Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [700,5,Mod(549,700)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(700, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("700.549");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 700.o (of order , degree , not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | |
Analytic rank: | |
Dimension: | |
Relative dimension: | over |
Coefficient field: | 12.0.32905425960566784.37 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
|
Coefficient ring: | |
Coefficient ring index: | |
Twist minimal: | no (minimal twist has level 28) |
Sato-Tate group: |
Embedding invariants
Embedding label | 649.3 | ||
Root | of defining polynomial | ||
Character | 700.649 | ||
Dual form | 700.5.o.a.549.3 |
-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 | |||||||||
−0.784623 | − | 1.35901i | −0.0871803 | − | 0.151001i | 0.819138 | − | 0.573597i | ||
−0.906318 | + | 0.422596i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−24.5667 | − | 42.3967i | −0.501361 | − | 0.865238i | |||||
0 | 0 | |||||||||
39.2687 | − | 68.0154i | 0.484799 | − | 0.839697i | |||||
0 | 0 | |||||||||
−11.7557 | − | 20.3615i | −0.0971545 | − | 0.168276i | 0.813351 | − | 0.581773i | ||
−0.910506 | + | 0.413496i | ||||||||
0 | 0 | |||||||||
136.269 | 0.806328 | 0.403164 | − | 0.915128i | ||||||
0.403164 | + | 0.915128i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
131.251 | + | 227.333i | 0.454154 | + | 0.786618i | 0.998639 | − | 0.0521523i | ||
−0.544485 | + | 0.838771i | ||||||||
0 | 0 | |||||||||
387.162 | + | 223.528i | 1.07247 | + | 0.619191i | 0.928855 | − | 0.370442i | ||
0.143615 | + | 0.989634i | ||||||||
0 | 0 | |||||||||
−38.3418 | + | 66.6517i | −0.0869429 | + | 0.151138i | |||||
0 | 0 | |||||||||
648.800 | + | 374.585i | 1.22646 | + | 0.708100i | 0.966288 | − | 0.257462i | ||
0.260176 | + | 0.965561i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−250.353 | −0.343420 | |||||||||
0 | 0 | |||||||||
−406.524 | −0.483382 | −0.241691 | − | 0.970353i | ||||||
−0.241691 | + | 0.970353i | ||||||||
0 | 0 | |||||||||
−584.199 | + | 337.287i | −0.607907 | + | 0.350975i | −0.772146 | − | 0.635445i | ||
0.164239 | + | 0.986421i | ||||||||
0 | 0 | |||||||||
−18.4476 | + | 31.9521i | −0.0169399 | + | 0.0293408i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
645.476 | + | 372.666i | 0.471495 | + | 0.272218i | 0.716865 | − | 0.697212i | ||
−0.245370 | + | 0.969429i | ||||||||
0 | 0 | |||||||||
−106.920 | − | 185.191i | −0.0702959 | − | 0.121756i | |||||
0 | 0 | |||||||||
− | 2476.20i | − | 1.47305i | −0.676410 | − | 0.736526i | ||||
0.676410 | − | 0.736526i | ||||||||
0 | 0 | |||||||||
− | 2636.68i | − | 1.42601i | −0.701161 | − | 0.713003i | ||||
0.701161 | − | 0.713003i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−334.343 | + | 579.099i | −0.151355 | + | 0.262154i | −0.931726 | − | 0.363163i | ||
0.780371 | + | 0.625317i | ||||||||
0 | 0 | |||||||||
−1193.96 | + | 2083.09i | −0.497275 | + | 0.867593i | |||||
0 | 0 | |||||||||
205.964 | − | 356.741i | 0.0791866 | − | 0.137155i | |||||
0 | 0 | |||||||||
−1757.36 | + | 1014.61i | −0.625617 | + | 0.361200i | −0.779053 | − | 0.626959i | ||
