | 0.0732264i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.19940 | − | 1.84717i | 0.116748 | − | 0.0674044i | −0.440489 | − | 0.897758i | \(-0.645195\pi\) |
0.557237 | + | 0.830354i | \(0.311862\pi\) | |||||||
\(752\) | 11.2229 | − | 3.70943i | 0.409256 | − | 0.135269i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 9.67739 | − | 6.66913i | 0.352430 | − | 0.242875i | ||||
\(755\) | 10.1617 | 0.369824 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.01887 | −0.0733772 | −0.0366886 | − | 0.999327i | \(-0.511681\pi\) | ||||
−0.0366886 | + | 0.999327i | \(0.511681\pi\) | |||||||
\(758\) | −24.6895 | + | 17.0146i | −0.896762 | + | 0.617999i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3.27835 | − | 3.42850i | −0.118918 | − | 0.124365i | ||||
\(761\) | 16.4382 | − | 9.49062i | 0.595886 | − | 0.344035i | −0.171536 | − | 0.985178i | \(-0.554873\pi\) |
0.767421 | + | 0.641143i | \(0.221540\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.37610 | − | 0.794490i | −0.0498181 | − | 0.0287625i | ||||
\(764\) | −33.1666 | − | 40.7461i | −1.19993 | − | 1.47414i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 7.10484 | − | 14.9442i | 0.256708 | − | 0.539957i | ||||
\(767\) | 17.6937 | − | 30.6464i | 0.638882 | − | 1.10658i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −11.1454 | − | 19.3043i | −0.401912 | − | 0.696131i | 0.592045 | − | 0.805905i | \(-0.298321\pi\) |
−0.993957 | + | 0.109774i | \(0.964987\pi\) | |||||||
\(770\) | −22.7440 | + | 1.81895i | −0.819639 | + | 0.0655504i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −32.4285 | + | 5.22031i | −1.16713 | + | 0.187883i | ||||
\(773\) | − | 38.1241i | − | 1.37123i | −0.727965 | − | 0.685614i | \(-0.759534\pi\) | ||
0.727965 | − | 0.685614i | \(-0.240466\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.43394i | 0.302956i | ||||||||
\(776\) | −9.76691 | + | 33.4381i | −0.350612 | + | 1.20036i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −2.68357 | − | 33.5552i | −0.0962107 | − | 1.20301i | ||||
\(779\) | −0.714239 | − | 1.23710i | −0.0255903 | − | 0.0443236i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −33.4097 | + | 57.8673i | −1.19549 | + | 2.07065i | ||||
\(782\) | −29.4566 | − | 14.0044i | −1.05337 | − | 0.500795i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.811836 | − | 3.91675i | 0.0289942 | − | 0.139884i | ||||
\(785\) | 17.1372 | + | 9.89416i | 0.611653 | + | 0.353138i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 14.7144 | − | 8.49538i | 0.524513 | − | 0.302828i | −0.214266 | − | 0.976775i | \(-0.568736\pi\) |
0.738779 | + | 0.673948i | \(0.235403\pi\) | |||||||
\(788\) | −10.8397 | − | 4.12952i | −0.386147 | − | 0.147108i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −5.05819 | − | 7.33980i | −0.179962 | − | 0.261138i | ||||
\(791\) | −6.42062 | −0.228291 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 30.8772 | 1.09648 | ||||||||
\(794\) | 7.28844 | + | 10.5761i | 0.258657 | + | 0.375330i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −47.0828 | − | 17.9368i | −1.66880 | − | 0.635754i | ||||
\(797\) | −17.5585 | + | 10.1374i | −0.621955 | + | 0.359086i | −0.777630 | − | 0.628723i | \(-0.783578\pi\) |
0.155675 | + | 0.987808i | \(0.450245\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −18.4929 | − | 10.6769i | −0.654233 | − | 0.377721i | ||||
\(800\) | 22.3411 | + | 16.9195i | 0.789878 | + | 0.598195i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −33.4582 | − | 15.9068i | −1.18145 | − | 0.561689i | ||||
