Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [804,2,Mod(499,804)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(804, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("804.499");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 804 = 2^{2} \cdot 3 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 804.j (of order \(6\), degree \(2\), 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: | \(6.41997232251\) |
Analytic rank: | \(0\) |
Dimension: | \(68\) |
Relative dimension: | \(34\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 499.4 | ||
Character | \(\chi\) | \(=\) | 804.499 |
Dual form | 804.2.j.b.775.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/804\mathbb{Z}\right)^\times\).
\(n\) | \(269\) | \(337\) | \(403\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.32266 | + | 0.500561i | −0.935264 | + | 0.353950i | ||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.49888 | − | 1.32415i | 0.749439 | − | 0.662074i | ||||
\(5\) | − | 3.14328i | − | 1.40572i | −0.711330 | − | 0.702858i | \(-0.751907\pi\) | ||
0.711330 | − | 0.702858i | \(-0.248093\pi\) | |||||||
\(6\) | −1.32266 | + | 0.500561i | −0.539975 | + | 0.204353i | ||||
\(7\) | 2.02612 | − | 3.50935i | 0.765803 | − | 1.32641i | −0.174018 | − | 0.984742i | \(-0.555675\pi\) |
0.939821 | − | 0.341667i | \(-0.110991\pi\) | |||||||
\(8\) | −1.31969 | + | 2.50168i | −0.466582 | + | 0.884478i | ||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.57340 | + | 4.15750i | 0.497554 | + | 1.31472i | ||||
\(11\) | −0.934262 | + | 1.61819i | −0.281690 | + | 0.487902i | −0.971801 | − | 0.235802i | \(-0.924228\pi\) |
0.690111 | + | 0.723704i | \(0.257562\pi\) | |||||||
\(12\) | 1.49888 | − | 1.32415i | 0.432689 | − | 0.382249i | ||||
\(13\) | 1.56836 | − | 0.905492i | 0.434984 | − | 0.251138i | −0.266483 | − | 0.963839i | \(-0.585862\pi\) |
0.701468 | + | 0.712701i | \(0.252528\pi\) | |||||||
\(14\) | −0.923236 | + | 5.65589i | −0.246745 | + | 1.51160i | ||||
\(15\) | − | 3.14328i | − | 0.811591i | ||||||
\(16\) | 0.493266 | − | 3.96947i | 0.123317 | − | 0.992367i | ||||
\(17\) | 3.63749 | + | 6.30032i | 0.882221 | + | 1.52805i | 0.848866 | + | 0.528609i | \(0.177286\pi\) |
0.0333558 | + | 0.999444i | \(0.489381\pi\) | |||||||
\(18\) | −1.32266 | + | 0.500561i | −0.311755 | + | 0.117983i | ||||
\(19\) | 3.35356 | − | 1.93618i | 0.769359 | − | 0.444190i | −0.0632869 | − | 0.997995i | \(-0.520158\pi\) |
0.832646 | + | 0.553806i | \(0.186825\pi\) | |||||||
\(20\) | −4.16216 | − | 4.71139i | −0.930688 | − | 1.05350i | ||||
\(21\) | 2.02612 | − | 3.50935i | 0.442136 | − | 0.765803i | ||||
\(22\) | 0.425712 | − | 2.60797i | 0.0907620 | − | 0.556022i | ||||
\(23\) | −0.543486 | + | 0.313782i | −0.113325 | + | 0.0654281i | −0.555591 | − | 0.831456i | \(-0.687508\pi\) |
0.442266 | + | 0.896884i | \(0.354175\pi\) | |||||||
\(24\) | −1.31969 | + | 2.50168i | −0.269381 | + | 0.510654i | ||||
\(25\) | −4.88020 | −0.976040 | ||||||||
\(26\) | −1.62116 | + | 1.98272i | −0.317935 | + | 0.388843i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −1.60999 | − | 7.94297i | −0.304259 | − | 1.50108i | ||||
\(29\) | 4.41834 | − | 7.65278i | 0.820464 | − | 1.42109i | −0.0848728 | − | 0.996392i | \(-0.527048\pi\) |
0.905337 | − | 0.424694i | \(-0.139618\pi\) | |||||||
\(30\) | 1.57340 | + | 4.15750i | 0.287263 | + | 0.759052i | ||||
\(31\) | −3.78697 | + | 6.55923i | −0.680160 | + | 1.17807i | 0.294771 | + | 0.955568i | \(0.404757\pi\) |
−0.974932 | + | 0.222505i | \(0.928577\pi\) | |||||||
\(32\) | 1.33454 | + | 5.49718i | 0.235915 | + | 0.971774i | ||||
\(33\) | −0.934262 | + | 1.61819i | −0.162634 | + | 0.281690i | ||||
\(34\) | −7.96487 | − | 6.51242i | −1.36596 | − | 1.11687i | ||||
\(35\) | −11.0309 | − | 6.36867i | −1.86456 | − | 1.07650i | ||||
\(36\) | 1.49888 | − | 1.32415i | 0.249813 | − | 0.220691i | ||||
\(37\) | −5.45660 | − | 9.45112i | −0.897060 | − | 1.55375i | −0.831234 | − | 0.555923i | \(-0.812365\pi\) |
−0.0658262 | − | 0.997831i | \(-0.520968\pi\) | |||||||
\(38\) | −3.46645 | + | 4.23957i | −0.562333 | + | 0.687749i | ||||
\(39\) | 1.56836 | − | 0.905492i | 0.251138 | − | 0.144995i | ||||
\(40\) | 7.86348 | + | 4.14816i | 1.24333 | + | 0.655882i | ||||
\(41\) | −2.51599 | − | 1.45261i | −0.392931 | − | 0.226859i | 0.290498 | − | 0.956876i | \(-0.406179\pi\) |
−0.683429 | + | 0.730017i | \(0.739512\pi\) | |||||||
\(42\) | −0.923236 | + | 5.65589i | −0.142458 | + | 0.872722i | ||||
\(43\) | −2.50287 | −0.381684 | −0.190842 | − | 0.981621i | \(-0.561122\pi\) | ||||
−0.190842 | + | 0.981621i | \(0.561122\pi\) | |||||||
\(44\) | 0.742377 | + | 3.66257i | 0.111918 | + | 0.552153i | ||||
\(45\) | − | 3.14328i | − | 0.468572i | ||||||
\(46\) | 0.561783 | − | 0.687076i | 0.0828303 | − | 0.101304i | ||||
\(47\) | −6.03173 | − | 3.48242i | −0.879818 | − | 0.507963i | −0.00921972 | − | 0.999957i | \(-0.502935\pi\) |
−0.870598 | + | 0.491994i | \(0.836268\pi\) | |||||||
\(48\) | 0.493266 | − | 3.96947i | 0.0711968 | − | 0.572944i | ||||
\(49\) | −4.71035 | − | 8.15857i | −0.672908 | − | 1.16551i | ||||
\(50\) | 6.45486 | − | 2.44284i | 0.912855 | − | 0.345470i | ||||
\(51\) | 3.63749 | + | 6.30032i | 0.509351 | + | 0.882221i | ||||
\(52\) | 1.15177 | − | 3.43396i | 0.159722 | − | 0.476204i | ||||
\(53\) | − | 3.73302i | − | 0.512769i | −0.966575 | − | 0.256385i | \(-0.917469\pi\) | ||
0.966575 | − | 0.256385i | \(-0.0825314\pi\) | |||||||
\(54\) | −1.32266 | + | 0.500561i | −0.179992 | + | 0.0681177i | ||||
\(55\) | 5.08642 | + | 2.93664i | 0.685852 | + | 0.395977i | ||||
\(56\) | 6.10541 | + | 9.69998i | 0.815870 | + | 1.29621i | ||||
\(57\) | 3.35356 | − | 1.93618i | 0.444190 | − | 0.256453i | ||||
\(58\) | −2.01329 | + | 12.3337i | −0.264357 | + | 1.61949i | ||||
\(59\) | 14.0628i | 1.83082i | 0.402522 | + | 0.915410i | \(0.368134\pi\) | ||||
−0.402522 | + | 0.915410i | \(0.631866\pi\) | |||||||
\(60\) | −4.16216 | − | 4.71139i | −0.537333 | − | 0.608238i | ||||
\(61\) | 2.09861 | − | 1.21163i | 0.268699 | − | 0.155134i | −0.359597 | − | 0.933108i | \(-0.617086\pi\) |
0.628296 | + | 0.777974i | \(0.283753\pi\) | |||||||
\(62\) | 1.72560 | − | 10.5713i | 0.219151 | − | 1.34255i | ||||
\(63\) | 2.02612 | − | 3.50935i | 0.255268 | − | 0.442136i | ||||
\(64\) | −4.51682 | − | 6.60290i | −0.564602 | − | 0.825363i | ||||
\(65\) | −2.84621 | − | 4.92979i | −0.353029 | − | 0.611465i | ||||
\(66\) | 0.425712 | − | 2.60797i | 0.0524015 | − | 0.321019i | ||||
\(67\) | 6.35908 | + | 5.15385i | 0.776885 | + | 0.629642i | ||||
\(68\) | 13.7947 | + | 4.62683i | 1.67285 | + | 0.561086i | ||||
\(69\) | −0.543486 | + | 0.313782i | −0.0654281 | + | 0.0377749i | ||||
\(70\) | 17.7780 | + | 2.90199i | 2.12488 | + | 0.346854i | ||||
\(71\) | −12.4110 | − | 7.16551i | −1.47292 | − | 0.850389i | −0.473382 | − | 0.880857i | \(-0.656967\pi\) |
−0.999536 | + | 0.0304681i | \(0.990300\pi\) | |||||||
\(72\) | −1.31969 | + | 2.50168i | −0.155527 | + | 0.294826i | ||||
\(73\) | 2.30070 | + | 3.98493i | 0.269276 | + | 0.466400i | 0.968675 | − | 0.248331i | \(-0.0798822\pi\) |
−0.699399 | + | 0.714732i | \(0.746549\pi\) | |||||||
\(74\) | 11.9481 | + | 9.76928i | 1.38894 | + | 1.13566i | ||||
\(75\) | −4.88020 | −0.563517 | ||||||||
\(76\) | 2.46279 | − | 7.34270i | 0.282501 | − | 0.842265i | ||||
\(77\) | 3.78586 | + | 6.55730i | 0.431439 | + | 0.747274i | ||||
\(78\) | −1.62116 | + | 1.98272i | −0.183560 | + | 0.224499i | ||||
\(79\) | 0.726008 | − | 1.25748i | 0.0816822 | − | 0.141478i | −0.822290 | − | 0.569068i | \(-0.807304\pi\) |
0.903973 | + | 0.427590i | \(0.140637\pi\) | |||||||
\(80\) | −12.4771 | − | 1.55047i | −1.39499 | − | 0.173348i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 4.05492 | + | 0.661904i | 0.447791 | + | 0.0730951i | ||||
\(83\) | −8.21115 | + | 4.74071i | −0.901291 | + | 0.520361i | −0.877619 | − | 0.479359i | \(-0.840869\pi\) |
−0.0236721 | + | 0.999720i | \(0.507536\pi\) | |||||||
\(84\) | −1.60999 | − | 7.94297i | −0.175664 | − | 0.866649i | ||||
\(85\) | 19.8037 | − | 11.4337i | 2.14801 | − | 1.24015i | ||||
\(86\) | 3.31045 | − | 1.25284i | 0.356975 | − | 0.135097i | ||||
\(87\) | 4.41834 | − | 7.65278i | 0.473695 | − | 0.820464i | ||||
\(88\) | −2.81525 | − | 4.47274i | −0.300107 | − | 0.476795i | ||||
\(89\) | 4.88846 | 0.518176 | 0.259088 | − | 0.965854i | \(-0.416578\pi\) | ||||
0.259088 | + | 0.965854i | \(0.416578\pi\) | |||||||
\(90\) | 1.57340 | + | 4.15750i | 0.165851 | + | 0.438239i | ||||
\(91\) | − | 7.33856i | − | 0.769290i | ||||||
\(92\) | −0.399126 | + | 1.18998i | −0.0416117 | + | 0.124064i | ||||
\(93\) | −3.78697 | + | 6.55923i | −0.392691 | + | 0.680160i | ||||
\(94\) | 9.72111 | + | 1.58682i | 1.00266 | + | 0.163668i | ||||
\(95\) | −6.08595 | − | 10.5412i | −0.624405 | − | 1.08150i | ||||
\(96\) | 1.33454 | + | 5.49718i | 0.136206 | + | 0.561054i | ||||
\(97\) | 1.88856 | − | 1.09036i | 0.191755 | − | 0.110710i | −0.401049 | − | 0.916057i | \(-0.631354\pi\) |
0.592804 | + | 0.805347i | \(0.298021\pi\) | |||||||
\(98\) | 10.3141 | + | 8.43322i | 1.04188 | + | 0.851884i | ||||
\(99\) | −0.934262 | + | 1.61819i | −0.0938968 | + | 0.162634i | ||||
\(100\) | −7.31482 | + | 6.46211i | −0.731482 | + | 0.646211i | ||||
\(101\) | 5.00651 | + | 2.89051i | 0.498167 | + | 0.287617i | 0.727956 | − | 0.685624i | \(-0.240470\pi\) |
−0.229789 | + | 0.973240i | \(0.573804\pi\) | |||||||
\(102\) | −7.96487 | − | 6.51242i | −0.788640 | − | 0.644825i | ||||
\(103\) | 8.68180 | + | 5.01244i | 0.855443 | + | 0.493890i | 0.862484 | − | 0.506085i | \(-0.168908\pi\) |
−0.00704068 | + | 0.999975i | \(0.502241\pi\) | |||||||
\(104\) | 0.195500 | + | 5.11850i | 0.0191704 | + | 0.501911i | ||||
\(105\) | −11.0309 | − | 6.36867i | −1.07650 | − | 0.621519i | ||||
\(106\) | 1.86860 | + | 4.93752i | 0.181495 | + | 0.479575i | ||||
\(107\) | 3.66590i | 0.354396i | 0.984175 | + | 0.177198i | \(0.0567033\pi\) | ||||
−0.984175 | + | 0.177198i | \(0.943297\pi\) | |||||||
\(108\) | 1.49888 | − | 1.32415i | 0.144230 | − | 0.127416i | ||||
\(109\) | 6.55918i | 0.628256i | 0.949381 | + | 0.314128i | \(0.101712\pi\) | ||||
−0.949381 | + | 0.314128i | \(0.898288\pi\) | |||||||