0.153436 | + | 0.988159i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
− | 701.541i | − | 0.215925i | |||||||
0 | 0 | |||||||||
1014.22 | − | 585.561i | 0.291359 | − | 0.168216i | −0.347195 | − | 0.937793i | ||
0.638555 | + | 0.769576i | ||||||||
0 | 0 | |||||||||
−2022.05 | − | 1167.43i | −0.543416 | − | 0.313741i | 0.203047 | − | 0.979169i | ||
−0.746462 | + | 0.665428i | ||||||||
0 | 0 | |||||||||
−3848.33 | + | 6.04891i | −0.969597 | + | 0.00152404i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
6546.78 | − | 3779.79i | 1.45841 | − | 0.842011i | 0.459472 | − | 0.888192i | ||
0.998933 | + | 0.0461815i | ||||||||
0 | 0 | |||||||||
− | 1175.63i | − | 0.246929i | |||||||
0 | 0 | |||||||||
7575.36 | 1.50275 | 0.751375 | − | 0.659876i | ||||||
0.751375 | + | 0.659876i | ||||||||
0 | 0 | |||||||||
1896.12 | + | 3284.18i | 0.355812 | + | 0.616284i | 0.987257 | − | 0.159137i | ||
−0.631445 | + | 0.775421i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−574.460 | + | 998.615i | −0.0968898 | + | 0.168429i | |||||
0 | 0 | |||||||||
3897.33 | − | 6750.37i | 0.624472 | − | 1.08162i | −0.364171 | − | 0.931332i | ||
0.988643 | − | 0.150285i | ||||||||
0 | 0 | |||||||||
−2984.33 | − | 5169.02i | −0.454860 | − | 0.787840i | |||||
0 | 0 | |||||||||
2181.41 | 0.316651 | 0.158326 | − | 0.987387i | ||||||
0.158326 | + | 0.987387i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
318.968 | + | 552.469i | 0.0421414 | + | 0.0729910i | |||||
0 | 0 | |||||||||
−8050.38 | − | 4647.89i | −1.01633 | − | 0.586781i | −0.103294 | − | 0.994651i | ||
−0.913040 | + | 0.407870i | ||||||||
0 | 0 | |||||||||
−3347.69 | − | 5777.37i | −0.404261 | − | 0.697666i | |||||
0 | 0 | |||||||||
916.751 | + | 529.287i | 0.105995 | + | 0.0611963i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
9981.90 | 1.06089 | 0.530444 | − | 0.847720i | ||||||
0.530444 | + | 0.847720i | ||||||||
0 | 0 | |||||||||
−1846.52 | −0.188402 | |||||||||
0 | 0 | |||||||||
−675.552 | + | 390.030i | −0.0662241 | + | 0.0382345i | −0.532746 | − | 0.846275i | ||
0.466522 | + | 0.884509i | ||||||||
0 | 0 | |||||||||
−1376.35 | + | 2383.90i | −0.129734 | + | 0.224706i | −0.923573 | − | 0.383422i | ||
0.793840 | + | 0.608127i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
12868.2 | + | 7429.46i | 1.12396 | + | 0.648917i | 0.942408 | − | 0.334464i | ||
0.181550 | + | 0.983382i | ||||||||
0 | 0 | |||||||||
1378.33 | + | 2387.33i | 0.116011 | + | 0.200937i | 0.918183 | − | 0.396155i | ||
−0.802172 | + | 0.597092i | ||||||||
0 | 0 | |||||||||
− | 1169.61i | − | 0.0949281i | |||||||
0 | 0 | |||||||||
6264.79i | 0.490625i | 0.969444 | + | 0.245312i | ||||||
−0.969444 | + | 0.245312i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
5351.13 | − | 9268.43i | 0.390907 | − | 0.677071i | |||||
0 | 0 | |||||||||
6413.76 | − | 11149.4i | 0.452917 | − | 0.787331i | |||||
0 | 0 | |||||||||
7044.11 | − | 12200.8i | 0.481122 | − | 0.833328i | |||||
0 | 0 | |||||||||
−3365.17 | + | 1942.88i | −0.222432 | + | 0.128421i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
− | 12855.0i | − | 0.797010i | −0.917166 | − | 0.398505i | ||||
0.917166 | − | 0.398505i | ||||||||
0 | 0 | |||||||||
−3583.27 | + | 2068.80i | −0.215328 | + | 0.124320i | |||||
0 | 0 | |||||||||