\(803\) | −16.8671 | + | 29.2147i | −0.595228 | + | 1.03096i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.03470 | − | 8.72035i | −0.177450 | − | 0.307352i | ||||
\(806\) | 0.915010 | + | 11.4412i | 0.0322299 | + | 0.403000i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 9.93239 | + | 2.90115i | 0.349420 | + | 0.102062i | ||||
\(809\) | 22.1960i | 0.780368i | 0.920737 | + | 0.390184i | \(0.127589\pi\) | ||||
−0.920737 | + | 0.390184i | \(0.872411\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 55.5158i | − | 1.94942i | −0.223463 | − | 0.974712i | \(-0.571736\pi\) | ||
0.223463 | − | 0.974712i | \(-0.428264\pi\) | |||||||
\(812\) | −3.44208 | + | 0.554104i | −0.120794 | + | 0.0194452i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −22.4478 | + | 1.79526i | −0.786795 | + | 0.0629237i | ||||
\(815\) | −27.7587 | − | 48.0794i | −0.972343 | − | 1.68415i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.34739 | − | 2.33375i | 0.0471393 | − | 0.0816476i | ||||
\(818\) | −5.61892 | + | 11.8188i | −0.196461 | + | 0.413233i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 10.7045 | + | 13.1508i | 0.373817 | + | 0.459245i | ||||
\(821\) | 26.1556 | + | 15.1010i | 0.912838 | + | 0.527027i | 0.881343 | − | 0.472477i | \(-0.156640\pi\) |
0.0314945 | + | 0.999504i | \(0.489973\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −20.0335 | + | 11.5664i | −0.698324 | + | 0.403178i | −0.806723 | − | 0.590930i | \(-0.798761\pi\) |
0.108399 | + | 0.994108i | \(0.465428\pi\) | |||||||
\(824\) | 6.18727 | − | 5.91630i | 0.215544 | − | 0.206104i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −8.64367 | + | 5.95675i | −0.300752 | + | 0.207262i | ||||
\(827\) | −26.5467 | −0.923119 | −0.461559 | − | 0.887109i | \(-0.652710\pi\) | ||||
−0.461559 | + | 0.887109i | \(0.652710\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 44.5548 | 1.54745 | 0.773727 | − | 0.633520i | \(-0.218390\pi\) | ||||
0.773727 | + | 0.633520i | \(0.218390\pi\) | |||||||
\(830\) | −24.1023 | + | 16.6100i | −0.836601 | + | 0.576540i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 32.1429 | + | 20.5287i | 1.11436 | + | 0.711703i | ||||
\(833\) | −6.25817 | + | 3.61316i | −0.216833 | + | 0.125188i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7.70370 | − | 4.44773i | −0.266597 | − | 0.153920i | ||||
\(836\) | 4.21639 | − | 3.43206i | 0.145827 | − | 0.118700i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 17.3843 | − | 36.5659i | 0.600530 | − | 1.26315i | ||||
\(839\) | 24.4985 | − | 42.4327i | 0.845782 | − | 1.46494i | −0.0391577 | − | 0.999233i | \(-0.512467\pi\) |
0.884940 | − | 0.465705i | \(-0.154199\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −12.9806 | − | 22.4831i | −0.447608 | − | 0.775280i | ||||
\(842\) | 19.2331 | − | 1.53816i | 0.662816 | − | 0.0530086i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −4.62617 | − | 28.7377i | −0.159239 | − | 0.989191i | ||||
\(845\) | 30.6921i | 1.05584i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 15.1499i | − | 0.520557i | ||||||
\(848\) | −36.4116 | + | 40.8530i | −1.25038 | + | 1.40290i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −4.03617 | − | 50.4680i | −0.138440 | − | 1.73104i | ||||
\(851\) | −4.96911 | − | 8.60676i | −0.170339 | − | 0.295036i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −17.4025 | + | 30.1421i | −0.595852 | + | 1.03205i | 0.397574 | + | 0.917570i | \(0.369852\pi\) |
−0.993426 | + | 0.114476i | \(0.963481\pi\) | |||||||