\(110\) | −8.19759 | − | 1.33813i | −0.781609 | − | 0.127586i | ||||
\(111\) | −5.45660 | − | 9.45112i | −0.517918 | − | 0.897060i | ||||
\(112\) | −12.9308 | − | 9.77368i | −1.22185 | − | 0.923526i | ||||
\(113\) | 0.372202 | + | 0.214891i | 0.0350138 | + | 0.0202153i | 0.517405 | − | 0.855741i | \(-0.326898\pi\) |
−0.482391 | + | 0.875956i | \(0.660232\pi\) | |||||||
\(114\) | −3.46645 | + | 4.23957i | −0.324663 | + | 0.397072i | ||||
\(115\) | 0.986304 | + | 1.70833i | 0.0919734 | + | 0.159303i | ||||
\(116\) | −3.51087 | − | 17.3211i | −0.325976 | − | 1.60822i | ||||
\(117\) | 1.56836 | − | 0.905492i | 0.144995 | − | 0.0837128i | ||||
\(118\) | −7.03929 | − | 18.6004i | −0.648019 | − | 1.71230i | ||||
\(119\) | 29.4800 | 2.70243 | ||||||||
\(120\) | 7.86348 | + | 4.14816i | 0.717834 | + | 0.378674i | ||||
\(121\) | 3.75431 | + | 6.50266i | 0.341301 | + | 0.591151i | ||||
\(122\) | −2.16926 | + | 2.65306i | −0.196395 | + | 0.240197i | ||||
\(123\) | −2.51599 | − | 1.45261i | −0.226859 | − | 0.130977i | ||||
\(124\) | 3.00918 | + | 14.8460i | 0.270232 | + | 1.33321i | ||||
\(125\) | − | 0.376563i | − | 0.0336808i | ||||||
\(126\) | −0.923236 | + | 5.65589i | −0.0822484 | + | 0.503866i | ||||
\(127\) | −1.52701 | − | 0.881617i | −0.135500 | − | 0.0782309i | 0.430718 | − | 0.902487i | \(-0.358260\pi\) |
−0.566218 | + | 0.824256i | \(0.691594\pi\) | |||||||
\(128\) | 9.27939 | + | 6.47248i | 0.820190 | + | 0.572092i | ||||
\(129\) | −2.50287 | −0.220365 | ||||||||
\(130\) | 6.23224 | + | 5.09575i | 0.546604 | + | 0.446926i | ||||
\(131\) | 6.98506i | 0.610287i | 0.952306 | + | 0.305144i | \(0.0987045\pi\) | ||||
−0.952306 | + | 0.305144i | \(0.901295\pi\) | |||||||
\(132\) | 0.742377 | + | 3.66257i | 0.0646156 | + | 0.318786i | ||||
\(133\) | − | 15.6917i | − | 1.36065i | ||||||
\(134\) | −10.9907 | − | 3.63370i | −0.949455 | − | 0.313904i | ||||
\(135\) | − | 3.14328i | − | 0.270530i | ||||||
\(136\) | −20.5618 | + | 0.785354i | −1.76316 | + | 0.0673435i | ||||
\(137\) | − | 20.0886i | − | 1.71628i | −0.513414 | − | 0.858141i | \(-0.671620\pi\) | ||
0.513414 | − | 0.858141i | \(-0.328380\pi\) | |||||||
\(138\) | 0.561783 | − | 0.687076i | 0.0478221 | − | 0.0584878i | ||||
\(139\) | 8.51721 | 0.722420 | 0.361210 | − | 0.932484i | \(-0.382364\pi\) | ||||
0.361210 | + | 0.932484i | \(0.382364\pi\) | |||||||
\(140\) | −24.9670 | + | 5.06063i | −2.11009 | + | 0.427702i | ||||
\(141\) | −6.03173 | − | 3.48242i | −0.507963 | − | 0.293273i | ||||
\(142\) | 20.0024 | + | 3.26508i | 1.67856 | + | 0.273999i | ||||
\(143\) | 3.38387i | 0.282973i | ||||||||
\(144\) | 0.493266 | − | 3.96947i | 0.0411055 | − | 0.330789i | ||||
\(145\) | −24.0548 | − | 13.8881i | −1.99764 | − | 1.15334i | ||||
\(146\) | −5.03775 | − | 4.11908i | −0.416927 | − | 0.340897i | ||||
\(147\) | −4.71035 | − | 8.15857i | −0.388503 | − | 0.672908i | ||||
\(148\) | −20.6935 | − | 6.94071i | −1.70099 | − | 0.570523i | ||||
\(149\) | −13.0609 | −1.06999 | −0.534995 | − | 0.844855i | \(-0.679686\pi\) | ||||
−0.534995 | + | 0.844855i | \(0.679686\pi\) | |||||||
\(150\) | 6.45486 | − | 2.44284i | 0.527037 | − | 0.199457i | ||||
\(151\) | −16.6270 | + | 9.59960i | −1.35309 | + | 0.781204i | −0.988680 | − | 0.150037i | \(-0.952061\pi\) |
−0.364405 | + | 0.931241i | \(0.618727\pi\) | |||||||
\(152\) | 0.418031 | + | 10.9447i | 0.0339068 | + | 0.887732i | ||||
\(153\) | 3.63749 | + | 6.30032i | 0.294074 | + | 0.509351i | ||||
\(154\) | −8.28975 | − | 6.77805i | −0.668007 | − | 0.546191i | ||||
\(155\) | 20.6175 | + | 11.9035i | 1.65604 | + | 0.956113i | ||||
\(156\) | 1.15177 | − | 3.43396i | 0.0922155 | − | 0.274937i | ||||
\(157\) | 12.1533 | + | 21.0501i | 0.969936 | + | 1.67998i | 0.695725 | + | 0.718309i | \(0.255083\pi\) |
0.274211 | + | 0.961669i | \(0.411583\pi\) | |||||||
\(158\) | −0.330817 | + | 2.02664i | −0.0263184 | + | 0.161231i | ||||
\(159\) | − | 3.73302i | − | 0.296047i | ||||||
\(160\) | 17.2792 | − | 4.19482i | 1.36604 | − | 0.331630i | ||||
\(161\) | 2.54304i | 0.200420i | ||||||||
\(162\) | −1.32266 | + | 0.500561i | −0.103918 | + | 0.0393278i | ||||
\(163\) | 2.27493 | + | 1.31343i | 0.178187 | + | 0.102876i | 0.586440 | − | 0.809992i | \(-0.300529\pi\) |
−0.408254 | + | 0.912868i | \(0.633862\pi\) | |||||||
\(164\) | −5.69462 | + | 1.15426i | −0.444675 | + | 0.0901327i | ||||
\(165\) | 5.08642 | + | 2.93664i | 0.395977 | + | 0.228617i | ||||
\(166\) | 8.48757 | − | 10.3805i | 0.658764 | − | 0.805687i | ||||
\(167\) | 5.03270 | + | 2.90563i | 0.389442 | + | 0.224845i | 0.681918 | − | 0.731428i | \(-0.261146\pi\) |
−0.292476 | + | 0.956273i | \(0.594479\pi\) | |||||||
\(168\) | 6.10541 | + | 9.69998i | 0.471043 | + | 0.748370i | ||||
\(169\) | −4.86017 | + | 8.41806i | −0.373859 | + | 0.647543i | ||||
\(170\) | −20.4703 | + | 25.0358i | −1.57000 | + | 1.92016i | ||||
\(171\) | 3.35356 | − | 1.93618i | 0.256453 | − | 0.148063i | ||||
\(172\) | −3.75149 | + | 3.31416i | −0.286048 | + | 0.252703i | ||||
\(173\) | 2.25366 | + | 3.90346i | 0.171343 | + | 0.296775i | 0.938890 | − | 0.344218i | \(-0.111856\pi\) |
−0.767547 | + | 0.640993i | \(0.778523\pi\) | |||||||
\(174\) | −2.01329 | + | 12.3337i | −0.152627 | + | 0.935015i | ||||
\(175\) | −9.88789 | + | 17.1263i | −0.747454 | + | 1.29463i | ||||
\(176\) | 5.96251 | + | 4.50672i | 0.449441 | + | 0.339707i | ||||
\(177\) | 14.0628i | 1.05702i | ||||||||
\(178\) | −6.46579 | + | 2.44697i | −0.484632 | + | 0.183408i | ||||
\(179\) | 18.3582 | 1.37216 | 0.686079 | − | 0.727527i | \(-0.259331\pi\) | ||||
0.686079 | + | 0.727527i | \(0.259331\pi\) | |||||||
\(180\) | −4.16216 | − | 4.71139i | −0.310229 | − | 0.351166i | ||||
\(181\) | 2.65528 | − | 4.59908i | 0.197365 | − | 0.341847i | −0.750308 | − | 0.661088i | \(-0.770095\pi\) |
0.947673 | + | 0.319242i | \(0.103428\pi\) | |||||||
\(182\) | 3.67340 | + | 9.70644i | 0.272290 | + | 0.719489i | ||||
\(183\) | 2.09861 | − | 1.21163i | 0.155134 | − | 0.0895665i | ||||
\(184\) | −0.0677472 | − | 1.77373i | −0.00499439 | − | 0.130761i | ||||
\(185\) | −29.7075 | + | 17.1516i | −2.18414 | + | 1.26101i | ||||
\(186\) | 1.72560 | − | 10.5713i | 0.126527 | − | 0.775123i | ||||
\(187\) | −13.5935 | −0.994054 | ||||||||
\(188\) | −13.6521 | + | 2.76718i | −0.995679 | + | 0.201817i | ||||
\(189\) | 2.02612 | − | 3.50935i | 0.147379 | − | 0.255268i | ||||
\(190\) | 13.3262 | + | 10.8960i | 0.966781 | + | 0.790481i | ||||
\(191\) | 4.16544 | + | 7.21475i | 0.301400 | + | 0.522041i | 0.976453 | − | 0.215728i | \(-0.0692126\pi\) |
−0.675053 | + | 0.737769i | \(0.735879\pi\) | |||||||
\(192\) | −4.51682 | − | 6.60290i | −0.325973 | − | 0.476524i | ||||
\(193\) | 21.1039 | 1.51909 | 0.759546 | − | 0.650453i | \(-0.225421\pi\) | ||||
0.759546 | + | 0.650453i | \(0.225421\pi\) | |||||||
\(194\) | −1.95214 | + | 2.38752i | −0.140156 | + | 0.171414i | ||||
\(195\) | −2.84621 | − | 4.92979i | −0.203822 | − | 0.353029i | ||||
\(196\) | −17.8634 | − | 5.99149i | −1.27596 | − | 0.427964i | ||||
\(197\) | 4.60979 | + | 2.66147i | 0.328434 | + | 0.189622i | 0.655146 | − | 0.755503i | \(-0.272607\pi\) |
−0.326712 | + | 0.945124i | \(0.605941\pi\) | |||||||
\(198\) | 0.425712 | − | 2.60797i | 0.0302540 | − | 0.185341i | ||||
\(199\) | −12.8058 | + | 7.39343i | −0.907779 | + | 0.524106i | −0.879716 | − | 0.475500i | \(-0.842267\pi\) |
−0.0280631 | + | 0.999606i | \(0.508934\pi\) | |||||||
\(200\) | 6.44037 | − | 12.2087i | 0.455403 | − | 0.863286i | ||||
\(201\) | 6.35908 | + | 5.15385i | 0.448535 | + | 0.363524i | ||||
\(202\) | −8.06881 | − | 1.31711i | −0.567720 | − | 0.0926715i | ||||
\(203\) | −17.9042 | − | 31.0110i | −1.25663 | − | 2.17654i | ||||
\(204\) | 13.7947 | + | 4.62683i | 0.965823 | + | 0.323943i | ||||
\(205\) | −4.56595 | + | 7.90845i | −0.318900 | + | 0.552350i | ||||
\(206\) | −13.9921 | − | 2.28400i | −0.974878 | − | 0.159134i | ||||
\(207\) | −0.543486 | + | 0.313782i | −0.0377749 | + | 0.0218094i | ||||
\(208\) | −2.82071 | − | 6.67220i | −0.195581 | − | 0.462634i | ||||
\(209\) | 7.23559i | 0.500496i | ||||||||
\(210\) | 17.7780 | + | 2.90199i | 1.22680 | + | 0.200256i | ||||
\(211\) | 12.0538 | − | 6.95929i | 0.829821 | − | 0.479097i | −0.0239703 | − | 0.999713i | \(-0.507631\pi\) |
0.853791 | + | 0.520615i | \(0.174297\pi\) | |||||||
\(212\) | −4.94306 | − | 5.59533i | −0.339491 | − | 0.384289i | ||||
\(213\) | −12.4110 | − | 7.16551i | −0.850389 | − | 0.490972i | ||||
\(214\) | −1.83501 | − | 4.84875i | −0.125438 | − | 0.331454i | ||||
\(215\) | 7.86721i | 0.536539i | ||||||||
\(216\) | −1.31969 | + | 2.50168i | −0.0897938 | + | 0.170218i | ||||
\(217\) | 15.3458 | + | 26.5796i | 1.04174 | + | 1.80434i | ||||
\(218\) | −3.28327 | − | 8.67559i | −0.222371 | − | 0.587585i | ||||
\(219\) | 2.30070 | + | 3.98493i | 0.155467 | + | 0.269276i | ||||
\(220\) | 11.5125 | − | 2.33350i | 0.776170 | − | 0.157324i | ||||
\(221\) | 11.4098 | + | 6.58744i | 0.767505 | + | 0.443119i | ||||
\(222\) | 11.9481 | + | 9.76928i | 0.801905 | + | 0.655671i | ||||
\(223\) | 22.7611i | 1.52420i | 0.647460 | + | 0.762099i | \(0.275831\pi\) | ||||
−0.647460 | + | 0.762099i | \(0.724169\pi\) | |||||||
\(224\) | 21.9955 | + | 6.45461i | 1.46963 | + | 0.431267i | ||||
\(225\) | −4.88020 | −0.325347 | ||||||||
\(226\) | −0.599864 | − | 0.0979186i | −0.0399024 | − | 0.00651345i | ||||
\(227\) | −8.68285 | − | 5.01304i | −0.576301 | − | 0.332727i | 0.183361 | − | 0.983046i | \(-0.441302\pi\) |
−0.759662 | + | 0.650318i | \(0.774636\pi\) | |||||||
\(228\) | 2.46279 | − | 7.34270i | 0.163102 | − | 0.486282i | ||||
\(229\) | −7.45156 | + | 4.30216i | −0.492413 | + | 0.284295i | −0.725575 | − | 0.688143i | \(-0.758426\pi\) |
0.233162 | + | 0.972438i | \(0.425093\pi\) | |||||||
\(230\) | −2.15967 | − | 1.76584i | −0.142405 | − | 0.116436i | ||||
\(231\) | 3.78586 | + | 6.55730i | 0.249091 | + | 0.431439i | ||||
\(232\) | 13.3140 | + | 21.1526i | 0.874105 | + | 1.38874i | ||||
\(233\) | −12.1603 | − | 7.02078i | −0.796651 | − | 0.459946i | 0.0456481 | − | 0.998958i | \(-0.485465\pi\) |
−0.842299 | + | 0.539011i | \(0.818798\pi\) | |||||||
\(234\) | −1.62116 | + | 1.98272i | −0.105978 | + | 0.129614i | ||||
