Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [162,5,Mod(53,162)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(162, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("162.53");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 162.d (of order , degree , 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: | |
Analytic rank: | |
Dimension: | |
Relative dimension: | over |
Coefficient field: | |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
|
Coefficient ring: | |
Coefficient ring index: | |
Twist minimal: | yes |
Sato-Tate group: |
Embedding invariants
Embedding label | 107.4 | ||
Root | of defining polynomial | ||
Character | 162.107 | ||
Dual form | 162.5.d.d.53.4 |
-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 on generators for .
Coefficient data
For each we display the coefficients of the -expansion , the Satake parameters , and the Satake angles .
2.44949 | + | 1.41421i | 0.612372 | + | 0.353553i | |||||
0 | 0 | |||||||||
4.00000 | + | 6.92820i | 0.250000 | + | 0.433013i | |||||
−7.97262 | + | 4.60300i | −0.318905 | + | 0.184120i | −0.650904 | − | 0.759160i | ||
0.331999 | + | 0.943280i | ||||||||
0 | 0 | |||||||||
−27.2750 | + | 47.2417i | −0.556632 | + | 0.964116i | 0.441142 | + | 0.897437i | ||
−0.997775 | + | 0.0666784i | ||||||||
22.6274i | 0.353553i | |||||||||
0 | 0 | |||||||||
−26.0385 | −0.260385 | |||||||||
−34.3164 | − | 19.8126i | −0.283607 | − | 0.163740i | 0.351448 | − | 0.936207i | ||
−0.635055 | + | 0.772467i | ||||||||
0 | 0 | |||||||||
−107.873 | − | 186.842i | −0.638302 | − | 1.10557i | −0.985805 | − | 0.167893i | ||
0.347503 | − | 0.937679i | ||||||||
−133.620 | + | 77.1453i | −0.681733 | + | 0.393599i | |||||
0 | 0 | |||||||||
−32.0000 | + | 55.4256i | −0.125000 | + | 0.216506i | |||||
− | 28.2272i | − | 0.0976719i | −0.998807 | − | 0.0488360i | ||||
0.998807 | − | 0.0488360i | ||||||||
0 | 0 | |||||||||
−254.435 | −0.704805 | −0.352402 | − | 0.935849i | ||||||
−0.352402 | + | 0.935849i | ||||||||
−63.7810 | − | 36.8240i | −0.159452 | − | 0.0920599i | |||||
0 | 0 | |||||||||
−56.0385 | − | 97.0615i | −0.115782 | − | 0.200540i | |||||
−801.737 | + | 462.883i | −1.51557 | + | 0.875015i | −0.515737 | + | 0.856747i | ||
−0.999833 | + | 0.0182680i | ||||||||
0 | 0 | |||||||||
−270.125 | + | 467.870i | −0.432200 | + | 0.748592i | |||||
− | 610.222i | − | 0.902696i | |||||||
0 | 0 | |||||||||
−436.400 | −0.556632 | |||||||||
1164.65 | + | 672.411i | 1.38484 | + | 0.799537i | 0.992728 | − | 0.120381i | ||
0.392111 | + | 0.919918i | ||||||||
0 | 0 | |||||||||
−588.296 | − | 1018.96i | −0.612171 | − | 1.06031i | −0.990874 | − | 0.134793i | ||
0.378703 | − | 0.925518i | ||||||||
−156.767 | + | 90.5097i | −0.153093 | + | 0.0883883i | |||||
0 | 0 | |||||||||
39.9193 | − | 69.1422i | 0.0345322 | − | 0.0598116i | |||||
− | 502.187i | − | 0.409948i | |||||||
0 | 0 | |||||||||
−2344.80 | −1.71279 | −0.856393 | − | 0.516325i | ||||||
−0.856393 | + | 0.516325i | ||||||||
−623.235 | − | 359.825i | −0.431603 | − | 0.249186i | |||||
0 | 0 | |||||||||
−104.154 | − | 180.400i | −0.0650962 | − | 0.112750i | |||||
1257.92 | − | 726.261i | 0.748317 | − | 0.432041i | −0.0767684 | − | 0.997049i | ||
0.825086 | + | 0.565008i | ||||||||
0 | 0 | |||||||||
−837.359 | + | 1450.35i | −0.452872 | + | 0.784397i | −0.998563 | − | 0.0535896i | ||
0.545691 | + | 0.837986i | ||||||||
− | 317.001i | − | 0.163740i | |||||||
0 | 0 | |||||||||
−2618.46 | −1.23746 | |||||||||
2878.47 | + | 1661.88i | 1.30306 | + | 0.752324i | 0.980928 | − | 0.194370i | ||
0.322134 | + | 0.946694i | ||||||||
0 | 0 | |||||||||
−287.350 | − | 497.705i | −0.119679 | − | 0.207291i | |||||
−1323.34 | + | 764.028i | −0.529334 | + | 0.305611i | |||||
0 | 0 | |||||||||
862.985 | − | 1494.73i | 0.319151 | − | 0.552786i | |||||
− | 1743.30i | − | 0.620611i | −0.950637 | − | 0.310305i | ||||
0.950637 | − | 0.310305i | ||||||||
0 | 0 | |||||||||
364.789 | 0.120591 | |||||||||
−1068.96 | − | 617.163i | −0.340866 | − | 0.196799i | |||||
0 | 0 | |||||||||
1901.86 | + | 3294.13i | 0.565358 | + | 0.979229i | |||||
709.264 | − | 409.494i | 0.203753 | − | 0.117637i | −0.394652 | − | 0.918831i | ||
0.598405 | + | 0.801194i | ||||||||
0 | 0 | |||||||||
−393.925 | + | 682.298i | −0.105865 | + | 0.183364i | −0.914091 | − | 0.405508i | ||
0.808226 | + | 0.588872i | ||||||||
− | 3327.91i | − | 0.865740i | |||||||
0 | 0 | |||||||||
−512.000 | −0.125000 | |||||||||
1720.06 | + | 993.079i | 0.407115 | + | 0.235048i | |||||
0 | 0 | |||||||||
−1428.92 | − | 2474.97i | −0.318317 | − | 0.551341i | 0.661820 | − | 0.749663i | ||
−0.980137 | + | 0.198322i | ||||||||
195.564 | − | 112.909i | 0.0422932 | − | 0.0244180i | |||||
0 | 0 | |||||||||
710.199 | − | 1230.10i | 0.144939 | − | 0.251041i | |||||
7906.95i | 1.56853i | 0.620427 | + | 0.784264i | ||||||
−0.620427 | + | 0.784264i | ||||||||
0 | 0 | |||||||||
7112.40 | 1.33466 | 0.667330 | − | 0.744762i | ||||||
0.667330 | + | 0.744762i | ||||||||
−5743.57 | − | 3316.05i | −1.04886 | − | 0.605561i | |||||
0 | 0 | |||||||||
−1017.74 | − | 1762.77i | −0.176201 | − | 0.305189i | |||||
1871.96 | − | 1080.78i | 0.315729 | − | 0.182286i | |||||
0 | 0 | |||||||||
1737.80 | − | 3009.96i | 0.278449 | − | 0.482288i | −0.692550 | − | 0.721370i | ||
0.971000 | + | 0.239081i | ||||||||
− | 589.183i | − | 0.0920599i | |||||||
0 | 0 | |||||||||
4108.35 | 0.610998 | |||||||||
996.961 | + | 575.596i | 0.144718 | + | 0.0835529i | 0.570611 | − | 0.821221i | ||
−0.425893 | + | 0.904774i | ||||||||
0 | 0 | |||||||||
129.930 | + | 225.045i | 0.0179833 | + | 0.0311481i | |||||
−4102.21 | + | 2368.41i | −0.554652 | + | 0.320229i | |||||
0 | 0 | |||||||||
448.308 | − | 776.492i | 0.0578910 | − | 0.100270i | |||||
10793.5i | 1.36265i | 0.731983 | + | 0.681323i | ||||||
−0.731983 | + | 0.681323i | ||||||||
0 | 0 | |||||||||
11768.9 | 1.42120 | |||||||||
−6413.89 | − | 3703.06i | −0.757785 | − | 0.437507i | |||||
0 | 0 | |||||||||
4700.51 | + | 8141.53i | 0.531973 | + | 0.921404i | |||||
2028.51 | − | 1171.16i | 0.224766 | − | 0.129769i | |||||
0 | 0 | |||||||||
−4982.60 | + | 8630.11i | −0.529556 | + | 0.917219i | 0.469849 | + | 0.882747i | ||
−0.999406 | + | 0.0344720i | ||||||||
− | 1625.50i | − | 0.169252i | |||||||
0 | 0 | |||||||||
−4322.00 | −0.432200 | |||||||||
−8556.31 | − | 4939.99i | −0.838772 | − | 0.484265i | 0.0180748 | − | 0.999837i | ||
−0.856847 | + | 0.515572i | ||||||||
0 | 0 | |||||||||
6752.51 | + | 11695.7i | 0.636489 | + | 1.10243i | 0.986198 | + | 0.165572i | ||
