Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [504,2,Mod(193,504)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(504, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("504.193");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 504.t (of order , degree , 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 |
Twist minimal: | yes |
Sato-Tate group: |
Embedding invariants
Embedding label | 457.8 | ||
Character | 504.457 | ||
Dual form | 504.2.t.d.193.8 |
-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 .
0 | 0 | |||||||||
0.577666 | + | 1.63288i | 0.333515 | + | 0.942745i | |||||
0 | 0 | |||||||||
1.85591 | 0.829990 | 0.414995 | − | 0.909824i | ||||||
0.414995 | + | 0.909824i | ||||||||
0 | 0 | |||||||||
−2.60465 | + | 0.464545i | −0.984465 | + | 0.175582i | |||||
0 | 0 | |||||||||
−2.33261 | + | 1.88652i | −0.777535 | + | 0.628840i | |||||
0 | 0 | |||||||||
−2.57601 | −0.776696 | −0.388348 | − | 0.921513i | ||||||
−0.388348 | + | 0.921513i | ||||||||
0 | 0 | |||||||||
2.82227 | + | 4.88832i | 0.782757 | + | 1.35578i | 0.930330 | + | 0.366724i | ||
−0.147573 | + | 0.989051i | ||||||||
0 | 0 | |||||||||
1.07210 | + | 3.03049i | 0.276814 | + | 0.782469i | |||||
0 | 0 | |||||||||
3.57951 | + | 6.19989i | 0.868158 | + | 1.50369i | 0.863876 | + | 0.503704i | ||
0.00428199 | + | 0.999991i | ||||||||
0 | 0 | |||||||||
0.636599 | − | 1.10262i | 0.146046 | − | 0.252959i | −0.783717 | − | 0.621118i | ||
0.929763 | + | 0.368160i | ||||||||
0 | 0 | |||||||||
−2.26316 | − | 3.98473i | −0.493863 | − | 0.869540i | |||||
0 | 0 | |||||||||
0.241277 | 0.0503098 | 0.0251549 | − | 0.999684i | ||||||
0.0251549 | + | 0.999684i | ||||||||
0 | 0 | |||||||||
−1.55558 | −0.311116 | |||||||||
0 | 0 | |||||||||
−4.42793 | − | 2.71909i | −0.852155 | − | 0.523289i | |||||
0 | 0 | |||||||||
0.923571 | − | 1.59967i | 0.171503 | − | 0.297051i | −0.767443 | − | 0.641118i | ||
0.938945 | + | 0.344066i | ||||||||
0 | 0 | |||||||||
1.49552 | − | 2.59031i | 0.268602 | − | 0.465233i | −0.699899 | − | 0.714242i | ||
0.968501 | + | 0.249009i | ||||||||
0 | 0 | |||||||||
−1.48807 | − | 4.20632i | −0.259040 | − | 0.732226i | |||||
0 | 0 | |||||||||
−4.83401 | + | 0.862156i | −0.817096 | + | 0.145731i | |||||
0 | 0 | |||||||||
0.338260 | − | 0.585884i | 0.0556097 | − | 0.0963188i | −0.836880 | − | 0.547386i | ||
0.892490 | + | 0.451067i | ||||||||
0 | 0 | |||||||||
−6.35171 | + | 7.43225i | −1.01709 | + | 1.19011i | |||||
0 | 0 | |||||||||
−0.733933 | − | 1.27121i | −0.114621 | − | 0.198529i | 0.803007 | − | 0.595969i | ||
−0.917628 | + | 0.397440i | ||||||||
0 | 0 | |||||||||
4.14269 | − | 7.17535i | 0.631754 | − | 1.09423i | −0.355439 | − | 0.934700i | ||
0.987193 | − | 0.159531i | ||||||||
0 | 0 | |||||||||
−4.32912 | + | 3.50122i | −0.645346 | + | 0.521931i | |||||
0 | 0 | |||||||||
6.15723 | + | 10.6646i | 0.898124 | + | 1.55560i | 0.829890 | + | 0.557928i | ||
0.0682346 | + | 0.997669i | ||||||||
0 | 0 | |||||||||
6.56840 | − | 2.41995i | 0.938342 | − | 0.345708i | |||||
0 | 0 | |||||||||
−8.05593 | + | 9.42638i | −1.12806 | + | 1.31996i | |||||
0 | 0 | |||||||||
3.35508 | + | 5.81117i | 0.460856 | + | 0.798226i | 0.999004 | − | 0.0446243i | ||
−0.538148 | + | 0.842851i | ||||||||
0 | 0 | |||||||||
−4.78085 | −0.644650 | |||||||||
0 | 0 | |||||||||
2.16819 | + | 0.402544i | 0.287184 | + | 0.0533182i | |||||
0 | 0 | |||||||||
−1.04139 | + | 1.80375i | −0.135578 | + | 0.234828i | −0.925818 | − | 0.377969i | ||
0.790240 | + | 0.612797i | ||||||||
0 | 0 | |||||||||
−6.47973 | − | 11.2232i | −0.829644 | − | 1.43699i | −0.898317 | − | 0.439347i | ||
0.0686730 | − | 0.997639i | ||||||||
0 | 0 | |||||||||
5.19925 | − | 5.99732i | 0.655043 | − | 0.755591i | |||||
0 | 0 | |||||||||
5.23789 | + | 9.07230i | 0.649681 | + | 1.12528i | |||||
0 | 0 | |||||||||
2.41551 | − | 4.18379i | 0.295102 | − | 0.511131i | −0.679907 | − | 0.733298i | ||
0.975009 | + | 0.222167i | ||||||||
0 | 0 | |||||||||
0.139378 | + | 0.393977i | 0.0167791 | + | 0.0474293i | |||||
0 | 0 | |||||||||
−1.53621 | −0.182314 | −0.0911572 | − | 0.995837i | ||||||
−0.0911572 | + | 0.995837i | ||||||||
0 | 0 | |||||||||
−6.55954 | − | 11.3615i | −0.767736 | − | 1.32976i | −0.938788 | − | 0.344496i | ||
0.171052 | − | 0.985262i | ||||||||
0 | 0 | |||||||||
−0.898606 | − | 2.54008i | −0.103762 | − | 0.293303i | |||||
0 | 0 | |||||||||
6.70960 | − | 1.19667i | 0.764630 | − | 0.136373i | |||||
0 | 0 | |||||||||
1.86009 | + | 3.22177i | 0.209277 | + | 0.362478i | 0.951487 | − | 0.307689i | ||
−0.742210 | + | 0.670167i | ||||||||
0 | 0 | |||||||||
1.88209 | − | 8.80101i | 0.209121 | − | 0.977890i | |||||
0 | 0 | |||||||||
−3.00173 | + | 5.19915i | −0.329483 | + | 0.570681i | −0.982409 | − | 0.186740i | ||
0.652926 | + | 0.757421i | ||||||||
0 | 0 | |||||||||
6.64326 | + | 11.5065i | 0.720563 | + | 1.24805i | |||||
0 | 0 | |||||||||
3.14559 | + | 0.584007i | 0.337242 | + | 0.0626121i | |||||
0 | 0 | |||||||||
6.60349 | − | 11.4376i | 0.699968 | − | 1.21238i | −0.268509 | − | 0.963277i | ||
0.968477 | − | 0.249103i | ||||||||
0 | 0 | |||||||||
−9.62187 | − | 11.4213i | −1.00865 | − | 1.19728i | |||||
0 | 0 | |||||||||
5.09357 | + | 0.945667i | 0.528179 | + | 0.0980611i | |||||
0 | 0 | |||||||||
1.18147 | − | 2.04637i | 0.121217 | − | 0.209953i | |||||
0 | 0 | |||||||||
6.40860 | − | 11.1000i | 0.650695 | − | 1.12704i | −0.332260 | − | 0.943188i | ||
0.982955 | − | 0.183848i | ||||||||
0 | 0 | |||||||||
6.00881 | − | 4.85969i | 0.603908 | − | 0.488417i | |||||
0 | 0 | |||||||||
12.2013 | 1.21408 | 0.607039 | − | 0.794672i | ||||||
0.607039 | + | 0.794672i | ||||||||
0 | 0 | |||||||||
13.6433 | 1.34431 | 0.672155 | − | 0.740411i | ||||||
0.672155 | + | 0.740411i | ||||||||
0 | 0 | |||||||||
−4.20024 | − | 7.39532i | −0.409901 | − | 0.721710i | |||||
0 | 0 | |||||||||
−6.48002 | + | 11.2237i | −0.626448 | + | 1.08504i | 0.361811 | + | 0.932251i | ||
−0.988259 | + | 0.152788i | ||||||||
0 | 0 | |||||||||
7.70089 | + | 13.3383i | 0.737612 | + | 1.27758i | 0.953568 | + | 0.301178i | ||
