Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [197,10,Mod(1,197)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(197, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("197.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 197.a (trivial) |
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: | yes |
Analytic conductor: | |
Analytic rank: | |
Dimension: | |
Twist minimal: | yes |
Fricke sign: | |
Sato-Tate group: |
Embedding invariants
Embedding label | 1.18 | ||
Character | 197.1 |
-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each we display the coefficients of the -expansion , the Satake parameters , and the Satake angles .
−27.2613 | −1.20479 | −0.602395 | − | 0.798198i | ||||||
−0.602395 | + | 0.798198i | ||||||||
−2.80973 | −0.0200272 | −0.0100136 | − | 0.999950i | ||||||
−0.0100136 | + | 0.999950i | ||||||||
231.177 | 0.451517 | |||||||||
1123.40 | 0.803836 | 0.401918 | − | 0.915676i | ||||||
0.401918 | + | 0.915676i | ||||||||
76.5969 | 0.0241285 | |||||||||
−8481.66 | −1.33518 | −0.667590 | − | 0.744529i | ||||||
−0.667590 | + | 0.744529i | ||||||||
7655.60 | 0.660806 | |||||||||
−19675.1 | −0.999599 | |||||||||
−30625.2 | −0.968453 | |||||||||
79300.8 | 1.63309 | 0.816546 | − | 0.577281i | ||||||
0.816546 | + | 0.577281i | ||||||||
−649.546 | −0.00904262 | |||||||||
−97256.2 | −0.944435 | −0.472218 | − | 0.881482i | ||||||
−0.472218 | + | 0.881482i | ||||||||
231221. | 1.60861 | |||||||||
−3156.44 | −0.0160986 | |||||||||
−327064. | −1.24765 | |||||||||
−37665.0 | −0.109375 | −0.0546875 | − | 0.998504i | ||||||
−0.0546875 | + | 0.998504i | ||||||||
536368. | 1.20431 | |||||||||
584746. | 1.02938 | 0.514691 | − | 0.857376i | ||||||
0.514691 | + | 0.857376i | ||||||||
259703. | 0.362946 | |||||||||
23831.2 | 0.0267399 | |||||||||
−2.16184e6 | −1.96753 | |||||||||
1.46262e6 | 1.08982 | 0.544910 | − | 0.838495i | ||||||
0.544910 | + | 0.838495i | ||||||||
−21510.2 | −0.0132341 | |||||||||
−691109. | −0.353848 | |||||||||
2.65133e6 | 1.13785 | |||||||||
110586. | 0.0400463 | |||||||||
−1.96076e6 | −0.602857 | |||||||||
−5.08723e6 | −1.33564 | −0.667822 | − | 0.744321i | ||||||
−0.667822 | + | 0.744321i | ||||||||
86048.6 | 0.0193954 | |||||||||
−226476. | −0.0440447 | −0.0220224 | − | 0.999757i | ||||||
−0.0220224 | + | 0.999757i | ||||||||
4.99651e6 | 0.842349 | |||||||||
−222814. | −0.0327062 | |||||||||
1.02680e6 | 0.131774 | |||||||||
−9.52825e6 | −1.07327 | |||||||||
−4.54843e6 | −0.451336 | |||||||||
7.07236e6 | 0.620378 | 0.310189 | − | 0.950675i | ||||||
0.310189 | + | 0.950675i | ||||||||
−1.59409e7 | −1.24019 | |||||||||
273264. | 0.0189144 | |||||||||
8.60026e6 | 0.531180 | |||||||||
−2.82852e7 | −1.56326 | −0.781632 | − | 0.623740i | ||||||
−0.781632 | + | 0.623740i | ||||||||
−649669. | −0.0322159 | |||||||||
2.12893e7 | 0.949627 | 0.474813 | − | 0.880087i | ||||||
0.474813 | + | 0.880087i | ||||||||
1.83325e7 | 0.737369 | |||||||||
−2.21029e7 | −0.803514 | |||||||||
−3.98727e7 | −1.31300 | |||||||||
4.37126e6 | 0.130667 | 0.0653335 | − | 0.997863i | ||||||
0.0653335 | + | 0.997863i | ||||||||
918963. | 0.0249869 | |||||||||
3.15849e7 | 0.782704 | |||||||||
1.88405e7 | 0.426312 | |||||||||
105829. | 0.00219047 | |||||||||
−2.24834e7 | −0.426429 | |||||||||
8.42582e7 | 1.46680 | 0.733400 | − | 0.679797i | ||||||
0.733400 | + | 0.679797i | ||||||||
−3.01471e6 | −0.0482474 | |||||||||
8.90861e7 | 1.31274 | |||||||||
−6.49321e7 | −0.882295 | |||||||||
−1.64298e6 | −0.0206156 | |||||||||
1.38684e8 | 1.60917 | |||||||||
−4.99543e7 | −0.536709 | −0.268354 | − | 0.963320i | ||||||
−0.268354 | + | 0.963320i | ||||||||
−729696. | −0.00726878 | |||||||||
1.38172e8 | 1.27772 | 0.638860 | − | 0.769323i | ||||||
0.638860 | + | 0.769323i | ||||||||
6.17401e6 | 0.0530646 | |||||||||
1.66878e8 | 1.33464 | |||||||||
3.12455e7 | 0.232797 | |||||||||
−1.09257e8 | −0.759171 | |||||||||
6.07420e6 | 0.0394041 | |||||||||
−2.30776e7 | −0.139912 | −0.0699559 | − | 0.997550i | ||||||
−0.0699559 | + | 0.997550i | ||||||||
−8.70728e6 | −0.0493847 | |||||||||
−4.10956e6 | −0.0218260 | |||||||||
2.59752e8 | 1.29306 | |||||||||
1.47748e8 | 0.690018 | 0.345009 | − | 0.938599i | ||||||
0.345009 | + | 0.938599i | ||||||||
−1.50625e8 | −0.660541 | |||||||||
1.64941e8 | 0.679791 | 0.339896 | − | 0.940463i | ||||||
0.339896 | + | 0.940463i | ||||||||
−1.92802e8 | −0.747425 | |||||||||
1.94183e6 | 0.00708657 | |||||||||
1.35180e8 | 0.464783 | |||||||||
−6.72602e8 | −2.18047 | |||||||||
−7.44953e6 | −0.0227878 | |||||||||
3.82858e8 | 1.10590 | 0.552949 | − | 0.833215i | ||||||
0.552949 | + | 0.833215i | ||||||||
−3.67422e8 | −1.00291 | |||||||||
3.86954e8 | 0.998797 | |||||||||
7.71091e8 | 1.88340 | |||||||||
−4.96417e7 | −0.114814 | −0.0574070 | − | 0.998351i | ||||||
−0.0574070 | + | 0.998351i | ||||||||
5.50922e6 | 0.0120735 | |||||||||
−4.23127e7 | −0.0879196 | |||||||||
−5.80373e8 | −1.14410 | |||||||||
1.42938e7 | 0.0267492 | |||||||||
6.07095e8 | 1.07916 | |||||||||
−2.48081e8 | −0.419120 | −0.209560 | − | 0.977796i | ||||||
−0.209560 | + | 0.977796i | ||||||||
6.02554e8 | 0.968065 | |||||||||
8.24894e8 | 1.26099 | |||||||||
3.38123e8 | 0.492073 | |||||||||
636336. | 0.000882091 0 | |||||||||
−1.19166e8 | −0.157426 | |||||||||
6.56901e8 | 0.827454 | |||||||||
−1.40389e7 | −0.0168699 | |||||||||
−1.11825e9 | −1.28253 | −0.641265 | − | 0.767319i | ||||||
−0.641265 | + | 0.767319i | ||||||||
−8.61045e8 | −0.942993 | |||||||||
−1.56025e9 | −1.63244 | |||||||||
−1.59768e8 | −0.159768 | |||||||||
−8.40721e7 | −0.0803907 | −0.0401953 | − | 0.999192i | ||||||
−0.0401953 | + | 0.999192i | ||||||||
−2.88503e6 | −0.00263906 | |||||||||
1.40068e8 | 0.122623 | 0.0613113 | − | 0.998119i | ||||||
0.0613113 | + | 0.998119i | ||||||||