\(854\) | −8.27223 | − | 3.93281i | −0.283070 | − | 0.134578i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 11.0133 | − | 2.68830i | 0.376426 | − | 0.0918842i | ||||
\(857\) | 16.9081 | + | 9.76190i | 0.577570 | + | 0.333460i | 0.760167 | − | 0.649728i | \(-0.225117\pi\) |
−0.182597 | + | 0.983188i | \(0.558450\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 17.6783 | − | 10.2066i | 0.603176 | − | 0.348244i | −0.167114 | − | 0.985938i | \(-0.553445\pi\) |
0.770290 | + | 0.637694i | \(0.220112\pi\) | |||||||
\(860\) | −11.3880 | + | 29.8925i | −0.388327 | + | 1.01933i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 9.62950 | + | 13.9731i | 0.327982 | + | 0.475926i | ||||
\(863\) | −38.2894 | −1.30339 | −0.651694 | − | 0.758482i | \(-0.725941\pi\) | ||||
−0.651694 | + | 0.758482i | \(0.725941\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −12.4238 | −0.422421 | ||||||||
\(866\) | −14.9846 | − | 21.7438i | −0.509199 | − | 0.738885i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.21212 | − | 3.18173i | 0.0411422 | − | 0.107995i | ||||
\(869\) | 8.84743 | − | 5.10807i | 0.300129 | − | 0.173279i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.23331 | − | 4.75350i | −0.278975 | − | 0.161066i | ||||
\(872\) | −4.36612 | + | 1.06576i | −0.147856 | + | 0.0360911i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 2.16686 | + | 1.03018i | 0.0732952 | + | 0.0348462i | ||||
\(875\) | −0.0723271 | + | 0.125274i | −0.00244510 | + | 0.00423504i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 28.5255 | + | 49.4076i | 0.963238 | + | 1.66838i | 0.714277 | + | 0.699863i | \(0.246756\pi\) |
0.248960 | + | 0.968514i | \(0.419911\pi\) | |||||||
\(878\) | 2.95020 | + | 36.8891i | 0.0995644 | + | 1.24495i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −42.9393 | + | 48.1770i | −1.44748 | + | 1.62405i | ||||
\(881\) | − | 42.6383i | − | 1.43652i | −0.695774 | − | 0.718261i | \(-0.744938\pi\) | ||
0.695774 | − | 0.718261i | \(-0.255062\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0.262142i | 0.00882176i | 0.999990 | + | 0.00441088i | \(0.00140403\pi\) | ||||
−0.999990 | + | 0.00441088i | \(0.998596\pi\) | |||||||
\(884\) | −10.9507 | − | 68.0255i | −0.368312 | − | 2.28795i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −48.8783 | + | 3.90903i | −1.64210 | + | 0.131327i | ||||
\(887\) | −8.58006 | − | 14.8611i | −0.288090 | − | 0.498987i | 0.685264 | − | 0.728295i | \(-0.259687\pi\) |
−0.973354 | + | 0.229308i | \(0.926354\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.57804 | − | 4.46529i | 0.0864645 | − | 0.149761i | ||||
\(890\) | −18.7349 | + | 39.4067i | −0.627995 | + | 1.32092i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −23.6327 | + | 19.2366i | −0.791282 | + | 0.644089i | ||||
\(893\) | 1.36036 | + | 0.785405i | 0.0455227 | + | 0.0262826i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.25894 | + | 1.88155i | −0.108934 | + | 0.0628933i | ||||
\(896\) | −5.99659 | − | 9.59379i | −0.200332 | − | 0.320506i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 16.9943 | − | 11.7115i | 0.567107 | − | 0.390819i | ||||
\(899\) | −2.96762 | −0.0989757 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 98.8641 | 3.29364 | ||||||||
\(902\) | −16.0020 | + | 11.0277i | −0.532808 | + | 0.367182i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −13.1254 | + | 12.5506i | −0.436546 | + | 0.417427i | ||||
\(905\) | −1.41025 | + | 0.814206i | −0.0468782 | + | 0.0270651i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −44.7570 | − | 25.8405i | −1.48613 | − | 0.858019i | −0.486257 | − | 0.873816i | \(-0.661638\pi\) |