−0.215956 | + | 0.976403i | ||||||||
0 | 0 | |||||||||
1.15208 | + | 0.213894i | 0.109351 | + | 0.0203019i | |||||
0 | 0 | |||||||||
−7.73446 | − | 13.3965i | −0.727597 | − | 1.26023i | −0.957896 | − | 0.287115i | ||
0.230299 | − | 0.973120i | ||||||||
0 | 0 | |||||||||
0.447790 | 0.0417566 | |||||||||
0 | 0 | |||||||||
−15.8051 | − | 6.07824i | −1.46119 | − | 0.561934i | |||||
0 | 0 | |||||||||
−12.2035 | − | 14.4857i | −1.11869 | − | 1.32790i | |||||
0 | 0 | |||||||||
−4.36418 | −0.396744 | |||||||||
0 | 0 | |||||||||
1.65177 | − | 1.93276i | 0.148935 | − | 0.174271i | |||||
0 | 0 | |||||||||
−12.1666 | −1.08821 | |||||||||
0 | 0 | |||||||||
−3.19404 | −0.283425 | −0.141713 | − | 0.989908i | ||||||
−0.141713 | + | 0.989908i | ||||||||
0 | 0 | |||||||||
14.1096 | + | 2.61957i | 1.24228 | + | 0.230640i | |||||
0 | 0 | |||||||||
14.0868 | 1.23077 | 0.615383 | − | 0.788229i | ||||||
0.615383 | + | 0.788229i | ||||||||
0 | 0 | |||||||||
−1.14590 | + | 3.16767i | −0.0993620 | + | 0.274672i | |||||
0 | 0 | |||||||||
−8.21785 | − | 5.04640i | −0.707280 | − | 0.434325i | |||||
0 | 0 | |||||||||
13.6964 | 1.17016 | 0.585079 | − | 0.810976i | ||||||
0.585079 | + | 0.810976i | ||||||||
0 | 0 | |||||||||
−4.94131 | − | 8.55859i | −0.419116 | − | 0.725931i | 0.576735 | − | 0.816932i | ||
−0.995851 | + | 0.0910010i | ||||||||
0 | 0 | |||||||||
−13.8573 | + | 16.2146i | −1.16699 | + | 1.36552i | |||||
0 | 0 | |||||||||
−7.27019 | − | 12.5923i | −0.607964 | − | 1.05302i | |||||
0 | 0 | |||||||||
1.71407 | − | 2.96885i | 0.142346 | − | 0.246550i | |||||
0 | 0 | |||||||||
7.74583 | + | 9.32749i | 0.638866 | + | 0.769318i | |||||
0 | 0 | |||||||||
−3.92029 | −0.321163 | −0.160581 | − | 0.987023i | ||||||
−0.160581 | + | 0.987023i | ||||||||
0 | 0 | |||||||||
19.5784 | 1.59327 | 0.796634 | − | 0.604462i | ||||||
0.796634 | + | 0.604462i | ||||||||
0 | 0 | |||||||||
−20.0458 | − | 7.70909i | −1.62061 | − | 0.623243i | |||||
0 | 0 | |||||||||
2.77555 | − | 4.80739i | 0.222937 | − | 0.386139i | |||||
0 | 0 | |||||||||
−7.39637 | + | 12.8109i | −0.590295 | + | 1.02242i | 0.403898 | + | 0.914804i | ||
−0.994193 | + | 0.107616i | ||||||||
0 | 0 | |||||||||
−7.55084 | + | 8.83537i | −0.598821 | + | 0.700690i | |||||
0 | 0 | |||||||||
−0.628443 | + | 0.112084i | −0.0495282 | + | 0.00883347i | |||||
0 | 0 | |||||||||
7.54686 | − | 13.0715i | 0.591116 | − | 1.02384i | −0.402967 | − | 0.915215i | ||
0.994082 | − | 0.108628i | ||||||||
0 | 0 | |||||||||
−2.76173 | − | 7.80656i | −0.215001 | − | 0.607740i | |||||
0 | 0 | |||||||||
1.92946 | + | 3.34192i | 0.149306 | + | 0.258605i | 0.930971 | − | 0.365093i | ||
−0.781665 | + | 0.623698i | ||||||||
0 | 0 | |||||||||
−9.43043 | + | 16.3340i | −0.725418 | + | 1.25646i | |||||
0 | 0 | |||||||||
0.595183 | + | 3.77293i | 0.0455147 | + | 0.288524i | |||||
0 | 0 | |||||||||
−0.325786 | − | 0.564277i | −0.0247690 | − | 0.0429012i | 0.853375 | − | 0.521297i | ||
−0.878144 | + | 0.478396i | ||||||||
0 | 0 | |||||||||
4.05174 | − | 0.722638i | 0.306283 | − | 0.0546263i | |||||
0 | 0 | |||||||||
−3.54688 | − | 0.658511i | −0.266600 | − | 0.0494967i | |||||
0 | 0 | |||||||||
10.9059 | + | 18.8896i | 0.815145 | + | 1.41187i | 0.909223 | + | 0.416308i | ||
−0.0940781 | + | 0.995565i | ||||||||
0 | 0 | |||||||||
−25.0338 | −1.86075 | −0.930374 | − | 0.366613i | ||||||
−0.930374 | + | 0.366613i | ||||||||
0 | 0 | |||||||||
14.5831 | − | 17.0639i | 1.07801 | − | 1.26140i | |||||
0 | 0 | |||||||||
0.627782 | − | 1.08735i | 0.0461555 | − | 0.0799436i | |||||
0 | 0 | |||||||||
−9.22085 | − | 15.9710i | −0.674295 | − | 1.16791i | |||||
0 | 0 | |||||||||
12.7963 | + | 5.02531i | 0.930797 | + | 0.365537i | |||||
0 | 0 | |||||||||
−4.33036 | − | 7.50041i | −0.313334 | − | 0.542711i | 0.665748 | − | 0.746177i | ||
−0.979082 | + | 0.203466i | ||||||||
0 | 0 | |||||||||
−0.808322 | + | 1.40006i | −0.0581843 | + | 0.100778i | −0.893650 | − | 0.448764i | ||
0.835466 | + | 0.549542i | ||||||||
0 | 0 | |||||||||
−11.7882 | + | 13.7936i | −0.844173 | + | 0.987781i | |||||
0 | 0 | |||||||||
10.7746 | 0.767659 | 0.383829 | − | 0.923404i | ||||||
0.383829 | + | 0.923404i | ||||||||
0 | 0 | |||||||||
2.38768 | + | 4.13558i | 0.169258 | + | 0.293163i | 0.938159 | − | 0.346204i | ||
−0.768901 | + | 0.639368i | ||||||||
0 | 0 | |||||||||
8.22699 | + | 1.52741i | 0.580287 | + | 0.107735i | |||||
0 | 0 | |||||||||
−1.66246 | + | 4.59562i | −0.116682 | + | 0.322549i | |||||
0 | 0 | |||||||||
−1.36212 | − | 2.35925i | −0.0951343 | − | 0.164777i | |||||
0 | 0 | |||||||||
−0.562805 | + | 0.455174i | −0.0391176 | + | 0.0316368i | |||||
0 | 0 | |||||||||
−1.63988 | + | 2.84036i | −0.113433 | + | 0.196472i | |||||
0 | 0 | |||||||||
2.42787 | + | 4.20520i | 0.167142 | + | 0.289498i | 0.937414 | − | 0.348218i | ||
−0.770272 | + | 0.637715i | ||||||||
0 | 0 | |||||||||
−0.887415 | − | 2.50845i | −0.0608046 | − | 0.171876i | |||||
0 | 0 | |||||||||
7.68848 | − | 13.3168i | 0.524350 | − | 0.908200i | |||||
0 | 0 | |||||||||
−2.69198 | + | 7.44158i | −0.182743 | + | 0.505167i | |||||
0 | 0 | |||||||||
14.7627 | − | 17.2741i | 0.997570 | − | 1.16727i | |||||
0 | 0 | |||||||||
−20.2047 | + | 34.9955i | −1.35911 | + | 2.35406i | |||||
0 | 0 | |||||||||
3.86187 | − | 6.68896i | 0.258610 | − | 0.447926i | −0.707260 | − | 0.706954i | ||
0.965870 | + | 0.259028i | ||||||||
0 | 0 | |||||||||
3.62856 | − | 2.93463i | 0.241904 | − | 0.195642i | |||||
0 | 0 | |||||||||
−13.9491 | −0.925837 | −0.462919 | − | 0.886401i | ||||||
−0.462919 | + | 0.886401i | ||||||||
0 | 0 | |||||||||
1.60027 | 0.105749 | 0.0528745 | − | 0.998601i | ||||||
0.0528745 | + | 0.998601i | ||||||||
0 | 0 | |||||||||
5.82993 | + | 10.2647i | 0.383581 | + | 0.675368i | |||||
0 | 0 | |||||||||
3.69939 | − | 6.40753i | 0.242355 | − | 0.419771i | −0.719030 | − | 0.694979i | ||
0.961385 | + | 0.275208i | ||||||||
0 | 0 | |||||||||
11.4273 | + | 19.7926i | 0.745434 | + | 1.29113i | |||||
0 | 0 | |||||||||
−4.18626 | + | 4.89841i | −0.271927 | + | 0.318186i | |||||
0 | 0 | |||||||||