\(235\) | −10.9462 | + | 18.9594i | −0.714053 | + | 1.23678i | ||||
\(236\) | 18.6212 | + | 21.0784i | 1.21214 | + | 1.37209i | ||||
\(237\) | 0.726008 | − | 1.25748i | 0.0471593 | − | 0.0816822i | ||||
\(238\) | −38.9922 | + | 14.7566i | −2.52749 | + | 0.956525i | ||||
\(239\) | −7.61571 | + | 13.1908i | −0.492619 | + | 0.853242i | −0.999964 | − | 0.00850144i | \(-0.997294\pi\) |
0.507344 | + | 0.861743i | \(0.330627\pi\) | |||||||
\(240\) | −12.4771 | − | 1.55047i | −0.805396 | − | 0.100083i | ||||
\(241\) | 1.87229 | 0.120605 | 0.0603024 | − | 0.998180i | \(-0.480794\pi\) | ||||
0.0603024 | + | 0.998180i | \(0.480794\pi\) | |||||||
\(242\) | −8.22067 | − | 6.72156i | −0.528444 | − | 0.432079i | ||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 1.54118 | − | 4.59496i | 0.0986638 | − | 0.294162i | ||||
\(245\) | −25.6447 | + | 14.8060i | −1.63838 | + | 0.945918i | ||||
\(246\) | 4.05492 | + | 0.661904i | 0.258533 | + | 0.0422014i | ||||
\(247\) | 3.50639 | − | 6.07324i | 0.223106 | − | 0.386431i | ||||
\(248\) | −11.4115 | − | 18.1300i | −0.724628 | − | 1.15125i | ||||
\(249\) | −8.21115 | + | 4.74071i | −0.520361 | + | 0.300430i | ||||
\(250\) | 0.188493 | + | 0.498066i | 0.0119213 | + | 0.0315005i | ||||
\(251\) | −2.42889 | − | 4.20697i | −0.153310 | − | 0.265542i | 0.779132 | − | 0.626860i | \(-0.215660\pi\) |
−0.932443 | + | 0.361318i | \(0.882327\pi\) | |||||||
\(252\) | −1.60999 | − | 7.94297i | −0.101420 | − | 0.500360i | ||||
\(253\) | − | 1.17262i | − | 0.0737219i | ||||||
\(254\) | 2.46102 | + | 0.401723i | 0.154418 | + | 0.0252064i | ||||
\(255\) | 19.8037 | − | 11.4337i | 1.24015 | − | 0.716003i | ||||
\(256\) | −15.5134 | − | 3.91601i | −0.969586 | − | 0.244751i | ||||
\(257\) | 4.52176 | − | 7.83191i | 0.282060 | − | 0.488541i | −0.689832 | − | 0.723969i | \(-0.742316\pi\) |
0.971892 | + | 0.235428i | \(0.0756491\pi\) | |||||||
\(258\) | 3.31045 | − | 1.25284i | 0.206100 | − | 0.0779982i | ||||
\(259\) | −44.2230 | −2.74788 | ||||||||
\(260\) | −10.7939 | − | 3.62034i | −0.669409 | − | 0.224524i | ||||
\(261\) | 4.41834 | − | 7.65278i | 0.273488 | − | 0.473695i | ||||
\(262\) | −3.49645 | − | 9.23888i | −0.216011 | − | 0.570780i | ||||
\(263\) | − | 27.8170i | − | 1.71527i | −0.514257 | − | 0.857636i | \(-0.671932\pi\) | ||
0.514257 | − | 0.857636i | \(-0.328068\pi\) | |||||||
\(264\) | −2.81525 | − | 4.47274i | −0.173267 | − | 0.275278i | ||||
\(265\) | −11.7339 | −0.720808 | ||||||||
\(266\) | 7.85467 | + | 20.7549i | 0.481601 | + | 1.27256i | ||||
\(267\) | 4.88846 | 0.299169 | ||||||||
\(268\) | 16.3559 | − | 0.695377i | 0.999097 | − | 0.0424769i | ||||
\(269\) | 28.3773 | 1.73019 | 0.865097 | − | 0.501605i | \(-0.167257\pi\) | ||||
0.865097 | + | 0.501605i | \(0.167257\pi\) | |||||||
\(270\) | 1.57340 | + | 4.15750i | 0.0957543 | + | 0.253017i | ||||
\(271\) | −11.4356 | −0.694661 | −0.347331 | − | 0.937743i | \(-0.612912\pi\) | ||||
−0.347331 | + | 0.937743i | \(0.612912\pi\) | |||||||
\(272\) | 26.8032 | − | 11.3312i | 1.62518 | − | 0.687054i | ||||
\(273\) | − | 7.33856i | − | 0.444150i | ||||||
\(274\) | 10.0556 | + | 26.5704i | 0.607478 | + | 1.60518i | ||||
\(275\) | 4.55938 | − | 7.89709i | 0.274941 | − | 0.476212i | ||||
\(276\) | −0.399126 | + | 1.18998i | −0.0240245 | + | 0.0716282i | ||||
\(277\) | −11.7684 | −0.707093 | −0.353547 | − | 0.935417i | \(-0.615024\pi\) | ||||
−0.353547 | + | 0.935417i | \(0.615024\pi\) | |||||||
\(278\) | −11.2654 | + | 4.26338i | −0.675654 | + | 0.255701i | ||||
\(279\) | −3.78697 | + | 6.55923i | −0.226720 | + | 0.392691i | ||||
\(280\) | 30.4897 | − | 19.1910i | 1.82211 | − | 1.14688i | ||||
\(281\) | −0.164511 | + | 0.0949807i | −0.00981393 | + | 0.00566607i | −0.504899 | − | 0.863178i | \(-0.668470\pi\) |
0.495085 | + | 0.868845i | \(0.335137\pi\) | |||||||
\(282\) | 9.72111 | + | 1.58682i | 0.578884 | + | 0.0944939i | ||||
\(283\) | − | 25.3856i | − | 1.50902i | −0.656290 | − | 0.754509i | \(-0.727875\pi\) | ||
0.656290 | − | 0.754509i | \(-0.272125\pi\) | |||||||
\(284\) | −28.0908 | + | 5.69381i | −1.66688 | + | 0.337866i | ||||
\(285\) | −6.08595 | − | 10.5412i | −0.360500 | − | 0.624405i | ||||
\(286\) | −1.69383 | − | 4.47572i | −0.100158 | − | 0.264655i | ||||
\(287\) | −10.1954 | + | 5.88632i | −0.601816 | + | 0.347459i | ||||
\(288\) | 1.33454 | + | 5.49718i | 0.0786383 | + | 0.323925i | ||||
\(289\) | −17.9627 | + | 31.1123i | −1.05663 | + | 1.83014i | ||||
\(290\) | 38.7683 | + | 6.32832i | 2.27655 | + | 0.371612i | ||||
\(291\) | 1.88856 | − | 1.09036i | 0.110710 | − | 0.0639182i | ||||
\(292\) | 8.72509 | + | 2.92645i | 0.510597 | + | 0.171258i | ||||
\(293\) | 9.67877 | 0.565440 | 0.282720 | − | 0.959202i | \(-0.408763\pi\) | ||||
0.282720 | + | 0.959202i | \(0.408763\pi\) | |||||||
\(294\) | 10.3141 | + | 8.43322i | 0.601529 | + | 0.491836i | ||||
\(295\) | 44.2033 | 2.57362 | ||||||||
\(296\) | 30.8447 | − | 1.17811i | 1.79281 | − | 0.0684762i | ||||
\(297\) | −0.934262 | + | 1.61819i | −0.0542114 | + | 0.0938968i | ||||
\(298\) | 17.2752 | − | 6.53777i | 1.00072 | − | 0.378723i | ||||
\(299\) | −0.568254 | + | 0.984245i | −0.0328630 | + | 0.0569204i | ||||
\(300\) | −7.31482 | + | 6.46211i | −0.422321 | + | 0.373090i | ||||
\(301\) | −5.07112 | + | 8.78343i | −0.292294 | + | 0.506269i | ||||
\(302\) | 17.1867 | − | 21.0199i | 0.988985 | − | 1.20956i | ||||
\(303\) | 5.00651 | + | 2.89051i | 0.287617 | + | 0.166056i | ||||
\(304\) | −6.03140 | − | 14.2669i | −0.345925 | − | 0.818263i | ||||
\(305\) | −3.80850 | − | 6.59651i | −0.218074 | − | 0.377715i | ||||
\(306\) | −7.96487 | − | 6.51242i | −0.455321 | − | 0.372290i | ||||
\(307\) | 18.3287 | − | 10.5821i | 1.04607 | − | 0.603950i | 0.124525 | − | 0.992217i | \(-0.460259\pi\) |
0.921547 | + | 0.388267i | \(0.126926\pi\) | |||||||
\(308\) | 14.3574 | + | 4.81555i | 0.818087 | + | 0.274392i | ||||
\(309\) | 8.68180 | + | 5.01244i | 0.493890 | + | 0.285148i | ||||
\(310\) | −33.2284 | − | 5.42403i | −1.88725 | − | 0.308064i | ||||
\(311\) | 22.5190 | 1.27694 | 0.638469 | − | 0.769648i | \(-0.279568\pi\) | ||||
0.638469 | + | 0.769648i | \(0.279568\pi\) | |||||||
\(312\) | 0.195500 | + | 5.11850i | 0.0110680 | + | 0.289778i | ||||
\(313\) | − | 28.6373i | − | 1.61868i | −0.587344 | − | 0.809338i | \(-0.699826\pi\) | ||
0.587344 | − | 0.809338i | \(-0.300174\pi\) | |||||||
\(314\) | −26.6115 | − | 21.7587i | −1.50177 | − | 1.22791i | ||||
\(315\) | −11.0309 | − | 6.36867i | −0.621519 | − | 0.358834i | ||||
\(316\) | −0.576896 | − | 2.84615i | −0.0324529 | − | 0.160109i | ||||
\(317\) | 11.5584 | + | 20.0198i | 0.649186 | + | 1.12442i | 0.983318 | + | 0.181896i | \(0.0582236\pi\) |
−0.334132 | + | 0.942526i | \(0.608443\pi\) | |||||||
\(318\) | 1.86860 | + | 4.93752i | 0.104786 | + | 0.276883i | ||||
\(319\) | 8.25576 | + | 14.2994i | 0.462234 | + | 0.800613i | ||||
\(320\) | −20.7548 | + | 14.1976i | −1.16023 | + | 0.793671i | ||||
\(321\) | 3.66590i | 0.204611i | ||||||||
\(322\) | −1.27295 | − | 3.36359i | −0.0709387 | − | 0.187446i | ||||
\(323\) | 24.3971 | + | 14.0857i | 1.35749 | + | 0.783747i | ||||
\(324\) | 1.49888 | − | 1.32415i | 0.0832710 | − | 0.0735638i | ||||
\(325\) | −7.65390 | + | 4.41898i | −0.424562 | + | 0.245121i | ||||
\(326\) | −3.66643 | − | 0.598487i | −0.203065 | − | 0.0331472i | ||||
\(327\) | 6.55918i | 0.362724i | ||||||||
\(328\) | 6.95429 | − | 4.37721i | 0.383987 | − | 0.241691i | ||||
\(329\) | −24.4421 | + | 14.1116i | −1.34753 | + | 0.777999i | ||||
\(330\) | −8.19759 | − | 1.33813i | −0.451262 | − | 0.0736616i | ||||
\(331\) | 5.59150 | − | 9.68477i | 0.307337 | − | 0.532323i | −0.670442 | − | 0.741962i | \(-0.733895\pi\) |
0.977779 | + | 0.209639i | \(0.0672288\pi\) | |||||||
\(332\) | −6.03011 | + | 17.9785i | −0.330945 | + | 0.986699i | ||||
\(333\) | −5.45660 | − | 9.45112i | −0.299020 | − | 0.517918i | ||||
\(334\) | −8.11102 | − | 1.32400i | −0.443815 | − | 0.0724460i | ||||
\(335\) | 16.2000 | − | 19.9884i | 0.885099 | − | 1.09208i | ||||
\(336\) | −12.9308 | − | 9.77368i | −0.705435 | − | 0.533198i | ||||
\(337\) | −2.03943 | + | 1.17747i | −0.111095 | + | 0.0641407i | −0.554518 | − | 0.832172i | \(-0.687097\pi\) |
0.443423 | + | 0.896312i | \(0.353764\pi\) | |||||||
\(338\) | 2.21461 | − | 13.5671i | 0.120459 | − | 0.737951i | ||||
\(339\) | 0.372202 | + | 0.214891i | 0.0202153 | + | 0.0116713i | ||||
\(340\) | 14.5434 | − | 43.3606i | 0.788728 | − | 2.35156i | ||||
\(341\) | −7.07605 | − | 12.2561i | −0.383189 | − | 0.663704i | ||||
\(342\) | −3.46645 | + | 4.23957i | −0.187444 | + | 0.229250i | ||||
\(343\) | −9.80930 | −0.529652 | ||||||||
\(344\) | 3.30302 | − | 6.26137i | 0.178087 | − | 0.337591i | ||||
\(345\) | 0.986304 | + | 1.70833i | 0.0531008 | + | 0.0919734i | ||||
\(346\) | −4.93476 | − | 4.03487i | −0.265294 | − | 0.216916i | ||||
\(347\) | 5.79554 | − | 10.0382i | 0.311121 | − | 0.538878i | −0.667484 | − | 0.744624i | \(-0.732629\pi\) |
0.978605 | + | 0.205746i | \(0.0659622\pi\) | |||||||
\(348\) | −3.51087 | − | 17.3211i | −0.188202 | − | 0.928509i | ||||
\(349\) | −16.4268 | −0.879304 | −0.439652 | − | 0.898168i | \(-0.644898\pi\) | ||||
−0.439652 | + | 0.898168i | \(0.644898\pi\) | |||||||
\(350\) | 4.50558 | − | 27.6019i | 0.240833 | − | 1.47538i | ||||
\(351\) | 1.56836 | − | 0.905492i | 0.0837128 | − | 0.0483316i | ||||
\(352\) | −10.1423 | − | 2.97627i | −0.540586 | − | 0.158636i | ||||
\(353\) | 25.1091 | − | 14.4967i | 1.33642 | − | 0.771584i | 0.350147 | − | 0.936695i | \(-0.386132\pi\) |
0.986275 | + | 0.165111i | \(0.0527983\pi\) | |||||||
\(354\) | −7.03929 | − | 18.6004i | −0.374134 | − | 0.988598i | ||||
\(355\) | −22.5232 | + | 39.0113i | −1.19541 | + | 2.07051i | ||||
\(356\) | 7.32721 | − | 6.47305i | 0.388341 | − | 0.343071i | ||||
\(357\) | 29.4800 | 1.56025 | ||||||||
\(358\) | −24.2817 | + | 9.18941i | −1.28333 | + | 0.485675i | ||||
\(359\) | − | 16.0771i | − | 0.848516i | −0.905541 | − | 0.424258i | \(-0.860535\pi\) | ||
0.905541 | − | 0.424258i | \(-0.139465\pi\) | |||||||
\(360\) | 7.86348 | + | 4.14816i | 0.414442 | + | 0.218627i | ||||