−7.44554e8 | −0.624089 | |||||||||
2.67719e7 | 0.0214945 | |||||||||
−2.29699e9 | −1.76719 | |||||||||
1.22164e9 | 0.900985 | 0.450492 | − | 0.892780i | ||||||
0.450492 | + | 0.892780i | ||||||||
2.55649e7 | 0.0180816 | |||||||||
−2.76698e9 | −1.87753 | −0.938765 | − | 0.344559i | ||||||
−0.938765 | + | 0.344559i | ||||||||
−2.42860e9 | −1.58157 | |||||||||
−1.98715e7 | −0.0124244 | |||||||||
2.77404e9 | 1.66584 | |||||||||
6.64574e8 | 0.383434 | 0.191717 | − | 0.981450i | ||||||
0.191717 | + | 0.981450i | ||||||||
4.47898e7 | 0.0248374 | |||||||||
1.64309e9 | 0.876037 | |||||||||
−1.17605e9 | −0.603066 | |||||||||
1.91353e9 | 0.944057 | |||||||||
1.36182e9 | 0.646621 | |||||||||
3.19462e8 | 0.146035 | |||||||||
−2.41644e7 | −0.0106380 | |||||||||
3.93067e9 | 1.66699 | |||||||||
−3.76674e9 | −1.53938 | |||||||||
7.94740e7 | 0.0313078 | |||||||||
−5.23559e7 | −0.0198870 | |||||||||
−2.97052e9 | −1.08827 | |||||||||
−4.54929e9 | −1.60796 | |||||||||
−1.43263e9 | −0.488671 | −0.244336 | − | 0.969691i | ||||||
−0.244336 | + | 0.969691i | ||||||||
−3.41000e9 | −1.12282 | |||||||||
−5.98172e7 | −0.0190183 | |||||||||
2.97849e9 | 0.914641 | |||||||||
3.69105e9 | 1.09504 | 0.547519 | − | 0.836793i | ||||||
0.547519 | + | 0.836793i | ||||||||
−5.15095e7 | −0.0147674 | |||||||||
−4.95962e9 | −1.37441 | |||||||||
6.29125e8 | 0.168564 | |||||||||
1.24232e8 | 0.0321907 | |||||||||
−2.88348e8 | −0.0722757 | |||||||||
−3.13654e9 | −0.760692 | −0.380346 | − | 0.924844i | ||||||
−0.380346 | + | 0.924844i | ||||||||
1.12032e8 | 0.0262958 | |||||||||
−3.50593e9 | −0.796594 | −0.398297 | − | 0.917257i | ||||||
−0.398297 | + | 0.917257i | ||||||||
−2.20271e9 | −0.484598 | |||||||||
−1.22821e7 | −0.00261689 | |||||||||
−4.02781e9 | −0.831326 | |||||||||
−7.71250e9 | −1.54235 | |||||||||
6.43501e9 | 1.24715 | |||||||||
−5.71497e9 | −1.07364 | |||||||||
−4.49650e9 | −0.819005 | |||||||||
−8.87453e7 | −0.0156753 | |||||||||
1.63497e9 | 0.280112 | |||||||||
−3.48521e9 | −0.579283 | −0.289641 | − | 0.957135i | ||||||
−0.289641 | + | 0.957135i | ||||||||
−5.29368e7 | −0.00853782 | |||||||||
9.00940e9 | 1.41026 | 0.705131 | − | 0.709077i | ||||||
0.705131 | + | 0.709077i | ||||||||
4.47658e9 | 0.680221 | |||||||||
7.41063e8 | 0.109331 | |||||||||
1.83360e10 | 2.62701 | |||||||||
−2.54422e8 | −0.0354047 | |||||||||
6.31724e7 | 0.00854017 | |||||||||
−1.39865e10 | −1.83721 | −0.918606 | − | 0.395174i | ||||||
−0.918606 | + | 0.395174i | ||||||||
−1.04372e10 | −1.33238 | |||||||||
−2.36743e8 | −0.0293759 | |||||||||
5.61305e9 | 0.677110 | |||||||||
−1.24054e10 | −1.45511 | |||||||||
−1.05489e10 | −1.20334 | |||||||||
−9.82245e8 | −0.108987 | −0.0544936 | − | 0.998514i | ||||||
−0.0544936 | + | 0.998514i | ||||||||
−6.53889e9 | −0.705841 | |||||||||
−2.50308e8 | −0.0262904 | |||||||||
1.35329e9 | 0.138327 | |||||||||
−1.90494e10 | −1.89521 | −0.947606 | − | 0.319441i | ||||||
−0.947606 | + | 0.319441i | ||||||||
1.82442e8 | 0.0176699 | |||||||||
−1.14573e9 | −0.108042 | |||||||||
1.15350e9 | 0.105925 | |||||||||
−1.15049e10 | −1.02897 | |||||||||
4.92159e9 | 0.428773 | |||||||||
−1.55325e10 | −1.31836 | −0.659180 | − | 0.751985i | ||||||
−0.659180 | + | 0.751985i | ||||||||
−3.89666e8 | −0.0322271 | |||||||||
5.86175e9 | 0.472450 | |||||||||
−2.59364e10 | −2.03753 | |||||||||
1.40358e8 | 0.0107488 | |||||||||
6.76301e9 | 0.504952 | |||||||||
−7.81980e9 | −0.569321 | −0.284660 | − | 0.958628i | ||||||
−0.284660 | + | 0.958628i | ||||||||
−5.10968e9 | −0.362800 | |||||||||
−2.49172e10 | −1.72562 | −0.862811 | − | 0.505527i | ||||||
−0.862811 | + | 0.505527i | ||||||||
−2.24877e10 | −1.51923 | |||||||||
−3.88227e8 | −0.0255891 | |||||||||
1.11972e10 | 0.720160 | |||||||||
7.94505e9 | 0.498682 | |||||||||
−1.73473e7 | −0.00106273 | |||||||||
−2.98687e9 | −0.178619 | |||||||||
1.01053e9 | 0.0589984 | |||||||||
−9.37951e8 | −0.0534690 | |||||||||
−1.79080e10 | −0.996907 | |||||||||
1.77428e10 | 0.964655 | 0.482328 | − | 0.875991i | ||||||
0.482328 | + | 0.875991i | ||||||||
−8.77915e7 | −0.00466226 | |||||||||
−4.69301e9 | −0.243469 | −0.121735 | − | 0.992563i | ||||||
−0.121735 | + | 0.992563i | ||||||||
3.04850e10 | 1.54518 | |||||||||
3.06984e8 | 0.0152041 | |||||||||
7.30170e9 | 0.353404 | |||||||||
−1.50614e9 | −0.0712470 | |||||||||
4.25344e10 | 1.96674 | |||||||||
−1.32204e10 | −0.597594 | −0.298797 | − | 0.954317i | ||||||
−0.298797 | + | 0.954317i | ||||||||
−5.29085e9 | −0.233825 | |||||||||
6.48420e7 | 0.00280204 | |||||||||
2.29191e9 | 0.0968538 | |||||||||
4.31482e10 | 1.78332 | |||||||||
2.44652e7 | 0.000989036 0 | |||||||||
−3.17755e10 | −1.25661 | |||||||||
−3.81842e9 | −0.147734 | |||||||||
−2.87771e10 | −1.08938 | |||||||||
3.18090e10 | 1.17832 | |||||||||
4.63708e10 | 1.68107 | |||||||||
−7.29835e8 | −0.0258963 | |||||||||
5.71933e10 | 1.98643 | 0.993216 | − | 0.116280i | ||||||
0.993216 | + | 0.116280i | ||||||||
1.94786e10 | 0.662286 | |||||||||
−4.15134e8 | −0.0138191 | |||||||||
−3.33036e10 | −1.08550 | |||||||||
2.39163e10 | 0.763344 | |||||||||
8.46600e8 | 0.0264629 | |||||||||
1.92089e9 | 0.0588076 | |||||||||
7.54314e10 | 2.26203 | |||||||||
−4.63440e8 | −0.0136143 | |||||||||
2.05947e10 | 0.592724 | |||||||||
3.66316e9 | 0.103298 | |||||||||
5.41721e8 | 0.0149688 | |||||||||
−5.71649e10 | −1.54795 | −0.773977 | − | 0.633214i | ||||||
−0.773977 | + | 0.633214i | ||||||||
−4.23787e10 | −1.12469 | |||||||||
1.35976e10 | 0.353706 | |||||||||
−1.81171e10 | −0.461957 | |||||||||
−1.80488e10 | −0.451163 | −0.225581 | − | 0.974224i | ||||||
−0.225581 | + | 0.974224i | ||||||||
−3.79819e8 | −0.00930830 | |||||||||
5.57660e10 | 1.34002 | 0.670008 | − | 0.742354i | ||||||
0.670008 | + | 0.742354i | ||||||||
−4.47928e10 | −1.05544 | |||||||||