−1.25117 | − | 2.16709i | −0.0809316 | − | 0.140178i | 0.822719 | − | 0.568449i | ||
−0.903650 | + | 0.428271i | ||||||||
0 | 0 | |||||||||
4.24297 | 0.273314 | 0.136657 | − | 0.990618i | ||||||
0.136657 | + | 0.990618i | ||||||||
0 | 0 | |||||||||
15.4582 | − | 2.01080i | 0.991645 | − | 0.128993i | |||||
0 | 0 | |||||||||
12.1904 | − | 4.49123i | 0.778815 | − | 0.286934i | |||||
0 | 0 | |||||||||
7.18661 | 0.457273 | |||||||||
0 | 0 | |||||||||
−10.2236 | − | 1.89810i | −0.647894 | − | 0.120287i | |||||
0 | 0 | |||||||||
−13.5381 | −0.854516 | −0.427258 | − | 0.904130i | ||||||
−0.427258 | + | 0.904130i | ||||||||
0 | 0 | |||||||||
−0.621532 | −0.0390754 | |||||||||
0 | 0 | |||||||||
−14.9511 | + | 17.4946i | −0.936275 | + | 1.09555i | |||||
0 | 0 | |||||||||
−6.15495 | −0.383935 | −0.191968 | − | 0.981401i | ||||||
−0.191968 | + | 0.981401i | ||||||||
0 | 0 | |||||||||
−0.608880 | + | 1.68316i | −0.0378340 | + | 0.104586i | |||||
0 | 0 | |||||||||
0.863485 | + | 5.47373i | 0.0534484 | + | 0.338816i | |||||
0 | 0 | |||||||||
−25.3411 | −1.56260 | −0.781300 | − | 0.624156i | ||||||
−0.781300 | + | 0.624156i | ||||||||
0 | 0 | |||||||||
6.22675 | + | 10.7850i | 0.382506 | + | 0.662520i | |||||
0 | 0 | |||||||||
22.4908 | + | 4.17562i | 1.37642 | + | 0.255544i | |||||
0 | 0 | |||||||||
−5.42092 | − | 9.38931i | −0.330519 | − | 0.572476i | 0.652095 | − | 0.758138i | ||
−0.982614 | + | 0.185662i | ||||||||
0 | 0 | |||||||||
−15.0184 | + | 26.0127i | −0.912306 | + | 1.58016i | −0.101507 | + | 0.994835i | ||
−0.810799 | + | 0.585325i | ||||||||
0 | 0 | |||||||||
13.0914 | − | 22.3091i | 0.792326 | − | 1.35021i | |||||
0 | 0 | |||||||||
4.00719 | 0.241643 | |||||||||
0 | 0 | |||||||||
19.7629 | 1.18744 | 0.593720 | − | 0.804672i | ||||||
0.593720 | + | 0.804672i | ||||||||
0 | 0 | |||||||||
1.39822 | + | 8.86348i | 0.0837092 | + | 0.530643i | |||||
0 | 0 | |||||||||
−3.98596 | + | 6.90388i | −0.237782 | + | 0.411851i | −0.960078 | − | 0.279734i | ||
0.722295 | + | 0.691585i | ||||||||
0 | 0 | |||||||||
−11.6063 | + | 20.1028i | −0.689926 | + | 1.19499i | 0.281936 | + | 0.959433i | ||
−0.971861 | + | 0.235553i | ||||||||
0 | 0 | |||||||||
4.02398 | + | 0.747087i | 0.238360 | + | 0.0442536i | |||||
0 | 0 | |||||||||
2.50217 | + | 2.97011i | 0.147698 | + | 0.175320i | |||||
0 | 0 | |||||||||
−17.1258 | + | 29.6627i | −1.00740 | + | 1.74486i | |||||
0 | 0 | |||||||||
21.8270 | + | 4.05239i | 1.27952 | + | 0.237555i | |||||
0 | 0 | |||||||||
11.8556 | + | 20.5345i | 0.692612 | + | 1.19964i | 0.970979 | + | 0.239164i | ||
−0.278367 | + | 0.960475i | ||||||||
0 | 0 | |||||||||
−1.93274 | + | 3.34760i | −0.112528 | + | 0.194905i | |||||
0 | 0 | |||||||||
11.4064 | + | 7.00440i | 0.661865 | + | 0.406437i | |||||
0 | 0 | |||||||||
0.680950 | + | 1.17944i | 0.0393803 | + | 0.0682088i | |||||
0 | 0 | |||||||||
−7.45698 | + | 20.6137i | −0.429813 | + | 1.18816i | |||||
0 | 0 | |||||||||
7.04829 | + | 19.9233i | 0.404913 | + | 1.14456i | |||||
0 | 0 | |||||||||
−12.0258 | − | 20.8293i | −0.688597 | − | 1.19268i | |||||
0 | 0 | |||||||||
3.87810 | 0.221335 | 0.110668 | − | 0.993857i | ||||||
0.110668 | + | 0.993857i | ||||||||
0 | 0 | |||||||||
7.88124 | + | 22.2778i | 0.448348 | + | 1.26734i | |||||
0 | 0 | |||||||||
3.46220 | − | 5.99670i | 0.196323 | − | 0.340042i | −0.751010 | − | 0.660290i | ||
0.947333 | + | 0.320249i | ||||||||
0 | 0 | |||||||||
−15.1157 | − | 26.1811i | −0.854388 | − | 1.47984i | −0.877212 | − | 0.480104i | ||
0.0228236 | − | 0.999740i | ||||||||
0 | 0 | |||||||||
9.64935 | − | 11.1305i | 0.543679 | − | 0.627133i | |||||
0 | 0 | |||||||||
−4.68699 | − | 8.11811i | −0.263248 | − | 0.455959i | 0.703855 | − | 0.710343i | ||
−0.967103 | + | 0.254385i | ||||||||
0 | 0 | |||||||||
−2.37913 | + | 4.12077i | −0.133205 | + | 0.230719i | |||||
0 | 0 | |||||||||
−22.0703 | − | 4.09755i | −1.23184 | − | 0.228703i | |||||
0 | 0 | |||||||||
9.11484 | 0.507163 | |||||||||
0 | 0 | |||||||||
−4.39027 | − | 7.60418i | −0.243529 | − | 0.421804i | |||||
0 | 0 | |||||||||
−17.3314 | + | 20.2797i | −0.958428 | + | 1.12147i | |||||
0 | 0 | |||||||||
−20.9916 | − | 24.9173i | −1.15731 | − | 1.37374i | |||||
0 | 0 | |||||||||
−13.7720 | − | 23.8539i | −0.756979 | − | 1.31113i | −0.944384 | − | 0.328844i | ||
0.187405 | − | 0.982283i | ||||||||
0 | 0 | |||||||||
0.316254 | + | 2.00477i | 0.0173306 | + | 0.109861i | |||||
0 | 0 | |||||||||
4.48298 | − | 7.76475i | 0.244931 | − | 0.424234i | |||||
0 | 0 | |||||||||
−3.41673 | − | 5.91796i | −0.186121 | − | 0.322372i | 0.757832 | − | 0.652449i | ||
−0.943954 | + | 0.330078i | ||||||||
0 | 0 | |||||||||
17.4069 | − | 20.3681i | 0.945415 | − | 1.10625i | |||||
0 | 0 | |||||||||
−3.85246 | + | 6.67266i | −0.208622 | + | 0.361345i | |||||
0 | 0 | |||||||||
−15.9842 | + | 9.35445i | −0.863065 | + | 0.505093i | |||||
0 | 0 | |||||||||
0.258673 | + | 0.731188i | 0.0139265 | + | 0.0393658i | |||||
0 | 0 | |||||||||
−10.0959 | + | 17.4867i | −0.541979 | + | 0.938735i | 0.456812 | + | 0.889564i | ||
−0.998790 | + | 0.0491714i | ||||||||
0 | 0 | |||||||||
−4.25154 | + | 7.36388i | −0.227580 | + | 0.394180i | −0.957090 | − | 0.289790i | ||
0.729511 | + | 0.683970i | ||||||||
0 | 0 | |||||||||
0.794966 | − | 29.3191i | 0.0424321 | − | 1.56494i | |||||
0 | 0 | |||||||||
4.70904 | 0.250637 | 0.125318 | − | 0.992117i | ||||||
0.125318 | + | 0.992117i | ||||||||
0 | 0 | |||||||||
−2.85107 | −0.151319 | |||||||||
0 | 0 | |||||||||
16.6039 | − | 28.2948i | 0.878771 | − | 1.49752i | |||||
0 | 0 | |||||||||
6.03357 | − | 10.4504i | 0.318440 | − | 0.551554i | −0.661723 | − | 0.749748i | ||
0.980163 | + | 0.198195i | ||||||||
0 | 0 | |||||||||
8.68948 | + | 15.0506i | 0.457341 | + | 0.792138i | |||||
0 | 0 | |||||||||
−2.52104 | − | 7.12619i | −0.132320 | − | 0.374028i | |||||
0 | 0 | |||||||||
−12.1739 | − | 21.0859i | −0.637213 | − | 1.10369i | |||||
0 | 0 | |||||||||
0.960711 | 0.0501487 | 0.0250744 | − | 0.999686i | ||||||
0.0250744 | + | 0.999686i | ||||||||
0 | 0 | |||||||||
4.11013 | + | 1.58065i | 0.213965 | + | 0.0822854i | |||||