\(361\) | −2.00243 | + | 3.46832i | −0.105391 | + | 0.182543i | ||||
\(362\) | −1.20992 | + | 7.41216i | −0.0635920 | + | 0.389574i | ||||
\(363\) | 3.75431 | + | 6.50266i | 0.197050 | + | 0.341301i | ||||
\(364\) | −9.71733 | − | 10.9996i | −0.509327 | − | 0.576535i | ||||
\(365\) | 12.5257 | − | 7.23173i | 0.655627 | − | 0.378526i | ||||
\(366\) | −2.16926 | + | 2.65306i | −0.113389 | + | 0.138678i | ||||
\(367\) | 3.79571 | − | 6.57436i | 0.198134 | − | 0.343179i | −0.749789 | − | 0.661677i | \(-0.769845\pi\) |
0.947924 | + | 0.318498i | \(0.103178\pi\) | |||||||
\(368\) | 0.977465 | + | 2.31213i | 0.0509539 | + | 0.120528i | ||||
\(369\) | −2.51599 | − | 1.45261i | −0.130977 | − | 0.0756197i | ||||
\(370\) | 30.7076 | − | 37.5562i | 1.59641 | − | 1.95246i | ||||
\(371\) | −13.1005 | − | 7.56355i | −0.680142 | − | 0.392680i | ||||
\(372\) | 3.00918 | + | 14.8460i | 0.156019 | + | 0.769729i | ||||
\(373\) | 2.90432 | + | 1.67681i | 0.150380 | + | 0.0868220i | 0.573302 | − | 0.819344i | \(-0.305662\pi\) |
−0.422922 | + | 0.906166i | \(0.638996\pi\) | |||||||
\(374\) | 17.9796 | − | 6.80437i | 0.929703 | − | 0.351845i | ||||
\(375\) | − | 0.376563i | − | 0.0194456i | ||||||
\(376\) | 16.6719 | − | 10.4937i | 0.859790 | − | 0.541173i | ||||
\(377\) | − | 16.0031i | − | 0.824200i | ||||||
\(378\) | −0.923236 | + | 5.65589i | −0.0474861 | + | 0.290907i | ||||
\(379\) | −9.02457 | − | 15.6310i | −0.463561 | − | 0.802911i | 0.535574 | − | 0.844488i | \(-0.320095\pi\) |
−0.999135 | + | 0.0415769i | \(0.986762\pi\) | |||||||
\(380\) | −23.0801 | − | 7.74122i | −1.18399 | − | 0.397116i | ||||
\(381\) | −1.52701 | − | 0.881617i | −0.0782309 | − | 0.0451666i | ||||
\(382\) | −9.12089 | − | 7.45763i | −0.466665 | − | 0.381565i | ||||
\(383\) | 2.02414 | + | 3.50592i | 0.103429 | + | 0.179144i | 0.913095 | − | 0.407746i | \(-0.133685\pi\) |
−0.809666 | + | 0.586890i | \(0.800352\pi\) | |||||||
\(384\) | 9.27939 | + | 6.47248i | 0.473537 | + | 0.330297i | ||||
\(385\) | 20.6114 | − | 11.9000i | 1.05046 | − | 0.606481i | ||||
\(386\) | −27.9134 | + | 10.5638i | −1.42075 | + | 0.537683i | ||||
\(387\) | −2.50287 | −0.127228 | ||||||||
\(388\) | 1.38692 | − | 4.13506i | 0.0704104 | − | 0.209926i | ||||
\(389\) | 6.54654 | + | 11.3389i | 0.331923 | + | 0.574907i | 0.982889 | − | 0.184200i | \(-0.0589694\pi\) |
−0.650966 | + | 0.759107i | \(0.725636\pi\) | |||||||
\(390\) | 6.23224 | + | 5.09575i | 0.315582 | + | 0.258033i | ||||
\(391\) | −3.95385 | − | 2.28276i | −0.199955 | − | 0.115444i | ||||
\(392\) | 26.6264 | − | 1.01699i | 1.34483 | − | 0.0513657i | ||||
\(393\) | 6.98506i | 0.352350i | ||||||||
\(394\) | −7.42943 | − | 1.21274i | −0.374289 | − | 0.0610969i | ||||
\(395\) | −3.95262 | − | 2.28204i | −0.198878 | − | 0.114822i | ||||
\(396\) | 0.742377 | + | 3.66257i | 0.0373059 | + | 0.184051i | ||||
\(397\) | 1.91018 | 0.0958692 | 0.0479346 | − | 0.998850i | \(-0.484736\pi\) | ||||
0.0479346 | + | 0.998850i | \(0.484736\pi\) | |||||||
\(398\) | 13.2369 | − | 16.1891i | 0.663506 | − | 0.811487i | ||||
\(399\) | − | 15.6917i | − | 0.785570i | ||||||
\(400\) | −2.40724 | + | 19.3718i | −0.120362 | + | 0.968590i | ||||
\(401\) | − | 0.717734i | − | 0.0358419i | −0.999839 | − | 0.0179210i | \(-0.994295\pi\) | ||
0.999839 | − | 0.0179210i | \(-0.00570473\pi\) | |||||||
\(402\) | −10.9907 | − | 3.63370i | −0.548168 | − | 0.181232i | ||||
\(403\) | 13.7163i | 0.683257i | ||||||||
\(404\) | 11.3316 | − | 2.29684i | 0.563769 | − | 0.114272i | ||||
\(405\) | − | 3.14328i | − | 0.156191i | ||||||
\(406\) | 39.2041 | + | 32.0549i | 1.94567 | + | 1.59086i | ||||
\(407\) | 20.3916 | 1.01077 | ||||||||
\(408\) | −20.5618 | + | 0.785354i | −1.01796 | + | 0.0388808i | ||||
\(409\) | −18.3698 | − | 10.6058i | −0.908328 | − | 0.524423i | −0.0284352 | − | 0.999596i | \(-0.509052\pi\) |
−0.879893 | + | 0.475172i | \(0.842386\pi\) | |||||||
\(410\) | 2.08055 | − | 12.7458i | 0.102751 | − | 0.629468i | ||||
\(411\) | − | 20.0886i | − | 0.990896i | ||||||
\(412\) | 19.6502 | − | 3.98295i | 0.968094 | − | 0.196226i | ||||
\(413\) | 49.3513 | + | 28.4930i | 2.42842 | + | 1.40205i | ||||
\(414\) | 0.561783 | − | 0.687076i | 0.0276101 | − | 0.0337680i | ||||
\(415\) | 14.9014 | + | 25.8099i | 0.731480 | + | 1.26696i | ||||
\(416\) | 7.07069 | + | 7.41314i | 0.346669 | + | 0.363459i | ||||
\(417\) | 8.51721 | 0.417090 | ||||||||
\(418\) | −3.62185 | − | 9.57025i | −0.177151 | − | 0.468096i | ||||
\(419\) | −24.3289 | + | 14.0463i | −1.18855 | + | 0.686208i | −0.957976 | − | 0.286848i | \(-0.907393\pi\) |
−0.230571 | + | 0.973056i | \(0.574059\pi\) | |||||||
\(420\) | −24.9670 | + | 5.06063i | −1.21826 | + | 0.246934i | ||||
\(421\) | 19.1695 | + | 33.2025i | 0.934264 | + | 1.61819i | 0.775942 | + | 0.630805i | \(0.217275\pi\) |
0.158322 | + | 0.987388i | \(0.449392\pi\) | |||||||
\(422\) | −12.4596 | + | 15.2385i | −0.606525 | + | 0.741798i | ||||
\(423\) | −6.03173 | − | 3.48242i | −0.293273 | − | 0.169321i | ||||
\(424\) | 9.33882 | + | 4.92644i | 0.453533 | + | 0.239249i | ||||
\(425\) | −17.7517 | − | 30.7468i | −0.861083 | − | 1.49144i | ||||
\(426\) | 20.0024 | + | 3.26508i | 0.969119 | + | 0.158194i | ||||
\(427\) | − | 9.81967i | − | 0.475207i | ||||||
\(428\) | 4.85419 | + | 5.49473i | 0.234636 | + | 0.265598i | ||||
\(429\) | 3.38387i | 0.163375i | ||||||||
\(430\) | −3.93802 | − | 10.4057i | −0.189908 | − | 0.501806i | ||||
\(431\) | −31.0841 | − | 17.9464i | −1.49727 | − | 0.864450i | −0.497275 | − | 0.867593i | \(-0.665666\pi\) |
−0.999995 | + | 0.00314323i | \(0.998999\pi\) | |||||||
\(432\) | 0.493266 | − | 3.96947i | 0.0237323 | − | 0.190981i | ||||
\(433\) | 19.3801 | + | 11.1891i | 0.931347 | + | 0.537714i | 0.887237 | − | 0.461313i | \(-0.152622\pi\) |
0.0441099 | + | 0.999027i | \(0.485955\pi\) | |||||||
\(434\) | −33.6020 | − | 27.4744i | −1.61295 | − | 1.31881i | ||||
\(435\) | −24.0548 | − | 13.8881i | −1.15334 | − | 0.665881i | ||||
\(436\) | 8.68533 | + | 9.83141i | 0.415952 | + | 0.470839i | ||||
\(437\) | −1.21508 | + | 2.10457i | −0.0581249 | + | 0.100675i | ||||
\(438\) | −5.03775 | − | 4.11908i | −0.240713 | − | 0.196817i | ||||
\(439\) | −5.92371 | + | 3.42006i | −0.282723 | + | 0.163230i | −0.634656 | − | 0.772795i | \(-0.718858\pi\) |
0.351932 | + | 0.936025i | \(0.385525\pi\) | |||||||
\(440\) | −14.0591 | + | 8.84913i | −0.670239 | + | 0.421866i | ||||
\(441\) | −4.71035 | − | 8.15857i | −0.224303 | − | 0.388503i | ||||
\(442\) | −18.3887 | − | 3.00167i | −0.874662 | − | 0.142775i | ||||
\(443\) | 18.5472 | − | 32.1247i | 0.881206 | − | 1.52629i | 0.0312039 | − | 0.999513i | \(-0.490066\pi\) |
0.850002 | − | 0.526780i | \(-0.176601\pi\) | |||||||
\(444\) | −20.6935 | − | 6.94071i | −0.982068 | − | 0.329392i | ||||
\(445\) | − | 15.3658i | − | 0.728409i | ||||||
\(446\) | −11.3933 | − | 30.1053i | −0.539490 | − | 1.42553i | ||||
\(447\) | −13.0609 | −0.617759 | ||||||||
\(448\) | −32.3235 | + | 2.47279i | −1.52714 | + | 0.116828i | ||||
\(449\) | −11.1349 | + | 19.2862i | −0.525487 | + | 0.910171i | 0.474072 | + | 0.880486i | \(0.342784\pi\) |
−0.999559 | + | 0.0296847i | \(0.990550\pi\) | |||||||
\(450\) | 6.45486 | − | 2.44284i | 0.304285 | − | 0.115157i | ||||
\(451\) | 4.70118 | − | 2.71423i | 0.221370 | − | 0.127808i | ||||
\(452\) | 0.842433 | − | 0.170755i | 0.0396247 | − | 0.00803166i | ||||
\(453\) | −16.6270 | + | 9.59960i | −0.781204 | + | 0.451028i | ||||
\(454\) | 13.9938 | + | 2.28427i | 0.656762 | + | 0.107206i | ||||
\(455\) | −23.0671 | −1.08140 | ||||||||
\(456\) | 0.418031 | + | 10.9447i | 0.0195761 | + | 0.512532i | ||||
\(457\) | −10.6263 | + | 18.4054i | −0.497079 | + | 0.860966i | −0.999994 | − | 0.00336952i | \(-0.998927\pi\) |
0.502915 | + | 0.864336i | \(0.332261\pi\) | |||||||
\(458\) | 7.70241 | − | 9.42027i | 0.359910 | − | 0.440180i | ||||
\(459\) | 3.63749 | + | 6.30032i | 0.169784 | + | 0.294074i | ||||
\(460\) | 3.74043 | + | 1.25456i | 0.174398 | + | 0.0584943i | ||||
\(461\) | −35.1560 | −1.63738 | −0.818689 | − | 0.574237i | \(-0.805299\pi\) | ||||
−0.818689 | + | 0.574237i | \(0.805299\pi\) | |||||||
\(462\) | −8.28975 | − | 6.77805i | −0.385674 | − | 0.315343i | ||||
\(463\) | 7.07547 | + | 12.2551i | 0.328825 | + | 0.569542i | 0.982279 | − | 0.187425i | \(-0.0600140\pi\) |
−0.653454 | + | 0.756966i | \(0.726681\pi\) | |||||||
\(464\) | −28.1981 | − | 21.3133i | −1.30906 | − | 0.989445i | ||||
\(465\) | 20.6175 | + | 11.9035i | 0.956113 | + | 0.552012i | ||||
\(466\) | 19.5984 | + | 3.19913i | 0.907877 | + | 0.148197i | ||||
\(467\) | 8.68690 | − | 5.01538i | 0.401982 | − | 0.232084i | −0.285357 | − | 0.958421i | \(-0.592112\pi\) |
0.687339 | + | 0.726337i | \(0.258779\pi\) | |||||||
\(468\) | 1.15177 | − | 3.43396i | 0.0532407 | − | 0.158735i | ||||
\(469\) | 30.9709 | − | 11.8739i | 1.43010 | − | 0.548286i | ||||
\(470\) | 4.98782 | − | 30.5562i | 0.230071 | − | 1.40945i | ||||
\(471\) | 12.1533 | + | 21.0501i | 0.559993 | + | 0.969936i | ||||
\(472\) | −35.1806 | − | 18.5586i | −1.61932 | − | 0.854228i | ||||
\(473\) | 2.33833 | − | 4.05011i | 0.107517 | − | 0.186224i | ||||
\(474\) | −0.330817 | + | 2.02664i | −0.0151949 | + | 0.0930865i | ||||
\(475\) | −16.3660 | + | 9.44893i | −0.750925 | + | 0.433547i | ||||
\(476\) | 44.1869 | − | 39.0359i | 2.02531 | − | 1.78921i | ||||
\(477\) | − | 3.73302i | − | 0.170923i | ||||||
\(478\) | 3.47022 | − | 21.2591i | 0.158724 | − | 0.972369i | ||||
\(479\) | −29.7525 | + | 17.1776i | −1.35943 | + | 0.784865i | −0.989546 | − | 0.144215i | \(-0.953934\pi\) |
−0.369880 | + | 0.929080i | \(0.620601\pi\) | |||||||
\(480\) | 17.2792 | − | 4.19482i | 0.788683 | − | 0.191467i | ||||
\(481\) | −17.1158 | − | 9.88182i | −0.780414 | − | 0.450572i | ||||
\(482\) | −2.47641 | + | 0.937195i | −0.112797 | + | 0.0426881i | ||||
\(483\) | 2.54304i | 0.115713i | ||||||||
\(484\) | 14.2377 | + | 4.77542i | 0.647169 | + | 0.217065i | ||||
\(485\) | −3.42731 | − | 5.93628i | −0.155626 | − | 0.269553i | ||||
\(486\) | −1.32266 | + | 0.500561i | −0.0599972 | + | 0.0227059i | ||||
\(487\) | 1.95720 | + | 3.38997i | 0.0886891 | + | 0.153614i | 0.906957 | − | 0.421223i | \(-0.138399\pi\) |