1.88983e9 | 0.0436687 | |||||||||
−3.89458e10 | −0.882601 | |||||||||
−5.29219e10 | −1.17634 | −0.588172 | − | 0.808736i | ||||||
−0.588172 | + | 0.808736i | ||||||||
−5.21652e10 | −1.13739 | |||||||||
4.91065e9 | 0.105035 | |||||||||
−1.15483e10 | −0.242333 | |||||||||
−1.07573e9 | −0.0221480 | |||||||||
−8.70894e9 | −0.175942 | |||||||||
1.79804e9 | 0.0356458 | 0.0178229 | − | 0.999841i | ||||||
0.0178229 | + | 0.999841i | ||||||||
1.03236e9 | 0.0200854 | |||||||||
−6.95213e10 | −1.32752 | −0.663760 | − | 0.747945i | ||||||
−0.663760 | + | 0.747945i | ||||||||
−1.07155e11 | −2.00837 | |||||||||
−3.26390e9 | −0.0600494 | |||||||||
3.19422e10 | 0.576913 | |||||||||
3.54824e10 | 0.629166 | |||||||||
−2.16656e9 | −0.0377193 | |||||||||
−5.68702e10 | −0.972184 | |||||||||
−1.73381e9 | −0.0291050 | |||||||||
1.39480e8 | 0.00229940 | |||||||||
8.09801e10 | 1.31114 | |||||||||
1.13858e11 | 1.81063 | 0.905317 | − | 0.424737i | ||||||
0.905317 | + | 0.424737i | ||||||||
3.85782e10 | 0.602615 | |||||||||
1.15987e11 | 1.77978 | |||||||||
3.90553e10 | 0.588746 | |||||||||
1.18887e8 | 0.00176078 | |||||||||
7.69634e10 | 1.11996 | |||||||||
−6.07005e9 | −0.0867947 | −0.0433974 | − | 0.999058i | ||||||
−0.0433974 | + | 0.999058i | ||||||||
1.63069e9 | 0.0229131 | |||||||||
−5.99853e10 | −0.828316 | |||||||||
−2.52577e10 | −0.342779 | |||||||||
1.00092e11 | 1.33511 | |||||||||
−1.00623e11 | −1.31929 | |||||||||
8.09083e10 | 1.04278 | 0.521390 | − | 0.853319i | ||||||
0.521390 | + | 0.853319i | ||||||||
−1.70578e9 | −0.0216125 | |||||||||
9.46553e10 | 1.17907 | |||||||||
1.35205e11 | 1.65587 | |||||||||
6.97042e8 | 0.00839380 | |||||||||
−5.33501e9 | −0.0631726 | |||||||||
−7.12863e10 | −0.830081 | −0.415041 | − | 0.909803i | ||||||
−0.415041 | + | 0.909803i | ||||||||
−3.38671e9 | −0.0387830 | |||||||||
1.47145e11 | 1.65723 | 0.828617 | − | 0.559816i | ||||||
0.828617 | + | 0.559816i | ||||||||
1.23189e10 | 0.136462 | |||||||||
−2.31773e9 | −0.0252541 | |||||||||
8.55062e10 | 0.916474 | |||||||||
−5.48055e10 | −0.577866 | |||||||||
−9.50035e8 | −0.00985482 | |||||||||
2.60482e10 | 0.265839 | 0.132919 | − | 0.991127i | ||||||
0.132919 | + | 0.991127i | ||||||||
9.55762e10 | 0.959728 | |||||||||
4.45593e9 | 0.0440271 | |||||||||
−7.29445e10 | −0.709220 | |||||||||
−6.02508e10 | −0.576480 | −0.288240 | − | 0.957558i | ||||||
−0.288240 | + | 0.957558i | ||||||||
3.34825e8 | 0.00315280 | |||||||||
−3.43541e10 | −0.318376 | −0.159188 | − | 0.987248i | ||||||
−0.159188 | + | 0.987248i | ||||||||
3.41560e10 | 0.311555 | |||||||||
−1.84572e9 | −0.0165716 | |||||||||
2.10252e11 | 1.85821 | |||||||||
2.39906e11 | 2.08724 | |||||||||
−9.83069e10 | −0.842011 | |||||||||
−1.17169e11 | −0.988037 | |||||||||
1.55797e11 | 1.29351 | |||||||||
3.14200e9 | 0.0256855 | |||||||||
3.81305e10 | 0.306937 | |||||||||
−7.28008e10 | −0.577075 | −0.288537 | − | 0.957469i | ||||||
−0.288537 | + | 0.957469i | ||||||||
2.41931e9 | 0.0188855 | |||||||||
−5.61184e10 | −0.431426 | |||||||||
5.41431e10 | 0.409950 | |||||||||
8.76955e9 | 0.0653993 | |||||||||
9.50112e10 | 0.697914 | |||||||||
−1.42248e11 | −1.02926 | |||||||||
4.48907e8 | 0.00319971 | |||||||||
−1.80568e11 | −1.26792 | |||||||||
−2.45608e11 | −1.69907 | |||||||||
2.36220e8 | 0.00161000 | |||||||||
−1.91249e11 | −1.28431 | |||||||||
1.55222e11 | 1.02708 | |||||||||
−2.02023e10 | −0.131721 | |||||||||
6.54927e10 | 0.420795 | 0.210397 | − | 0.977616i | ||||||
0.210397 | + | 0.977616i | ||||||||
−1.55490e11 | −0.984520 | |||||||||
−3.93553e8 | −0.00245578 | |||||||||
6.93586e9 | 0.0426552 | |||||||||
−1.93043e11 | −1.17013 | −0.585064 | − | 0.810987i | ||||||
−0.585064 | + | 0.810987i | ||||||||
2.09200e9 | 0.0124987 | |||||||||
−2.03390e11 | −1.19779 | −0.598895 | − | 0.800828i | ||||||
−0.598895 | + | 0.800828i | ||||||||
3.81289e11 | 2.21345 | |||||||||
1.87469e11 | 1.07283 | |||||||||
8.85078e10 | 0.499332 | |||||||||
−3.09712e11 | −1.72263 | −0.861314 | − | 0.508073i | ||||||
−0.861314 | + | 0.508073i | ||||||||
6.45392e9 | 0.0353917 | |||||||||
−4.03422e11 | −2.18123 | |||||||||
3.51010e10 | 0.187130 | |||||||||
−3.43249e9 | −0.0180442 | |||||||||
3.38187e11 | 1.75310 | |||||||||
−2.20245e10 | −0.112589 | |||||||||
8.94549e10 | 0.450974 | |||||||||
6.72146e10 | 0.334186 | |||||||||
2.67772e10 | 0.131307 | |||||||||
7.77448e9 | 0.0376016 | |||||||||
−2.16540e11 | −1.03301 | |||||||||
−3.70755e10 | −0.174464 | |||||||||
6.82372e9 | 0.0316744 | |||||||||
−3.55412e11 | −1.62744 | −0.813722 | − | 0.581255i | ||||||
−0.813722 | + | 0.581255i | ||||||||
−1.14760e10 | −0.0518405 | |||||||||
−1.39149e11 | −0.620129 | |||||||||
5.19312e11 | 2.28333 | |||||||||
−2.59253e10 | −0.112466 | |||||||||
−7.79433e9 | −0.0333620 | |||||||||
−3.56501e10 | −0.150566 | −0.0752829 | − | 0.997162i | ||||||
−0.0752829 | + | 0.997162i | ||||||||
3.12340e10 | 0.130168 | |||||||||
−1.86728e9 | −0.00767910 | |||||||||
−9.78172e9 | −0.0396972 | |||||||||
−1.79597e10 | −0.0719291 | |||||||||
3.13639e11 | 1.23969 | |||||||||
7.43729e10 | 0.290129 | |||||||||
1.62982e11 | 0.627519 | |||||||||
−4.61666e9 | −0.0175445 | |||||||||
4.23436e11 | 1.58835 | |||||||||
−2.35582e11 | −0.872288 | −0.436144 | − | 0.899877i | ||||||
−0.436144 | + | 0.899877i | ||||||||
3.30439e9 | 0.0120777 | |||||||||
−1.61378e11 | −0.582276 | −0.291138 | − | 0.956681i | ||||||
−0.291138 | + | 0.956681i | ||||||||
−1.59799e11 | −0.569203 | |||||||||
−1.07552e10 | −0.0378212 | |||||||||
3.96227e11 | 1.37563 | |||||||||
−3.84760e11 | −1.31888 | −0.659438 | − | 0.751759i | ||||||
−0.659438 | + | 0.751759i | ||||||||
−3.82634e9 | −0.0129500 | |||||||||
1.65980e11 | 0.554661 | |||||||||
−5.73506e10 | −0.189240 | |||||||||
−8.97603e8 | −0.00292467 | |||||||||
2.13178e11 | 0.685912 | |||||||||