−0.349709 | + | 0.936858i | ||||||||
4227.74 | − | 2440.89i | 0.390879 | − | 0.225674i | |||||
0 | 0 | |||||||||
2465.39 | − | 4270.18i | 0.219419 | − | 0.380045i | |||||
− | 9.72286i | − | 0.000849233i | −1.00000 | 0.000424616i | |||||
1.00000 | 0.000424616i | |||||||||
0 | 0 | |||||||||
18929.2 | 1.59324 | 0.796618 | − | 0.604484i | ||||||
0.796618 | + | 0.604484i | ||||||||
893.547 | + | 515.890i | 0.0738469 | + | 0.0426355i | |||||
0 | 0 | |||||||||
−1745.60 | − | 3023.47i | −0.139158 | − | 0.241029i | |||||
5106.30 | − | 2948.13i | 0.399898 | − | 0.230881i | −0.286542 | − | 0.958068i | ||
0.686440 | + | 0.727186i | ||||||||
0 | 0 | |||||||||
4261.30 | − | 7380.78i | 0.322215 | − | 0.558093i | |||||
10758.6i | 0.799537i | |||||||||
0 | 0 | |||||||||
2316.45 | 0.166363 | |||||||||
1333.50 | + | 769.896i | 0.0941670 | + | 0.0543674i | |||||
0 | 0 | |||||||||
−6535.42 | − | 11319.7i | −0.446378 | − | 0.773150i | |||||
−1929.83 | + | 1114.19i | −0.129658 | + | 0.0748581i | |||||
0 | 0 | |||||||||
4706.37 | − | 8151.67i | 0.306085 | − | 0.530155i | |||||
− | 10727.3i | − | 0.686546i | |||||||
0 | 0 | |||||||||
−20216.9 | −1.25345 | −0.626724 | − | 0.779241i | ||||||
−0.626724 | + | 0.779241i | ||||||||
−1254.14 | − | 724.077i | −0.0765466 | − | 0.0441942i | |||||
0 | 0 | |||||||||
2808.85 | + | 4865.07i | 0.166204 | + | 0.287874i | |||||
12179.1 | − | 7031.58i | 0.709694 | − | 0.409742i | −0.101254 | − | 0.994861i | ||
0.810948 | + | 0.585119i | ||||||||
0 | 0 | |||||||||
6939.70 | − | 12019.9i | 0.392317 | − | 0.679513i | |||||
− | 8083.22i | − | 0.450168i | |||||||
0 | 0 | |||||||||
638.708 | 0.0345322 | |||||||||
12773.7 | + | 7374.92i | 0.680576 | + | 0.392931i | 0.800072 | − | 0.599904i | ||
−0.119496 | + | 0.992835i | ||||||||
0 | 0 | |||||||||
7069.12 | + | 12244.1i | 0.365878 | + | 0.633719i | 0.988917 | − | 0.148472i | ||
−0.623039 | + | 0.782191i | ||||||||
3479.25 | − | 2008.75i | 0.177513 | − | 0.102487i | |||||
0 | 0 | |||||||||
−11182.1 | + | 19368.0i | −0.554559 | + | 0.960524i | |||||
8548.98i | 0.418064i | |||||||||
0 | 0 | |||||||||
−12380.4 | −0.588843 | |||||||||
17421.8 | + | 10058.5i | 0.817309 | + | 0.471873i | |||||
0 | 0 | |||||||||
−9379.22 | − | 16245.3i | −0.428196 | − | 0.741658i | |||||
−9451.21 | + | 5456.66i | −0.425711 | + | 0.245784i | −0.697518 | − | 0.716567i | ||
0.271807 | + | 0.962352i | ||||||||
0 | 0 | |||||||||
−1394.36 | + | 2415.10i | −0.0611534 | + | 0.105921i | −0.894981 | − | 0.446104i | ||
0.833828 | + | 0.552025i | ||||||||
− | 5757.20i | − | 0.249186i | |||||||
0 | 0 | |||||||||
6113.80 | 0.257792 | |||||||||
9380.53 | + | 5415.85i | 0.390449 | + | 0.225426i | |||||
0 | 0 | |||||||||
1238.42 | + | 2145.01i | 0.0502423 | + | 0.0870222i | 0.890053 | − | 0.455857i | ||
−0.839811 | + | 0.542880i | ||||||||
8513.46 | − | 4915.25i | 0.341029 | − | 0.196893i | |||||
0 | 0 | |||||||||
833.231 | − | 1443.20i | 0.0325481 | − | 0.0563750i | |||||
− | 50500.5i | − | 1.94825i | |||||||
0 | 0 | |||||||||
−35547.0 | −1.33791 | −0.668957 | − | 0.743301i | ||||||
−0.668957 | + | 0.743301i | ||||||||
10063.4 | + | 5810.09i | 0.374159 | + | 0.216021i | |||||
0 | 0 | |||||||||
1628.03 | + | 2819.83i | 0.0590808 | + | 0.102331i | |||||
−45892.8 | + | 26496.2i | −1.64555 | + | 0.950060i | −0.666743 | + | 0.745287i | ||
−0.978810 | + | 0.204773i | ||||||||
0 | 0 | |||||||||
−8992.70 | + | 15575.8i | −0.314859 | + | 0.545352i | |||||
734.993i | 0.0254323i | |||||||||
0 | 0 | |||||||||
−13397.8 | −0.452872 | |||||||||
−46242.8 | − | 26698.3i | −1.54508 | − | 0.892054i | −0.998506 | − | 0.0546443i | ||
−0.546576 | − | 0.837409i | ||||||||
0 | 0 | |||||||||
−14735.3 | − | 25522.3i | −0.481153 | − | 0.833381i | |||||
2196.25 | − | 1268.01i | 0.0709017 | − | 0.0409351i | |||||
0 | 0 | |||||||||
−15264.3 | + | 26438.6i | −0.481768 | + | 0.834447i | |||||
32448.3i | 1.01271i | 0.862324 | + | 0.506356i | ||||||
−0.862324 | + | 0.506356i | ||||||||
0 | 0 | |||||||||
−50381.3 | −1.53784 | −0.768921 | − | 0.639344i | ||||||
−0.768921 | + | 0.639344i | ||||||||
28827.9 | + | 16643.8i | 0.870303 | + | 0.502470i | |||||
0 | 0 | |||||||||
−10473.8 | − | 18141.2i | −0.309364 | − | 0.535835i | |||||
18694.2 | − | 10793.1i | 0.546216 | − | 0.315358i | |||||
0 | 0 | |||||||||
−559.254 | + | 968.656i | −0.0159928 | + | 0.0277004i | |||||
26590.1i | 0.752324i | |||||||||
0 | 0 | |||||||||
6625.09 | 0.183520 | |||||||||
1953.74 | + | 1127.99i | 0.0535551 | + | 0.0309201i | 0.526538 | − | 0.850151i | ||
−0.472983 | + | 0.881071i | ||||||||
0 | 0 | |||||||||
−12016.0 | − | 20812.3i | −0.322586 | − | 0.558736i | 0.658435 | − | 0.752638i | ||
−0.981021 | + | 0.193902i | ||||||||
−24409.6 | + | 14092.9i | −0.648572 | + | 0.374453i | |||||
0 | 0 | |||||||||
2298.80 | − | 3981.64i | 0.0598397 | − | 0.103645i | |||||
− | 66824.6i | − | 1.72189i | −0.508702 | − | 0.860943i | ||||
0.508702 | − | 0.860943i | ||||||||
0 | 0 | |||||||||
−8425.29 | −0.212754 | −0.106377 | − | 0.994326i | ||||||
−0.106377 | + | 0.994326i | ||||||||
−10586.7 | − | 6112.23i | −0.264667 | − | 0.152806i | |||||
0 | 0 | |||||||||
−13972.4 | − | 24200.9i | −0.342427 | − | 0.593101i | |||||
−63531.6 | + | 36680.0i | −1.54169 | + | 0.890097i | |||||
0 | 0 | |||||||||
−6685.95 | + | 11580.4i | −0.159095 | + | 0.275560i | |||||
38197.9i | 0.900131i | |||||||||
0 | 0 | |||||||||
13807.8 | 0.319151 | |||||||||
8731.28 | + | 5041.01i | 0.199887 | + | 0.115405i | |||||
0 | 0 | |||||||||
16850.0 | + | 29185.0i | 0.378473 | + | 0.655534i | 0.990840 | − | 0.135039i | ||
−0.612367 | + | 0.790573i | ||||||||
12077.9 | − | 6973.18i | 0.268732 | − | 0.155153i | |||||
0 | 0 | |||||||||
13.7502 | − | 23.8161i | 0.000300249 | − | 0.000520047i | |||||
− | 15417.4i | − | 0.333531i | |||||||
0 | 0 | |||||||||
64183.1 | 1.36302 | |||||||||
46367.0 | + | 26770.0i | 0.975653 | + | 0.563294i | |||||
0 | 0 | |||||||||
1459.16 | + | 2527.33i | 0.0301479 | + | 0.0522176i | |||||
−5274.01 | + | 3044.95i | −0.107983 | + | 0.0623442i | |||||
0 | 0 | |||||||||
10265.6 | − | 17780.6i | 0.206432 | − | 0.357550i | −0.744156 | − | 0.668006i | ||
0.950588 | + | 0.310455i | ||||||||
− | 9874.60i | − | 0.196799i | |||||||
0 | 0 | |||||||||
16677.1 | 0.326516 | |||||||||
−50720.2 | − | 29283.3i | −0.984305 | − | 0.568289i | −0.0807378 | − | 0.996735i | ||
−0.903567 | + | 0.428447i | ||||||||
0 | 0 | |||||||||
3644.28 | + | 6312.07i | 0.0694929 | + | 0.120365i | 0.898678 | − | 0.438609i | ||