−0.818268 | + | 0.574837i | \(0.805066\pi\) | |||||||
\(488\) | 0.261598 | + | 6.84903i | 0.0118420 | + | 0.310041i | ||||
\(489\) | 2.27493 | + | 1.31343i | 0.102876 | + | 0.0593955i | ||||
\(490\) | 26.5080 | − | 32.4200i | 1.19751 | − | 1.46459i | ||||
\(491\) | 34.4636i | 1.55532i | 0.628684 | + | 0.777661i | \(0.283594\pi\) | ||||
−0.628684 | + | 0.777661i | \(0.716406\pi\) | |||||||
\(492\) | −5.69462 | + | 1.15426i | −0.256733 | + | 0.0520381i | ||||
\(493\) | 64.2866 | 2.89532 | ||||||||
\(494\) | −1.59774 | + | 9.78801i | −0.0718858 | + | 0.440384i | ||||
\(495\) | 5.08642 | + | 2.93664i | 0.228617 | + | 0.131992i | ||||
\(496\) | 24.1687 | + | 18.2677i | 1.08521 | + | 0.820245i | ||||
\(497\) | −50.2925 | + | 29.0364i | −2.25593 | + | 1.30246i | ||||
\(498\) | 8.48757 | − | 10.3805i | 0.380337 | − | 0.465163i | ||||
\(499\) | 19.3059 | + | 33.4388i | 0.864251 | + | 1.49693i | 0.867789 | + | 0.496932i | \(0.165540\pi\) |
−0.00353889 | + | 0.999994i | \(0.501126\pi\) | |||||||
\(500\) | −0.498625 | − | 0.564422i | −0.0222992 | − | 0.0252417i | ||||
\(501\) | 5.03270 | + | 2.90563i | 0.224845 | + | 0.129814i | ||||
\(502\) | 5.31846 | + | 4.34859i | 0.237374 | + | 0.194087i | ||||
\(503\) | −6.50316 | + | 11.2638i | −0.289961 | + | 0.502228i | −0.973800 | − | 0.227405i | \(-0.926976\pi\) |
0.683839 | + | 0.729633i | \(0.260309\pi\) | |||||||
\(504\) | 6.10541 | + | 9.69998i | 0.271957 | + | 0.432071i | ||||
\(505\) | 9.08569 | − | 15.7369i | 0.404308 | − | 0.700282i | ||||
\(506\) | 0.586967 | + | 1.55098i | 0.0260939 | + | 0.0689494i | ||||
\(507\) | −4.86017 | + | 8.41806i | −0.215848 | + | 0.373859i | ||||
\(508\) | −3.45619 | + | 0.700545i | −0.153343 | + | 0.0310817i | ||||
\(509\) | 18.6072 | 0.824749 | 0.412375 | − | 0.911014i | \(-0.364699\pi\) | ||||
0.412375 | + | 0.911014i | \(0.364699\pi\) | |||||||
\(510\) | −20.4703 | + | 25.0358i | −0.906442 | + | 1.10860i | ||||
\(511\) | 18.6460 | 0.824850 | ||||||||
\(512\) | 22.4792 | − | 2.58583i | 0.993449 | − | 0.114279i | ||||
\(513\) | 3.35356 | − | 1.93618i | 0.148063 | − | 0.0854843i | ||||
\(514\) | −2.06041 | + | 12.6224i | −0.0908809 | + | 0.556750i | ||||
\(515\) | 15.7555 | − | 27.2893i | 0.694270 | − | 1.20251i | ||||
\(516\) | −3.75149 | + | 3.31416i | −0.165150 | + | 0.145898i | ||||
\(517\) | 11.2704 | − | 6.50698i | 0.495673 | − | 0.286177i | ||||
\(518\) | 58.4922 | − | 22.1363i | 2.57000 | − | 0.972614i | ||||
\(519\) | 2.25366 | + | 3.90346i | 0.0989249 | + | 0.171343i | ||||
\(520\) | 16.0889 | − | 0.614513i | 0.705544 | − | 0.0269482i | ||||
\(521\) | − | 28.3049i | − | 1.24006i | −0.784577 | − | 0.620031i | \(-0.787120\pi\) | ||
0.784577 | − | 0.620031i | \(-0.212880\pi\) | |||||||
\(522\) | −2.01329 | + | 12.3337i | −0.0881191 | + | 0.539831i | ||||
\(523\) | 13.9278 | − | 8.04122i | 0.609021 | − | 0.351618i | −0.163561 | − | 0.986533i | \(-0.552298\pi\) |
0.772582 | + | 0.634915i | \(0.218965\pi\) | |||||||
\(524\) | 9.24925 | + | 10.4697i | 0.404055 | + | 0.457373i | ||||
\(525\) | −9.88789 | + | 17.1263i | −0.431543 | + | 0.747454i | ||||
\(526\) | 13.9241 | + | 36.7926i | 0.607121 | + | 1.60423i | ||||
\(527\) | −55.1003 | −2.40021 | ||||||||
\(528\) | 5.96251 | + | 4.50672i | 0.259485 | + | 0.196130i | ||||
\(529\) | −11.3031 | + | 19.5775i | −0.491438 | + | 0.851196i | ||||
\(530\) | 15.5200 | − | 5.87354i | 0.674146 | − | 0.255130i | ||||
\(531\) | 14.0628i | 0.610274i | ||||||||
\(532\) | −20.7782 | − | 23.5200i | −0.900848 | − | 1.01972i | ||||
\(533\) | −5.26130 | −0.227892 | ||||||||
\(534\) | −6.46579 | + | 2.44697i | −0.279802 | + | 0.105891i | ||||
\(535\) | 11.5229 | 0.498180 | ||||||||
\(536\) | −21.2853 | + | 9.10689i | −0.919385 | + | 0.393358i | ||||
\(537\) | 18.3582 | 0.792216 | ||||||||
\(538\) | −37.5336 | + | 14.2046i | −1.61819 | + | 0.612402i | ||||
\(539\) | 17.6028 | 0.758207 | ||||||||
\(540\) | −4.16216 | − | 4.71139i | −0.179111 | − | 0.202746i | ||||
\(541\) | − | 35.5470i | − | 1.52828i | −0.645049 | − | 0.764142i | \(-0.723163\pi\) | ||
0.645049 | − | 0.764142i | \(-0.276837\pi\) | |||||||
\(542\) | 15.1254 | − | 5.72420i | 0.649692 | − | 0.245876i | ||||
\(543\) | 2.65528 | − | 4.59908i | 0.113949 | − | 0.197365i | ||||
\(544\) | −29.7796 | + | 28.4040i | −1.27679 | + | 1.21781i | ||||
\(545\) | 20.6173 | 0.883150 | ||||||||
\(546\) | 3.67340 | + | 9.70644i | 0.157207 | + | 0.415397i | ||||
\(547\) | −3.78761 | + | 6.56033i | −0.161946 | + | 0.280499i | −0.935567 | − | 0.353150i | \(-0.885110\pi\) |
0.773620 | + | 0.633649i | \(0.218444\pi\) | |||||||
\(548\) | −26.6002 | − | 30.1103i | −1.13631 | − | 1.28625i | ||||
\(549\) | 2.09861 | − | 1.21163i | 0.0895665 | − | 0.0517112i | ||||
\(550\) | −2.07756 | + | 12.7274i | −0.0885874 | + | 0.542700i | ||||
\(551\) | − | 34.2187i | − | 1.45777i | ||||||
\(552\) | −0.0677472 | − | 1.77373i | −0.00288351 | − | 0.0754948i | ||||
\(553\) | −2.94196 | − | 5.09563i | −0.125105 | − | 0.216688i | ||||
\(554\) | 15.5656 | − | 5.89079i | 0.661319 | − | 0.250276i | ||||
\(555\) | −29.7075 | + | 17.1516i | −1.26101 | + | 0.728046i | ||||
\(556\) | 12.7663 | − | 11.2780i | 0.541410 | − | 0.478296i | ||||
\(557\) | −15.2481 | + | 26.4105i | −0.646083 | + | 1.11905i | 0.337967 | + | 0.941158i | \(0.390261\pi\) |
−0.984050 | + | 0.177891i | \(0.943073\pi\) | |||||||
\(558\) | 1.72560 | − | 10.5713i | 0.0730503 | − | 0.447517i | ||||
\(559\) | −3.92539 | + | 2.26633i | −0.166026 | + | 0.0958554i | ||||
\(560\) | −30.7214 | + | 40.6452i | −1.29822 | + | 1.71757i | ||||
\(561\) | −13.5935 | −0.573917 | ||||||||
\(562\) | 0.170050 | − | 0.207976i | 0.00717311 | − | 0.00877292i | ||||
\(563\) | 31.9971 | 1.34852 | 0.674258 | − | 0.738496i | \(-0.264464\pi\) | ||||
0.674258 | + | 0.738496i | \(0.264464\pi\) | |||||||
\(564\) | −13.6521 | + | 2.76718i | −0.574855 | + | 0.116519i | ||||
\(565\) | 0.675463 | − | 1.16994i | 0.0284169 | − | 0.0492196i | ||||
\(566\) | 12.7070 | + | 33.5766i | 0.534117 | + | 1.41133i | ||||
\(567\) | 2.02612 | − | 3.50935i | 0.0850892 | − | 0.147379i | ||||
\(568\) | 34.3046 | − | 21.5922i | 1.43939 | − | 0.905987i | ||||
\(569\) | 3.32706 | − | 5.76263i | 0.139477 | − | 0.241582i | −0.787822 | − | 0.615904i | \(-0.788791\pi\) |
0.927299 | + | 0.374322i | \(0.122124\pi\) | |||||||
\(570\) | 13.3262 | + | 10.8960i | 0.558171 | + | 0.456384i | ||||
\(571\) | −10.4964 | − | 6.06010i | −0.439261 | − | 0.253607i | 0.264023 | − | 0.964516i | \(-0.414950\pi\) |
−0.703284 | + | 0.710909i | \(0.748284\pi\) | |||||||
\(572\) | 4.48074 | + | 5.07200i | 0.187349 | + | 0.212071i | ||||
\(573\) | 4.16544 | + | 7.21475i | 0.174014 | + | 0.301400i | ||||
\(574\) | 10.5386 | − | 12.8890i | 0.439874 | − | 0.537978i | ||||
\(575\) | 2.65232 | − | 1.53132i | 0.110610 | − | 0.0638604i | ||||
\(576\) | −4.51682 | − | 6.60290i | −0.188201 | − | 0.275121i | ||||
\(577\) | 2.06577 | + | 1.19267i | 0.0859990 | + | 0.0496516i | 0.542383 | − | 0.840131i | \(-0.317522\pi\) |
−0.456384 | + | 0.889783i | \(0.650856\pi\) | |||||||
\(578\) | 8.18499 | − | 50.1425i | 0.340451 | − | 2.08565i | ||||
\(579\) | 21.1039 | 0.877048 | ||||||||
\(580\) | −54.4451 | + | 11.0356i | −2.26071 | + | 0.458230i | ||||
\(581\) | 38.4211i | 1.59397i | ||||||||
\(582\) | −1.95214 | + | 2.38752i | −0.0809188 | + | 0.0989661i | ||||
\(583\) | 6.04072 | + | 3.48761i | 0.250181 | + | 0.144442i | ||||
\(584\) | −13.0052 | + | 0.496733i | −0.538160 | + | 0.0205549i | ||||
\(585\) | −2.84621 | − | 4.92979i | −0.117676 | − | 0.203822i | ||||
\(586\) | −12.8018 | + | 4.84482i | −0.528836 | + | 0.200138i | ||||
\(587\) | 11.4631 | + | 19.8546i | 0.473132 | + | 0.819489i | 0.999527 | − | 0.0307515i | \(-0.00979006\pi\) |
−0.526395 | + | 0.850240i | \(0.676457\pi\) | |||||||
\(588\) | −17.8634 | − | 5.99149i | −0.736674 | − | 0.247085i | ||||
\(589\) | 29.3290i | 1.20848i | ||||||||
\(590\) | −58.4661 | + | 22.1265i | −2.40701 | + | 0.910932i | ||||
\(591\) | 4.60979 | + | 2.66147i | 0.189622 | + | 0.109478i | ||||
\(592\) | −40.2075 | + | 16.9979i | −1.65252 | + | 0.698610i | ||||
\(593\) | 26.0828 | − | 15.0589i | 1.07109 | − | 0.618396i | 0.142613 | − | 0.989778i | \(-0.454449\pi\) |
0.928480 | + | 0.371383i | \(0.121116\pi\) | |||||||
\(594\) | 0.425712 | − | 2.60797i | 0.0174672 | − | 0.107006i | ||||
\(595\) | − | 92.6640i | − | 3.79885i | ||||||
\(596\) | −19.5767 | + | 17.2945i | −0.801891 | + | 0.708412i | ||||
\(597\) | −12.8058 | + | 7.39343i | −0.524106 | + | 0.302593i | ||||
\(598\) | 0.258934 | − | 1.58627i | 0.0105886 | − | 0.0648675i | ||||
\(599\) | −13.7306 | + | 23.7821i | −0.561016 | + | 0.971708i | 0.436392 | + | 0.899757i | \(0.356256\pi\) |
−0.997408 | + | 0.0719518i | \(0.977077\pi\) | |||||||
\(600\) | 6.44037 | − | 12.2087i | 0.262927 | − | 0.498418i | ||||
\(601\) | −9.04377 | − | 15.6643i | −0.368903 | − | 0.638959i | 0.620491 | − | 0.784213i | \(-0.286933\pi\) |
−0.989394 | + | 0.145254i | \(0.953600\pi\) | |||||||
\(602\) | 2.31074 | − | 14.1559i | 0.0941786 | − | 0.576952i | ||||
\(603\) | 6.35908 | + | 5.15385i | 0.258962 | + | 0.209881i | ||||
\(604\) | −12.2105 | + | 36.4052i | −0.496839 | + | 1.48131i | ||||
\(605\) | 20.4397 | − | 11.8008i | 0.830990 | − | 0.479773i | ||||
\(606\) | −8.06881 | − | 1.31711i | −0.327773 | − | 0.0535039i | ||||
\(607\) | 9.00353 | + | 5.19819i | 0.365442 | + | 0.210988i | 0.671465 | − | 0.741036i | \(-0.265665\pi\) |
−0.306023 | + | 0.952024i | \(0.598999\pi\) | |||||||
\(608\) | 15.1190 | + | 15.8512i | 0.613155 | + | 0.642852i | ||||
\(609\) | −17.9042 | − | 31.0110i | −0.725514 | − | 1.25663i | ||||
\(610\) | 8.33932 | + | 6.81858i | 0.337649 | + | 0.276076i | ||||
\(611\) | −12.6132 | −0.510276 | ||||||||
\(612\) | 13.7947 | + | 4.62683i | 0.557618 | + | 0.187029i | ||||
\(613\) | 2.48491 | + | 4.30399i | 0.100365 | + | 0.173837i | 0.911835 | − | 0.410557i | \(-0.134666\pi\) |
−0.811470 | + | 0.584394i | \(0.801332\pi\) | |||||||
\(614\) | −18.9457 | + | 23.1711i | −0.764585 | + | 0.935110i | ||||
\(615\) | −4.56595 | + | 7.90845i | −0.184117 | + | 0.318900i | ||||
\(616\) | −21.4004 | + | 0.817387i | −0.862249 | + | 0.0329335i | ||||