−2.52817e11 | −0.803308 | −0.401654 | − | 0.915792i | ||||||
−0.401654 | + | 0.915792i | ||||||||
−1.69211e11 | −0.530967 | |||||||||
1.92403e10 | 0.0596253 | |||||||||
6.79274e11 | 2.07901 | |||||||||
−1.10441e10 | −0.0333851 | |||||||||
1.90696e11 | 0.569359 | |||||||||
1.85294e11 | 0.546441 | |||||||||
1.05836e10 | 0.0308295 | |||||||||
−1.71582e11 | −0.493713 | −0.246856 | − | 0.969052i | ||||||
−0.246856 | + | 0.969052i | ||||||||
−4.78368e11 | −1.35971 | |||||||||
5.56515e11 | 1.56264 | |||||||||
−2.16592e11 | −0.600807 | |||||||||
−7.14650e11 | −1.95844 | |||||||||
1.47106e8 | 0.000398279 0 | |||||||||
−5.28558e10 | −0.141385 | −0.0706924 | − | 0.997498i | ||||||
−0.0706924 | + | 0.997498i | ||||||||
8.14258e10 | 0.215199 | |||||||||
8.34637e9 | 0.0217950 | |||||||||
3.34646e10 | 0.0863455 | |||||||||
4.94765e11 | 1.26143 | |||||||||
2.55697e10 | 0.0644189 | |||||||||
−4.80261e11 | −1.19564 | −0.597821 | − | 0.801630i | ||||||
−0.597821 | + | 0.801630i | ||||||||
1.51860e11 | 0.373610 | |||||||||
4.02531e9 | 0.00978670 | |||||||||
−4.83691e11 | −1.16221 | |||||||||
−4.19884e11 | −0.997092 | −0.498546 | − | 0.866863i | ||||||
−0.498546 | + | 0.866863i | ||||||||
9.58121e9 | 0.0224869 | |||||||||
−7.55598e11 | −1.75274 | |||||||||
1.27937e11 | 0.293329 | |||||||||
−4.18869e11 | −0.949246 | |||||||||
−2.58515e11 | −0.579085 | |||||||||
8.83759e11 | 1.95686 | 0.978432 | − | 0.206569i | ||||||
0.978432 | + | 0.206569i | ||||||||
−8.36876e9 | −0.0183177 | |||||||||
−5.50894e10 | −0.119199 | |||||||||
2.41801e11 | 0.517216 | |||||||||
−1.03709e10 | −0.0219305 | |||||||||
4.10592e10 | 0.0858377 | |||||||||
4.30100e11 | 0.888961 | |||||||||
−3.60694e11 | −0.737073 | |||||||||
5.53182e11 | 1.11766 | 0.558832 | − | 0.829281i | ||||||
0.558832 | + | 0.829281i | ||||||||
3.60405e11 | 0.719975 | |||||||||
1.39352e10 | 0.0275255 | |||||||||
2.26037e11 | 0.441478 | |||||||||
3.82922e11 | 0.739538 | 0.369769 | − | 0.929124i | ||||||
0.369769 | + | 0.929124i | ||||||||
−1.76767e9 | −0.00337587 | |||||||||
2.20262e10 | 0.0415974 | |||||||||
−1.94355e10 | −0.0362978 | |||||||||
4.34703e11 | 0.802869 | |||||||||
−1.17627e12 | −2.14853 | |||||||||
5.60844e11 | 1.01313 | |||||||||
8.10182e8 | 0.00144748 | |||||||||
7.80488e11 | 1.37915 | 0.689575 | − | 0.724214i | ||||||
0.689575 | + | 0.724214i | ||||||||
8.66240e11 | 1.51395 | |||||||||
8.81286e9 | 0.0152345 | |||||||||
3.23804e10 | 0.0553662 | |||||||||
4.23695e11 | 0.716602 | |||||||||
7.84501e11 | 1.31248 | |||||||||
−5.57672e10 | −0.0922916 | |||||||||
−4.85942e11 | −0.795544 | |||||||||
9.85074e9 | 0.0159535 | |||||||||
−1.26413e12 | −2.02534 | |||||||||
−2.67523e11 | −0.424032 | −0.212016 | − | 0.977266i | ||||||
−0.212016 | + | 0.977266i | ||||||||
6.18904e9 | 0.00970513 | |||||||||
−1.20251e11 | −0.186560 | −0.0932801 | − | 0.995640i | ||||||
−0.0932801 | + | 0.995640i | ||||||||
−1.55916e12 | −2.39323 | |||||||||
−8.60049e10 | −0.130615 | |||||||||
6.45047e11 | 0.969271 | |||||||||
2.60306e10 | 0.0387021 | |||||||||
1.13171e10 | 0.0166491 | |||||||||
−1.17193e12 | −1.70599 | |||||||||
2.82416e11 | 0.406810 | |||||||||
2.16701e10 | 0.0308889 | |||||||||
−6.51988e11 | −0.919669 | |||||||||
5.43676e10 | 0.0758914 | 0.0379457 | − | 0.999280i | ||||||
0.0379457 | + | 0.999280i | ||||||||
−3.61686e10 | −0.0499638 | |||||||||
7.13709e11 | 0.975721 | 0.487860 | − | 0.872922i | ||||||
0.487860 | + | 0.872922i | ||||||||
−5.23659e10 | −0.0708508 | |||||||||
1.60576e10 | 0.0215019 | |||||||||
−6.39662e11 | −0.847737 | |||||||||
8.55259e11 | 1.12184 | |||||||||
1.26340e10 | 0.0164024 | |||||||||
−3.91017e10 | −0.0502464 | −0.0251232 | − | 0.999684i | ||||||
−0.0251232 | + | 0.999684i | ||||||||
6.82007e11 | 0.867465 | |||||||||
−6.21437e11 | −0.782390 | |||||||||
−9.98623e10 | −0.124452 | |||||||||
9.76650e10 | 0.120482 | 0.0602410 | − | 0.998184i | ||||||
0.0602410 | + | 0.998184i | ||||||||
−4.59382e9 | −0.00560984 | |||||||||
−2.78693e11 | −0.336904 | |||||||||
1.55839e12 | 1.86496 | |||||||||
9.79251e9 | 0.0116014 | |||||||||
−2.65013e11 | −0.310826 | |||||||||
−4.90259e11 | −0.569268 | −0.284634 | − | 0.958636i | ||||||
−0.284634 | + | 0.958636i | ||||||||
−3.70689e11 | −0.426141 | |||||||||
−2.24304e12 | −2.55295 | |||||||||
1.53634e11 | 0.173127 | |||||||||
−2.53140e10 | −0.0282436 | |||||||||
4.92035e11 | 0.543556 | |||||||||
9.26682e11 | 1.01363 | |||||||||
−1.25780e10 | −0.0136229 | |||||||||
1.12239e12 | 1.20371 | 0.601855 | − | 0.798606i | ||||||
0.601855 | + | 0.798606i | ||||||||
−1.52025e12 | −1.61444 | |||||||||
−4.16522e9 | −0.00438007 | |||||||||
3.79845e11 | 0.395546 | |||||||||
−5.53487e11 | −0.570759 | −0.285380 | − | 0.958415i | ||||||
−0.285380 | + | 0.958415i | ||||||||
−5.15193e10 | −0.0526115 | |||||||||
−1.15064e12 | −1.16366 | −0.581829 | − | 0.813311i | ||||||
−0.581829 | + | 0.813311i | ||||||||
1.66385e12 | 1.66641 | |||||||||
7.14857e8 | 0.000709057 0 | |||||||||
1.44272e12 | 1.41725 | |||||||||
−1.20682e12 | −1.17413 | −0.587067 | − | 0.809538i | ||||||
−0.587067 | + | 0.809538i | ||||||||
4.42363e11 | 0.426258 | |||||||||
1.95736e11 | 0.186807 | |||||||||
−1.33870e11 | −0.126545 | |||||||||
3.92982e10 | 0.0367942 | |||||||||
−3.82430e11 | −0.354660 | |||||||||
1.68826e12 | 1.55083 | |||||||||
2.93257e10 | 0.0266837 | |||||||||
−4.04123e11 | −0.364244 | |||||||||
7.38522e10 | 0.0659375 | |||||||||
−1.65779e12 | −1.46621 | |||||||||
−4.90167e10 | −0.0429456 | |||||||||
−5.88600e11 | −0.510870 | −0.255435 | − | 0.966826i | ||||||
−0.255435 | + | 0.966826i | ||||||||
−1.57712e10 | −0.0135606 | |||||||||
−6.87831e11 | −0.585907 | |||||||||
1.89524e12 | 1.59938 | |||||||||
3.48559e10 | 0.0291416 | |||||||||
9.08680e11 | 0.752674 | |||||||||