−0.829185 | + | 0.558974i | ||||||||
20876.0 | − | 12052.8i | 0.394631 | − | 0.227841i | |||||
0 | 0 | |||||||||
−15214.9 | + | 26353.0i | −0.282679 | + | 0.489615i | |||||
13584.9i | 0.250232i | 0.992142 | + | 0.125116i | ||||||
−0.992142 | + | 0.125116i | ||||||||
0 | 0 | |||||||||
−30598.6 | −0.554071 | |||||||||
5674.11 | + | 3275.95i | 0.101876 | + | 0.0588184i | |||||
0 | 0 | |||||||||
2177.60 | + | 3771.71i | 0.0384435 | + | 0.0665862i | |||||
22418.8 | − | 12943.5i | 0.392479 | − | 0.226598i | −0.290755 | − | 0.956798i | ||
0.683234 | + | 0.730200i | ||||||||
0 | 0 | |||||||||
4680.48 | − | 8106.84i | 0.0805855 | − | 0.139578i | −0.822916 | − | 0.568163i | ||
0.903502 | + | 0.428585i | ||||||||
− | 36969.9i | − | 0.631274i | |||||||
0 | 0 | |||||||||
−6302.80 | −0.105865 | |||||||||
4581.87 | + | 2645.34i | 0.0763327 | + | 0.0440707i | |||||
0 | 0 | |||||||||
27446.6 | + | 47539.0i | 0.449878 | + | 0.779212i | |||||
23056.4 | − | 13311.6i | 0.374877 | − | 0.216435i | |||||
0 | 0 | |||||||||
15170.7 | − | 26276.4i | 0.242731 | − | 0.420422i | |||||
109546.i | 1.73879i | 0.494117 | + | 0.869396i | ||||||
−0.494117 | + | 0.869396i | ||||||||
0 | 0 | |||||||||
36683.6 | 0.573101 | |||||||||
−49521.0 | − | 28591.0i | −0.767577 | − | 0.443161i | |||||
0 | 0 | |||||||||
−2048.00 | − | 3547.24i | −0.0312500 | − | 0.0541266i | |||||
83266.7 | − | 48074.1i | 1.26068 | − | 0.727855i | 0.287475 | − | 0.957788i | ||
0.973206 | + | 0.229933i | ||||||||
0 | 0 | |||||||||
63954.5 | − | 110772.i | 0.953392 | − | 1.65132i | |||||
15889.3i | 0.235048i | |||||||||
0 | 0 | |||||||||
39776.6 | 0.579463 | |||||||||
11913.5 | + | 6878.28i | 0.172238 | + | 0.0994417i | 0.583641 | − | 0.812012i | ||
−0.411403 | + | 0.911454i | ||||||||
0 | 0 | |||||||||
8024.38 | + | 13898.6i | 0.114267 | + | 0.197916i | |||||
33997.4 | − | 19628.4i | 0.480489 | − | 0.277410i | |||||
0 | 0 | |||||||||
11431.4 | − | 19799.8i | 0.159158 | − | 0.275670i | |||||
− | 65136.7i | − | 0.900163i | −0.892988 | − | 0.450081i | ||||
0.892988 | − | 0.450081i | ||||||||
0 | 0 | |||||||||
9569.63 | 0.130304 | 0.0651518 | − | 0.997875i | ||||||
0.0651518 | + | 0.997875i | ||||||||
1564.51 | + | 903.270i | 0.0211466 | + | 0.0122090i | |||||
0 | 0 | |||||||||
20859.4 | + | 36129.6i | 0.277844 | + | 0.481240i | |||||
18539.4 | − | 10703.7i | 0.245150 | − | 0.141537i | |||||
0 | 0 | |||||||||
−22168.3 | + | 38396.6i | −0.288916 | + | 0.500418i | −0.973551 | − | 0.228468i | ||
0.684635 | + | 0.728886i | ||||||||
39989.0i | 0.517429i | |||||||||
0 | 0 | |||||||||
11363.2 | 0.144939 | |||||||||
−105192. | − | 60732.4i | −1.33220 | − | 0.769145i | −0.346561 | − | 0.938027i | ||
−0.985636 | + | 0.168883i | ||||||||
0 | 0 | |||||||||
58191.1 | + | 100790.i | 0.726581 | + | 1.25848i | 0.958320 | + | 0.285697i | ||
−0.231739 | + | 0.972778i | ||||||||
−54781.0 | + | 31627.8i | −0.679193 | + | 0.392132i | |||||
0 | 0 | |||||||||
−12090.1 | + | 20940.6i | −0.147808 | + | 0.256011i | |||||
79235.1i | 0.961952i | |||||||||
0 | 0 | |||||||||
82724.2 | 0.990460 | |||||||||
−30325.7 | − | 17508.6i | −0.360591 | − | 0.208187i | |||||
0 | 0 | |||||||||
28449.6 | + | 49276.2i | 0.333665 | + | 0.577925i | |||||
137541. | − | 79409.4i | 1.60213 | − | 0.924990i | 0.611068 | − | 0.791578i | ||
0.991061 | − | 0.133412i | ||||||||
0 | 0 | |||||||||
−3769.79 | + | 6529.47i | −0.0433185 | + | 0.0750299i | |||||
− | 53056.9i | − | 0.605561i | |||||||
0 | 0 | |||||||||
−30867.5 | −0.347592 | |||||||||
172972. | + | 99865.2i | 1.93478 | + | 1.11705i | |||||
0 | 0 | |||||||||
−45677.9 | − | 79116.5i | −0.504166 | − | 0.873241i | |||||
−6830.94 | + | 3943.84i | −0.0748973 | + | 0.0432420i | |||||
0 | 0 | |||||||||
8141.91 | − | 14102.2i | 0.0881006 | − | 0.152595i | |||||
− | 7252.94i | − | 0.0779676i | |||||||
0 | 0 | |||||||||
100162. | 1.06274 | 0.531370 | − | 0.847140i | ||||||
0.531370 | + | 0.847140i | ||||||||
14975.7 | + | 8646.21i | 0.157865 | + | 0.0911432i | |||||
0 | 0 | |||||||||
15318.3 | + | 26532.1i | 0.159400 | + | 0.276089i | |||||
−46738.2 | + | 26984.3i | −0.483227 | + | 0.278991i | −0.721760 | − | 0.692143i | ||
0.238534 | + | 0.971134i | ||||||||
0 | 0 | |||||||||
−37756.9 | + | 65396.9i | −0.385396 | + | 0.667526i | −0.991824 | − | 0.127613i | ||
0.606428 | + | 0.795139i | ||||||||
7005.58i | 0.0710534i | |||||||||
0 | 0 | |||||||||
27804.8 | 0.278449 | |||||||||
−57648.6 | − | 33283.4i | −0.573680 | − | 0.331215i | 0.184938 | − | 0.982750i | ||
−0.758618 | + | 0.651536i | ||||||||
0 | 0 | |||||||||
−26644.4 | − | 46149.5i | −0.261833 | − | 0.453508i | |||||
4081.98 | − | 2356.73i | 0.0398631 | − | 0.0230150i | |||||
0 | 0 | |||||||||
71418.5 | − | 123700.i | 0.688809 | − | 1.19305i | |||||
7181.97i | 0.0688397i | |||||||||
0 | 0 | |||||||||
116557. | 1.10350 | |||||||||
−87072.1 | − | 50271.1i | −0.819302 | − | 0.473024i | |||||
0 | 0 | |||||||||
16433.4 | + | 28463.5i | 0.152750 | + | 0.264570i | |||||
−157020. | + | 90655.7i | −1.45065 | + | 0.837535i | |||||
0 | 0 | |||||||||
34710.1 | − | 60119.7i | 0.316811 | − | 0.548732i | −0.663010 | − | 0.748611i | ||
0.979821 | + | 0.199878i | ||||||||
9209.53i | 0.0835529i | |||||||||
0 | 0 | |||||||||
−149885. | −1.34359 | |||||||||
22784.5 | + | 13154.7i | 0.203026 | + | 0.117217i | |||||
0 | 0 | |||||||||
−44393.0 | − | 76890.9i | −0.390890 | − | 0.677041i | 0.601677 | − | 0.798739i | ||
−0.992567 | + | 0.121698i | ||||||||
−44055.0 | + | 25435.2i | −0.385622 | + | 0.222639i | |||||
0 | 0 | |||||||||
−1039.44 | + | 1800.36i | −0.00899167 | + | 0.0155740i | |||||
46622.7i | 0.400948i | |||||||||
0 | 0 | |||||||||
−99624.6 | −0.846795 | |||||||||
−32817.7 | − | 18947.3i | −0.277326 | − | 0.160114i | |||||
0 | 0 | |||||||||
−75514.1 | − | 130794.i | −0.630777 | − | 1.09254i | |||||
95033.8 | − | 54867.8i | 0.789259 | − | 0.455679i | −0.0504428 | − | 0.998727i | ||
0.839701 | + | 0.543048i | ||||||||
0 | 0 | |||||||||
−69389.6 | + | 120186.i | −0.569696 | + | 0.986743i | 0.426899 | + | 0.904299i | ||
−0.996596 | + | 0.0824438i | ||||||||
− | 83355.5i | − | 0.680453i | |||||||
0 | 0 | |||||||||
7172.92 | 0.0578910 | |||||||||
67397.6 | + | 38912.0i | 0.540873 | + | 0.312273i | 0.745433 | − | 0.666581i | ||
−0.204560 | + | 0.978854i | ||||||||
0 | 0 | |||||||||
−36395.7 | − | 63039.2i | −0.288797 | − | 0.500212i | |||||
−74779.7 | + | 43174.1i | −0.590043 | + | 0.340662i | |||||
0 | 0 | |||||||||
−45888.9 | + | 79481.8i | −0.358048 | + | 0.620157i | |||||