−21412.5 | − | 12362.5i | −1.24774 | − | 0.720383i | −0.277082 | − | 0.960846i | ||
−0.970658 | + | 0.240464i | ||||||||
0 | 0 | |||||||||
−34.4320 | − | 21905.7i | −0.00194652 | − | 1.23838i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1145.02 | + | 661.078i | −0.0610059 | + | 0.0352218i | −0.530193 | − | 0.847877i | ||
0.469187 | + | 0.883099i | ||||||||
0 | 0 | |||||||||
5119.78i | 0.264985i | 0.991184 | + | 0.132493i | ||||||
−0.991184 | + | 0.132493i | ||||||||
0 | 0 | |||||||||
1049.33 | 0.0527807 | |||||||||
0 | 0 | |||||||||
−1601.94 | − | 2774.64i | −0.0783384 | − | 0.135686i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
3767.74 | − | 11.8445i | 0.174360 | − | 0.000548128i | |||||
0 | 0 | |||||||||
5104.93 | − | 8842.00i | 0.229942 | − | 0.398270i | −0.727849 | − | 0.685737i | ||
0.957791 | + | 0.287467i | ||||||||
0 | 0 | |||||||||
−14672.1 | − | 25412.8i | −0.643483 | − | 1.11455i | −0.984650 | − | 0.174543i | ||
0.341166 | − | 0.940003i | ||||||||
0 | 0 | |||||||||
20616.2 | 0.880695 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
15030.2 | + | 26033.1i | 0.609770 | + | 1.05615i | 0.991278 | + | 0.131787i | ||
−0.381508 | + | 0.924366i | ||||||||
0 | 0 | |||||||||
2757.73 | + | 1592.17i | 0.109083 | + | 0.0629791i | |||||
0 | 0 | |||||||||
−57.7005 | − | 36709.3i | −0.00222602 | − | 1.41620i | |||||
0 | 0 | |||||||||
−26742.3 | − | 15439.7i | −1.00652 | − | 0.581115i | −0.0963500 | − | 0.995348i | ||
−0.910171 | + | 0.414232i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
12858.8 | 0.461070 | 0.230535 | − | 0.973064i | ||||||
0.230535 | + | 0.973064i | ||||||||
0 | 0 | |||||||||
−9991.63 | −0.349835 | |||||||||
0 | 0 | |||||||||
30406.7 | − | 17555.3i | 1.03987 | − | 0.600367i | |||||
0 | 0 | |||||||||
−7845.51 | + | 13588.8i | −0.262137 | + | 0.454035i | −0.966810 | − | 0.255498i | ||
0.704672 | + | 0.709533i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1591.56 | − | 918.890i | −0.0508016 | − | 0.0293303i | |||||
0 | 0 | |||||||||
−15993.2 | − | 27701.0i | −0.499148 | − | 0.864550i | 0.500851 | − | 0.865533i | ||
−1.00000 | 0.000983488i | |||||||||
0 | 0 | |||||||||
− | 47967.6i | − | 1.46417i | −0.681215 | − | 0.732083i | ||||
0.681215 | − | 0.732083i | ||||||||
0 | 0 | |||||||||
3663.97i | 0.109408i | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
3085.88 | − | 5344.91i | 0.0882462 | − | 0.152847i | |||||
0 | 0 | |||||||||
6150.35 | + | 10614.2i | 0.172177 | + | 0.297141i | |||||
0 | 0 | |||||||||
−2227.93 | + | 3858.88i | −0.0610709 | + | 0.105778i | −0.894944 | − | 0.446178i | ||
0.833873 | + | 0.551956i | ||||||||
0 | 0 | |||||||||
−25460.9 | + | 14699.9i | −0.683533 | + | 0.394638i | −0.801185 | − | 0.598417i | ||
0.117652 | + | 0.993055i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
− | 23816.0i | − | 0.613671i | −0.951763 | − | 0.306836i | ||||
0.951763 | − | 0.306836i | ||||||||
0 | 0 | |||||||||
42280.9 | − | 24410.9i | 1.06767 | − | 0.616421i | 0.140128 | − | 0.990133i | ||
0.927545 | + | 0.373713i | ||||||||
0 | 0 | |||||||||
−10273.5 | − | 5931.41i | −0.254288 | − | 0.146813i | |||||
0 | 0 | |||||||||
9986.94 | + | 17235.3i | 0.242349 | + | 0.418241i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