−1.25624e12 | −1.03094 | |||||||||
8.89781e10 | 0.0723469 | |||||||||
8.90630e11 | 0.717492 | 0.358746 | − | 0.933435i | ||||||
0.358746 | + | 0.933435i | ||||||||
1.05779e12 | 0.844325 | |||||||||
2.75985e9 | 0.00218271 | |||||||||
−9.67294e11 | −0.758012 | |||||||||
−1.75078e11 | −0.135946 | −0.0679729 | − | 0.997687i | ||||||
−0.0679729 | + | 0.997687i | ||||||||
1.83726e10 | 0.0141360 | |||||||||
1.91611e11 | 0.146086 | |||||||||
1.55035e12 | 1.17128 | |||||||||
−1.75278e12 | −1.31221 | |||||||||
7.40720e10 | 0.0549524 | |||||||||
−1.25315e12 | −0.921298 | |||||||||
−3.80240e9 | −0.00277029 | |||||||||
2.13513e12 | 1.54160 | 0.770801 | − | 0.637076i | ||||||
0.770801 | + | 0.637076i | ||||||||
−6.86715e11 | −0.491373 | |||||||||
5.35239e10 | 0.0379558 | |||||||||
−3.10391e12 | −2.18143 | |||||||||
−1.85502e12 | −1.29209 | −0.646044 | − | 0.763300i | ||||||
−0.646044 | + | 0.763300i | ||||||||
1.27755e12 | 0.881941 | |||||||||
−9.44462e10 | −0.0646209 | |||||||||
−3.16194e12 | −2.14425 | |||||||||
3.21919e9 | 0.00216377 | |||||||||
−3.31191e11 | −0.220644 | |||||||||
−6.25773e11 | −0.413225 | −0.206613 | − | 0.978423i | ||||||
−0.206613 | + | 0.978423i | ||||||||
−3.24102e9 | −0.00212137 | |||||||||
−1.39897e12 | −0.907643 | |||||||||
−3.52197e11 | −0.226501 | |||||||||
6.46646e10 | 0.0412229 | |||||||||
1.65477e11 | 0.104569 | |||||||||
1.57351e11 | 0.0985685 | |||||||||
−1.38284e10 | −0.00858711 | |||||||||
3.46644e11 | 0.213391 | |||||||||
1.63528e12 | 0.997947 | |||||||||
4.36422e10 | 0.0264030 | |||||||||
−8.36429e11 | −0.501665 | |||||||||
−7.06921e11 | −0.420341 | −0.210170 | − | 0.977665i | ||||||
−0.210170 | + | 0.977665i | ||||||||
−2.72863e12 | −1.60852 | |||||||||
8.82998e11 | 0.516062 | 0.258031 | − | 0.966137i | ||||||
0.258031 | + | 0.966137i | ||||||||
8.53286e11 | 0.494429 | |||||||||
−1.64700e10 | −0.00946184 | |||||||||
−2.20566e12 | −1.25633 | |||||||||
8.53021e9 | 0.00481739 | |||||||||
7.28745e10 | 0.0408059 | |||||||||
3.38090e11 | 0.187708 | |||||||||
−2.58042e12 | −1.42053 | |||||||||
9.82856e11 | 0.536493 | |||||||||
−1.14655e12 | −0.620569 | |||||||||
2.75092e12 | 1.47640 | |||||||||
−1.90023e10 | −0.0101128 | |||||||||
1.37239e12 | 0.724244 | |||||||||
−1.76673e11 | −0.0924546 | |||||||||
2.19716e10 | 0.0114019 | |||||||||
1.94335e12 | 1.00007 | |||||||||
2.50471e12 | 1.27823 | |||||||||
2.87195e10 | 0.0145346 | |||||||||
1.66056e12 | 0.833427 | 0.416713 | − | 0.909038i | ||||||
0.416713 | + | 0.909038i | ||||||||
−4.01136e12 | −1.99662 | |||||||||
7.00107e10 | 0.0345593 | |||||||||
−1.88194e11 | −0.0921319 | |||||||||
−3.10841e12 | −1.50923 | |||||||||
6.31844e10 | 0.0304258 | |||||||||
−2.25202e12 | −1.07555 | −0.537773 | − | 0.843090i | ||||||
−0.537773 | + | 0.843090i | ||||||||
−7.25096e11 | −0.343466 | |||||||||
−2.71855e12 | −1.27721 | |||||||||
1.49407e12 | 0.696206 | |||||||||
−2.97474e12 | −1.37489 | |||||||||
−3.14611e10 | −0.0144228 | |||||||||
−3.24727e12 | −1.47657 | |||||||||
−7.10106e11 | −0.320279 | |||||||||
−2.23235e10 | −0.00998720 | |||||||||
−8.10491e11 | −0.359676 | |||||||||
2.43310e12 | 1.07105 | 0.535527 | − | 0.844518i | ||||||
0.535527 | + | 0.844518i | ||||||||
−1.21474e11 | −0.0530433 | |||||||||
−2.07051e12 | −0.896861 | |||||||||
3.11635e12 | 1.33906 | |||||||||
8.39230e9 | 0.00357724 | |||||||||
1.64251e12 | 0.694537 | |||||||||
−1.87650e12 | −0.787154 | −0.393577 | − | 0.919292i | ||||||
−0.393577 | + | 0.919292i | ||||||||
−2.83933e9 | −0.00118157 | |||||||||
7.46579e11 | 0.308218 | |||||||||
9.36536e11 | 0.383575 | |||||||||
−3.28202e12 | −1.33357 | |||||||||
1.13110e12 | 0.455968 | |||||||||
6.80557e11 | 0.272182 | 0.136091 | − | 0.990696i | ||||||
0.136091 | + | 0.990696i | ||||||||
5.03166e10 | 0.0199652 | |||||||||
−1.66287e12 | −0.654628 | −0.327314 | − | 0.944916i | ||||||
−0.327314 | + | 0.944916i | ||||||||
−1.78295e12 | −0.696397 | |||||||||
−4.98526e10 | −0.0193193 | |||||||||
−6.54013e12 | −2.51468 | |||||||||
−1.01083e12 | −0.385630 | |||||||||
−6.14758e11 | −0.232703 | |||||||||
2.72131e12 | 1.02208 | 0.511042 | − | 0.859556i | ||||||
0.511042 | + | 0.859556i | ||||||||
3.19418e12 | 1.19038 | |||||||||
1.31861e10 | 0.00487600 | |||||||||
−1.32117e12 | −0.484766 | |||||||||
4.21044e11 | 0.153297 | |||||||||
−8.56549e10 | −0.0309456 | |||||||||
6.68175e12 | 2.39542 | |||||||||
1.26272e12 | 0.449210 | |||||||||
2.14965e12 | 0.758867 | |||||||||
1.98464e12 | 0.695253 | |||||||||
4.16725e12 | 1.44870 | 0.724349 | − | 0.689433i | ||||||
0.724349 | + | 0.689433i | ||||||||
−2.05159e10 | −0.00707769 | |||||||||
−1.32431e11 | −0.0453388 | |||||||||
1.52986e12 | 0.519777 | |||||||||
4.23185e9 | 0.00142688 | |||||||||
−2.31311e12 | −0.774015 | |||||||||
−3.32259e11 | −0.110339 | −0.0551696 | − | 0.998477i | ||||||
−0.0551696 | + | 0.998477i | ||||||||
−2.39069e11 | −0.0787924 | |||||||||
3.58882e11 | 0.117388 | |||||||||
−8.05700e11 | −0.261556 | |||||||||
3.71459e10 | 0.0119681 | |||||||||
3.87787e12 | 1.24005 | |||||||||
3.49811e12 | 1.11023 | 0.555115 | − | 0.831773i | ||||||
0.555115 | + | 0.831773i | ||||||||
1.48659e10 | 0.00468285 | |||||||||
4.68251e12 | 1.46401 | 0.732004 | − | 0.681301i | ||||||
0.732004 | + | 0.681301i | ||||||||
4.92252e12 | 1.52758 | |||||||||
4.54054e11 | 0.139856 | |||||||||
2.08277e12 | 0.636758 | |||||||||
4.41570e12 | 1.33998 | |||||||||
−6.43967e9 | −0.00193971 | |||||||||
−3.49070e12 | −1.04367 | −0.521836 | − | 0.853046i | ||||||
−0.521836 | + | 0.853046i | ||||||||
2.92169e12 | 0.867098 | |||||||||
−1.21235e11 | −0.0357149 | |||||||||
−4.23154e12 | −1.23741 | |||||||||
−4.25132e11 | −0.123407 | |||||||||
1.71317e11 | 0.0493649 | |||||||||
3.63680e12 | 1.04027 | 0.520136 | − | 0.854084i | ||||||
0.520136 | + | 0.854084i | ||||||||