195283.i | 1.51522i | 0.652708 | + | 0.757610i | ||||||
−0.652708 | + | 0.757610i | ||||||||
0 | 0 | |||||||||
−65584.1 | −0.503250 | |||||||||
−123408. | − | 71249.8i | −0.941732 | − | 0.543709i | |||||
0 | 0 | |||||||||
47075.8 | + | 81537.7i | 0.355300 | + | 0.615397i | |||||
−56704.5 | + | 32738.4i | −0.425630 | + | 0.245737i | |||||
0 | 0 | |||||||||
−42902.7 | + | 74309.6i | −0.318531 | + | 0.551713i | −0.980182 | − | 0.198100i | ||
0.661650 | + | 0.749812i | ||||||||
− | 59249.0i | − | 0.437507i | |||||||
0 | 0 | |||||||||
61055.1 | 0.445983 | |||||||||
82356.2 | + | 47548.4i | 0.598340 | + | 0.345452i | |||||
0 | 0 | |||||||||
−6159.02 | − | 10667.7i | −0.0442684 | − | 0.0766751i | 0.843042 | − | 0.537847i | ||
−0.887311 | + | 0.461172i | ||||||||
−2739.77 | + | 1581.81i | −0.0195872 | + | 0.0113086i | |||||
0 | 0 | |||||||||
−37604.1 | + | 65132.2i | −0.265987 | + | 0.460702i | |||||
− | 290140.i | − | 2.04139i | |||||||
0 | 0 | |||||||||
−216174. | −1.50496 | −0.752479 | − | 0.658617i | ||||||
−0.752479 | + | 0.658617i | ||||||||
16228.1 | + | 9369.29i | 0.112383 | + | 0.0648843i | |||||
0 | 0 | |||||||||
3190.45 | + | 5526.02i | 0.0218638 | + | 0.0378692i | |||||
−205867. | + | 118857.i | −1.40342 | + | 0.810266i | −0.994742 | − | 0.102411i | ||
−0.408680 | + | 0.912678i | ||||||||
0 | 0 | |||||||||
−9949.62 | + | 17233.2i | −0.0671251 | + | 0.116264i | |||||
− | 67972.8i | − | 0.456206i | |||||||
0 | 0 | |||||||||
−79721.5 | −0.529556 | |||||||||
161345. | + | 93152.6i | 1.06624 | + | 0.615596i | 0.927153 | − | 0.374684i | ||
0.139091 | + | 0.990280i | ||||||||
0 | 0 | |||||||||
13065.9 | + | 22630.8i | 0.0854644 | + | 0.148029i | |||||
11261.8 | − | 6501.99i | 0.0732884 | − | 0.0423131i | |||||
0 | 0 | |||||||||
94504.3 | − | 163686.i | 0.608778 | − | 1.05444i | |||||
31996.4i | 0.205072i | |||||||||
0 | 0 | |||||||||
5004.70 | 0.0317539 | 0.0158769 | − | 0.999874i | ||||||
0.0158769 | + | 0.999874i | ||||||||
−20637.7 | − | 11915.2i | −0.130285 | − | 0.0752200i | |||||
0 | 0 | |||||||||
−17288.0 | − | 29943.7i | −0.108050 | − | 0.187148i | |||||
152835. | − | 88239.4i | 0.950461 | − | 0.548749i | 0.0572371 | − | 0.998361i | ||
0.893224 | + | 0.449612i | ||||||||
0 | 0 | |||||||||
−126923. | + | 219836.i | −0.781500 | + | 1.35360i | |||||
− | 79039.8i | − | 0.484265i | |||||||
0 | 0 | |||||||||
−207493. | −1.25879 | |||||||||
80465.3 | + | 46456.6i | 0.485758 | + | 0.280452i | |||||
0 | 0 | |||||||||
−94356.8 | − | 163431.i | −0.564062 | − | 0.976984i | −0.997136 | − | 0.0756254i | ||
0.433075 | − | 0.901358i | ||||||||
−32754.3 | + | 18910.7i | −0.194850 | + | 0.112497i | |||||
0 | 0 | |||||||||
−54020.1 | + | 93565.5i | −0.318244 | + | 0.551215i | |||||
44675.7i | 0.261922i | |||||||||
0 | 0 | |||||||||
−10597.9 | −0.0615349 | |||||||||
33821.9 | + | 19527.1i | 0.195439 | + | 0.112837i | |||||
0 | 0 | |||||||||
14258.1 | + | 24695.8i | 0.0816037 | + | 0.141342i | |||||
−10397.0 | + | 6002.70i | −0.0592215 | + | 0.0341915i | −0.529318 | − | 0.848423i | ||
0.470097 | + | 0.882615i | ||||||||
0 | 0 | |||||||||
27797.6 | − | 48146.8i | 0.156835 | − | 0.271646i | −0.776891 | − | 0.629635i | ||
0.933726 | + | 0.357989i | ||||||||
95317.9i | 0.535241i | |||||||||
0 | 0 | |||||||||
39446.3 | 0.219419 | |||||||||
13206.7 | + | 7624.87i | 0.0731164 | + | 0.0422138i | |||||
0 | 0 | |||||||||
−21488.6 | − | 37219.3i | −0.117856 | − | 0.204133i | |||||
67.3620 | − | 38.8915i | 0.000367728 | − | 0.000212308i | |||||
0 | 0 | |||||||||
21803.6 | − | 37764.9i | 0.117921 | − | 0.204245i | |||||
− | 52071.6i | − | 0.280315i | −0.990129 | − | 0.140158i | ||||
0.990129 | − | 0.140158i | ||||||||
0 | 0 | |||||||||
−205361. | −1.09532 | −0.547662 | − | 0.836700i | ||||||
−0.547662 | + | 0.836700i | ||||||||
157216. | + | 90768.6i | 0.834674 | + | 0.481899i | |||||
0 | 0 | |||||||||
75716.9 | + | 131146.i | 0.398309 | + | 0.689891i | |||||
203990. | − | 117773.i | 1.06818 | − | 0.616715i | |||||
0 | 0 | |||||||||
162282. | − | 281081.i | 0.842058 | − | 1.45849i | −0.0460931 | − | 0.998937i | ||
0.888152 | − | 0.459551i | ||||||||
8254.24i | 0.0426355i | |||||||||
0 | 0 | |||||||||
−17224.9 | −0.0881680 | |||||||||
−148975. | − | 86010.6i | −0.759111 | − | 0.438273i | 0.0698657 | − | 0.997556i | ||
−0.828976 | + | 0.559284i | ||||||||
0 | 0 | |||||||||
−49682.5 | − | 86052.7i | −0.250890 | − | 0.434555i | |||||
50291.2 | − | 29035.6i | 0.252826 | − | 0.145969i | |||||
0 | 0 | |||||||||
13964.8 | − | 24187.7i | 0.0695791 | − | 0.120514i | |||||
− | 121635.i | − | 0.603345i | −0.953412 | − | 0.301672i | ||||
0.953412 | − | 0.301672i | ||||||||
0 | 0 | |||||||||
−57556.5 | −0.282970 | |||||||||
40850.4 | + | 23585.0i | 0.199949 | + | 0.115441i | |||||
0 | 0 | |||||||||
−82825.8 | − | 143459.i | −0.401841 | − | 0.696009i | |||||
−93829.4 | + | 54172.4i | −0.453227 | + | 0.261671i | |||||
0 | 0 | |||||||||
−23274.4 | + | 40312.4i | −0.111441 | + | 0.193022i | −0.916352 | − | 0.400375i | ||
0.804910 | + | 0.593396i | ||||||||
20615.1i | 0.0982778i | |||||||||
0 | 0 | |||||||||
68180.7 | 0.322215 | |||||||||
176904. | + | 102136.i | 0.832409 | + | 0.480591i | 0.854677 | − | 0.519161i | ||
−0.0222679 | + | 0.999752i | ||||||||
0 | 0 | |||||||||
8635.53 | + | 14957.2i | 0.0402835 | + | 0.0697731i | 0.885464 | − | 0.464708i | ||
−0.845181 | + | 0.534481i | ||||||||
−74537.6 | + | 43034.3i | −0.346210 | + | 0.199884i | |||||
0 | 0 | |||||||||
−19211.9 | + | 33276.0i | −0.0884705 | + | 0.153235i | |||||
− | 219664.i | − | 1.00722i | −0.863930 | − | 0.503611i | ||||
0.863930 | − | 0.503611i | ||||||||
0 | 0 | |||||||||
155896. | 0.708742 | |||||||||
−74950.9 | − | 43272.9i | −0.339298 | − | 0.195894i | |||||
0 | 0 | |||||||||
9265.78 | + | 16048.8i | 0.0415909 | + | 0.0720375i | |||||
57470.4 | − | 33180.5i | 0.256875 | − | 0.148307i | |||||
0 | 0 | |||||||||
68729.1 | − | 119042.i | 0.304617 | − | 0.527611i | |||||
12318.3i | 0.0543674i | |||||||||
0 | 0 | |||||||||
73219.4 | 0.320457 | |||||||||
−78854.6 | − | 45526.7i | −0.343682 | − | 0.198425i | 0.318217 | − | 0.948018i | ||
−0.661899 | + | 0.749593i | ||||||||
0 | 0 | |||||||||
252941. | + | 438107.i | 1.09327 | + | 1.89361i | |||||
22929.6 | − | 13238.4i | 0.0986966 | − | 0.0569825i | |||||
0 | 0 | |||||||||
52283.4 | − | 90557.5i | 0.223189 | − | 0.386575i | |||||
− | 91739.5i | − | 0.390007i | |||||||
0 | 0 | |||||||||
146600. | 0.618126 | 0.309063 | − | 0.951042i | ||||||
0.309063 | + | 0.951042i | ||||||||