50955.1 | − | 29418.9i | 1.18918 | − | 0.686572i | |||||
0 | 0 | |||||||||
− | 10510.9i | − | 0.240629i | |||||||
0 | 0 | |||||||||
−9582.07 | −0.215226 | −0.107613 | − | 0.994193i | ||||||
−0.107613 | + | 0.994193i | ||||||||
0 | 0 | |||||||||
−5943.80 | − | 10295.0i | −0.131010 | − | 0.226916i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
28651.7 | + | 16482.1i | 0.608458 | + | 0.350019i | |||||
0 | 0 | |||||||||
2975.48 | − | 5153.68i | 0.0620396 | − | 0.107456i | |||||
0 | 0 | |||||||||
17885.5 | + | 30978.5i | 0.366197 | + | 0.634273i | |||||
0 | 0 | |||||||||
54978.9 | 1.10557 | 0.552785 | − | 0.833324i | ||||||
0.552785 | + | 0.833324i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
4340.66 | + | 7518.24i | 0.0842372 | + | 0.145903i | 0.905066 | − | 0.425271i | ||
−0.820829 | + | 0.571174i | ||||||||
0 | 0 | |||||||||
6262.86 | + | 3615.86i | 0.119427 | + | 0.0689511i | 0.558523 | − | 0.829489i | ||
−0.439097 | + | 0.898440i | ||||||||
0 | 0 | |||||||||
1807.86 | − | 2.84164i | 0.0338798 | − | 5.32531e-5i | |||||
0 | 0 | |||||||||
−7660.79 | − | 4422.96i | −0.141111 | − | 0.0814707i | 0.427782 | − | 0.903882i | ||
−0.568894 | + | 0.822411i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−12231.7 | −0.217767 | |||||||||
0 | 0 | |||||||||
−88491.7 | −1.54920 | −0.774599 | − | 0.632453i | ||||||
−0.774599 | + | 0.632453i | ||||||||
0 | 0 | |||||||||
−53365.8 | + | 30810.7i | −0.918816 | + | 0.530479i | −0.883257 | − | 0.468889i | ||
−0.0355589 | + | 0.999368i | ||||||||
0 | 0 | |||||||||
−14822.5 | + | 25673.3i | −0.251020 | + | 0.434779i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
52758.4 | + | 30460.0i | 0.864763 | + | 0.499271i | |||||
0 | 0 | |||||||||
−1711.59 | − | 2964.55i | −0.0276058 | − | 0.0478146i | |||||
0 | 0 | |||||||||
− | 57796.3i | − | 0.917386i | −0.888595 | − | 0.458693i | ||||
0.888595 | − | 0.458693i | ||||||||
0 | 0 | |||||||||
− | 17614.0i | − | 0.275180i | |||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
35065.0 | − | 60734.3i | 0.530893 | − | 0.919534i | −0.468457 | − | 0.883486i | ||
0.999350 | − | 0.0360479i | ||||||||
0 | 0 | |||||||||
−57.4050 | − | 36521.2i | −0.000855756 | − | 0.544435i | |||||
0 | 0 | |||||||||
−15963.7 | + | 27649.9i | −0.234343 | + | 0.405894i | |||||
0 | 0 | |||||||||
19262.0 | − | 11120.9i | 0.278477 | − | 0.160779i | −0.354257 | − | 0.935148i | ||
0.632734 | + | 0.774369i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
14587.4i | 0.204623i | |||||||||
0 | 0 | |||||||||
−40332.3 | + | 23285.9i | −0.557376 | + | 0.321801i | −0.752092 | − | 0.659058i | ||
0.194715 | + | 0.980860i | ||||||||
0 | 0 | |||||||||
71958.3 | + | 41545.1i | 0.979811 | + | 0.565694i | 0.902213 | − | 0.431291i | ||
0.0775980 | + | 0.996985i | ||||||||
0 | 0 | |||||||||
−5224.82 | + | 9082.59i | −0.0701045 | + | 0.121866i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
7818.59 | − | 4514.06i | 0.101899 | − | 0.0588313i | −0.448185 | − | 0.893941i | ||
0.550083 | + | 0.835110i | ||||||||
0 | 0 | |||||||||
52979.4i | 0.680610i | |||||||||
0 | 0 | |||||||||
64188.4 | 0.812912 | 0.406456 | − | 0.913670i | ||||||
0.406456 | + | 0.913670i | ||||||||
0 | 0 | |||||||||
11295.1 | + | 19563.7i | 0.141032 | + | 0.244274i | 0.927885 | − | 0.372865i | ||