−1.78542e12 | −0.506969 | |||||||||
8.92807e10 | 0.0251663 | |||||||||
−5.14917e12 | −1.44087 | |||||||||
6.36043e11 | 0.176686 | 0.0883432 | − | 0.996090i | ||||||
0.0883432 | + | 0.996090i | ||||||||
1.07288e10 | 0.00295870 | |||||||||
1.92995e12 | 0.528369 | 0.264185 | − | 0.964472i | ||||||
0.264185 | + | 0.964472i | ||||||||
−5.88164e10 | −0.0159858 | |||||||||
1.61745e11 | 0.0436433 | |||||||||
5.26261e12 | 1.40976 | |||||||||
2.10414e12 | 0.559601 | |||||||||
−8.93748e10 | −0.0235985 | |||||||||
−1.98724e12 | −0.520944 | |||||||||
5.54468e12 | 1.44308 | |||||||||
−1.30290e11 | −0.0336671 | |||||||||
−3.23335e12 | −0.829533 | |||||||||
−2.66381e11 | −0.0678539 | |||||||||
−5.11065e12 | −1.29254 | |||||||||
−3.98525e11 | −0.100075 | −0.0500373 | − | 0.998747i | ||||||
−0.0500373 | + | 0.998747i | ||||||||
2.93100e12 | 0.730785 | |||||||||
−1.60698e11 | −0.0397826 | |||||||||
8.44315e12 | 2.07540 | |||||||||
−1.60941e12 | −0.392812 | |||||||||
−5.47296e10 | −0.0132637 | |||||||||
−3.07183e12 | −0.739213 | |||||||||
1.09978e13 | 2.62792 | |||||||||
−2.90697e12 | −0.689741 | |||||||||
−3.83078e12 | −0.902563 | |||||||||
−5.02329e12 | −1.17524 | −0.587621 | − | 0.809136i | ||||||
−0.587621 | + | 0.809136i | ||||||||
9.35742e10 | 0.0217394 | |||||||||
5.97878e10 | 0.0137931 | 0.00689657 | − | 0.999976i | ||||||
0.00689657 | + | 0.999976i | ||||||||
−2.86784e12 | −0.657005 | |||||||||
−6.71984e10 | −0.0152876 | |||||||||
6.00415e11 | 0.135646 | |||||||||
−7.37249e12 | −1.65404 | −0.827018 | − | 0.562176i | ||||||
−0.827018 | + | 0.562176i | ||||||||
2.96237e12 | 0.660011 | |||||||||
−3.96141e12 | −0.876494 | |||||||||
−1.83236e12 | −0.402624 | |||||||||
−5.39719e9 | −0.00117775 | |||||||||
−2.27072e11 | −0.0492096 | |||||||||
8.15737e12 | 1.75566 | 0.877831 | − | 0.478971i | ||||||
0.877831 | + | 0.478971i | ||||||||
−2.11942e11 | −0.0453020 | |||||||||
4.14651e12 | 0.880232 | |||||||||
9.25108e12 | 1.95041 | |||||||||
−3.24523e12 | −0.679519 | |||||||||
1.01073e12 | 0.210192 | |||||||||
6.17339e12 | 1.27508 | 0.637542 | − | 0.770415i | ||||||
0.637542 | + | 0.770415i | ||||||||
−5.78655e10 | −0.0118706 | |||||||||
−1.02154e12 | −0.208136 | −0.104068 | − | 0.994570i | ||||||
−0.104068 | + | 0.994570i | ||||||||
9.68898e12 | 1.96073 | |||||||||
−1.02925e10 | −0.00206876 | |||||||||
−3.80036e11 | −0.0758698 | |||||||||
−5.57161e12 | −1.10480 | |||||||||
3.79339e12 | 0.747125 | |||||||||
−7.44066e12 | −1.45561 | |||||||||
−4.40379e12 | −0.855721 | |||||||||
1.60618e11 | 0.0310011 | |||||||||
7.06756e11 | 0.135498 | |||||||||
1.09572e13 | 2.08663 | |||||||||
1.19073e11 | 0.0225243 | |||||||||
−8.94337e12 | −1.68048 | −0.840241 | − | 0.542214i | ||||||
−0.840241 | + | 0.542214i | ||||||||
9.71867e11 | 0.181400 | |||||||||
−7.64268e10 | −0.0141703 | |||||||||
−2.64866e11 | −0.0487827 | |||||||||
−6.62513e12 | −1.21212 | −0.606060 | − | 0.795419i | ||||||
−0.606060 | + | 0.795419i | ||||||||
5.09044e10 | 0.00925169 | |||||||||
9.48465e12 | 1.71241 | |||||||||
−3.23929e11 | −0.0580978 | |||||||||
5.07125e10 | 0.00903551 | |||||||||
4.89604e11 | 0.0866594 | |||||||||
−4.28043e11 | −0.0752653 | −0.0376326 | − | 0.999292i | ||||||
−0.0376326 | + | 0.999292i | ||||||||
−2.65968e12 | −0.464597 | |||||||||
−3.52358e12 | −0.611472 | |||||||||
−2.02750e12 | −0.349545 | |||||||||
−1.56688e11 | −0.0268367 | |||||||||
−6.96295e12 | −1.18480 | |||||||||
−8.19464e12 | −1.38530 | |||||||||
1.25856e11 | 0.0211375 | |||||||||
2.03772e12 | 0.340012 | 0.170006 | − | 0.985443i | ||||||
0.170006 | + | 0.985443i | ||||||||
−3.59076e12 | −0.595263 | |||||||||
1.32335e13 | 2.17960 | |||||||||
6.42227e12 | 1.05092 | |||||||||
−3.93855e12 | −0.640331 | |||||||||
1.09427e11 | 0.0176760 | |||||||||
1.06536e12 | 0.170982 | |||||||||
4.39936e12 | 0.701520 | |||||||||
1.48697e11 | 0.0235588 | |||||||||
1.35510e12 | 0.213319 | |||||||||
9.06293e12 | 1.41755 | 0.708774 | − | 0.705436i | ||||||
0.708774 | + | 0.705436i | ||||||||
2.93199e11 | 0.0455665 | |||||||||
4.13553e12 | 0.638606 | |||||||||
2.47779e12 | 0.380179 | |||||||||
−1.37976e10 | −0.00210355 | |||||||||
1.04891e13 | 1.58897 | |||||||||
7.13071e11 | 0.107336 | |||||||||
3.24476e10 | 0.00485325 | |||||||||
−1.97637e12 | −0.293738 | −0.146869 | − | 0.989156i | ||||||
−0.146869 | + | 0.989156i | ||||||||
−4.52482e12 | −0.668250 | |||||||||
−7.53276e12 | −1.10546 | |||||||||
−1.89921e12 | −0.276957 | |||||||||
−3.31247e11 | −0.0480008 | |||||||||
2.44698e10 | 0.00352362 | |||||||||
−8.66418e12 | −1.23980 | |||||||||
−1.80776e12 | −0.257058 | |||||||||
−5.05200e9 | −0.000713884 0 | |||||||||
6.89213e12 | 0.967817 | |||||||||
−1.30533e12 | −0.182154 | −0.0910771 | − | 0.995844i | ||||||
−0.0910771 | + | 0.995844i | ||||||||
7.22906e12 | 1.00250 | |||||||||
−1.18801e12 | −0.163723 | |||||||||
−5.24516e11 | −0.0718359 | |||||||||
1.95336e11 | 0.0265865 | |||||||||
−5.76028e12 | −0.779148 | |||||||||
3.51583e12 | 0.472614 | |||||||||
3.01077e11 | 0.0402220 | |||||||||
1.26168e13 | 1.67511 | 0.837557 | − | 0.546350i | ||||||
0.837557 | + | 0.546350i | ||||||||
6.31505e12 | 0.833270 | |||||||||
−7.60725e12 | −0.997594 | |||||||||
−5.05134e12 | −0.658346 | |||||||||
−8.01861e11 | −0.103865 | |||||||||
−8.97490e10 | −0.0115539 | |||||||||
−1.05610e13 | −1.35125 | −0.675627 | − | 0.737243i | ||||||
−0.675627 | + | 0.737243i | ||||||||
4.67754e12 | 0.594820 | |||||||||
−9.96960e10 | −0.0126004 | |||||||||
7.30797e12 | 0.918008 | |||||||||
−1.83007e12 | −0.228489 | |||||||||
−1.51713e13 | −1.88265 | |||||||||
3.02384e12 | 0.372957 | 0.186479 | − | 0.982459i | ||||||
0.186479 | + | 0.982459i | ||||||||
1.83671e12 | 0.225164 | |||||||||
1.59790e11 | 0.0194701 | |||||||||
1.94823e13 | 2.35951 | |||||||||