−15438.6 | − | 8913.50i | −0.0648290 | − | 0.0374290i | |||||
0 | 0 | |||||||||
7482.16 | + | 12959.5i | 0.0311627 | + | 0.0539754i | |||||
41966.3 | − | 24229.2i | 0.174075 | − | 0.100502i | −0.410431 | − | 0.911892i | ||
0.584506 | + | 0.811389i | ||||||||
0 | 0 | |||||||||
18980.3 | − | 32874.8i | 0.0780924 | − | 0.135260i | |||||
155262.i | 0.636224i | |||||||||
0 | 0 | |||||||||
75301.9 | 0.306085 | |||||||||
−373538. | − | 215662.i | −1.51224 | − | 0.873094i | |||||
0 | 0 | |||||||||
124007. | + | 214786.i | 0.498016 | + | 0.862590i | 0.999997 | − | 0.00228889i | ||
−0.501981 | + | 0.864879i | ||||||||
74320.8 | − | 42909.1i | 0.297283 | − | 0.171636i | |||||
0 | 0 | |||||||||
−154921. | + | 268331.i | −0.614755 | + | 1.06479i | |||||
486322.i | 1.92215i | 0.276286 | + | 0.961076i | ||||||
−0.276286 | + | 0.961076i | ||||||||
0 | 0 | |||||||||
90955.0 | 0.356651 | |||||||||
89856.2 | + | 51878.5i | 0.350951 | + | 0.202622i | |||||
0 | 0 | |||||||||
−80867.4 | − | 140066.i | −0.313362 | − | 0.542759i | |||||
−246292. | + | 142196.i | −0.950635 | + | 0.548850i | −0.893278 | − | 0.449504i | ||
−0.0573571 | + | 0.998354i | ||||||||
0 | 0 | |||||||||
−193991. | + | 336002.i | −0.742915 | + | 1.28677i | |||||
− | 11585.2i | − | 0.0441942i | |||||||
0 | 0 | |||||||||
271948. | 1.02934 | |||||||||
−107670. | − | 62163.5i | −0.405959 | − | 0.234380i | |||||
0 | 0 | |||||||||
−65852.4 | − | 114060.i | −0.246372 | − | 0.426728i | |||||
313312. | − | 180891.i | 1.16766 | − | 0.674150i | |||||
0 | 0 | |||||||||
−22470.8 | + | 38920.6i | −0.0831021 | + | 0.143937i | |||||
248390.i | 0.915079i | 0.889189 | + | 0.457539i | ||||||
−0.889189 | + | 0.457539i | ||||||||
0 | 0 | |||||||||
113565. | 0.415186 | 0.207593 | − | 0.978215i | ||||||
0.207593 | + | 0.978215i | ||||||||
97432.5 | + | 56252.7i | 0.354847 | + | 0.204871i | |||||
0 | 0 | |||||||||
19454.7 | + | 33696.6i | 0.0703159 | + | 0.121791i | |||||
−28762.3 | + | 16605.9i | −0.103563 | + | 0.0597919i | |||||
0 | 0 | |||||||||
288601. | − | 499871.i | 1.03130 | − | 1.78627i | |||||
45392.8i | 0.161598i | |||||||||
0 | 0 | |||||||||
111035. | 0.392317 | |||||||||
−271392. | − | 156688.i | −0.955305 | − | 0.551546i | |||||
0 | 0 | |||||||||
44.7543 | + | 77.5167i | 0.000156361 | + | 0.000270824i | |||||
56002.2 | − | 32332.9i | 0.194928 | − | 0.112542i | |||||
0 | 0 | |||||||||
92117.2 | − | 159552.i | 0.318256 | − | 0.551235i | |||||
22772.6i | 0.0783854i | |||||||||
0 | 0 | |||||||||
68803.4 | 0.235080 | 0.117540 | − | 0.993068i | ||||||
0.117540 | + | 0.993068i | ||||||||
23440.7 | + | 13533.5i | 0.0797943 | + | 0.0460693i | |||||
0 | 0 | |||||||||
2554.83 | + | 4425.10i | 0.00863306 | + | 0.0149529i | |||||
−150916. | + | 87131.2i | −0.508091 | + | 0.293346i | |||||
0 | 0 | |||||||||
70749.2 | − | 122541.i | 0.236454 | − | 0.409551i | −0.723240 | − | 0.690597i | ||
0.959694 | + | 0.281046i | ||||||||
117999.i | 0.392931i | |||||||||
0 | 0 | |||||||||
60549.5 | 0.200164 | |||||||||
−296327. | − | 171085.i | −0.976041 | − | 0.563518i | |||||
0 | 0 | |||||||||
94797.1 | + | 164193.i | 0.309988 | + | 0.536915i | |||||
−108602. | + | 62701.3i | −0.353849 | + | 0.204295i | |||||
0 | 0 | |||||||||
−56553.0 | + | 97952.7i | −0.182939 | + | 0.316859i | |||||
59163.4i | 0.190697i | 0.995444 | + | 0.0953483i | ||||||
−0.995444 | + | 0.0953483i | ||||||||
0 | 0 | |||||||||
361314. | 1.15628 | |||||||||
27834.0 | + | 16070.0i | 0.0887564 | + | 0.0512435i | |||||
0 | 0 | |||||||||
−171777. | − | 297527.i | −0.543867 | − | 0.942006i | |||||
359369. | − | 207482.i | 1.13377 | − | 0.654580i | 0.188886 | − | 0.981999i | ||
0.944879 | + | 0.327419i | ||||||||
0 | 0 | |||||||||
−27140.4 | + | 47008.6i | −0.0850197 | + | 0.147258i | |||||
329179.i | 1.02754i | |||||||||
0 | 0 | |||||||||
−178914. | −0.554559 | |||||||||
−229601. | − | 132560.i | −0.709169 | − | 0.409439i | 0.101584 | − | 0.994827i | ||
−0.810753 | + | 0.585388i | ||||||||
0 | 0 | |||||||||
16370.1 | + | 28353.8i | 0.0502086 | + | 0.0869639i | 0.890037 | − | 0.455887i | ||
−0.839829 | + | 0.542851i | ||||||||
−59229.1 | + | 34195.9i | −0.181027 | + | 0.104516i | |||||
0 | 0 | |||||||||
−112055. | + | 194085.i | −0.340102 | + | 0.589073i | |||||
− | 500145.i | − | 1.51272i | |||||||
0 | 0 | |||||||||
136483. | 0.409946 | 0.204973 | − | 0.978768i | ||||||
0.204973 | + | 0.978768i | ||||||||
202632. | + | 116990.i | 0.606531 | + | 0.350181i | |||||
0 | 0 | |||||||||
−49521.7 | − | 85774.0i | −0.147211 | − | 0.254976i | |||||
−54384.2 | + | 31398.7i | −0.161109 | + | 0.0930165i | |||||
0 | 0 | |||||||||
−34539.2 | + | 59823.7i | −0.101619 | + | 0.176009i | |||||
160935.i | 0.471873i | |||||||||
0 | 0 | |||||||||
449208. | 1.30813 | |||||||||
249463. | + | 144027.i | 0.723984 | + | 0.417992i | 0.816217 | − | 0.577745i | ||
−0.0922331 | + | 0.995737i | ||||||||
0 | 0 | |||||||||
149683. | + | 259258.i | 0.431461 | + | 0.747312i | |||||
−18468.1 | + | 10662.6i | −0.0530541 | + | 0.0306308i | |||||
0 | 0 | |||||||||
75033.7 | − | 129962.i | 0.214098 | − | 0.370829i | |||||
272778.i | 0.775711i | 0.921720 | + | 0.387856i | ||||||
−0.921720 | + | 0.387856i | ||||||||
0 | 0 | |||||||||
−14175.3 | −0.0400404 | |||||||||
−75609.7 | − | 43653.3i | −0.212856 | − | 0.122892i | |||||
0 | 0 | |||||||||
282461. | + | 489238.i | 0.789872 | + | 1.36810i | |||||
−68974.2 | + | 39822.3i | −0.192235 | + | 0.110987i | −0.593029 | − | 0.805181i | ||
0.400793 | + | 0.916169i | ||||||||
0 | 0 | |||||||||
−59878.8 | + | 103713.i | −0.165777 | + | 0.287134i | −0.936931 | − | 0.349515i | ||
0.771154 | + | 0.636649i | ||||||||
− | 258393.i | − | 0.712998i | |||||||
0 | 0 | |||||||||
−22309.7 | −0.0611534 | |||||||||
104209. | + | 60165.0i | 0.284704 | + | 0.164374i | |||||
0 | 0 | |||||||||
−57220.1 | − | 99108.1i | −0.155300 | − | 0.268987i | 0.777868 | − | 0.628427i | ||
−0.933168 | + | 0.359440i | ||||||||
39887.0 | − | 23028.8i | 0.107901 | − | 0.0622965i | |||||
0 | 0 | |||||||||
10257.2 | − | 17766.0i | 0.0275657 | − | 0.0477452i | |||||
− | 717090.i | − | 1.92084i | |||||||
0 | 0 | |||||||||
−598912. | −1.59383 | −0.796915 | − | 0.604091i | ||||||
−0.796915 | + | 0.604091i | ||||||||
245346. | + | 141651.i | 0.650793 | + | 0.375735i | |||||
0 | 0 | |||||||||
24455.2 | + | 42357.6i | 0.0644480 | + | 0.111627i | |||||
−150704. | + | 87008.9i | −0.395871 | + | 0.228556i | −0.684701 | − | 0.728824i | ||
0.288830 | + | 0.957381i | ||||||||
0 | 0 | |||||||||