−0.786854 | + | 0.617140i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−104983. | + | 60832.0i | −1.27454 | + | 0.738530i | |||||
0 | 0 | |||||||||
7307.06 | − | 12656.2i | 0.0874877 | − | 0.151533i | |||||
0 | 0 | |||||||||
−7832.02 | − | 13565.5i | −0.0924885 | − | 0.160195i | |||||
0 | 0 | |||||||||
−130473. | −1.51980 | −0.759900 | − | 0.650040i | ||||||
−0.759900 | + | 0.650040i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
2943.08 | + | 5097.56i | 0.0333648 | + | 0.0577896i | |||||
0 | 0 | |||||||||
88411.6 | + | 51044.5i | 0.988933 | + | 0.570961i | |||||
0 | 0 | |||||||||
−111787. | + | 64774.5i | −1.23383 | + | 0.714943i | |||||
0 | 0 | |||||||||
1060.11 | + | 612.053i | 0.0115469 | + | 0.00666659i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−56173.9 | −0.596015 | −0.298008 | − | 0.954563i | ||||||
−0.298008 | + | 0.954563i | ||||||||
0 | 0 | |||||||||
4319.65 | 0.0452410 | |||||||||
0 | 0 | |||||||||
40087.2 | − | 23144.4i | 0.414462 | − | 0.239290i | −0.278243 | − | 0.960511i | ||
0.692705 | + | 0.721221i | ||||||||
0 | 0 | |||||||||
69174.4 | − | 119814.i | 0.706085 | − | 1.22298i | −0.260213 | − | 0.965551i | ||
0.966299 | − | 0.257424i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−50493.9 | − | 29152.7i | −0.502482 | − | 0.290108i | 0.227256 | − | 0.973835i | ||
−0.729738 | + | 0.683727i | ||||||||
0 | 0 | |||||||||
4778.97 | + | 8277.42i | 0.0469627 | + | 0.0813418i | |||||
0 | 0 | |||||||||
− | 23317.3i | − | 0.226291i | |||||||
0 | 0 | |||||||||
117353.i | 1.12483i | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
2162.93 | − | 3746.31i | 0.0202278 | − | 0.0350355i | |||||
0 | 0 | |||||||||
32765.6 | − | 51.5018i | 0.302709 | − | 0.000475806i | |||||
0 | 0 | |||||||||
−494.602 | + | 856.675i | −0.00451440 | + | 0.00781916i | −0.868274 | − | 0.496085i | ||
0.863759 | + | 0.503904i | ||||||||
0 | 0 | |||||||||
50694.1 | − | 29268.2i | 0.457161 | − | 0.263942i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
55958.7i | 0.492728i | 0.969177 | + | 0.246364i | ||||||
−0.969177 | + | 0.246364i | ||||||||
0 | 0 | |||||||||
8513.89 | − | 4915.49i | 0.0740847 | − | 0.0427728i | |||||
0 | 0 | |||||||||
13735.3 | + | 7930.09i | 0.118122 | + | 0.0681976i | |||||
0 | 0 | |||||||||
117648. | − | 554.769i | 0.999989 | − | 0.00471546i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−113141. | + | 65322.2i | −0.939641 | + | 0.542502i | −0.889848 | − | 0.456257i | ||
−0.0497936 | + | 0.998760i | ||||||||
0 | 0 | |||||||||
110948.i | 0.910899i | 0.890262 | + | 0.455450i | ||||||
−0.890262 | + | 0.455450i | ||||||||
0 | 0 | |||||||||
−34115.5 | −0.276910 | |||||||||
0 | 0 | |||||||||
8503.18 | + | 14727.9i | 0.0682389 | + | 0.118193i | 0.898126 | − | 0.439738i | ||
−0.829887 | + | 0.557931i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−20184.5 | + | 31.7265i | −0.158373 | + | 0.000248935i | |||||
0 | 0 | |||||||||
35732.4 | − | 61890.3i | 0.277251 | − | 0.480212i | −0.693450 | − | 0.720505i | ||
0.970701 | + | 0.240293i | ||||||||
0 | 0 | |||||||||
34769.0 | + | 60221.8i | 0.266795 | + | 0.462103i | |||||
0 | 0 | |||||||||