1.45200e13 | 1.74790 | 0.873952 | − | 0.486012i | ||||||
0.873952 | + | 0.486012i | ||||||||
4.87153e9 | 0.000582891 0 | |||||||||
−3.91527e12 | −0.465648 | |||||||||
1.44091e12 | 0.170339 | |||||||||
9.76705e11 | 0.114768 | |||||||||
−6.90495e11 | −0.0806498 | |||||||||
−1.03616e13 | −1.20298 | |||||||||
−2.27533e11 | −0.0262584 | |||||||||
4.67153e12 | 0.535895 | 0.267948 | − | 0.963434i | ||||||
0.267948 | + | 0.963434i | ||||||||
−1.42968e12 | −0.163027 | |||||||||
−3.19910e11 | −0.0362619 | |||||||||
−1.34879e13 | −1.51976 | |||||||||
1.01211e13 | 1.13362 | |||||||||
−2.16833e11 | −0.0241422 | |||||||||
5.33315e12 | 0.590272 | 0.295136 | − | 0.955455i | ||||||
0.295136 | + | 0.955455i | ||||||||
1.30925e13 | 1.44050 | |||||||||
−3.25891e11 | −0.0356439 | |||||||||
5.02897e12 | 0.546786 | |||||||||
−2.66730e12 | −0.288298 | −0.144149 | − | 0.989556i | ||||||
−0.144149 | + | 0.989556i | ||||||||
−1.09735e11 | −0.0117909 | |||||||||
2.34686e13 | 2.50684 | |||||||||
4.10173e12 | 0.435558 | |||||||||
8.32507e11 | 0.0878843 | |||||||||
1.14466e13 | 1.20129 | |||||||||
4.85836e12 | 0.506887 | |||||||||
−2.16247e11 | −0.0224297 | |||||||||
−1.16350e13 | −1.19977 | −0.599883 | − | 0.800087i | ||||||
−0.599883 | + | 0.800087i | ||||||||
2.05986e13 | 2.11168 | |||||||||
1.70552e10 | 0.00173825 | |||||||||
−1.08492e12 | −0.109930 | |||||||||
−5.34961e12 | −0.538908 | −0.269454 | − | 0.963013i | ||||||
−0.269454 | + | 0.963013i | ||||||||
1.14189e13 | 1.14364 | |||||||||
1.56519e11 | 0.0155851 | |||||||||
−8.56090e12 | −0.847504 | |||||||||
1.68543e11 | 0.0165888 | |||||||||
−2.40924e13 | −2.35761 | |||||||||
−1.65397e13 | −1.60919 | |||||||||
7.09675e10 | 0.00686489 | |||||||||
1.17166e13 | 1.12686 | |||||||||
1.50181e12 | 0.143610 | |||||||||
−5.62576e11 | −0.0534876 | |||||||||
−1.03303e13 | −0.976540 | |||||||||
−1.57123e13 | −1.47682 | |||||||||
2.82723e11 | 0.0264217 | |||||||||
−1.16579e13 | −1.08326 | −0.541632 | − | 0.840615i | ||||||
−0.541632 | + | 0.840615i | ||||||||
−3.48184e11 | −0.0321693 | |||||||||
−2.27331e11 | −0.0208839 | |||||||||
−1.17251e13 | −1.07101 | |||||||||
−5.63669e12 | −0.511953 | |||||||||
−1.19447e13 | −1.07872 | |||||||||
−1.34381e13 | −1.20672 | |||||||||
−1.50805e13 | −1.34655 | |||||||||
−2.65956e11 | −0.0236134 | |||||||||
−3.05625e12 | −0.269824 | |||||||||
−1.16078e13 | −1.01903 | −0.509514 | − | 0.860463i | ||||||
−0.509514 | + | 0.860463i | ||||||||
−3.79891e11 | −0.0331624 | |||||||||
−1.64643e11 | −0.0142917 | |||||||||
−3.45313e12 | −0.298063 | |||||||||
4.88102e12 | 0.418952 | |||||||||
−1.04389e13 | −0.890988 | |||||||||
1.30799e13 | 1.11016 | |||||||||
1.49900e10 | 0.00126517 | |||||||||
−1.39362e13 | −1.16967 | |||||||||
−6.00461e11 | −0.0501161 | |||||||||
2.00296e11 | 0.0166242 | |||||||||
−6.43622e11 | −0.0531227 | |||||||||
3.30393e12 | 0.271183 | 0.135591 | − | 0.990765i | ||||||
0.135591 | + | 0.990765i | ||||||||
−1.18505e13 | −0.967288 | |||||||||
−3.66102e12 | −0.297172 | −0.148586 | − | 0.988899i | ||||||
−0.148586 | + | 0.988899i | ||||||||
9.97486e12 | 0.805201 | |||||||||
−4.13438e11 | −0.0331897 | |||||||||
−1.52893e13 | −1.22061 | |||||||||
−1.10345e12 | −0.0876078 | |||||||||
−3.46128e10 | −0.00273294 | |||||||||
1.24488e13 | 0.977528 | |||||||||
−2.12771e13 | −1.66159 | |||||||||
−1.62299e13 | −1.26048 | |||||||||
−7.34576e12 | −0.567380 | |||||||||
1.09783e13 | 0.843321 | 0.421660 | − | 0.906754i | ||||||
0.421660 | + | 0.906754i | ||||||||
−2.40250e11 | −0.0183544 | |||||||||
−1.81105e13 | −1.37604 | −0.688019 | − | 0.725693i | ||||||
−0.688019 | + | 0.725693i | ||||||||
1.07230e12 | 0.0810298 | |||||||||
1.53989e11 | 0.0115730 | |||||||||
−1.15505e13 | −0.863355 | |||||||||
−5.02389e12 | −0.373478 | −0.186739 | − | 0.982410i | ||||||
−0.186739 | + | 0.982410i | ||||||||
−6.65260e12 | −0.491875 | |||||||||
2.49772e13 | 1.83674 | 0.918371 | − | 0.395721i | ||||||
0.918371 | + | 0.395721i | ||||||||
1.52028e12 | 0.111192 | |||||||||
−7.31884e10 | −0.00532400 | |||||||||
−3.03882e12 | −0.219862 | |||||||||
−1.18965e12 | −0.0856083 | |||||||||
−2.68544e11 | −0.0192206 | |||||||||
−2.14000e13 | −1.52344 | |||||||||
1.07199e13 | 0.759034 | |||||||||
−2.50450e10 | −0.00176383 | |||||||||
7.29302e12 | 0.510869 | |||||||||
−1.68612e13 | −1.17479 | −0.587393 | − | 0.809302i | ||||||
−0.587393 | + | 0.809302i | ||||||||
2.04955e11 | 0.0142037 | |||||||||
1.13728e13 | 0.783944 | |||||||||
3.27819e12 | 0.224766 | |||||||||
1.69289e11 | 0.0115453 | |||||||||
1.32218e13 | 0.896909 | |||||||||
−1.28711e12 | −0.0868479 | |||||||||
2.34460e12 | 0.157363 | |||||||||
−3.33386e13 | −2.22573 | |||||||||
−2.75578e13 | −1.83005 | |||||||||
9.65259e10 | 0.00637616 | |||||||||
−7.09628e11 | −0.0466279 | |||||||||
1.03441e13 | 0.676101 | |||||||||
−9.59694e10 | −0.00623957 | |||||||||
−2.96077e12 | −0.191485 | −0.0957424 | − | 0.995406i | ||||||
−0.0957424 | + | 0.995406i | ||||||||
3.19482e13 | 2.05535 | |||||||||
−1.29246e13 | −0.827122 | |||||||||
9.35241e12 | 0.595376 | |||||||||
−2.12923e13 | −1.34837 | −0.674186 | − | 0.738562i | ||||||
−0.674186 | + | 0.738562i | ||||||||
−5.90754e11 | −0.0372146 | |||||||||
1.10479e13 | 0.692325 | 0.346163 | − | 0.938174i | ||||||
0.346163 | + | 0.938174i | ||||||||
5.52889e12 | 0.344663 | |||||||||
−6.74071e11 | −0.0418015 | |||||||||
−1.48213e12 | −0.0914332 | |||||||||
−5.45410e12 | −0.334714 | −0.167357 | − | 0.985896i | ||||||
−0.167357 | + | 0.985896i | ||||||||
5.52543e11 | 0.0337330 | |||||||||
−1.74491e13 | −1.05975 | |||||||||
−1.94566e13 | −1.17554 | |||||||||
3.29214e11 | 0.0197876 | |||||||||
4.44065e11 | 0.0265526 | |||||||||
3.03609e13 | 1.80603 | |||||||||
−4.37749e11 | −0.0259053 | |||||||||
2.24444e12 | 0.132138 | |||||||||
−2.11829e13 | −1.24068 | |||||||||