368424. | − | 638130.i | 0.961540 | − | 1.66544i | 0.242902 | − | 0.970051i | ||
0.718638 | − | 0.695384i | ||||||||
86653.6i | 0.225426i | |||||||||
0 | 0 | |||||||||
−152646. | −0.394553 | |||||||||
−509904. | − | 294393.i | −1.31375 | − | 0.758493i | |||||
0 | 0 | |||||||||
−119450. | − | 206894.i | −0.305793 | − | 0.529649i | |||||
−184970. | + | 106793.i | −0.472012 | + | 0.272516i | |||||
0 | 0 | |||||||||
−9907.38 | + | 17160.1i | −0.0251212 | + | 0.0435111i | |||||
66187.2i | 0.167291i | |||||||||
0 | 0 | |||||||||
−26188.6 | −0.0657739 | −0.0328869 | − | 0.999459i | ||||||
−0.0328869 | + | 0.999459i | ||||||||
68107.6 | + | 39322.0i | 0.170515 | + | 0.0984467i | |||||
0 | 0 | |||||||||
−94139.7 | − | 163055.i | −0.234204 | − | 0.405653i | |||||
161181. | − | 93058.1i | 0.399731 | − | 0.230785i | |||||
0 | 0 | |||||||||
−61994.7 | + | 107378.i | −0.152783 | + | 0.264628i | |||||
− | 150724.i | − | 0.370288i | |||||||
0 | 0 | |||||||||
13331.7 | 0.0325481 | |||||||||
343687. | + | 198428.i | 0.836462 | + | 0.482932i | 0.856060 | − | 0.516876i | ||
−0.0195978 | + | 0.999808i | ||||||||
0 | 0 | |||||||||
32175.0 | + | 55728.7i | 0.0778209 | + | 0.134790i | 0.902309 | − | 0.431089i | ||
−0.824489 | + | 0.565879i | ||||||||
349878. | − | 202002.i | 0.843616 | − | 0.487062i | |||||
0 | 0 | |||||||||
−10156.8 | + | 17592.2i | −0.0243385 | + | 0.0421555i | |||||
16209.2i | 0.0387215i | 0.999813 | + | 0.0193607i | ||||||
−0.999813 | + | 0.0193607i | ||||||||
0 | 0 | |||||||||
−32452.5 | −0.0770476 | |||||||||
285505. | + | 164836.i | 0.675751 | + | 0.390145i | |||||
0 | 0 | |||||||||
−142188. | − | 246277.i | −0.334478 | − | 0.579334i | |||||
96132.7 | − | 55502.2i | 0.225447 | − | 0.130162i | −0.383023 | − | 0.923739i | ||
0.608470 | + | 0.793577i | ||||||||
0 | 0 | |||||||||
−64732.7 | + | 112120.i | −0.150883 | + | 0.261337i | |||||
92961.4i | 0.216021i | |||||||||
0 | 0 | |||||||||
−512826. | −1.18445 | |||||||||
625726. | + | 361263.i | 1.44083 | + | 0.831865i | 0.997905 | − | 0.0646920i | ||
0.442928 | + | 0.896557i | ||||||||
0 | 0 | |||||||||
−1621.86 | − | 2809.15i | −0.00371203 | − | 0.00642942i | 0.864163 | − | 0.503211i | ||
−0.867875 | + | 0.496782i | ||||||||
170044. | − | 98175.0i | 0.388012 | − | 0.224019i | |||||
0 | 0 | |||||||||
−13024.2 | + | 22558.6i | −0.0295404 | + | 0.0511655i | |||||
127774.i | 0.288934i | |||||||||
0 | 0 | |||||||||
−1.24499e6 | −2.79843 | |||||||||
−367143. | − | 211970.i | −0.822776 | − | 0.475030i | |||||
0 | 0 | |||||||||
37207.0 | + | 64444.4i | 0.0828848 | + | 0.143561i | |||||
27036.2 | − | 15609.3i | 0.0600482 | − | 0.0346689i | |||||
0 | 0 | |||||||||
−340188. | + | 589223.i | −0.751085 | + | 1.30092i | 0.196212 | + | 0.980561i | ||
−0.947297 | + | 0.320356i | ||||||||
− | 251125.i | − | 0.552802i | |||||||
0 | 0 | |||||||||
−143883. | −0.314859 | |||||||||
71954.5 | + | 41542.9i | 0.156993 | + | 0.0906400i | 0.576438 | − | 0.817141i | ||
−0.419445 | + | 0.907781i | ||||||||
0 | 0 | |||||||||
−271801. | − | 470772.i | −0.589537 | − | 1.02111i | |||||
−5092.18 | + | 2939.97i | −0.0110125 | + | 0.00635807i | |||||
0 | 0 | |||||||||
−65934.4 | + | 114202.i | −0.141757 | + | 0.245530i | |||||
− | 6386.51i | − | 0.0136906i | −0.999977 | − | 0.00684529i | ||||
0.999977 | − | 0.00684529i | ||||||||
0 | 0 | |||||||||
−135787. | −0.289385 | |||||||||
−244029. | − | 140890.i | −0.518554 | − | 0.299387i | |||||
0 | 0 | |||||||||
−53591.0 | − | 92822.3i | −0.113218 | − | 0.196099i | |||||
−325720. | + | 188055.i | −0.686130 | + | 0.396137i | |||||
0 | 0 | |||||||||
−224531. | + | 388900.i | −0.470242 | + | 0.814483i | −0.999421 | − | 0.0340275i | ||
0.529179 | + | 0.848510i | ||||||||
− | 427172.i | − | 0.892054i | |||||||
0 | 0 | |||||||||
310379. | 0.644427 | |||||||||
−112719. | − | 65078.3i | −0.233360 | − | 0.134731i | |||||
0 | 0 | |||||||||
−20500.3 | − | 35507.6i | −0.0421983 | − | 0.0730896i | |||||
−339938. | + | 196263.i | −0.697733 | + | 0.402836i | |||||
0 | 0 | |||||||||
117882. | − | 204178.i | 0.240576 | − | 0.416691i | |||||
408122.i | 0.830527i | 0.909701 | + | 0.415264i | ||||||
−0.909701 | + | 0.415264i | ||||||||
0 | 0 | |||||||||
596599. | 1.20718 | |||||||||
17570.0 | + | 10144.0i | 0.0354508 | + | 0.0204676i | |||||
0 | 0 | |||||||||
110060. | + | 190629.i | 0.220810 | + | 0.382455i | |||||
466747. | − | 269476.i | 0.933775 | − | 0.539115i | |||||
0 | 0 | |||||||||
425844. | − | 737584.i | 0.847146 | − | 1.46730i | −0.0365985 | − | 0.999330i | ||
0.883744 | − | 0.467970i | ||||||||
− | 205885.i | − | 0.408421i | |||||||
0 | 0 | |||||||||
−244230. | −0.481768 | |||||||||
943317. | + | 544624.i | 1.85558 | + | 1.07132i | |||||
0 | 0 | |||||||||
−39350.9 | − | 68157.8i | −0.0769738 | − | 0.133323i | |||||
−224809. | + | 129793.i | −0.438517 | + | 0.253178i | |||||
0 | 0 | |||||||||
−276172. | + | 478344.i | −0.535711 | + | 0.927879i | |||||
− | 951431.i | − | 1.84043i | −0.391412 | − | 0.920215i | ||||
0.391412 | − | 0.920215i | ||||||||
0 | 0 | |||||||||
−736698. | −1.41716 | |||||||||
−160647. | − | 92749.9i | −0.308176 | − | 0.177926i | |||||
0 | 0 | |||||||||
−201525. | − | 349052.i | −0.384461 | − | 0.665905i | |||||
−629202. | + | 363270.i | −1.19705 | + | 0.691120i | |||||
0 | 0 | |||||||||
−410863. | + | 711636.i | −0.777371 | + | 1.34645i | 0.156081 | + | 0.987744i | ||
−0.933452 | + | 0.358702i | ||||||||
266301.i | 0.502470i | |||||||||
0 | 0 | |||||||||
−185196. | −0.347525 | |||||||||
40939.3 | + | 23636.3i | 0.0766135 | + | 0.0442328i | |||||
0 | 0 | |||||||||
224965. | + | 389651.i | 0.418704 | + | 0.725217i | 0.995809 | − | 0.0914530i | ||
−0.577105 | + | 0.816670i | ||||||||
−210179. | + | 121347.i | −0.390120 | + | 0.225236i | |||||
0 | 0 | |||||||||
83790.8 | − | 145130.i | 0.154682 | − | 0.267917i | |||||
113243.i | 0.208485i | |||||||||
0 | 0 | |||||||||
533367. | 0.976647 | 0.488323 | − | 0.872663i | ||||||
0.488323 | + | 0.872663i | ||||||||
149554. | + | 86345.0i | 0.273108 | + | 0.157679i | |||||
0 | 0 | |||||||||
134487. | + | 232938.i | 0.244271 | + | 0.423091i | |||||
−505677. | + | 291952.i | −0.915999 | + | 0.528852i | −0.882357 | − | 0.470581i | ||
−0.0336428 | + | 0.999434i | ||||||||
0 | 0 | |||||||||
50234.0 | − | 87007.8i | 0.0905076 | − | 0.156764i | |||||
− | 34840.7i | − | 0.0626050i | |||||||
0 | 0 | |||||||||
−8948.06 | −0.0159928 | |||||||||
459.324 | + | 265.191i | 0.000818758 | + | 0.000472710i | |||||
0 | 0 | |||||||||
−296313. | − | 513229.i | −0.525377 | − | 0.909979i | −0.999563 | − | 0.0295548i | ||