0 | 0 | |||||||||
−11.4384 | − | 13.5775i | −0.593850 | − | 0.704908i | |||||
0 | 0 | |||||||||
−7.04998 | −0.365034 | −0.182517 | − | 0.983203i | ||||||
−0.182517 | + | 0.983203i | ||||||||
0 | 0 | |||||||||
−7.02822 | − | 19.8666i | −0.362936 | − | 1.02591i | |||||
0 | 0 | |||||||||
10.4263 | 0.536980 | |||||||||
0 | 0 | |||||||||
−37.1330 | −1.90739 | −0.953697 | − | 0.300769i | ||||||
−0.953697 | + | 0.300769i | ||||||||
0 | 0 | |||||||||
−1.84509 | − | 5.21549i | −0.0945267 | − | 0.267198i | |||||
0 | 0 | |||||||||
32.1975 | 1.64522 | 0.822608 | − | 0.568609i | ||||||
0.822608 | + | 0.568609i | ||||||||
0 | 0 | |||||||||
12.4524 | − | 2.22092i | 0.634635 | − | 0.113189i | |||||
0 | 0 | |||||||||
3.87317 | + | 24.5525i | 0.196884 | + | 1.24807i | |||||
0 | 0 | |||||||||
−25.7426 | −1.30520 | −0.652600 | − | 0.757702i | ||||||
−0.652600 | + | 0.757702i | ||||||||
0 | 0 | |||||||||
0.863654 | + | 1.49589i | 0.0436769 | + | 0.0756506i | |||||
0 | 0 | |||||||||
8.13743 | + | 23.0020i | 0.410479 | + | 1.16030i | |||||
0 | 0 | |||||||||
3.45217 | + | 5.97933i | 0.173697 | + | 0.300853i | |||||
0 | 0 | |||||||||
9.44903 | − | 16.3662i | 0.474233 | − | 0.821396i | −0.525332 | − | 0.850898i | ||
0.999565 | + | 0.0295016i | ||||||||
0 | 0 | |||||||||
−5.83438 | − | 0.0412635i | −0.292084 | − | 0.00206576i | |||||
0 | 0 | |||||||||
15.2039 | 0.759245 | 0.379622 | − | 0.925142i | ||||||
0.379622 | + | 0.925142i | ||||||||
0 | 0 | |||||||||
16.8830 | 0.841002 | |||||||||
0 | 0 | |||||||||
3.49300 | − | 16.3339i | 0.173569 | − | 0.811639i | |||||
0 | 0 | |||||||||
−0.871362 | + | 1.50924i | −0.0431918 | + | 0.0748104i | |||||
0 | 0 | |||||||||
14.9729 | − | 25.9339i | 0.740363 | − | 1.28235i | −0.211967 | − | 0.977277i | ||
0.952330 | − | 0.305070i | ||||||||
0 | 0 | |||||||||
7.91191 | + | 22.3645i | 0.390266 | + | 1.10316i | |||||
0 | 0 | |||||||||
1.87454 | − | 5.18191i | 0.0922403 | − | 0.254985i | |||||
0 | 0 | |||||||||
−5.57096 | + | 9.64918i | −0.273468 | + | 0.473660i | |||||
0 | 0 | |||||||||
11.1207 | − | 13.0126i | 0.544585 | − | 0.637229i | |||||
0 | 0 | |||||||||
−12.2660 | − | 21.2453i | −0.599231 | − | 1.03790i | −0.992935 | − | 0.118661i | ||
0.393704 | − | 0.919237i | ||||||||
0 | 0 | |||||||||
−2.37791 | + | 4.11866i | −0.115892 | + | 0.200731i | −0.918136 | − | 0.396265i | ||
0.802244 | + | 0.596996i | ||||||||
0 | 0 | |||||||||
−34.4814 | − | 13.2606i | −1.67654 | − | 0.644755i | |||||
0 | 0 | |||||||||
−5.56822 | − | 9.64444i | −0.270098 | − | 0.467824i | |||||
0 | 0 | |||||||||
22.0911 | + | 26.2224i | 1.06906 | + | 1.26899i | |||||
0 | 0 | |||||||||
16.3621 | − | 19.1455i | 0.789968 | − | 0.924355i | |||||
0 | 0 | |||||||||
1.36446 | + | 2.36331i | 0.0657237 | + | 0.113837i | 0.897015 | − | 0.442000i | ||
−0.831291 | + | 0.555837i | ||||||||
0 | 0 | |||||||||
14.5592 | 0.699672 | 0.349836 | − | 0.936811i | ||||||
0.349836 | + | 0.936811i | ||||||||
0 | 0 | |||||||||
5.83794 | + | 1.08387i | 0.279908 | + | 0.0519674i | |||||
0 | 0 | |||||||||
0.153597 | − | 0.266037i | 0.00734753 | − | 0.0127263i | |||||
0 | 0 | |||||||||
1.44066 | + | 2.49529i | 0.0687587 | + | 0.119094i | 0.898355 | − | 0.439270i | ||
−0.829596 | + | 0.558363i | ||||||||
0 | 0 | |||||||||
−10.7562 | + | 18.0362i | −0.512199 | + | 0.858867i | |||||
0 | 0 | |||||||||
−12.4865 | − | 21.6273i | −0.593254 | − | 1.02755i | −0.993791 | − | 0.111265i | ||
0.400537 | − | 0.916281i | ||||||||
0 | 0 | |||||||||
12.2555 | − | 21.2272i | 0.580967 | − | 1.00626i | |||||
0 | 0 | |||||||||
−2.26462 | − | 6.40138i | −0.107113 | − | 0.302775i | |||||
0 | 0 | |||||||||
−2.99154 | −0.141180 | −0.0705898 | − | 0.997505i | ||||||
−0.0705898 | + | 0.997505i | ||||||||
0 | 0 | |||||||||
1.89062 | + | 3.27464i | 0.0890257 | + | 0.154197i | |||||
0 | 0 | |||||||||
11.3098 | + | 31.9692i | 0.531379 | + | 1.50205i | |||||
0 | 0 | |||||||||
−17.8574 | − | 21.1969i | −0.837166 | − | 0.993727i | |||||
0 | 0 | |||||||||
12.8085 | + | 22.1850i | 0.599158 | + | 1.03777i | 0.992946 | + | 0.118571i | ||
−0.393788 | + | 0.919201i | ||||||||
0 | 0 | |||||||||
1.00826 | − | 37.1857i | 0.0470616 | − | 1.73568i | |||||
0 | 0 | |||||||||
−6.45759 | + | 11.1849i | −0.300760 | + | 0.520931i | −0.976308 | − | 0.216384i | ||
0.675548 | + | 0.737316i | ||||||||
0 | 0 | |||||||||
−12.2457 | − | 21.2102i | −0.569108 | − | 0.985724i | −0.996654 | − | 0.0817305i | ||
0.427547 | − | 0.903993i | ||||||||
0 | 0 | |||||||||
9.45324 | + | 1.75508i | 0.438383 | + | 0.0813898i | |||||
0 | 0 | |||||||||
−10.4087 | + | 18.0283i | −0.481655 | + | 0.834251i | −0.999778 | − | 0.0210550i | ||
0.518123 | + | 0.855306i | ||||||||
0 | 0 | |||||||||
−4.34800 | + | 12.0194i | −0.200772 | + | 0.555005i | |||||
0 | 0 | |||||||||
−25.1913 | − | 4.67699i | −1.16075 | − | 0.215504i | |||||
0 | 0 | |||||||||
−10.6716 | + | 18.4838i | −0.490681 | + | 0.849884i | |||||
0 | 0 | |||||||||
−0.990281 | + | 1.71522i | −0.0454372 | + | 0.0786996i | |||||
0 | 0 | |||||||||
−18.7890 | − | 7.22575i | −0.860288 | − | 0.330844i | |||||
0 | 0 | |||||||||
27.4873 | 1.25592 | 0.627962 | − | 0.778244i | ||||||
0.627962 | + | 0.778244i | ||||||||
0 | 0 | |||||||||
3.81865 | 0.174115 | |||||||||
0 | 0 | |||||||||
−0.546050 | − | 0.961425i | −0.0248461 | − | 0.0437464i | |||||
0 | 0 | |||||||||
11.8938 | − | 20.6007i | 0.540070 | − | 0.935429i | |||||
0 | 0 | |||||||||
−6.32927 | − | 10.9626i | −0.286807 | − | 0.496763i | 0.686239 | − | 0.727376i | ||
−0.973046 | + | 0.230613i | ||||||||
0 | 0 | |||||||||
25.7038 | + | 4.77215i | 1.16237 | + | 0.215804i | |||||
0 | 0 | |||||||||
−1.40618 | − | 2.43557i | −0.0634598 | − | 0.109916i | 0.832550 | − | 0.553950i | ||
−0.896010 | + | 0.444034i | ||||||||
0 | 0 | |||||||||
13.2237 | 0.595566 | |||||||||
0 | 0 | |||||||||
11.1518 | − | 9.01917i | 0.501238 | − | 0.405381i | |||||
0 | 0 | |||||||||
4.00128 | − | 0.713638i | 0.179482 | − | 0.0320110i | |||||
0 | 0 | |||||||||
−4.24205 | −0.189900 | −0.0949502 | − | 0.995482i | ||||||
−0.0949502 | + | 0.995482i | ||||||||