−0.999875 | + | 0.0157966i | \(0.994972\pi\) | |||||||
\(908\) | −7.33481 | − | 9.01102i | −0.243414 | − | 0.299041i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 9.13331 | − | 19.2109i | 0.302766 | − | 0.636835i | ||||
\(911\) | −15.9334 | + | 27.5975i | −0.527898 | + | 0.914347i | 0.471573 | + | 0.881827i | \(0.343687\pi\) |
−0.999471 | + | 0.0325198i | \(0.989647\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −16.7737 | − | 29.0530i | −0.555130 | − | 0.961513i | ||||
\(914\) | −0.0309596 | + | 0.00247599i | −0.00102405 | + | 8.18984e-5i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 29.5016 | − | 4.74914i | 0.974759 | − | 0.156916i | ||||
\(917\) | 14.9631i | 0.494125i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 49.4568i | 1.63143i | 0.578455 | + | 0.815714i | \(0.303656\pi\) | ||||
−0.578455 | + | 0.815714i | \(0.696344\pi\) | |||||||
\(920\) | −27.3382 | − | 7.98521i | −0.901314 | − | 0.263265i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0.913135 | + | 11.4178i | 0.0300725 | + | 0.376025i | ||||
\(923\) | −31.1471 | − | 53.9484i | −1.02522 | − | 1.77573i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.71342 | − | 13.3600i | 0.253616 | − | 0.439275i | ||||
\(926\) | 41.1253 | + | 19.5519i | 1.35146 | + | 0.642517i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −5.95341 | + | 7.86109i | −0.195430 | + | 0.258053i | ||||
\(929\) | −20.6955 | − | 11.9486i | −0.678998 | − | 0.392020i | 0.120479 | − | 0.992716i | \(-0.461557\pi\) |
−0.799477 | + | 0.600696i | \(0.794890\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.460358 | − | 0.265788i | 0.0150876 | − | 0.00871084i | ||||
\(932\) | −1.00312 | − | 0.382153i | −0.0328583 | − | 0.0125178i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −9.32390 | − | 13.5297i | −0.305087 | − | 0.442704i | ||||
\(935\) | 116.588 | 3.81284 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 35.2010 | 1.14997 | 0.574983 | − | 0.818165i | \(-0.305009\pi\) | ||||
0.574983 | + | 0.818165i | \(0.305009\pi\) | |||||||
\(938\) | 1.60031 | + | 2.32217i | 0.0522520 | + | 0.0758214i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −17.4246 | − | 6.63814i | −0.568327 | − | 0.216512i | ||||
\(941\) | −13.0422 | + | 7.52990i | −0.425163 | + | 0.245468i | −0.697284 | − | 0.716795i | \(-0.745608\pi\) |
0.272121 | + | 0.962263i | \(0.412275\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7.42746 | − | 4.28824i | −0.241871 | − | 0.139644i | ||||
\(944\) | −6.02610 | + | 29.0732i | −0.196133 | + | 0.946254i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −33.1100 | − | 15.7413i | −1.07650 | − | 0.511793i | ||||
\(947\) | 1.64196 | − | 2.84396i | 0.0533565 | − | 0.0924162i | −0.838114 | − | 0.545496i | \(-0.816341\pi\) |
0.891470 | + | 0.453080i | \(0.149675\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −15.7249 | − | 27.2362i | −0.510450 | − | 0.884126i | ||||
\(950\) | 0.296905 | + | 3.71249i | 0.00963288 | + | 0.120449i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −5.73059 | + | 19.6193i | −0.185730 | + | 0.635865i | ||||
\(953\) | − | 15.4731i | − | 0.501222i | −0.968088 | − | 0.250611i | \(-0.919368\pi\) | ||
0.968088 | − | 0.250611i | \(-0.0806316\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 82.8797i | 2.68192i | ||||||||
\(956\) | 39.4983 | − | 6.35840i | 1.27747 | − | 0.205645i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 8.60701 | − | 0.688344i | 0.278080 | − | 0.0222394i | ||||
\(959\) | −0.272612 | − | 0.472178i | −0.00880310 | − | 0.0152474i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14.0509 | + | 24.3369i | −0.453255 | + | 0.785061i | ||||