0.474186 | − | 0.880424i | ||||||||
−184222. | + | 106361.i | −0.325766 | + | 0.188081i | |||||
0 | 0 | |||||||||
410320. | − | 710695.i | 0.721739 | − | 1.25009i | |||||
− | 25672.9i | − | 0.0450382i | |||||||
0 | 0 | |||||||||
−30185.2 | −0.0526747 | −0.0263373 | − | 0.999653i | ||||||
−0.0263373 | + | 0.999653i | ||||||||
−529515. | − | 305716.i | −0.921594 | − | 0.532083i | |||||
0 | 0 | |||||||||
26500.4 | + | 45900.0i | 0.0458801 | + | 0.0794667i | |||||
265213. | − | 153121.i | 0.457957 | − | 0.264402i | −0.253228 | − | 0.967407i | ||
0.711185 | + | 0.703005i | ||||||||
0 | 0 | |||||||||
−516295. | + | 894248.i | −0.886846 | + | 1.53606i | |||||
18047.9i | 0.0309201i | |||||||||
0 | 0 | |||||||||
−672358. | −1.14589 | |||||||||
−153021. | − | 88346.6i | −0.260112 | − | 0.150176i | |||||
0 | 0 | |||||||||
−444182. | − | 769346.i | −0.751118 | − | 1.30097i | −0.947281 | − | 0.320403i | ||
0.196163 | − | 0.980571i | ||||||||
−48743.0 | + | 28141.8i | −0.0822111 | + | 0.0474646i | |||||
0 | 0 | |||||||||
96128.1 | − | 166499.i | 0.161293 | − | 0.279368i | |||||
456476.i | 0.763939i | 0.924175 | + | 0.381970i | ||||||
−0.924175 | + | 0.381970i | ||||||||
0 | 0 | |||||||||
635654. | 1.05832 | |||||||||
−195277. | − | 112743.i | −0.324286 | − | 0.187226i | |||||
0 | 0 | |||||||||
263475. | + | 456353.i | 0.435292 | + | 0.753948i | |||||
−320059. | + | 184786.i | −0.527418 | + | 0.304505i | |||||
0 | 0 | |||||||||
156657. | − | 271338.i | 0.256832 | − | 0.444845i | |||||
73911.8i | 0.120865i | |||||||||
0 | 0 | |||||||||
36780.8 | 0.0598397 | |||||||||
−19747.0 | − | 11400.9i | −0.0320450 | − | 0.0185012i | |||||
0 | 0 | |||||||||
−269736. | − | 467196.i | −0.435501 | − | 0.754310i | 0.561835 | − | 0.827249i | ||
−0.997336 | + | 0.0729393i | ||||||||
462975. | − | 267299.i | 0.745598 | − | 0.430471i | |||||
0 | 0 | |||||||||
−45249.7 | + | 78374.8i | −0.0725039 | + | 0.125581i | |||||
321640.i | 0.514064i | |||||||||
0 | 0 | |||||||||
169975. | 0.270296 | |||||||||
12258.9 | + | 7077.71i | 0.0194452 | + | 0.0112267i | |||||
0 | 0 | |||||||||
−33701.1 | − | 58372.1i | −0.0531886 | − | 0.0921254i | |||||
435416. | − | 251387.i | 0.685468 | − | 0.395755i | −0.116444 | − | 0.993197i | ||
0.801912 | + | 0.597442i | ||||||||
0 | 0 | |||||||||
46910.3 | − | 81251.0i | 0.0734809 | − | 0.127273i | |||||
− | 97795.6i | − | 0.152806i | |||||||
0 | 0 | |||||||||
499157. | 0.776048 | |||||||||
−244072. | − | 140915.i | −0.378519 | − | 0.218538i | |||||
0 | 0 | |||||||||
232454. | + | 402621.i | 0.358711 | + | 0.621305i | |||||
−621791. | + | 358991.i | −0.957138 | + | 0.552604i | |||||
0 | 0 | |||||||||
111779. | − | 193607.i | 0.171214 | − | 0.296551i | |||||
699315.i | 1.06850i | 0.845326 | + | 0.534251i | ||||||
−0.845326 | + | 0.534251i | ||||||||
0 | 0 | |||||||||
741168. | 1.12687 | 0.563437 | − | 0.826159i | ||||||
0.563437 | + | 0.826159i | ||||||||
−508253. | − | 293440.i | −0.770846 | − | 0.445048i | |||||
0 | 0 | |||||||||
131399. | + | 227590.i | 0.198310 | + | 0.343483i | |||||
283403. | − | 163623.i | 0.426667 | − | 0.246336i | |||||
0 | 0 | |||||||||
213053. | − | 369019.i | 0.319186 | − | 0.552846i | |||||
− | 533763.i | − | 0.797704i | |||||||
0 | 0 | |||||||||
−106975. | −0.159095 | |||||||||
58936.9 | + | 34027.3i | 0.0874382 | + | 0.0504825i | 0.543082 | − | 0.839680i | ||
−0.455643 | + | 0.890162i | ||||||||
0 | 0 | |||||||||
−325915. | − | 564502.i | −0.481177 | − | 0.833423i | 0.518590 | − | 0.855023i | ||
−0.999767 | + | 0.0216000i | ||||||||
−264643. | + | 152792.i | −0.389768 | + | 0.225033i | |||||
0 | 0 | |||||||||
−63181.0 | + | 109433.i | −0.0926033 | + | 0.160394i | |||||
− | 36453.4i | − | 0.0532999i | −0.999645 | − | 0.0266500i | ||||
0.999645 | − | 0.0266500i | ||||||||
0 | 0 | |||||||||
78480.8 | 0.114197 | 0.0570984 | − | 0.998369i | ||||||
0.0570984 | + | 0.998369i | ||||||||
−25959.3 | − | 14987.6i | −0.0376823 | − | 0.0217559i | |||||
0 | 0 | |||||||||
55231.0 | + | 95662.9i | 0.0797878 | + | 0.138196i | |||||
−14048.8 | + | 8111.09i | −0.0202465 | + | 0.0116893i | |||||
0 | 0 | |||||||||
243924. | − | 422489.i | 0.349850 | − | 0.605958i | |||||
80656.1i | 0.115405i | |||||||||
0 | 0 | |||||||||
−33956.4 | −0.0483541 | |||||||||
59633.8 | + | 34429.6i | 0.0847166 | + | 0.0489111i | 0.541760 | − | 0.840533i | ||
−0.457043 | + | 0.889444i | ||||||||
0 | 0 | |||||||||
550632. | + | 953723.i | 0.778520 | + | 1.34844i | |||||
136180. | − | 78623.4i | 0.192083 | − | 0.110899i | |||||
0 | 0 | |||||||||
−134800. | + | 233480.i | −0.189236 | + | 0.327767i | |||||
− | 165573.i | − | 0.231887i | |||||||
0 | 0 | |||||||||
713014. | 0.993874 | |||||||||
96623.2 | + | 55785.5i | 0.134366 | + | 0.0775763i | |||||
0 | 0 | |||||||||
21566.4 | + | 37354.1i | 0.0298497 | + | 0.0517011i | |||||
1.87992e6 | − | 1.08537e6i | 2.59585 | − | 1.49871i | |||||
0 | 0 | |||||||||
−412386. | + | 714273.i | −0.566768 | + | 0.981671i | 0.430115 | + | 0.902774i | ||
−0.996883 | + | 0.0788970i | ||||||||
− | 121558.i | − | 0.166674i | |||||||
0 | 0 | |||||||||
220.003 | 0.000300249 | |||||||||
561077. | + | 323938.i | 0.763942 | + | 0.441062i | 0.830709 | − | 0.556706i | ||
−0.0667670 | + | 0.997769i | ||||||||
0 | 0 | |||||||||
657566. | + | 1.13894e6i | 0.891154 | + | 1.54352i | 0.838493 | + | 0.544912i | ||
0.0526607 | + | 0.998612i | ||||||||
106815. | − | 61669.8i | 0.144423 | − | 0.0833826i | |||||
0 | 0 | |||||||||
73640.4 | − | 127549.i | 0.0991063 | − | 0.171657i | |||||
1.27319e6i | 1.70951i | 0.519028 | + | 0.854757i | ||||||
−0.519028 | + | 0.854757i | ||||||||
0 | 0 | |||||||||
491568. | 0.656979 | |||||||||
−503030. | − | 290424.i | −0.670746 | − | 0.387255i | |||||
0 | 0 | |||||||||
256732. | + | 444673.i | 0.340754 | + | 0.590203i | |||||
−119270. | + | 68860.7i | −0.157940 | + | 0.0911868i | |||||
0 | 0 | |||||||||
−308285. | + | 533965.i | −0.406365 | + | 0.703844i | |||||
428320.i | 0.563294i | |||||||||
0 | 0 | |||||||||
666227. | 0.872166 | |||||||||
506775. | + | 292586.i | 0.661910 | + | 0.382154i | |||||
0 | 0 | |||||||||
352514. | + | 610572.i | 0.458329 | + | 0.793848i | 0.998873 | − | 0.0474673i | ||
−0.540544 | + | 0.841316i | ||||||||
795018. | − | 459004.i | 1.03131 | − | 0.595425i | |||||
0 | 0 | |||||||||
−11673.3 | + | 20218.7i | −0.0150739 | + | 0.0261088i | |||||
750647.i | 0.967128i | 0.875309 | + | 0.483564i | ||||||
−0.875309 | + | 0.483564i | ||||||||
0 | 0 | |||||||||