−22107.9 | −0.167777 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−85183.8 | − | 147543.i | −0.632448 | − | 1.09543i | −0.987050 | − | 0.160415i | ||
0.354602 | − | 0.935017i | ||||||||
0 | 0 | |||||||||
−168420. | − | 97237.2i | −1.23692 | − | 0.714134i | |||||
0 | 0 | |||||||||
86188.6 | + | 49580.5i | 0.626184 | + | 0.360216i | |||||
0 | 0 | |||||||||
−130503. | − | 75346.0i | −0.938001 | − | 0.541555i | −0.0486680 | − | 0.998815i | ||
−0.889333 | + | 0.457260i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−55396.8 | −0.389764 | |||||||||
0 | 0 | |||||||||
211477. | 1.47226 | 0.736129 | − | 0.676841i | ||||||
0.736129 | + | 0.676841i | ||||||||
0 | 0 | |||||||||
−17470.0 | + | 10086.3i | −0.120349 | + | 0.0694836i | |||||
0 | 0 | |||||||||
59333.6 | − | 102769.i | 0.404486 | − | 0.700590i | −0.589776 | − | 0.807567i | ||
0.994261 | + | 0.106977i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−179335. | − | 103539.i | −1.19741 | − | 0.691326i | |||||
0 | 0 | |||||||||
107858. | + | 186816.i | 0.712778 | + | 1.23457i | 0.963810 | + | 0.266588i | ||
−0.251033 | + | 0.967979i | ||||||||
0 | 0 | |||||||||
196658.i | 1.28635i | |||||||||
0 | 0 | |||||||||
38799.6i | 0.251213i | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−77371.1 | + | 134011.i | −0.490905 | + | 0.850273i | −0.999945 | − | 0.0104699i | ||
0.509040 | + | 0.860743i | ||||||||
0 | 0 | |||||||||
−29743.0 | + | 17234.5i | −0.186827 | + | 0.108256i | |||||
0 | 0 | |||||||||
−100029. | + | 173255.i | −0.622067 | + | 1.07745i | 0.367033 | + | 0.930208i | ||
−0.989100 | + | 0.147244i | ||||||||
0 | 0 | |||||||||
−79608.5 | + | 45962.0i | −0.490173 | + | 0.283001i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
− | 17523.8i | − | 0.105789i | |||||||
0 | 0 | |||||||||
−190382. | + | 109917.i | −1.13810 | + | 0.657080i | −0.945958 | − | 0.324288i | ||
−0.192137 | + | 0.981368i | ||||||||
0 | 0 | |||||||||
1796.82 | + | 1037.39i | 0.0106370 | + | 0.00614129i | |||||
0 | 0 | |||||||||
−49741.9 | − | 28614.4i | −0.291623 | − | 0.167758i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
6957.81 | − | 4017.10i | 0.0400130 | − | 0.0231015i | |||||
0 | 0 | |||||||||
31359.8i | 0.178626i | 0.996004 | + | 0.0893132i | ||||||
−0.996004 | + | 0.0893132i | ||||||||
0 | 0 | |||||||||
−73690.7 | −0.415766 | −0.207883 | − | 0.978154i | ||||||
−0.207883 | + | 0.978154i | ||||||||
0 | 0 | |||||||||
26258.5 | + | 45481.0i | 0.146753 | + | 0.254184i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
179.830 | + | 114408.i | 0.000986291 | + | 0.627481i | |||||
0 | 0 | |||||||||
−2513.84 | + | 4354.10i | −0.0136591 | + | 0.0236583i | |||||
0 | 0 | |||||||||
132586. | + | 229646.i | 0.713746 | + | 1.23624i | 0.963441 | + | 0.267920i | ||
−0.249695 | + | 0.968325i | ||||||||
0 | 0 | |||||||||
124873. | 0.666027 | 0.333014 | − | 0.942922i | ||||||
0.333014 | + | 0.942922i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
167460. | + | 290050.i | 0.876898 | + | 1.51883i | |||||
0 | 0 | |||||||||
120989. | + | 69852.8i | 0.627792 | + | 0.362456i | 0.779896 | − | 0.625909i | ||
−0.152105 | + | 0.988364i | ||||||||
0 | 0 | |||||||||
94797.1 | + | 163008.i | 0.487437 | + | 0.838169i | |||||
0 | 0 | |||||||||
191556. | + | 110595.i | 0.976087 | + | 0.563544i | 0.901087 | − | 0.433639i | ||