0 | 0 | |||||||||
−4.34237 | + | 5.08108i | −0.194003 | + | 0.227006i | |||||
0 | 0 | |||||||||
22.2162 | 0.990570 | 0.495285 | − | 0.868730i | ||||||
0.495285 | + | 0.868730i | ||||||||
0 | 0 | |||||||||
22.6446 | 1.00767 | |||||||||
0 | 0 | |||||||||
−32.1191 | − | 5.96319i | −1.42646 | − | 0.264835i | |||||
0 | 0 | |||||||||
−4.85469 | −0.215180 | −0.107590 | − | 0.994195i | ||||||
−0.107590 | + | 0.994195i | ||||||||
0 | 0 | |||||||||
22.3632 | + | 26.5454i | 0.989290 | + | 1.17430i | |||||
0 | 0 | |||||||||
−5.81694 | + | 3.15136i | −0.256824 | + | 0.139136i | |||||
0 | 0 | |||||||||
25.3207 | 1.11576 | |||||||||
0 | 0 | |||||||||
−15.8611 | − | 27.4722i | −0.697569 | − | 1.20823i | |||||
0 | 0 | |||||||||
0.733203 | − | 0.857933i | 0.0321840 | − | 0.0376591i | |||||
0 | 0 | |||||||||
7.92316 | + | 13.7233i | 0.347120 | + | 0.601229i | 0.985737 | − | 0.168296i | ||
−0.638617 | + | 0.769525i | ||||||||
0 | 0 | |||||||||
10.7605 | − | 18.6377i | 0.470524 | − | 0.814972i | −0.528908 | − | 0.848679i | ||
0.999432 | + | 0.0337078i | ||||||||
0 | 0 | |||||||||
3.52054 | + | 6.19858i | 0.153649 | + | 0.270528i | |||||
0 | 0 | |||||||||
21.4128 | 0.932758 | |||||||||
0 | 0 | |||||||||
−22.9418 | −0.997469 | |||||||||
0 | 0 | |||||||||
−0.973643 | − | 6.17204i | −0.0422525 | − | 0.267844i | |||||
0 | 0 | |||||||||
4.14271 | − | 7.17539i | 0.179441 | − | 0.310801i | |||||
0 | 0 | |||||||||
−12.0264 | + | 20.8303i | −0.519945 | + | 0.900572i | |||||
0 | 0 | |||||||||
−24.5445 | + | 28.7199i | −1.05917 | + | 1.23936i | |||||
0 | 0 | |||||||||
−16.9202 | + | 6.23382i | −0.728806 | + | 0.268510i | |||||
0 | 0 | |||||||||
7.55977 | − | 13.0939i | 0.325020 | − | 0.562951i | −0.656497 | − | 0.754329i | ||
0.981516 | + | 0.191378i | ||||||||
0 | 0 | |||||||||
−14.4612 | − | 40.8772i | −0.620588 | − | 1.75421i | |||||
0 | 0 | |||||||||
14.2922 | + | 24.7548i | 0.612211 | + | 1.06038i | |||||
0 | 0 | |||||||||
−19.4532 | + | 33.6939i | −0.831757 | + | 1.44065i | 0.0648863 | + | 0.997893i | ||
−0.896644 | + | 0.442753i | ||||||||
0 | 0 | |||||||||
36.2875 | + | 13.9552i | 1.54871 | + | 0.595594i | |||||
0 | 0 | |||||||||
−1.17589 | − | 2.03670i | −0.0500945 | − | 0.0867662i | |||||
0 | 0 | |||||||||
−6.34154 | − | 7.52749i | −0.269670 | − | 0.320101i | |||||
0 | 0 | |||||||||
2.13816 | + | 0.396969i | 0.0907600 | + | 0.0168504i | |||||
0 | 0 | |||||||||
−5.37036 | − | 9.30173i | −0.227549 | − | 0.394127i | 0.729532 | − | 0.683947i | ||
−0.957081 | + | 0.289820i | ||||||||
0 | 0 | |||||||||
46.7672 | 1.97804 | |||||||||
0 | 0 | |||||||||
20.7521 | − | 24.2824i | 0.876156 | − | 1.02520i | |||||
0 | 0 | |||||||||
11.7380 | − | 20.3308i | 0.494697 | − | 0.856840i | −0.505285 | − | 0.862953i | ||
0.999981 | + | 0.00611281i | ||||||||
0 | 0 | |||||||||
−14.3545 | − | 24.8627i | −0.603898 | − | 1.04598i | |||||
0 | 0 | |||||||||
−0.813726 | + | 23.7979i | −0.0341733 | + | 0.999416i | |||||
0 | 0 | |||||||||
18.9681 | + | 32.8537i | 0.795183 | + | 1.37730i | 0.922723 | + | 0.385463i | ||
−0.127540 | + | 0.991833i | ||||||||
0 | 0 | |||||||||
2.15815 | − | 3.73803i | 0.0903158 | − | 0.156432i | −0.817328 | − | 0.576172i | ||
0.907644 | + | 0.419741i | ||||||||
0 | 0 | |||||||||
9.74578 | − | 11.4037i | 0.407136 | − | 0.476396i | |||||
0 | 0 | |||||||||
−0.375326 | −0.0156522 | |||||||||
0 | 0 | |||||||||
−5.05923 | − | 8.76284i | −0.210618 | − | 0.364802i | 0.741290 | − | 0.671185i | ||
−0.951908 | + | 0.306383i | ||||||||
0 | 0 | |||||||||
−2.75306 | − | 0.511131i | −0.114413 | − | 0.0212419i | |||||
0 | 0 | |||||||||
5.40322 | − | 14.9364i | 0.224163 | − | 0.619667i | |||||
0 | 0 | |||||||||
−8.64272 | − | 14.9696i | −0.357945 | − | 0.619979i | |||||
0 | 0 | |||||||||
−29.3330 | − | 11.2807i | −1.21277 | − | 0.466400i | |||||
0 | 0 | |||||||||
−4.10992 | + | 7.11859i | −0.169635 | + | 0.293816i | −0.938291 | − | 0.345846i | ||
0.768657 | + | 0.639661i | ||||||||
0 | 0 | |||||||||
−1.90409 | − | 3.29797i | −0.0784565 | − | 0.135891i | |||||
0 | 0 | |||||||||
6.22412 | + | 17.5937i | 0.256026 | + | 0.723706i | |||||
0 | 0 | |||||||||
21.8434 | − | 37.8339i | 0.897002 | − | 1.55365i | 0.0656957 | − | 0.997840i | ||
0.831307 | − | 0.555814i | ||||||||
0 | 0 | |||||||||
−22.6486 | − | 26.8842i | −0.928504 | − | 1.10215i | |||||
0 | 0 | |||||||||
−5.37363 | + | 6.28778i | −0.219928 | + | 0.257342i | |||||
0 | 0 | |||||||||
7.63946 | − | 13.2319i | 0.312140 | − | 0.540642i | −0.666686 | − | 0.745339i | ||
0.978825 | + | 0.204697i | ||||||||
0 | 0 | |||||||||
7.65696 | − | 13.2622i | 0.312334 | − | 0.540978i | −0.666533 | − | 0.745475i | ||
0.978867 | + | 0.204497i | ||||||||
0 | 0 | |||||||||
2.25836 | + | 14.3160i | 0.0919676 | + | 0.582994i | |||||
0 | 0 | |||||||||
−8.09955 | −0.329293 | |||||||||
0 | 0 | |||||||||
−2.66981 | −0.108364 | −0.0541821 | − | 0.998531i | ||||||
−0.0541821 | + | 0.998531i | ||||||||
0 | 0 | |||||||||
−8.46445 | − | 0.0598647i | −0.342997 | − | 0.00242584i | |||||
0 | 0 | |||||||||
−34.7547 | + | 60.1970i | −1.40603 | + | 2.43531i | |||||
0 | 0 | |||||||||
−13.5875 | − | 23.5343i | −0.548796 | − | 0.950542i | −0.998357 | − | 0.0572929i | ||
0.449562 | − | 0.893249i | ||||||||
0 | 0 | |||||||||
3.06554 | − | 3.58703i | 0.123614 | − | 0.144643i | |||||
0 | 0 | |||||||||
−17.6058 | − | 30.4942i | −0.708785 | − | 1.22765i | −0.965308 | − | 0.261113i | ||
0.256524 | − | 0.966538i | ||||||||
0 | 0 | |||||||||
−31.2681 | −1.25677 | −0.628385 | − | 0.777902i | ||||||
−0.628385 | + | 0.777902i | ||||||||
0 | 0 | |||||||||
−1.06836 | − | 0.656055i | −0.0428717 | − | 0.0263266i | |||||
0 | 0 | |||||||||
−11.8865 | + | 32.8585i | −0.476223 | + | 1.31645i | |||||
0 | 0 | |||||||||
−14.8023 | −0.592090 | |||||||||
0 | 0 | |||||||||
−5.58528 | − | 1.03696i | −0.223055 | − | 0.0414121i | |||||
0 | 0 | |||||||||
4.84322 | 0.193112 | |||||||||
0 | 0 | |||||||||
15.5090 | 0.617403 | 0.308702 | − | 0.951159i | ||||||
0.308702 | + | 0.951159i | ||||||||
0 | 0 | |||||||||
−5.46409 | + | 6.39363i | −0.217178 | + | 0.254124i | |||||