\(962\) | 9.01434 | − | 18.9607i | 0.290634 | − | 0.611316i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 20.3881 | + | 25.0474i | 0.656658 | + | 0.806723i | ||||
\(965\) | 44.8730 | + | 25.9074i | 1.44451 | + | 0.833989i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 30.8548 | − | 17.8141i | 0.992225 | − | 0.572861i | 0.0862862 | − | 0.996270i | \(-0.472500\pi\) |
0.905939 | + | 0.423409i | \(0.139167\pi\) | |||||||
\(968\) | −29.6140 | − | 30.9704i | −0.951831 | − | 0.995427i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 45.2488 | − | 31.1830i | 1.45285 | − | 1.00123i | ||||
\(971\) | −10.9461 | −0.351278 | −0.175639 | − | 0.984455i | \(-0.556199\pi\) | ||||
−0.175639 | + | 0.984455i | \(0.556199\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −10.3921 | −0.333154 | ||||||||
\(974\) | 21.7455 | − | 14.9858i | 0.696769 | − | 0.480175i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −24.5982 | + | 8.13029i | −0.787370 | + | 0.260244i | ||||
\(977\) | −30.9200 | + | 17.8516i | −0.989217 | + | 0.571125i | −0.905040 | − | 0.425326i | \(-0.860159\pi\) |
−0.0841770 | + | 0.996451i | \(0.526826\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −43.3081 | − | 25.0039i | −1.38413 | − | 0.799129i | ||||
\(980\) | −4.89376 | + | 3.98343i | −0.156325 | + | 0.127246i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −2.03995 | + | 4.29081i | −0.0650975 | + | 0.136925i | ||||
\(983\) | 7.62459 | − | 13.2062i | 0.243187 | − | 0.421212i | −0.718433 | − | 0.695596i | \(-0.755141\pi\) |
0.961620 | + | 0.274384i | \(0.0884739\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9.14926 | + | 15.8470i | 0.291520 | + | 0.504927i | ||||
\(986\) | 17.7580 | − | 1.42019i | 0.565530 | − | 0.0452282i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.805546 | + | 5.00403i | 0.0256278 | + | 0.159200i | ||||
\(989\) | − | 16.1793i | − | 0.514472i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 35.4971i | − | 1.12760i | −0.825911 | − | 0.563801i | \(-0.809339\pi\) | ||
0.825911 | − | 0.563801i | \(-0.190661\pi\) | |||||||
\(992\) | −3.74153 | − | 8.87368i | −0.118794 | − | 0.281740i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.47316 | + | 18.4203i | 0.0467259 | + | 0.584258i | ||||
\(995\) | 39.7404 | + | 68.8324i | 1.25985 | + | 2.18213i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 23.0368 | − | 39.9010i | 0.729584 | − | 1.26368i | −0.227475 | − | 0.973784i | \(-0.573047\pi\) |
0.957059 | − | 0.289893i | \(-0.0936196\pi\) | |||||||
\(998\) | −55.4418 | − | 26.3583i | −1.75498 | − | 0.834358i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 756.2.ba.a.575.11 | 72 | ||
3.2 | odd | 2 | 252.2.ba.a.155.26 | ✓ | 72 | ||
4.3 | odd | 2 | inner | 756.2.ba.a.575.2 | 72 | ||
9.4 | even | 3 | 252.2.ba.a.239.35 | yes | 72 | ||
9.5 | odd | 6 | inner | 756.2.ba.a.71.2 | 72 | ||
12.11 | even | 2 | 252.2.ba.a.155.35 | yes | 72 | ||
36.23 | even | 6 | inner | 756.2.ba.a.71.11 | 72 | ||
36.31 | odd | 6 | 252.2.ba.a.239.26 | yes | 72 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
252.2.ba.a.155.26 | ✓ | 72 | 3.2 | odd | 2 | ||
252.2.ba.a.155.35 | yes | 72 | 12.11 | even | 2 | ||
252.2.ba.a.239.26 | yes | 72 | 36.31 | odd | 6 | ||
252.2.ba.a.239.35 | yes | 72 | 9.4 | even | 3 | ||
756.2.ba.a.71.2 | 72 | 9.5 | odd | 6 | inner | ||
756.2.ba.a.71.11 | 72 | 36.23 | even | 6 | inner | ||
756.2.ba.a.575.2 | 72 | 4.3 | odd | 2 | inner | ||
756.2.ba.a.575.11 | 72 | 1.1 | even | 1 | trivial |