\(617\) | −12.7043 | −0.511456 | −0.255728 | − | 0.966749i | \(-0.582315\pi\) | ||||
−0.255728 | + | 0.966749i | \(0.582315\pi\) | |||||||
\(618\) | −13.9921 | − | 2.28400i | −0.562846 | − | 0.0918759i | ||||
\(619\) | −29.0492 | + | 16.7715i | −1.16758 | + | 0.674105i | −0.953110 | − | 0.302624i | \(-0.902137\pi\) |
−0.214475 | + | 0.976730i | \(0.568804\pi\) | |||||||
\(620\) | 46.6651 | − | 9.45869i | 1.87412 | − | 0.379870i | ||||
\(621\) | −0.543486 | + | 0.313782i | −0.0218094 | + | 0.0125916i | ||||
\(622\) | −29.7851 | + | 11.2722i | −1.19427 | + | 0.451972i | ||||
\(623\) | 9.90463 | − | 17.1553i | 0.396821 | − | 0.687313i | ||||
\(624\) | −2.82071 | − | 6.67220i | −0.112919 | − | 0.267102i | ||||
\(625\) | −25.5846 | −1.02339 | ||||||||
\(626\) | 14.3347 | + | 37.8775i | 0.572930 | + | 1.51389i | ||||
\(627\) | 7.23559i | 0.288961i | ||||||||
\(628\) | 46.0896 | + | 15.4588i | 1.83918 | + | 0.616871i | ||||
\(629\) | 39.6967 | − | 68.7567i | 1.58281 | − | 2.74151i | ||||
\(630\) | 17.7780 | + | 2.90199i | 0.708294 | + | 0.115618i | ||||
\(631\) | −2.02430 | − | 3.50619i | −0.0805862 | − | 0.139579i | 0.822916 | − | 0.568164i | \(-0.192346\pi\) |
−0.903502 | + | 0.428584i | \(0.859013\pi\) | |||||||
\(632\) | 2.18771 | + | 3.47573i | 0.0870225 | + | 0.138257i | ||||
\(633\) | 12.0538 | − | 6.95929i | 0.479097 | − | 0.276607i | ||||
\(634\) | −25.3090 | − | 20.6937i | −1.00515 | − | 0.821853i | ||||
\(635\) | −2.77117 | + | 4.79981i | −0.109971 | + | 0.190475i | ||||
\(636\) | −4.94306 | − | 5.59533i | −0.196005 | − | 0.221869i | ||||
\(637\) | −14.7750 | − | 8.53037i | −0.585409 | − | 0.337986i | ||||
\(638\) | −18.0773 | − | 14.7808i | −0.715688 | − | 0.585177i | ||||
\(639\) | −12.4110 | − | 7.16551i | −0.490972 | − | 0.283463i | ||||
\(640\) | 20.3448 | − | 29.1677i | 0.804199 | − | 1.15295i | ||||
\(641\) | 1.95122 | + | 1.12654i | 0.0770686 | + | 0.0444956i | 0.538039 | − | 0.842920i | \(-0.319165\pi\) |
−0.460971 | + | 0.887415i | \(0.652499\pi\) | |||||||
\(642\) | −1.83501 | − | 4.84875i | −0.0724219 | − | 0.191365i | ||||
\(643\) | 5.18604i | 0.204517i | 0.994758 | + | 0.102259i | \(0.0326070\pi\) | ||||
−0.994758 | + | 0.102259i | \(0.967393\pi\) | |||||||
\(644\) | 3.36737 | + | 3.81171i | 0.132693 | + | 0.150202i | ||||
\(645\) | 7.86721i | 0.309771i | ||||||||
\(646\) | −39.3199 | − | 6.41836i | −1.54702 | − | 0.252527i | ||||
\(647\) | 12.9463 | + | 22.4236i | 0.508970 | + | 0.881562i | 0.999946 | + | 0.0103890i | \(0.00330699\pi\) |
−0.490976 | + | 0.871173i | \(0.663360\pi\) | |||||||
\(648\) | −1.31969 | + | 2.50168i | −0.0518425 | + | 0.0982753i | ||||
\(649\) | −22.7563 | − | 13.1383i | −0.893262 | − | 0.515725i | ||||
\(650\) | 7.91157 | − | 9.67607i | 0.310317 | − | 0.379527i | ||||
\(651\) | 15.3458 | + | 26.5796i | 0.601447 | + | 1.04174i | ||||
\(652\) | 5.14903 | − | 1.04367i | 0.201651 | − | 0.0408734i | ||||
\(653\) | −36.9411 | + | 21.3280i | −1.44562 | + | 0.834628i | −0.998216 | − | 0.0597050i | \(-0.980984\pi\) |
−0.447402 | + | 0.894333i | \(0.647651\pi\) | |||||||
\(654\) | −3.28327 | − | 8.67559i | −0.128386 | − | 0.339242i | ||||
\(655\) | 21.9560 | 0.857891 | ||||||||
\(656\) | −7.00713 | + | 9.27062i | −0.273582 | + | 0.361957i | ||||
\(657\) | 2.30070 | + | 3.98493i | 0.0897588 | + | 0.155467i | ||||
\(658\) | 25.2649 | − | 30.8997i | 0.984928 | − | 1.20459i | ||||
\(659\) | 32.0427 | + | 18.4998i | 1.24821 | + | 0.720652i | 0.970751 | − | 0.240087i | \(-0.0771760\pi\) |
0.277454 | + | 0.960739i | \(0.410509\pi\) | |||||||
\(660\) | 11.5125 | − | 2.33350i | 0.448122 | − | 0.0908313i | ||||
\(661\) | 25.8331i | 1.00479i | 0.864638 | + | 0.502395i | \(0.167548\pi\) | ||||
−0.864638 | + | 0.502395i | \(0.832452\pi\) | |||||||
\(662\) | −2.54786 | + | 15.6086i | −0.0990254 | + | 0.606645i | ||||
\(663\) | 11.4098 | + | 6.58744i | 0.443119 | + | 0.255835i | ||||
\(664\) | −1.02354 | − | 26.7980i | −0.0397212 | − | 1.03996i | ||||
\(665\) | −49.3235 | −1.91268 | ||||||||
\(666\) | 11.9481 | + | 9.76928i | 0.462980 | + | 0.378552i | ||||
\(667\) | 5.54558i | 0.214726i | ||||||||
\(668\) | 11.3909 | − | 2.30885i | 0.440727 | − | 0.0893323i | ||||
\(669\) | 22.7611i | 0.879997i | ||||||||
\(670\) | −11.4217 | + | 34.5469i | −0.441260 | + | 1.33466i | ||||
\(671\) | 4.52793i | 0.174799i | ||||||||
\(672\) | 21.9955 | + | 6.45461i | 0.848494 | + | 0.248992i | ||||
\(673\) | − | 8.71971i | − | 0.336120i | −0.985777 | − | 0.168060i | \(-0.946250\pi\) | ||
0.985777 | − | 0.168060i | \(-0.0537503\pi\) | |||||||
\(674\) | 2.10809 | − | 2.57825i | 0.0812005 | − | 0.0993106i | ||||
\(675\) | −4.88020 | −0.187839 | ||||||||
\(676\) | 3.86196 | + | 19.0532i | 0.148537 | + | 0.732816i | ||||
\(677\) | −28.6454 | − | 16.5384i | −1.10093 | − | 0.635623i | −0.164466 | − | 0.986383i | \(-0.552590\pi\) |
−0.936466 | + | 0.350759i | \(0.885923\pi\) | |||||||
\(678\) | −0.599864 | − | 0.0979186i | −0.0230377 | − | 0.00376054i | ||||
\(679\) | − | 8.83684i | − | 0.339127i | ||||||
\(680\) | 2.46859 | + | 64.6314i | 0.0946659 | + | 2.47850i | ||||
\(681\) | −8.68285 | − | 5.01304i | −0.332727 | − | 0.192100i | ||||
\(682\) | 15.4941 | + | 12.6687i | 0.593301 | + | 0.485108i | ||||
\(683\) | −13.5254 | − | 23.4267i | −0.517535 | − | 0.896396i | −0.999793 | − | 0.0203671i | \(-0.993517\pi\) |
0.482258 | − | 0.876029i | \(-0.339817\pi\) | |||||||
\(684\) | 2.46279 | − | 7.34270i | 0.0941670 | − | 0.280755i | ||||
\(685\) | −63.1440 | −2.41261 | ||||||||
\(686\) | 12.9744 | − | 4.91015i | 0.495365 | − | 0.187471i | ||||
\(687\) | −7.45156 | + | 4.30216i | −0.284295 | + | 0.164138i | ||||
\(688\) | −1.23458 | + | 9.93505i | −0.0470679 | + | 0.378770i | ||||
\(689\) | −3.38022 | − | 5.85471i | −0.128776 | − | 0.223047i | ||||
\(690\) | −2.15967 | − | 1.76584i | −0.0822173 | − | 0.0672243i | ||||
\(691\) | −7.22794 | − | 4.17306i | −0.274964 | − | 0.158751i | 0.356177 | − | 0.934418i | \(-0.384080\pi\) |
−0.631141 | + | 0.775668i | \(0.717413\pi\) | |||||||
\(692\) | 8.54672 | + | 2.86662i | 0.324898 | + | 0.108973i | ||||
\(693\) | 3.78586 | + | 6.55730i | 0.143813 | + | 0.249091i | ||||
\(694\) | −2.64083 | + | 16.1782i | −0.100245 | + | 0.614114i | ||||
\(695\) | − | 26.7720i | − | 1.01552i | ||||||
\(696\) | 13.3140 | + | 21.1526i | 0.504665 | + | 0.801787i | ||||
\(697\) | − | 21.1354i | − | 0.800560i | ||||||
\(698\) | 21.7271 | − | 8.22260i | 0.822382 | − | 0.311230i | ||||
\(699\) | −12.1603 | − | 7.02078i | −0.459946 | − | 0.265550i | ||||
\(700\) | 7.85705 | + | 38.7633i | 0.296969 | + | 1.46511i | ||||
\(701\) | −22.8985 | − | 13.2205i | −0.864866 | − | 0.499330i | 0.000773032 | − | 1.00000i | \(-0.499754\pi\) |
−0.865639 | + | 0.500669i | \(0.833087\pi\) | |||||||
\(702\) | −1.62116 | + | 1.98272i | −0.0611866 | + | 0.0748330i | ||||
\(703\) | −36.5981 | − | 21.1299i | −1.38032 | − | 0.796930i | ||||
\(704\) | 14.9046 | − | 1.14022i | 0.561740 | − | 0.0429738i | ||||
\(705\) | −10.9462 | + | 18.9594i | −0.412258 | + | 0.714053i | ||||
\(706\) | −25.9544 | + | 31.7429i | −0.976806 | + | 1.19466i | ||||
\(707\) | 20.2876 | − | 11.7131i | 0.762995 | − | 0.440515i | ||||
\(708\) | 18.6212 | + | 21.0784i | 0.699828 | + | 0.792175i | ||||
\(709\) | 3.22465 | + | 5.58526i | 0.121104 | + | 0.209759i | 0.920203 | − | 0.391440i | \(-0.128023\pi\) |
−0.799099 | + | 0.601199i | \(0.794690\pi\) | |||||||
\(710\) | 10.2631 | − | 62.8731i | 0.385166 | − | 2.35958i | ||||
\(711\) | 0.726008 | − | 1.25748i | 0.0272274 | − | 0.0471593i | ||||
\(712\) | −6.45127 | + | 12.2294i | −0.241772 | + | 0.458315i | ||||
\(713\) | − | 4.75314i | − | 0.178006i | ||||||
\(714\) | −38.9922 | + | 14.7566i | −1.45924 | + | 0.552250i | ||||
\(715\) | 10.6364 | 0.397780 | ||||||||
\(716\) | 27.5167 | − | 24.3090i | 1.02835 | − | 0.908470i | ||||
\(717\) | −7.61571 | + | 13.1908i | −0.284414 | + | 0.492619i | ||||
\(718\) | 8.04757 | + | 21.2646i | 0.300332 | + | 0.793587i | ||||
\(719\) | −1.98014 | + | 1.14323i | −0.0738468 | + | 0.0426355i | −0.536469 | − | 0.843920i | \(-0.680242\pi\) |
0.462622 | + | 0.886556i | \(0.346909\pi\) | |||||||
\(720\) | −12.4771 | − | 1.55047i | −0.464996 | − | 0.0577827i | ||||
\(721\) | 35.1808 | − | 20.3116i | 1.31020 | − | 0.756445i | ||||
\(722\) | 0.912441 | − | 5.58975i | 0.0339575 | − | 0.208029i | ||||
\(723\) | 1.87229 | 0.0696312 | ||||||||
\(724\) | −2.10992 | − | 10.4094i | −0.0784146 | − | 0.386863i | ||||
\(725\) | −21.5624 | + | 37.3471i | −0.800806 | + | 1.38704i | ||||
\(726\) | −8.22067 | − | 6.72156i | −0.305098 | − | 0.249461i | ||||
\(727\) | −24.7885 | − | 42.9349i | −0.919353 | − | 1.59237i | −0.800400 | − | 0.599467i | \(-0.795379\pi\) |
−0.118954 | − | 0.992900i | \(-0.537954\pi\) | |||||||
\(728\) | 18.3587 | + | 9.68464i | 0.680420 | + | 0.358937i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −12.9474 | + | 15.8350i | −0.479205 | + | 0.586081i | ||||
\(731\) | −9.10416 | − | 15.7689i | −0.336729 | − | 0.583232i | ||||
\(732\) | 1.54118 | − | 4.59496i | 0.0569635 | − | 0.169834i | ||||
\(733\) | 24.0051 | + | 13.8593i | 0.886648 | + | 0.511906i | 0.872845 | − | 0.487998i | \(-0.162273\pi\) |
0.0138033 | + | 0.999905i | \(0.495606\pi\) | |||||||
\(734\) | −1.72958 | + | 10.5956i | −0.0638398 | + | 0.391093i | ||||
\(735\) | −25.6447 | + | 14.8060i | −0.945918 | + | 0.546126i | ||||
\(736\) | −2.45022 | − | 2.56889i | −0.0903163 | − | 0.0946905i | ||||
\(737\) | −14.2809 | + | 5.47515i | −0.526045 | + | 0.201680i | ||||
\(738\) | 4.05492 | + | 0.661904i | 0.149264 | + | 0.0243650i | ||||
\(739\) | 22.6623 | + | 39.2522i | 0.833645 | + | 1.44392i | 0.895129 | + | 0.445807i | \(0.147083\pi\) |
−0.0614842 | + | 0.998108i | \(0.519583\pi\) | |||||||
\(740\) | −21.8166 | + | 65.0453i | −0.801994 | + | 2.39111i | ||||
\(741\) | 3.50639 | − | 6.07324i | 0.128810 | − | 0.223106i | ||||
\(742\) | 21.1135 | + | 3.44646i | 0.775101 | + | 0.126523i | ||||
\(743\) | 6.31070 | − | 3.64348i | 0.231517 | − | 0.133666i | −0.379755 | − | 0.925087i | \(-0.623992\pi\) |
0.611272 | + | 0.791421i | \(0.290658\pi\) | |||||||
\(744\) | −11.4115 | − | 18.1300i | −0.418364 | − | 0.664677i | ||||