0 | 0 | |||||||||
−5.92787 | −0.235240 | |||||||||
0 | 0 | |||||||||
30.3673 | + | 25.2786i | 1.20320 | + | 1.00158i | |||||
0 | 0 | |||||||||
3.58337 | − | 2.89809i | 0.141756 | − | 0.114647i | |||||
0 | 0 | |||||||||
−33.5310 | −1.32440 | −0.662198 | − | 0.749329i | ||||||
−0.662198 | + | 0.749329i | ||||||||
0 | 0 | |||||||||
−10.2721 | − | 17.7918i | −0.405093 | − | 0.701641i | 0.589239 | − | 0.807958i | ||
−0.994332 | + | 0.106317i | ||||||||
0 | 0 | |||||||||
26.1862 | + | 4.86170i | 1.03108 | + | 0.191429i | |||||
0 | 0 | |||||||||
−16.8855 | − | 29.2465i | −0.663836 | − | 1.14980i | −0.979599 | − | 0.200960i | ||
0.315763 | − | 0.948838i | ||||||||
0 | 0 | |||||||||
2.68264 | − | 4.64647i | 0.105303 | − | 0.182390i | |||||
0 | 0 | |||||||||
−13.7063 | − | 0.0969374i | −0.537191 | − | 0.00379928i | |||||
0 | 0 | |||||||||
18.0115 | 0.704845 | 0.352423 | − | 0.935841i | ||||||
0.352423 | + | 0.935841i | ||||||||
0 | 0 | |||||||||
26.1438 | 1.02152 | |||||||||
0 | 0 | |||||||||
36.7344 | + | 14.1271i | 1.43315 | + | 0.551150i | |||||
0 | 0 | |||||||||
1.42710 | − | 2.47180i | 0.0555918 | − | 0.0962878i | −0.836890 | − | 0.547371i | ||
0.892482 | + | 0.451083i | ||||||||
0 | 0 | |||||||||
−7.02746 | + | 12.1719i | −0.273337 | + | 0.473433i | −0.969714 | − | 0.244243i | ||
0.696378 | + | 0.717676i | ||||||||
0 | 0 | |||||||||
−68.8151 | − | 12.7761i | −2.67256 | − | 0.496184i | |||||
0 | 0 | |||||||||
−2.12669 | + | 5.87892i | −0.0824695 | + | 0.227975i | |||||
0 | 0 | |||||||||
0.222837 | − | 0.385964i | 0.00862827 | − | 0.0149446i | |||||
0 | 0 | |||||||||
13.1532 | + | 2.44200i | 0.508530 | + | 0.0944132i | |||||
0 | 0 | |||||||||
16.6918 | + | 28.9111i | 0.644381 | + | 1.11610i | |||||
0 | 0 | |||||||||
−7.54157 | + | 13.0624i | −0.290706 | + | 0.503518i | −0.973977 | − | 0.226647i | ||
0.683271 | + | 0.730165i | ||||||||
0 | 0 | |||||||||
6.88800 | + | 4.22977i | 0.265119 | + | 0.162804i | |||||
0 | 0 | |||||||||
18.1093 | + | 31.3663i | 0.695998 | + | 1.20550i | 0.969843 | + | 0.243731i | ||
−0.273845 | + | 0.961774i | ||||||||
0 | 0 | |||||||||
−11.5357 | + | 31.8887i | −0.442699 | + | 1.22378i | |||||
0 | 0 | |||||||||
−8.05794 | − | 22.7773i | −0.308781 | − | 0.872828i | |||||
0 | 0 | |||||||||
8.84350 | + | 15.3174i | 0.338387 | + | 0.586104i | 0.984130 | − | 0.177452i | ||
−0.645742 | + | 0.763555i | ||||||||
0 | 0 | |||||||||
25.4193 | 0.971220 | |||||||||
0 | 0 | |||||||||
0.924422 | + | 2.61305i | 0.0352689 | + | 0.0996942i | |||||
0 | 0 | |||||||||
−18.9379 | + | 32.8014i | −0.721477 | + | 1.24963i | |||||
0 | 0 | |||||||||
−11.2049 | − | 19.4074i | −0.426253 | − | 0.738292i | 0.570283 | − | 0.821448i | ||
−0.996537 | + | 0.0831559i | ||||||||
0 | 0 | |||||||||
−13.3933 | + | 15.4491i | −0.508769 | + | 0.586865i | |||||
0 | 0 | |||||||||
−9.17064 | − | 15.8840i | −0.347862 | − | 0.602515i | |||||
0 | 0 | |||||||||
5.25424 | − | 9.10061i | 0.199018 | − | 0.344710i | |||||
0 | 0 | |||||||||
12.5997 | + | 2.33925i | 0.476566 | + | 0.0884787i | |||||
0 | 0 | |||||||||
−31.1776 | −1.17756 | −0.588781 | − | 0.808293i | ||||||
−0.588781 | + | 0.808293i | ||||||||
0 | 0 | |||||||||
−0.430672 | − | 0.745946i | −0.0162431 | − | 0.0281339i | |||||
0 | 0 | |||||||||
−25.7179 | + | 30.0929i | −0.968592 | + | 1.13337i | |||||
0 | 0 | |||||||||
−31.7802 | + | 5.66806i | −1.19522 | + | 0.213170i | |||||
0 | 0 | |||||||||
4.02492 | + | 6.97137i | 0.151159 | + | 0.261815i | 0.931654 | − | 0.363347i | ||
−0.780495 | + | 0.625162i | ||||||||
0 | 0 | |||||||||
−10.4168 | − | 4.00602i | −0.390660 | − | 0.150238i | |||||
0 | 0 | |||||||||
0.360834 | − | 0.624982i | 0.0135133 | − | 0.0234058i | |||||
0 | 0 | |||||||||
−13.4929 | − | 23.3703i | −0.504604 | − | 0.874000i | |||||
0 | 0 | |||||||||
2.81585 | − | 3.29487i | 0.105160 | − | 0.123049i | |||||
0 | 0 | |||||||||
−20.9980 | + | 36.3696i | −0.783093 | + | 1.35636i | 0.147039 | + | 0.989131i | ||
−0.930132 | + | 0.367226i | ||||||||
0 | 0 | |||||||||
−35.5359 | + | 6.33791i | −1.32343 | + | 0.236036i | |||||
0 | 0 | |||||||||
2.45102 | + | 6.92827i | 0.0911543 | + | 0.257665i | |||||
0 | 0 | |||||||||
−1.43669 | + | 2.48842i | −0.0533573 | + | 0.0924176i | |||||
0 | 0 | |||||||||
0.668774 | − | 1.15835i | 0.0248035 | − | 0.0429609i | −0.853357 | − | 0.521327i | ||
0.878161 | + | 0.478366i | ||||||||
0 | 0 | |||||||||
12.2131 | + | 24.0799i | 0.452337 | + | 0.891847i | |||||
0 | 0 | |||||||||
59.3152 | 2.19385 | |||||||||
0 | 0 | |||||||||
29.4749 | 1.08868 | 0.544340 | − | 0.838865i | ||||||
0.544340 | + | 0.838865i | ||||||||
0 | 0 | |||||||||
14.3756 | + | 17.3110i | 0.530252 | + | 0.638527i | |||||
0 | 0 | |||||||||
−6.22238 | + | 10.7775i | −0.229204 | + | 0.396993i | |||||
0 | 0 | |||||||||
9.52146 | + | 16.4916i | 0.350252 | + | 0.606655i | 0.986294 | − | 0.165000i | ||
−0.636041 | + | 0.771655i | ||||||||
0 | 0 | |||||||||
4.15146 | + | 11.7349i | 0.152508 | + | 0.431092i | |||||
0 | 0 | |||||||||
21.6613 | + | 37.5185i | 0.794676 | + | 1.37642i | 0.923045 | + | 0.384693i | ||
−0.128369 | + | 0.991726i | ||||||||
0 | 0 | |||||||||
−7.27573 | −0.266562 | |||||||||
0 | 0 | |||||||||
−2.80645 | − | 17.7904i | −0.102682 | − | 0.650917i | |||||
0 | 0 | |||||||||
11.6643 | − | 32.2441i | 0.426203 | − | 1.17818i | |||||
0 | 0 | |||||||||
34.8763 | 1.27265 | 0.636327 | − | 0.771420i | ||||||
0.636327 | + | 0.771420i | ||||||||
0 | 0 | |||||||||
−7.82049 | − | 22.1061i | −0.284994 | − | 0.805591i | |||||
0 | 0 | |||||||||
36.3358 | 1.32240 | |||||||||
0 | 0 | |||||||||
8.67255 | 0.315209 | 0.157605 | − | 0.987502i | ||||||
0.157605 | + | 0.987502i | ||||||||
0 | 0 | |||||||||
−0.359038 | − | 1.01489i | −0.0130322 | − | 0.0368381i | |||||
0 | 0 | |||||||||
−5.48977 | −0.199004 | −0.0995021 | − | 0.995037i | ||||||
−0.0995021 | + | 0.995037i | ||||||||
0 | 0 | |||||||||
−26.2544 | − | 31.1643i | −0.950473 | − | 1.12822i | |||||
0 | 0 | |||||||||
−37.2033 | − | 14.3074i | −1.34509 | − | 0.517285i | |||||
0 | 0 | |||||||||
−11.7564 | −0.424499 | |||||||||