2.20018e13 | 1.28202 | |||||||||
−2.33154e13 | −1.35158 | |||||||||
2.51949e13 | 1.45304 | |||||||||
−1.07137e11 | −0.00614709 | |||||||||
−6.93874e12 | −0.396079 | −0.198040 | − | 0.980194i | ||||||
−0.198040 | + | 0.980194i | ||||||||
1.06596e12 | 0.0605363 | |||||||||
2.04551e11 | 0.0115572 | |||||||||
−2.91368e13 | −1.63784 | |||||||||
−1.10273e13 | −0.616705 | −0.308352 | − | 0.951272i | ||||||
−0.308352 | + | 0.951272i | ||||||||
1.69412e13 | 0.942615 | |||||||||
−1.09368e13 | −0.605434 | −0.302717 | − | 0.953081i | ||||||
−0.302717 | + | 0.953081i | ||||||||
8.46837e11 | 0.0466407 | |||||||||
1.57678e11 | 0.00864024 | |||||||||
−2.66247e12 | −0.145155 | |||||||||
−2.59031e13 | −1.40506 | −0.702532 | − | 0.711653i | ||||||
−0.702532 | + | 0.711653i | ||||||||
−1.52128e11 | −0.00821014 | |||||||||
1.21511e13 | 0.652464 | |||||||||
7.59753e12 | 0.405898 | |||||||||
3.06858e13 | 1.63113 | |||||||||
−1.32152e13 | −0.698928 | |||||||||
2.55608e12 | 0.134506 | |||||||||
−2.66956e11 | −0.0139772 | |||||||||
−8.78473e12 | −0.457641 | |||||||||
2.89225e13 | 1.49917 | |||||||||
3.99680e11 | 0.0206133 | |||||||||
1.33651e13 | 0.685848 | |||||||||
1.15213e12 | 0.0588280 | |||||||||
3.14346e12 | 0.159704 | |||||||||
−3.17359e12 | −0.160431 | |||||||||
6.11482e13 | 3.07577 | |||||||||
5.07349e11 | 0.0253929 | |||||||||
5.08771e12 | 0.253375 | |||||||||
−2.79919e13 | −1.38712 | |||||||||
6.90093e11 | 0.0340275 | |||||||||
−1.56389e12 | −0.0767316 | −0.0383658 | − | 0.999264i | ||||||
−0.0383658 | + | 0.999264i | ||||||||
−4.17248e12 | −0.203708 | |||||||||
1.65413e12 | 0.0803585 | |||||||||
−2.52625e13 | −1.22121 | |||||||||
2.44644e13 | 1.17680 | 0.588398 | − | 0.808571i | ||||||
0.588398 | + | 0.808571i | ||||||||
5.37360e11 | 0.0257210 | |||||||||
−3.93662e12 | −0.187502 | |||||||||
−3.05978e13 | −1.45022 | |||||||||
−4.36132e11 | −0.0205695 | |||||||||
1.28918e13 | 0.605040 | |||||||||
−3.13063e13 | −1.46207 | |||||||||
1.13549e11 | 0.00527706 | |||||||||
−9.29278e12 | −0.429760 | −0.214880 | − | 0.976640i | ||||||
−0.214880 | + | 0.976640i | ||||||||
1.25789e13 | 0.578890 | |||||||||
−1.84017e11 | −0.00842733 | |||||||||
1.50888e13 | 0.687645 | |||||||||
−1.43695e13 | −0.651678 | |||||||||
4.36886e11 | 0.0197172 | |||||||||
−4.88777e12 | −0.219519 | |||||||||
3.13679e13 | 1.40196 | |||||||||
−2.75585e12 | −0.122573 | |||||||||
−2.54184e13 | −1.12508 | |||||||||
3.95256e12 | 0.174104 | 0.0870518 | − | 0.996204i | ||||||
0.0870518 | + | 0.996204i | ||||||||
−1.94879e10 | −0.000854264 0 | |||||||||
1.84692e13 | 0.805701 | |||||||||
−1.22343e13 | −0.531139 | |||||||||
5.42401e11 | 0.0234343 | |||||||||
3.28996e13 | 1.41459 | |||||||||
−3.35543e12 | −0.143581 | |||||||||
1.46492e13 | 0.623838 | |||||||||
3.11102e12 | 0.131848 | 0.0659242 | − | 0.997825i | ||||||
0.0659242 | + | 0.997825i | ||||||||
−5.33602e12 | −0.225063 | |||||||||
5.71473e11 | 0.0239884 | |||||||||
1.13523e12 | 0.0474250 | |||||||||
−2.78496e13 | −1.15789 | −0.578943 | − | 0.815368i | ||||||
−0.578943 | + | 0.815368i | ||||||||
−1.07132e12 | −0.0443292 | |||||||||
−4.13704e13 | −1.70368 | |||||||||
1.63382e13 | 0.669624 | |||||||||
−1.05369e12 | −0.0429803 | |||||||||
−4.60240e13 | −1.86842 | |||||||||
4.90336e12 | 0.198116 | 0.0990578 | − | 0.995082i | ||||||
0.0990578 | + | 0.995082i | ||||||||
−2.48684e11 | −0.0100002 | |||||||||
−1.60415e13 | −0.642019 | |||||||||
1.10169e13 | 0.438837 | |||||||||
8.70209e11 | 0.0344994 | |||||||||
2.44567e12 | 0.0965010 | |||||||||
3.31980e13 | 1.30375 | 0.651875 | − | 0.758327i | ||||||
0.651875 | + | 0.758327i | ||||||||
4.51935e13 | 1.76648 | |||||||||
1.99322e13 | 0.775425 | |||||||||
4.15664e11 | 0.0160947 | |||||||||
1.13351e12 | 0.0436838 | |||||||||
1.60460e13 | 0.615490 | |||||||||
2.66031e13 | 1.01566 | |||||||||
−9.86245e10 | −0.00374769 | |||||||||
−2.63883e13 | −0.998060 | |||||||||
1.87511e13 | 0.705895 | |||||||||
−2.40360e13 | −0.900624 | |||||||||
−1.60717e13 | −0.599399 | |||||||||
−5.27211e12 | −0.195709 | |||||||||
−9.50216e11 | −0.0351095 | |||||||||
−4.01878e13 | −1.47800 | −0.739001 | − | 0.673704i | ||||||
−0.739001 | + | 0.673704i | ||||||||
3.00916e13 | 1.10156 | |||||||||
6.18829e10 | 0.00225483 | |||||||||
3.42467e13 | 1.24207 | |||||||||
8.15723e12 | 0.294480 | 0.147240 | − | 0.989101i | ||||||
0.147240 | + | 0.989101i | ||||||||
−7.54538e11 | −0.0271133 | |||||||||
2.97361e13 | 1.06360 | |||||||||
−2.42797e13 | −0.864427 | |||||||||
−1.88855e11 | −0.00669281 | |||||||||
−4.51911e13 | −1.59415 | |||||||||
9.16012e12 | 0.321644 | 0.160822 | − | 0.986983i | ||||||
0.160822 | + | 0.986983i | ||||||||
−7.52369e10 | −0.00262970 | |||||||||
−1.96730e13 | −0.684462 | |||||||||
8.20270e12 | 0.284079 | |||||||||
5.44406e13 | 1.87678 | |||||||||
4.77286e12 | 0.163786 | |||||||||
−3.83289e13 | −1.30929 | −0.654645 | − | 0.755937i | ||||||
−0.654645 | + | 0.755937i | ||||||||
6.08421e11 | 0.0206884 | |||||||||
−1.69199e12 | −0.0572709 | |||||||||
−5.22355e12 | −0.176003 | |||||||||
1.04172e11 | 0.00349402 | |||||||||
−1.31471e13 | −0.438958 | |||||||||
3.11380e13 | 1.03492 | |||||||||
4.77830e13 | 1.58094 | |||||||||
5.86162e13 | 1.93057 | 0.965287 | − | 0.261191i | ||||||
0.965287 | + | 0.261191i | ||||||||
−1.13159e12 | −0.0371010 | |||||||||
9.98613e11 | 0.0325931 | |||||||||
3.41625e13 | 1.10997 | |||||||||
−1.48518e13 | −0.480368 | |||||||||
3.22445e10 | 0.00103822 | |||||||||
2.00858e13 | 0.643814 | 0.321907 | − | 0.946771i | ||||||
0.321907 | + | 0.946771i | ||||||||
−5.82064e13 | −1.85730 | |||||||||
7.82103e11 | 0.0248439 |
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 197.10.a.a.1.18 | ✓ | 71 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
197.10.a.a.1.18 | ✓ | 71 | 1.1 | even | 1 | trivial |