\(745\) | 41.0540i | 1.50410i | ||||||||
\(746\) | −4.68079 | − | 0.764066i | −0.171376 | − | 0.0279744i | ||||
\(747\) | −8.21115 | + | 4.74071i | −0.300430 | + | 0.173454i | ||||
\(748\) | −20.3750 | + | 17.9998i | −0.744982 | + | 0.658137i | ||||
\(749\) | 12.8649 | + | 7.42756i | 0.470074 | + | 0.271397i | ||||
\(750\) | 0.188493 | + | 0.498066i | 0.00688279 | + | 0.0181868i | ||||
\(751\) | 46.9172i | 1.71203i | 0.516948 | + | 0.856017i | \(0.327068\pi\) | ||||
−0.516948 | + | 0.856017i | \(0.672932\pi\) | |||||||
\(752\) | −16.7986 | + | 22.2250i | −0.612582 | + | 0.810463i | ||||
\(753\) | −2.42889 | − | 4.20697i | −0.0885139 | − | 0.153310i | ||||
\(754\) | 8.01051 | + | 21.1667i | 0.291726 | + | 0.770845i | ||||
\(755\) | 30.1742 | + | 52.2633i | 1.09815 | + | 1.90205i | ||||
\(756\) | −1.60999 | − | 7.94297i | −0.0585546 | − | 0.288883i | ||||
\(757\) | −28.3909 | − | 16.3915i | −1.03188 | − | 0.595759i | −0.114361 | − | 0.993439i | \(-0.536482\pi\) |
−0.917524 | + | 0.397680i | \(0.869815\pi\) | |||||||
\(758\) | 19.7607 | + | 16.1572i | 0.717743 | + | 0.586857i | ||||
\(759\) | − | 1.17262i | − | 0.0425633i | ||||||
\(760\) | 34.4022 | − | 1.31399i | 1.24790 | − | 0.0476633i | ||||
\(761\) | 8.25537 | 0.299257 | 0.149629 | − | 0.988742i | \(-0.452192\pi\) | ||||
0.149629 | + | 0.988742i | \(0.452192\pi\) | |||||||
\(762\) | 2.46102 | + | 0.401723i | 0.0891533 | + | 0.0145529i | ||||
\(763\) | 23.0185 | + | 13.2897i | 0.833324 | + | 0.481120i | ||||
\(764\) | 15.7969 | + | 5.29837i | 0.571511 | + | 0.191688i | ||||
\(765\) | 19.8037 | − | 11.4337i | 0.716003 | − | 0.413385i | ||||
\(766\) | −4.43219 | − | 3.62394i | −0.160141 | − | 0.130938i | ||||
\(767\) | 12.7338 | + | 22.0555i | 0.459789 | + | 0.796378i | ||||
\(768\) | −15.5134 | − | 3.91601i | −0.559791 | − | 0.141307i | ||||
\(769\) | −11.8707 | − | 6.85356i | −0.428069 | − | 0.247146i | 0.270455 | − | 0.962733i | \(-0.412826\pi\) |
−0.698524 | + | 0.715587i | \(0.746159\pi\) | |||||||
\(770\) | −21.3053 | + | 26.0570i | −0.767789 | + | 0.939028i | ||||
\(771\) | 4.52176 | − | 7.83191i | 0.162847 | − | 0.282060i | ||||
\(772\) | 31.6322 | − | 27.9447i | 1.13847 | − | 1.00575i | ||||
\(773\) | 12.0932 | − | 20.9461i | 0.434963 | − | 0.753379i | −0.562329 | − | 0.826913i | \(-0.690095\pi\) |
0.997293 | + | 0.0735347i | \(0.0234280\pi\) | |||||||
\(774\) | 3.31045 | − | 1.25284i | 0.118992 | − | 0.0450323i | ||||
\(775\) | 18.4812 | − | 32.0104i | 0.663864 | − | 1.14985i | ||||
\(776\) | 0.235415 | + | 6.16353i | 0.00845091 | + | 0.221258i | ||||
\(777\) | −44.2230 | −1.58649 | ||||||||
\(778\) | −14.3347 | − | 11.7207i | −0.513924 | − | 0.420206i | ||||
\(779\) | −11.2500 | −0.403074 | ||||||||
\(780\) | −10.7939 | − | 3.62034i | −0.386483 | − | 0.129629i | ||||
\(781\) | 23.1903 | − | 13.3889i | 0.829814 | − | 0.479093i | ||||
\(782\) | 6.37228 | + | 1.04018i | 0.227872 | + | 0.0371966i | ||||
\(783\) | 4.41834 | − | 7.65278i | 0.157898 | − | 0.273488i | ||||
\(784\) | −34.7087 | + | 14.6733i | −1.23959 | + | 0.524045i | ||||
\(785\) | 66.1662 | − | 38.2011i | 2.36157 | − | 1.36346i | ||||
\(786\) | −3.49645 | − | 9.23888i | −0.124714 | − | 0.329540i | ||||
\(787\) | −24.2313 | − | 41.9698i | −0.863752 | − | 1.49606i | −0.868281 | − | 0.496072i | \(-0.834775\pi\) |
0.00452974 | − | 0.999990i | \(-0.498558\pi\) | |||||||
\(788\) | 10.4337 | − | 2.11484i | 0.371685 | − | 0.0753379i | ||||
\(789\) | − | 27.8170i | − | 0.990313i | ||||||
\(790\) | 6.37028 | + | 1.03985i | 0.226645 | + | 0.0369962i | ||||
\(791\) | 1.50826 | − | 0.870792i | 0.0536274 | − | 0.0309618i | ||||
\(792\) | −2.81525 | − | 4.47274i | −0.100036 | − | 0.158932i | ||||
\(793\) | 2.19425 | − | 3.80055i | 0.0779200 | − | 0.134961i | ||||
\(794\) | −2.52653 | + | 0.956162i | −0.0896630 | + | 0.0339329i | ||||
\(795\) | −11.7339 | −0.416159 | ||||||||
\(796\) | −9.40433 | + | 28.0386i | −0.333327 | + | 0.993802i | ||||
\(797\) | 0.165324 | − | 0.286349i | 0.00585608 | − | 0.0101430i | −0.863083 | − | 0.505063i | \(-0.831469\pi\) |
0.868939 | + | 0.494920i | \(0.164803\pi\) | |||||||
\(798\) | 7.85467 | + | 20.7549i | 0.278052 | + | 0.734715i | ||||
\(799\) | − | 50.6691i | − | 1.79254i | ||||||
\(800\) | −6.51281 | − | 26.8274i | −0.230263 | − | 0.948490i | ||||
\(801\) | 4.88846 | 0.172725 | ||||||||
\(802\) | 0.359270 | + | 0.949321i | 0.0126863 | + | 0.0335217i | ||||
\(803\) | −8.59781 | −0.303410 | ||||||||
\(804\) | 16.3559 | − | 0.695377i | 0.576829 | − | 0.0245240i | ||||
\(805\) | 7.99350 | 0.281734 | ||||||||
\(806\) | −6.86584 | − | 18.1420i | −0.241839 | − | 0.639026i | ||||
\(807\) | 28.3773 | 0.998928 | ||||||||
\(808\) | −13.8382 | + | 8.71011i | −0.486826 | + | 0.306421i | ||||
\(809\) | 52.3857i | 1.84178i | 0.389817 | + | 0.920892i | \(0.372538\pi\) | ||||
−0.389817 | + | 0.920892i | \(0.627462\pi\) | |||||||
\(810\) | 1.57340 | + | 4.15750i | 0.0552837 | + | 0.146080i | ||||
\(811\) | 4.90019 | − | 8.48737i | 0.172069 | − | 0.298032i | −0.767074 | − | 0.641558i | \(-0.778288\pi\) |
0.939143 | + | 0.343526i | \(0.111622\pi\) | |||||||
\(812\) | −67.8993 | − | 22.7738i | −2.38280 | − | 0.799205i | ||||
\(813\) | −11.4356 | −0.401063 | ||||||||
\(814\) | −26.9712 | + | 10.2072i | −0.945340 | + | 0.357763i | ||||
\(815\) | 4.12849 | − | 7.15075i | 0.144615 | − | 0.250480i | ||||
\(816\) | 26.8032 | − | 11.3312i | 0.938299 | − | 0.396671i | ||||
\(817\) | −8.39351 | + | 4.84599i | −0.293652 | + | 0.169540i | ||||
\(818\) | 29.6059 | + | 4.83271i | 1.03515 | + | 0.168972i | ||||
\(819\) | − | 7.33856i | − | 0.256430i | ||||||
\(820\) | 3.62816 | + | 17.8998i | 0.126701 | + | 0.625088i | ||||
\(821\) | −0.331997 | − | 0.575036i | −0.0115868 | − | 0.0200689i | 0.860174 | − | 0.510001i | \(-0.170355\pi\) |
−0.871761 | + | 0.489932i | \(0.837022\pi\) | |||||||
\(822\) | 10.0556 | + | 26.5704i | 0.350728 | + | 0.926749i | ||||
\(823\) | −30.9660 | + | 17.8782i | −1.07941 | + | 0.623195i | −0.930736 | − | 0.365692i | \(-0.880832\pi\) |
−0.148669 | + | 0.988887i | \(0.547499\pi\) | |||||||
\(824\) | −23.9968 | + | 15.1042i | −0.835969 | + | 0.526180i | ||||
\(825\) | 4.55938 | − | 7.89709i | 0.158737 | − | 0.274941i | ||||
\(826\) | −79.5376 | − | 12.9833i | −2.76747 | − | 0.451746i | ||||
\(827\) | −0.826546 | + | 0.477207i | −0.0287418 | + | 0.0165941i | −0.514302 | − | 0.857609i | \(-0.671949\pi\) |
0.485560 | + | 0.874203i | \(0.338616\pi\) | |||||||
\(828\) | −0.399126 | + | 1.18998i | −0.0138706 | + | 0.0413546i | ||||
\(829\) | −9.78843 | −0.339966 | −0.169983 | − | 0.985447i | \(-0.554371\pi\) | ||||
−0.169983 | + | 0.985447i | \(0.554371\pi\) | |||||||
\(830\) | −32.6290 | − | 26.6788i | −1.13257 | − | 0.926035i | ||||
\(831\) | −11.7684 | −0.408240 | ||||||||
\(832\) | −13.0629 | − | 6.26578i | −0.452873 | − | 0.217227i | ||||
\(833\) | 34.2677 | − | 59.3535i | 1.18731 | − | 2.05648i | ||||
\(834\) | −11.2654 | + | 4.26338i | −0.390089 | + | 0.147629i | ||||
\(835\) | 9.13321 | − | 15.8192i | 0.316068 | − | 0.547445i | ||||
\(836\) | 9.58098 | + | 10.8453i | 0.331365 | + | 0.375091i | ||||
\(837\) | −3.78697 | + | 6.55923i | −0.130897 | + | 0.226720i | ||||
\(838\) | 25.1480 | − | 30.7567i | 0.868722 | − | 1.06247i | ||||
\(839\) | −6.65466 | − | 3.84207i | −0.229745 | − | 0.132643i | 0.380710 | − | 0.924695i | \(-0.375680\pi\) |
−0.610454 | + | 0.792052i | \(0.709013\pi\) | |||||||
\(840\) | 30.4897 | − | 19.1910i | 1.05200 | − | 0.662153i | ||||
\(841\) | −24.5434 | − | 42.5104i | −0.846323 | − | 1.46587i | ||||
\(842\) | −41.9747 | − | 34.3203i | −1.44654 | − | 1.18275i | ||||
\(843\) | −0.164511 | + | 0.0949807i | −0.00566607 | + | 0.00327131i | ||||
\(844\) | 8.85211 | − | 26.3922i | 0.304702 | − | 0.908457i | ||||
\(845\) | 26.4603 | + | 15.2769i | 0.910262 | + | 0.525540i | ||||
\(846\) | 9.72111 | + | 1.58682i | 0.334219 | + | 0.0545561i | ||||
\(847\) | 30.4268 | 1.04548 | ||||||||
\(848\) | −14.8181 | − | 1.84137i | −0.508855 | − | 0.0632329i | ||||
\(849\) | − | 25.3856i | − | 0.871232i | ||||||
\(850\) | 38.8702 | + | 31.7819i | 1.33324 | + | 1.09011i | ||||
\(851\) | 5.93118 | + | 3.42437i | 0.203318 | + | 0.117386i | ||||
\(852\) | −28.0908 | + | 5.69381i | −0.962375 | + | 0.195067i | ||||
\(853\) | −13.9172 | − | 24.1052i | −0.476515 | − | 0.825348i | 0.523123 | − | 0.852257i | \(-0.324767\pi\) |
−0.999638 | + | 0.0269093i | \(0.991433\pi\) | |||||||
\(854\) | 4.91534 | + | 12.9881i | 0.168200 | + | 0.444444i | ||||
\(855\) | −6.08595 | − | 10.5412i | −0.208135 | − | 0.360500i | ||||
\(856\) | −9.17091 | − | 4.83786i | −0.313455 | − | 0.165355i | ||||
\(857\) | 22.2953i | 0.761592i | 0.924659 | + | 0.380796i | \(0.124350\pi\) | ||||
−0.924659 | + | 0.380796i | \(0.875650\pi\) | |||||||
\(858\) | −1.69383 | − | 4.47572i | −0.0578265 | − | 0.152798i | ||||
\(859\) | 3.49725 | + | 2.01914i | 0.119325 | + | 0.0688920i | 0.558474 | − | 0.829522i | \(-0.311387\pi\) |
−0.439150 | + | 0.898414i | \(0.644720\pi\) | |||||||
\(860\) | 10.4173 | + | 11.7920i | 0.355228 | + | 0.402103i | ||||
\(861\) | −10.1954 | + | 5.88632i | −0.347459 | + | 0.200605i | ||||
\(862\) | 50.0971 | + | 8.17759i | 1.70632 | + | 0.278530i | ||||
\(863\) | 10.3501i | 0.352322i | 0.984361 | + | 0.176161i | \(0.0563680\pi\) | ||||
−0.984361 | + | 0.176161i | \(0.943632\pi\) | |||||||
\(864\) | 1.33454 | + | 5.49718i | 0.0454019 | + | 0.187018i | ||||
\(865\) | 12.2697 | − | 7.08389i | 0.417181 | − | 0.240860i | ||||
\(866\) | −31.2342 | − | 5.09849i | −1.06138 | − | 0.173254i | ||||
\(867\) | −17.9627 | + | 31.1123i | −0.610045 | + | 1.05663i | ||||
\(868\) | 58.1967 | + | 19.5195i | 1.97533 | + | 0.662537i | ||||
\(869\) | 1.35656 | + | 2.34963i | 0.0460182 | + | 0.0797059i | ||||
\(870\) | 38.7683 | + | 6.32832i | 1.31437 | + | 0.214550i | ||||
\(871\) | 14.6401 | + | 2.32498i | 0.496060 | + | 0.0787790i | ||||
\(872\) | −16.4090 | − | 8.65611i | −0.555678 | − | 0.293133i | ||||
\(873\) | 1.88856 | − | 1.09036i | 0.0639182 | − | 0.0369032i | ||||
\(874\) | 0.553669 | − | 3.39186i | 0.0187281 | − | 0.114731i | ||||
\(875\) | −1.32149 | − | 0.762963i | −0.0446746 | − | 0.0257929i | ||||