−638249. | −0.818594 | −0.409297 | − | 0.912401i | ||||||
−0.409297 | + | 0.912401i | ||||||||
−42192.1 | − | 24359.6i | −0.0539917 | − | 0.0311721i | |||||
0 | 0 | |||||||||
−243275. | − | 421364.i | −0.309906 | − | 0.536772i | |||||
−985132. | + | 568766.i | −1.25212 | + | 0.722914i | −0.971531 | − | 0.236914i | ||
−0.280592 | + | 0.959827i | ||||||||
0 | 0 | |||||||||
551415. | − | 955078.i | 0.697710 | − | 1.20847i | |||||
− | 281047.i | − | 0.354812i | |||||||
0 | 0 | |||||||||
164250. | 0.206432 | |||||||||
−732381. | − | 422840.i | −0.918405 | − | 0.530241i | |||||
0 | 0 | |||||||||
−149359. | − | 258698.i | −0.186460 | − | 0.322959i | |||||
68413.2 | − | 39498.4i | 0.0852166 | − | 0.0491998i | |||||
0 | 0 | |||||||||
172018. | − | 297944.i | 0.213315 | − | 0.369472i | |||||
− | 1.58231e6i | − | 1.95781i | |||||||
0 | 0 | |||||||||
−49208.3 | −0.0606162 | |||||||||
−140984. | − | 81397.1i | −0.173283 | − | 0.100045i | |||||
0 | 0 | |||||||||
66708.5 | + | 115542.i | 0.0816289 | + | 0.141385i | |||||
401671. | − | 231905.i | 0.490425 | − | 0.283147i | |||||
0 | 0 | |||||||||
652106. | − | 1.12948e6i | 0.792690 | − | 1.37298i | −0.131606 | − | 0.991302i | ||
0.924296 | − | 0.381677i | ||||||||
− | 468534.i | − | 0.568289i | |||||||
0 | 0 | |||||||||
−306445. | −0.370059 | |||||||||
−936156. | − | 540490.i | −1.12801 | − | 0.651254i | −0.184573 | − | 0.982819i | ||
−0.943433 | + | 0.331564i | ||||||||
0 | 0 | |||||||||
−22808.1 | − | 39504.8i | −0.0273620 | − | 0.0473923i | |||||
−114021. | + | 65829.8i | −0.136487 | + | 0.0788008i | |||||
0 | 0 | |||||||||
−29154.2 | + | 50496.6i | −0.0347465 | + | 0.0601826i | |||||
767145.i | 0.912303i | |||||||||
0 | 0 | |||||||||
558574. | 0.661378 | 0.330689 | − | 0.943740i | ||||||
0.330689 | + | 0.943740i | ||||||||
167008. | + | 96422.1i | 0.197316 | + | 0.113920i | |||||
0 | 0 | |||||||||
288884. | + | 500361.i | 0.339829 | + | 0.588602i | |||||
1.47735e6 | − | 852947.i | 1.73412 | − | 1.00120i | |||||
0 | 0 | |||||||||
633390. | − | 1.09706e6i | 0.740266 | − | 1.28218i | |||||
48849.9i | 0.0569695i | |||||||||
0 | 0 | |||||||||
−243439. | −0.282679 | |||||||||
764452. | + | 441357.i | 0.885765 | + | 0.511397i | 0.872555 | − | 0.488516i | ||
0.0132104 | + | 0.999913i | ||||||||
0 | 0 | |||||||||
73111.8 | + | 126633.i | 0.0843506 | + | 0.146100i | |||||
−94118.7 | + | 54339.5i | −0.108354 | + | 0.0625581i | |||||
0 | 0 | |||||||||
310652. | − | 538065.i | 0.356107 | − | 0.616795i | |||||
− | 10297.0i | − | 0.0117784i | |||||||
0 | 0 | |||||||||
893683. | 1.01790 | 0.508949 | − | 0.860797i | ||||||
0.508949 | + | 0.860797i | ||||||||
381865. | + | 220470.i | 0.434014 | + | 0.250578i | |||||
0 | 0 | |||||||||
−122394. | − | 211993.i | −0.138518 | − | 0.239920i | |||||
−408726. | + | 235978.i | −0.461587 | + | 0.266497i | −0.712711 | − | 0.701458i | ||
0.251125 | + | 0.967955i | ||||||||
0 | 0 | |||||||||
−672348. | + | 1.16454e6i | −0.756085 | + | 1.30958i | |||||
52415.2i | 0.0588184i | |||||||||
0 | 0 | |||||||||
187697. | 0.209737 | |||||||||
−629058. | − | 363187.i | −0.701441 | − | 0.404977i | 0.106443 | − | 0.994319i | ||
−0.807884 | + | 0.589342i | ||||||||
0 | 0 | |||||||||
−767237. | − | 1.32889e6i | −0.851916 | − | 1.47556i | |||||
336702. | − | 194395.i | 0.373078 | − | 0.215396i | |||||
0 | 0 | |||||||||
−17420.8 | + | 30173.7i | −0.0192218 | + | 0.0332931i | |||||
41574.8i | 0.0457767i | 0.999738 | + | 0.0228884i | ||||||
−0.999738 | + | 0.0228884i | ||||||||
0 | 0 | |||||||||
−20768.6 | −0.0227720 | |||||||||
179350. | + | 103548.i | 0.196239 | + | 0.113299i | |||||
0 | 0 | |||||||||
−128769. | − | 223035.i | −0.140307 | − | 0.243020i | |||||
−696807. | + | 402302.i | −0.757662 | + | 0.437436i | |||||
0 | 0 | |||||||||
−230424. | + | 399106.i | −0.249506 | + | 0.432157i | |||||
1.43085e6i | 1.54612i | |||||||||
0 | 0 | |||||||||
74887.7 | 0.0805855 | |||||||||
191598. | + | 110619.i | 0.205749 | + | 0.118789i | |||||
0 | 0 | |||||||||
600282. | + | 1.03972e6i | 0.641952 | + | 1.11189i | 0.984996 | + | 0.172575i | ||
−0.343044 | + | 0.939319i | ||||||||
256135. | − | 147880.i | 0.273350 | − | 0.157819i | |||||
0 | 0 | |||||||||
129739. | − | 224715.i | 0.137888 | − | 0.238830i | |||||
− | 1.38244e6i | − | 1.46625i | −0.680092 | − | 0.733127i | ||||
0.680092 | − | 0.733127i | ||||||||
0 | 0 | |||||||||
−771241. | −0.814638 | |||||||||
359096. | + | 207324.i | 0.378523 | + | 0.218541i | |||||
0 | 0 | |||||||||
−25211.2 | − | 43667.1i | −0.0264663 | − | 0.0458410i | |||||
−124404. | + | 71824.7i | −0.130330 | + | 0.0752463i | −0.563748 | − | 0.825947i | ||
0.433417 | + | 0.901193i | ||||||||
0 | 0 | |||||||||
213848. | − | 370395.i | 0.223120 | − | 0.386456i | |||||
42325.5i | 0.0440707i | |||||||||
0 | 0 | |||||||||
137061. | 0.142132 | |||||||||
−492098. | − | 284113.i | −0.509266 | − | 0.294025i | 0.223266 | − | 0.974758i | ||
−0.732532 | + | 0.680733i | ||||||||
0 | 0 | |||||||||
307594. | + | 532768.i | 0.317033 | + | 0.549118i | |||||
92983.9 | − | 53684.3i | 0.0956432 | − | 0.0552196i | |||||
0 | 0 | |||||||||
−219573. | + | 380312.i | −0.224939 | + | 0.389606i | |||||
− | 1.55040e6i | − | 1.58508i | |||||||
0 | 0 | |||||||||
−920749. | −0.937549 | −0.468774 | − | 0.883318i | ||||||
−0.468774 | + | 0.883318i | ||||||||
184451. | + | 106493.i | 0.187438 | + | 0.108218i | |||||
0 | 0 | |||||||||
−609985. | − | 1.05652e6i | −0.617371 | − | 1.06932i | |||||
67171.6 | − | 38781.6i | 0.0678484 | − | 0.0391723i | |||||
0 | 0 | |||||||||
−500709. | + | 867254.i | −0.503727 | + | 0.872481i | 0.496264 | + | 0.868172i | ||
−0.999991 | + | 0.00430895i | ||||||||
701487.i | 0.704302i | |||||||||
0 | 0 |
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 162.5.d.d.107.4 | 8 | ||
3.2 | odd | 2 | inner | 162.5.d.d.107.1 | 8 | ||
9.2 | odd | 6 | 162.5.b.a.161.3 | yes | 4 | ||
9.4 | even | 3 | inner | 162.5.d.d.53.1 | 8 | ||
9.5 | odd | 6 | inner | 162.5.d.d.53.4 | 8 | ||
9.7 | even | 3 | 162.5.b.a.161.2 | ✓ | 4 | ||
36.7 | odd | 6 | 1296.5.e.b.161.2 | 4 | |||
36.11 | even | 6 | 1296.5.e.b.161.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
162.5.b.a.161.2 | ✓ | 4 | 9.7 | even | 3 | ||
162.5.b.a.161.3 | yes | 4 | 9.2 | odd | 6 | ||
162.5.d.d.53.1 | 8 | 9.4 | even | 3 | inner | ||
162.5.d.d.53.4 | 8 | 9.5 | odd | 6 | inner | ||
162.5.d.d.107.1 | 8 | 3.2 | odd | 2 | inner | ||
162.5.d.d.107.4 | 8 | 1.1 | even | 1 | trivial | ||
1296.5.e.b.161.2 | 4 | 36.7 | odd | 6 | |||
1296.5.e.b.161.3 | 4 | 36.11 | even | 6 |