0 | 0 | |||||||||
1.81365 | + | 3.14134i | 0.0654021 | + | 0.113280i | 0.896872 | − | 0.442290i | ||
−0.831470 | + | 0.555569i | ||||||||
0 | 0 | |||||||||
−3.55550 | − | 10.0503i | −0.128048 | − | 0.361953i | |||||
0 | 0 | |||||||||
−6.96717 | − | 12.0675i | −0.250592 | − | 0.434037i | 0.713097 | − | 0.701065i | ||
−0.963689 | + | 0.267028i | ||||||||
0 | 0 | |||||||||
−2.32640 | + | 4.02944i | −0.0835666 | + | 0.144742i | |||||
0 | 0 | |||||||||
−3.10013 | − | 0.0219256i | −0.111217 | − | 0.000786577i | |||||
0 | 0 | |||||||||
−1.86888 | −0.0669597 | |||||||||
0 | 0 | |||||||||
3.95729 | 0.141603 | |||||||||
0 | 0 | |||||||||
−8.43916 | + | 4.57196i | −0.301591 | + | 0.163388i | |||||
0 | 0 | |||||||||
−13.7270 | + | 23.7759i | −0.489939 | + | 0.848599i | |||||
0 | 0 | |||||||||
−8.78923 | + | 15.2234i | −0.313302 | + | 0.542655i | −0.979075 | − | 0.203499i | ||
0.665773 | + | 0.746154i | ||||||||
0 | 0 | |||||||||
−14.6387 | − | 41.3790i | −0.521151 | − | 1.47313i | |||||
0 | 0 | |||||||||
26.3688 | + | 31.3001i | 0.937567 | + | 1.11290i | |||||
0 | 0 | |||||||||
36.5751 | − | 63.3499i | 1.29882 | − | 2.24962i | |||||
0 | 0 | |||||||||
−14.0137 | + | 16.3977i | −0.497015 | + | 0.581566i | |||||
0 | 0 | |||||||||
5.57971 | + | 9.66434i | 0.197644 | + | 0.342329i | 0.947764 | − | 0.318973i | ||
−0.750120 | + | 0.661301i | ||||||||
0 | 0 | |||||||||
−44.0797 | + | 76.3483i | −1.55943 | + | 2.70101i | |||||
0 | 0 | |||||||||
6.17388 | + | 39.1370i | 0.218143 | + | 1.38284i | |||||
0 | 0 | |||||||||
16.8974 | + | 29.2672i | 0.596297 | + | 1.03282i | |||||
0 | 0 | |||||||||
−1.16634 | + | 0.208019i | −0.0411079 | + | 0.00733169i | |||||
0 | 0 | |||||||||
12.2001 | − | 14.2756i | 0.429466 | − | 0.502525i | |||||
0 | 0 | |||||||||
14.3481 | + | 24.8517i | 0.504453 | + | 0.873738i | 0.999987 | + | 0.00514935i | ||
−0.495534 | + | 0.868589i | ||||||||
0 | 0 | |||||||||
47.1695 | 1.65635 | 0.828173 | − | 0.560473i | ||||||
0.828173 | + | 0.560473i | ||||||||
0 | 0 | |||||||||
−51.1513 | − | 9.49670i | −1.79396 | − | 0.333064i | |||||
0 | 0 | |||||||||
14.0063 | − | 24.2597i | 0.490620 | − | 0.849779i | |||||
0 | 0 | |||||||||
−5.27446 | − | 9.13563i | −0.184530 | − | 0.319615i | |||||
0 | 0 | |||||||||
43.9905 | + | 8.48949i | 1.53715 | + | 0.296647i | |||||
0 | 0 | |||||||||
19.3854 | + | 33.5765i | 0.676554 | + | 1.17183i | 0.976012 | + | 0.217717i | ||
−0.299458 | + | 0.954110i | ||||||||
0 | 0 | |||||||||
11.3920 | − | 19.7316i | 0.397101 | − | 0.687799i | −0.596266 | − | 0.802787i | ||
0.993367 | + | 0.114988i | ||||||||
0 | 0 | |||||||||
2.31482 | + | 6.54327i | 0.0805916 | + | 0.227807i | |||||
0 | 0 | |||||||||
−1.55152 | −0.0539515 | −0.0269758 | − | 0.999636i | ||||||
−0.0269758 | + | 0.999636i | ||||||||
0 | 0 | |||||||||
−23.8972 | − | 41.3911i | −0.829983 | − | 1.43757i | −0.898051 | − | 0.439892i | ||
0.0680673 | − | 0.997681i | ||||||||
0 | 0 | |||||||||
11.4164 | + | 32.2706i | 0.396030 | + | 1.11945i | |||||
0 | 0 | |||||||||
38.5151 | + | 32.0611i | 1.33447 | + | 1.11085i | |||||
0 | 0 | |||||||||
3.58090 | + | 6.20231i | 0.123922 | + | 0.214640i | |||||
0 | 0 | |||||||||
−13.6653 | + | 7.40326i | −0.472342 | + | 0.255894i | |||||
0 | 0 | |||||||||
19.5804 | − | 33.9142i | 0.675990 | − | 1.17085i | −0.300188 | − | 0.953880i | ||
0.976178 | − | 0.216970i | ||||||||
0 | 0 | |||||||||
12.7940 | + | 22.1599i | 0.441174 | + | 0.764135i | |||||
0 | 0 | |||||||||
−13.5758 | − | 2.52046i | −0.467574 | − | 0.0868093i | |||||
0 | 0 | |||||||||
−17.5021 | + | 30.3145i | −0.602089 | + | 1.04285i | |||||
0 | 0 | |||||||||
11.3672 | − | 2.02736i | 0.390580 | − | 0.0696609i | |||||
0 | 0 | |||||||||
−39.5301 | − | 7.33911i | −1.35667 | − | 0.251877i | |||||
0 | 0 | |||||||||
0.0816145 | − | 0.141361i | 0.00279771 | − | 0.00484578i | |||||
0 | 0 | |||||||||
14.5234 | − | 25.1552i | 0.497270 | − | 0.861298i | −0.502725 | − | 0.864447i | ||
0.999995 | + | 0.00314895i | ||||||||
0 | 0 | |||||||||
1.10461 | + | 7.00224i | 0.0377768 | + | 0.239472i | |||||
0 | 0 | |||||||||
−48.2584 | −1.64848 | −0.824239 | − | 0.566243i | ||||||
−0.824239 | + | 0.566243i | ||||||||
0 | 0 | |||||||||
−10.1506 | −0.346332 | −0.173166 | − | 0.984893i | ||||||
−0.173166 | + | 0.984893i | ||||||||
0 | 0 | |||||||||
−3.40442 | + | 5.80148i | −0.116022 | + | 0.197714i | |||||
0 | 0 | |||||||||
25.7981 | − | 44.6837i | 0.878179 | − | 1.52105i | 0.0248411 | − | 0.999691i | ||
0.853338 | − | 0.521359i | ||||||||
0 | 0 | |||||||||
−0.604630 | − | 1.04725i | −0.0205580 | − | 0.0356076i | |||||
0 | 0 | |||||||||
−58.3287 | − | 10.8292i | −1.98094 | − | 0.367780i | |||||
0 | 0 | |||||||||
−4.79161 | − | 8.29931i | −0.162544 | − | 0.281535i | |||||
0 | 0 | |||||||||
27.2689 | 0.923972 | |||||||||
0 | 0 | |||||||||
5.99167 | + | 37.9819i | 0.202787 | + | 1.28549i | |||||
0 | 0 | |||||||||
31.6897 | − | 5.65193i | 1.07131 | − | 0.191070i | |||||
0 | 0 | |||||||||
−10.3978 | −0.351109 | −0.175555 | − | 0.984470i | ||||||
−0.175555 | + | 0.984470i | ||||||||
0 | 0 | |||||||||
−26.6819 | + | 31.2209i | −0.899957 | + | 1.05305i | |||||
0 | 0 | |||||||||
23.6562 | 0.796996 | 0.398498 | − | 0.917169i | ||||||
0.398498 | + | 0.917169i | ||||||||
0 | 0 | |||||||||
41.8601 | 1.40871 | 0.704353 | − | 0.709850i | ||||||
0.704353 | + | 0.709850i | ||||||||
0 | 0 | |||||||||
−6.58271 | − | 1.22214i | −0.221276 | − | 0.0410818i | |||||
0 | 0 | |||||||||
42.2505 | 1.41863 | 0.709316 | − | 0.704891i | ||||||
0.709316 | + | 0.704891i | ||||||||
0 | 0 | |||||||||
8.31936 | − | 1.48378i | 0.279022 | − | 0.0497643i | |||||
0 | 0 | |||||||||
−4.84829 | + | 22.6715i | −0.162424 | + | 0.759523i | |||||
0 | 0 | |||||||||
15.6787 | 0.524669 | |||||||||
0 | 0 | |||||||||
20.2404 | + | 35.0574i | 0.676563 | + | 1.17184i | |||||
0 | 0 | |||||||||
−1.53252 | + | 1.79323i | −0.0511695 | + | 0.0598743i | |||||
0 | 0 | |||||||||
−2.76243 | − | 4.78467i | −0.0921321 | − | 0.159578i | |||||
0 | 0 | |||||||||
−24.0191 | + | 41.6023i | −0.800192 | + | 1.38597i | |||||
0 | 0 | |||||||||