\(876\) | 8.72509 | + | 2.92645i | 0.294794 | + | 0.0988756i | ||||
\(877\) | 15.5723 | + | 26.9720i | 0.525839 | + | 0.910780i | 0.999547 | + | 0.0300981i | \(0.00958197\pi\) |
−0.473708 | + | 0.880682i | \(0.657085\pi\) | |||||||
\(878\) | 6.12313 | − | 7.48876i | 0.206646 | − | 0.252733i | ||||
\(879\) | 9.67877 | 0.326457 | ||||||||
\(880\) | 14.1659 | − | 18.7418i | 0.477532 | − | 0.631787i | ||||
\(881\) | 11.0849 | + | 19.1996i | 0.373459 | + | 0.646850i | 0.990095 | − | 0.140398i | \(-0.0448384\pi\) |
−0.616636 | + | 0.787248i | \(0.711505\pi\) | |||||||
\(882\) | 10.3141 | + | 8.43322i | 0.347293 | + | 0.283961i | ||||
\(883\) | 15.0761 | − | 26.1126i | 0.507352 | − | 0.878759i | −0.492612 | − | 0.870249i | \(-0.663958\pi\) |
0.999964 | − | 0.00851011i | \(-0.00270888\pi\) | |||||||
\(884\) | 25.8246 | − | 5.23447i | 0.868575 | − | 0.176054i | ||||
\(885\) | 44.2033 | 1.48588 | ||||||||
\(886\) | −8.45135 | + | 51.7743i | −0.283929 | + | 1.73939i | ||||
\(887\) | −0.569415 | + | 0.328752i | −0.0191191 | + | 0.0110384i | −0.509529 | − | 0.860453i | \(-0.670180\pi\) |
0.490410 | + | 0.871492i | \(0.336847\pi\) | |||||||
\(888\) | 30.8447 | − | 1.17811i | 1.03508 | − | 0.0395348i | ||||
\(889\) | −6.18781 | + | 3.57253i | −0.207532 | + | 0.119819i | ||||
\(890\) | 7.69152 | + | 20.3238i | 0.257820 | + | 0.681255i | ||||
\(891\) | −0.934262 | + | 1.61819i | −0.0312989 | + | 0.0542114i | ||||
\(892\) | 30.1391 | + | 34.1162i | 1.00913 | + | 1.14229i | ||||
\(893\) | −26.9703 | −0.902528 | ||||||||
\(894\) | 17.2752 | − | 6.53777i | 0.577768 | − | 0.218656i | ||||
\(895\) | − | 57.7050i | − | 1.92887i | ||||||
\(896\) | 41.5154 | − | 19.4506i | 1.38693 | − | 0.649798i | ||||
\(897\) | −0.568254 | + | 0.984245i | −0.0189735 | + | 0.0328630i | ||||
\(898\) | 5.07379 | − | 31.0828i | 0.169315 | − | 1.03725i | ||||
\(899\) | 33.4642 | + | 57.9618i | 1.11609 | + | 1.93313i | ||||
\(900\) | −7.31482 | + | 6.46211i | −0.243827 | + | 0.215404i | ||||
\(901\) | 23.5192 | − | 13.5788i | 0.783538 | − | 0.452376i | ||||
\(902\) | −4.85945 | + | 5.94324i | −0.161802 | + | 0.197888i | ||||
\(903\) | −5.07112 | + | 8.78343i | −0.168756 | + | 0.292294i | ||||
\(904\) | −1.02878 | + | 0.647541i | −0.0342168 | + | 0.0215369i | ||||
\(905\) | −14.4562 | − | 8.34628i | −0.480540 | − | 0.277440i | ||||
\(906\) | 17.1867 | − | 21.0199i | 0.570991 | − | 0.698338i | ||||
\(907\) | −14.3152 | − | 8.26487i | −0.475327 | − | 0.274430i | 0.243140 | − | 0.969991i | \(-0.421823\pi\) |
−0.718467 | + | 0.695561i | \(0.755156\pi\) | |||||||
\(908\) | −19.6525 | + | 3.98343i | −0.652192 | + | 0.132195i | ||||
\(909\) | 5.00651 | + | 2.89051i | 0.166056 | + | 0.0958723i | ||||
\(910\) | 30.5100 | − | 11.5465i | 1.01140 | − | 0.382763i | ||||
\(911\) | − | 19.3823i | − | 0.642165i | −0.947051 | − | 0.321082i | \(-0.895953\pi\) | ||
0.947051 | − | 0.321082i | \(-0.104047\pi\) | |||||||
\(912\) | −6.03140 | − | 14.2669i | −0.199720 | − | 0.472424i | ||||
\(913\) | − | 17.7163i | − | 0.586322i | ||||||
\(914\) | 4.84206 | − | 29.6632i | 0.160161 | − | 0.981172i | ||||
\(915\) | −3.80850 | − | 6.59651i | −0.125905 | − | 0.218074i | ||||
\(916\) | −5.47228 | + | 16.3154i | −0.180809 | + | 0.539075i | ||||
\(917\) | 24.5130 | + | 14.1526i | 0.809491 | + | 0.467360i | ||||
\(918\) | −7.96487 | − | 6.51242i | −0.262880 | − | 0.214942i | ||||
\(919\) | −15.6638 | − | 27.1305i | −0.516700 | − | 0.894951i | −0.999812 | − | 0.0193924i | \(-0.993827\pi\) |
0.483112 | − | 0.875559i | \(-0.339507\pi\) | |||||||
\(920\) | −5.57531 | + | 0.212948i | −0.183813 | + | 0.00702070i | ||||
\(921\) | 18.3287 | − | 10.5821i | 0.603950 | − | 0.348691i | ||||
\(922\) | 46.4996 | − | 17.5977i | 1.53138 | − | 0.579550i | ||||
\(923\) | −25.9532 | −0.854261 | ||||||||
\(924\) | 14.3574 | + | 4.81555i | 0.472323 | + | 0.158420i | ||||
\(925\) | 26.6293 | + | 46.1233i | 0.875567 | + | 1.51653i | ||||
\(926\) | −15.4929 | − | 12.6676i | −0.509128 | − | 0.416284i | ||||
\(927\) | 8.68180 | + | 5.01244i | 0.285148 | + | 0.164630i | ||||
\(928\) | 47.9652 | + | 14.0755i | 1.57453 | + | 0.462050i | ||||
\(929\) | 14.8164i | 0.486112i | 0.970012 | + | 0.243056i | \(0.0781498\pi\) | ||||
−0.970012 | + | 0.243056i | \(0.921850\pi\) | |||||||
\(930\) | −33.2284 | − | 5.42403i | −1.08960 | − | 0.177861i | ||||
\(931\) | −31.5929 | − | 18.2402i | −1.03541 | − | 0.597797i | ||||
\(932\) | −27.5234 | + | 5.57881i | −0.901559 | + | 0.182740i | ||||
\(933\) | 22.5190 | 0.737241 | ||||||||
\(934\) | −8.97934 | + | 10.9820i | −0.293813 | + | 0.359341i | ||||
\(935\) | 42.7281i | 1.39736i | ||||||||
\(936\) | 0.195500 | + | 5.11850i | 0.00639013 | + | 0.167304i | ||||
\(937\) | − | 6.07853i | − | 0.198577i | −0.995059 | − | 0.0992885i | \(-0.968343\pi\) | ||
0.995059 | − | 0.0992885i | \(-0.0316567\pi\) | |||||||
\(938\) | −35.0205 | + | 31.2080i | −1.14346 | + | 1.01898i | ||||
\(939\) | − | 28.6373i | − | 0.934543i | ||||||
\(940\) | 8.69802 | + | 42.9122i | 0.283698 | + | 1.39964i | ||||
\(941\) | − | 21.1508i | − | 0.689496i | −0.938695 | − | 0.344748i | \(-0.887964\pi\) | ||
0.938695 | − | 0.344748i | \(-0.112036\pi\) | |||||||
\(942\) | −26.6115 | − | 21.7587i | −0.867050 | − | 0.708937i | ||||
\(943\) | 1.82321 | 0.0593718 | ||||||||
\(944\) | 55.8219 | + | 6.93670i | 1.81685 | + | 0.225770i | ||||
\(945\) | −11.0309 | − | 6.36867i | −0.358834 | − | 0.207173i | ||||
\(946\) | −1.06550 | + | 6.52741i | −0.0346424 | + | 0.212224i | ||||
\(947\) | − | 28.0752i | − | 0.912322i | −0.889897 | − | 0.456161i | \(-0.849224\pi\) | ||
0.889897 | − | 0.456161i | \(-0.150776\pi\) | |||||||
\(948\) | −0.576896 | − | 2.84615i | −0.0187367 | − | 0.0924387i | ||||
\(949\) | 7.21664 | + | 4.16653i | 0.234262 | + | 0.135251i | ||||
\(950\) | 16.9170 | − | 20.6900i | 0.548860 | − | 0.671271i | ||||
\(951\) | 11.5584 | + | 20.0198i | 0.374808 | + | 0.649186i | ||||
\(952\) | −38.9046 | + | 73.7496i | −1.26091 | + | 2.39024i | ||||
\(953\) | −26.2947 | −0.851768 | −0.425884 | − | 0.904778i | \(-0.640037\pi\) | ||||
−0.425884 | + | 0.904778i | \(0.640037\pi\) | |||||||
\(954\) | 1.86860 | + | 4.93752i | 0.0604982 | + | 0.159858i | ||||
\(955\) | 22.6780 | − | 13.0931i | 0.733842 | − | 0.423684i | ||||
\(956\) | 6.05155 | + | 29.8557i | 0.195721 | + | 0.965603i | ||||
\(957\) | 8.25576 | + | 14.2994i | 0.266871 | + | 0.462234i | ||||
\(958\) | 30.7541 | − | 37.6131i | 0.993620 | − | 1.21523i | ||||
\(959\) | −70.4978 | − | 40.7019i | −2.27649 | − | 1.31433i | ||||
\(960\) | −20.7548 | + | 14.1976i | −0.669857 | + | 0.458226i | ||||
\(961\) | −13.1823 | − | 22.8325i | −0.425237 | − | 0.736531i | ||||
\(962\) | 27.5849 | + | 4.50281i | 0.889374 | + | 0.145177i | ||||
\(963\) | 3.66590i | 0.118132i | ||||||||
\(964\) | 2.80633 | − | 2.47919i | 0.0903859 | − | 0.0798492i | ||||
\(965\) | − | 66.3355i | − | 2.13541i | ||||||
\(966\) | −1.27295 | − | 3.36359i | −0.0409565 | − | 0.108222i | ||||
\(967\) | 31.7410 | + | 18.3257i | 1.02072 | + | 0.589314i | 0.914313 | − | 0.405009i | \(-0.132732\pi\) |
0.106409 | + | 0.994322i | \(0.466065\pi\) | |||||||
\(968\) | −21.2221 | + | 0.810575i | −0.682105 | + | 0.0260529i | ||||
\(969\) | 24.3971 | + | 14.0857i | 0.783747 | + | 0.452497i | ||||
\(970\) | 7.50465 | + | 6.13612i | 0.240960 | + | 0.197019i | ||||
\(971\) | 37.8112 | + | 21.8303i | 1.21342 | + | 0.700567i | 0.963502 | − | 0.267700i | \(-0.0862637\pi\) |
0.249916 | + | 0.968268i | \(0.419597\pi\) | |||||||
\(972\) | 1.49888 | − | 1.32415i | 0.0480765 | − | 0.0424721i | ||||
\(973\) | 17.2569 | − | 29.8899i | 0.553232 | − | 0.958225i | ||||
\(974\) | −4.28560 | − | 3.50409i | −0.137319 | − | 0.112278i | ||||
\(975\) | −7.65390 | + | 4.41898i | −0.245121 | + | 0.141521i | ||||
\(976\) | −3.77437 | − | 8.92802i | −0.120815 | − | 0.285779i | ||||
\(977\) | 0.214926 | + | 0.372263i | 0.00687609 | + | 0.0119097i | 0.869443 | − | 0.494033i | \(-0.164478\pi\) |
−0.862567 | + | 0.505943i | \(0.831145\pi\) | |||||||
\(978\) | −3.66643 | − | 0.598487i | −0.117239 | − | 0.0191375i | ||||
\(979\) | −4.56710 | + | 7.91046i | −0.145965 | + | 0.252819i | ||||
\(980\) | −18.8329 | + | 56.1496i | −0.601596 | + | 1.79363i | ||||
\(981\) | 6.55918i | 0.209419i | ||||||||
\(982\) | −17.2512 | − | 45.5838i | −0.550506 | − | 1.45464i | ||||
\(983\) | −48.8806 | −1.55905 | −0.779524 | − | 0.626372i | \(-0.784539\pi\) | ||||
−0.779524 | + | 0.626372i | \(0.784539\pi\) | |||||||
\(984\) | 6.95429 | − | 4.37721i | 0.221695 | − | 0.139540i | ||||
\(985\) | 8.36573 | − | 14.4899i | 0.266554 | − | 0.461685i | ||||
\(986\) | −85.0296 | + | 32.1794i | −2.70789 | + | 1.02480i | ||||
\(987\) | −24.4421 | + | 14.1116i | −0.777999 | + | 0.449178i | ||||
\(988\) | −2.78622 | − | 13.7460i | −0.0886416 | − | 0.437319i | ||||
\(989\) | 1.36027 | − | 0.785354i | 0.0432542 | − | 0.0249728i | ||||
\(990\) | −8.19759 | − | 1.33813i | −0.260536 | − | 0.0425286i | ||||
\(991\) | 45.0902 | 1.43234 | 0.716169 | − | 0.697927i | \(-0.245894\pi\) | ||||
0.716169 | + | 0.697927i | \(0.245894\pi\) | |||||||
\(992\) | −41.1111 | − | 12.0641i | −1.30528 | − | 0.383037i | ||||
\(993\) | 5.59150 | − | 9.68477i | 0.177441 | − | 0.307337i | ||||
\(994\) | 51.9856 | − | 63.5799i | 1.64888 | − | 2.01663i | ||||
\(995\) | 23.2396 | + | 40.2522i | 0.736745 | + | 1.27608i | ||||
\(996\) | −6.03011 | + | 17.9785i | −0.191071 | + | 0.569671i | ||||
\(997\) | 22.3360 | 0.707389 | 0.353694 | − | 0.935361i | \(-0.384925\pi\) | ||||
0.353694 | + | 0.935361i | \(0.384925\pi\) | |||||||
\(998\) | −42.2734 | − | 34.5645i | −1.33814 | − | 1.09412i | ||||
\(999\) | −5.45660 | − | 9.45112i | −0.172639 | − | 0.299020i |
(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 | 804.2.j.b.499.4 | yes | 68 | |
4.3 | odd | 2 | 804.2.j.a.499.8 | ✓ | 68 | ||
67.38 | odd | 6 | 804.2.j.a.775.8 | yes | 68 | ||
268.239 | even | 6 | inner | 804.2.j.b.775.4 | yes | 68 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
804.2.j.a.499.8 | ✓ | 68 | 4.3 | odd | 2 | ||
804.2.j.a.775.8 | yes | 68 | 67.38 | odd | 6 | ||
804.2.j.b.499.4 | yes | 68 | 1.1 | even | 1 | trivial | |
804.2.j.b.775.4 | yes | 68 | 268.239 | even | 6 | inner |