−37.9674 | − | 0.268524i | −1.26348 | − | 0.00893592i | |||||
0 | 0 | |||||||||
−46.4606 | −1.54440 | |||||||||
0 | 0 | |||||||||
−40.8807 | −1.35742 | −0.678711 | − | 0.734405i | ||||||
−0.678711 | + | 0.734405i | ||||||||
0 | 0 | |||||||||
−28.4609 | + | 23.0180i | −0.943988 | + | 0.763460i | |||||
0 | 0 | |||||||||
14.4235 | − | 24.9823i | 0.477873 | − | 0.827701i | −0.521805 | − | 0.853065i | ||
0.999678 | + | 0.0253641i | ||||||||
0 | 0 | |||||||||
7.73249 | − | 13.3931i | 0.255908 | − | 0.443246i | |||||
0 | 0 | |||||||||
27.0649 | − | 31.6691i | 0.894739 | − | 1.04695i | |||||
0 | 0 | |||||||||
−36.6910 | + | 6.54393i | −1.21165 | + | 0.216100i | |||||
0 | 0 | |||||||||
21.8195 | − | 37.7925i | 0.719760 | − | 1.24666i | −0.241335 | − | 0.970442i | ||
0.961095 | − | 0.276219i | ||||||||
0 | 0 | |||||||||
2.24025 | + | 6.33248i | 0.0738186 | + | 0.208662i | |||||
0 | 0 | |||||||||
−4.33560 | − | 7.50947i | −0.142708 | − | 0.247177i | |||||
0 | 0 | |||||||||
−0.526192 | + | 0.911391i | −0.0173011 | + | 0.0299663i | |||||
0 | 0 | |||||||||
−31.8243 | + | 25.7383i | −1.04525 | + | 0.845355i | |||||
0 | 0 | |||||||||
13.7377 | + | 23.7944i | 0.450719 | + | 0.780668i | 0.998431 | − | 0.0559990i | ||
−0.547712 | + | 0.836667i | ||||||||
0 | 0 | |||||||||
1.51314 | − | 8.78299i | 0.0495911 | − | 0.287851i | |||||
0 | 0 | |||||||||
11.7919 | + | 2.18927i | 0.386049 | + | 0.0716735i | |||||
0 | 0 | |||||||||
−17.1131 | − | 29.6408i | −0.559658 | − | 0.969356i | |||||
0 | 0 | |||||||||
−3.11920 | −0.101900 | −0.0509500 | − | 0.998701i | ||||||
−0.0509500 | + | 0.998701i | ||||||||
0 | 0 | |||||||||
34.0188 | − | 39.8060i | 1.11016 | − | 1.29902i | |||||
0 | 0 | |||||||||
13.0608 | − | 22.6219i | 0.425769 | − | 0.737454i | −0.570723 | − | 0.821143i | ||
0.996492 | + | 0.0836892i | ||||||||
0 | 0 | |||||||||
−0.177081 | − | 0.306714i | −0.00576656 | − | 0.00998797i | |||||
0 | 0 | |||||||||
23.7489 | + | 9.32654i | 0.772552 | + | 0.303392i | |||||
0 | 0 | |||||||||
3.59015 | + | 6.21833i | 0.116664 | + | 0.202068i | 0.918444 | − | 0.395551i | ||
−0.801780 | + | 0.597620i | ||||||||
0 | 0 | |||||||||
37.0256 | − | 64.1302i | 1.20190 | − | 2.08176i | |||||
0 | 0 | |||||||||
10.5484 | − | 12.3429i | 0.342055 | − | 0.400245i | |||||
0 | 0 | |||||||||
−32.1187 | −1.04043 | −0.520214 | − | 0.854036i | ||||||
−0.520214 | + | 0.854036i | ||||||||
0 | 0 | |||||||||
−8.03678 | − | 13.9201i | −0.260064 | − | 0.450444i | |||||
0 | 0 | |||||||||
−8.10306 | − | 1.50441i | −0.261935 | − | 0.0486305i | |||||
0 | 0 | |||||||||
−35.6742 | + | 6.36257i | −1.15198 | + | 0.205458i | |||||
0 | 0 | |||||||||
11.0269 | + | 19.0991i | 0.355705 | + | 0.616100i | |||||
0 | 0 | |||||||||
−6.05844 | − | 38.4052i | −0.195231 | − | 1.23759i | |||||
0 | 0 | |||||||||
−1.50018 | + | 2.59838i | −0.0482924 | + | 0.0836449i | |||||
0 | 0 | |||||||||
−27.4860 | − | 47.6071i | −0.883890 | − | 1.53094i | −0.846981 | − | 0.531623i | ||
−0.0369085 | − | 0.999319i | ||||||||
0 | 0 | |||||||||
5.26533 | + | 14.8835i | 0.169147 | + | 0.478126i | |||||
0 | 0 | |||||||||
20.8518 | − | 36.1163i | 0.669165 | − | 1.15903i | −0.308973 | − | 0.951071i | ||
0.978138 | − | 0.207957i | ||||||||
0 | 0 | |||||||||
16.8462 | + | 19.9967i | 0.540065 | + | 0.641064i | |||||
0 | 0 | |||||||||
9.88061 | − | 11.5615i | 0.316433 | − | 0.370263i | |||||
0 | 0 | |||||||||
−2.61437 | + | 4.52823i | −0.0836412 | + | 0.144871i | −0.904811 | − | 0.425813i | ||
0.821170 | + | 0.570683i | ||||||||
0 | 0 | |||||||||
−17.0106 | + | 29.4633i | −0.543662 | + | 0.941651i | |||||
0 | 0 | |||||||||
−43.1262 | − | 16.5852i | −1.37691 | − | 0.529525i | |||||
0 | 0 | |||||||||
6.90697 | 0.220298 | 0.110149 | − | 0.993915i | ||||||
0.110149 | + | 0.993915i | ||||||||
0 | 0 | |||||||||
19.9967 | 0.637149 | |||||||||
0 | 0 | |||||||||
28.5609 | − | 48.6707i | 0.909103 | − | 1.54921i | |||||
0 | 0 | |||||||||
0.999537 | − | 1.73125i | 0.0317834 | − | 0.0550505i | |||||
0 | 0 | |||||||||
2.19861 | + | 3.80811i | 0.0698412 | + | 0.120968i | 0.898831 | − | 0.438295i | ||
−0.828990 | + | 0.559263i | ||||||||
0 | 0 | |||||||||
30.9949 | − | 36.2676i | 0.983593 | − | 1.15092i | |||||
0 | 0 | |||||||||
4.43133 | + | 7.67528i | 0.140482 | + | 0.243323i | |||||
0 | 0 | |||||||||
−28.0359 | −0.887907 | −0.443954 | − | 0.896050i | ||||||
−0.443954 | + | 0.896050i | ||||||||
0 | 0 | |||||||||
−3.09086 | + | 1.67449i | −0.0977906 | + | 0.0529786i |
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 504.2.t.d.457.8 | yes | 22 | |
3.2 | odd | 2 | 1512.2.t.d.289.3 | 22 | |||
4.3 | odd | 2 | 1008.2.t.k.961.4 | 22 | |||
7.4 | even | 3 | 504.2.q.d.25.7 | ✓ | 22 | ||
9.4 | even | 3 | 504.2.q.d.121.7 | yes | 22 | ||
9.5 | odd | 6 | 1512.2.q.c.793.9 | 22 | |||
12.11 | even | 2 | 3024.2.t.l.289.3 | 22 | |||
21.11 | odd | 6 | 1512.2.q.c.1369.9 | 22 | |||
28.11 | odd | 6 | 1008.2.q.k.529.5 | 22 | |||
36.23 | even | 6 | 3024.2.q.k.2305.9 | 22 | |||
36.31 | odd | 6 | 1008.2.q.k.625.5 | 22 | |||
63.4 | even | 3 | inner | 504.2.t.d.193.8 | yes | 22 | |
63.32 | odd | 6 | 1512.2.t.d.361.3 | 22 | |||
84.11 | even | 6 | 3024.2.q.k.2881.9 | 22 | |||
252.67 | odd | 6 | 1008.2.t.k.193.4 | 22 | |||
252.95 | even | 6 | 3024.2.t.l.1873.3 | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.q.d.25.7 | ✓ | 22 | 7.4 | even | 3 | ||
504.2.q.d.121.7 | yes | 22 | 9.4 | even | 3 | ||
504.2.t.d.193.8 | yes | 22 | 63.4 | even | 3 | inner | |
504.2.t.d.457.8 | yes | 22 | 1.1 | even | 1 | trivial | |
1008.2.q.k.529.5 | 22 | 28.11 | odd | 6 | |||
1008.2.q.k.625.5 | 22 | 36.31 | odd | 6 | |||
1008.2.t.k.193.4 | 22 | 252.67 | odd | 6 | |||
1008.2.t.k.961.4 | 22 | 4.3 | odd | 2 | |||
1512.2.q.c.793.9 | 22 | 9.5 | odd | 6 | |||
1512.2.q.c.1369.9 | 22 | 21.11 | odd | 6 | |||
1512.2.t.d.289.3 | 22 | 3.2 | odd | 2 | |||
1512.2.t.d.361.3 | 22 | 63.32 | odd | 6 | |||
3024.2.q.k.2305.9 | 22 | 36.23 | even | 6 | |||
3024.2.q.k.2881.9 | 22 | 84.11 | even | 6 | |||
3024.2.t.l.289.3 | 22 | 12.11 | even | 2 | |||
3024.2.t.l.1873.3 | 22 | 252.95 | even | 6 |