0.0750005 | + | 0.997183i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−16021.8 | −0.0801855 | |||||||||
0 | 0 | |||||||||
−255878. | −1.26923 | −0.634615 | − | 0.772828i | ||||||
−0.634615 | + | 0.772828i | ||||||||
0 | 0 | |||||||||
−50419.0 | + | 29109.4i | −0.247880 | + | 0.143114i | |||||
0 | 0 | |||||||||
−23024.1 | + | 39878.9i | −0.112198 | + | 0.194333i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−277065. | − | 159964.i | −1.32663 | − | 0.765929i | −0.341852 | − | 0.939754i | ||
−0.984777 | + | 0.173825i | ||||||||
0 | 0 | |||||||||
−32859.0 | − | 56913.5i | −0.155966 | − | 0.270141i | |||||
0 | 0 | |||||||||
369557.i | 1.73892i | 0.494002 | + | 0.869461i | ||||||
−0.494002 | + | 0.869461i | ||||||||
0 | 0 | |||||||||
32715.0i | 0.152611i | 0.997084 | + | 0.0763053i | ||||||
−0.997084 | + | 0.0763053i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
153186. | − | 265325.i | 0.702400 | − | 1.21659i | −0.265222 | − | 0.964187i | ||
0.967622 | − | 0.252405i | ||||||||
0 | 0 | |||||||||
−321083. | − | 184705.i | −1.45973 | − | 0.839717i | |||||
0 | 0 | |||||||||
23586.1 | − | 40852.3i | 0.106320 | − | 0.184151i | |||||
0 | 0 | |||||||||
−53686.7 | + | 30996.0i | −0.239963 | + | 0.138543i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
159370.i | 0.700438i | |||||||||
0 | 0 | |||||||||
226801. | − | 130944.i | 0.988493 | − | 0.570707i | 0.0836697 | − | 0.996494i | ||
0.904824 | + | 0.425787i | ||||||||
0 | 0 | |||||||||
87958.7 | + | 50783.0i | 0.380180 | + | 0.219497i | |||||
0 | 0 | |||||||||
−49842.8 | + | 28881.3i | −0.213653 | + | 0.123801i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−71235.3 | + | 41127.7i | −0.300357 | + | 0.173411i | −0.642603 | − | 0.766199i | ||
0.342246 | + | 0.939610i | ||||||||
0 | 0 | |||||||||
48457.2i | 0.202647i | |||||||||
0 | 0 | |||||||||
−102923. | −0.426924 | −0.213462 | − | 0.976951i | ||||||
−0.213462 | + | 0.976951i | ||||||||
0 | 0 | |||||||||
−53356.5 | − | 92416.2i | −0.219530 | − | 0.380237i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−186101. | − | 321170.i | −0.753420 | − | 1.30024i | |||||
0 | 0 | |||||||||
75028.2 | − | 129953.i | 0.301317 | − | 0.521896i | −0.675118 | − | 0.737710i | ||
0.976434 | + | 0.215814i | ||||||||
0 | 0 | |||||||||
−10089.3 | − | 17475.2i | −0.0401962 | − | 0.0696219i | |||||
0 | 0 | |||||||||
91806.6 | 0.362859 | 0.181430 | − | 0.983404i | ||||||
0.181430 | + | 0.983404i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
7839.66 | + | 13578.7i | 0.0304987 | + | 0.0528253i | |||||
0 | 0 | |||||||||
412600. | + | 238215.i | 1.59255 | + | 0.919460i | 0.992867 | + | 0.119224i | ||
0.599684 | + | 0.800237i | ||||||||
0 | 0 | |||||||||
92656.9 | − | 161071.i | 0.354843 | − | 0.616843i | |||||
0 | 0 | |||||||||
−96927.3 | − | 55961.0i | −0.368308 | − | 0.212643i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
15721.7 | 0.0588192 | |||||||||
0 | 0 | |||||||||
24623.1 | 0.0914128 | |||||||||
0 | 0 | |||||||||
147768. | − | 85314.0i | 0.544384 | − | 0.314300i | −0.202470 | − | 0.979289i | ||
0.746854 | + | 0.664988i | ||||||||
0 | 0 | |||||||||
−49098.2 | + | 85040.5i | −0.179499 | + | 0.310901i | −0.941709 | − | 0.336428i | ||
0.762210 | + | 0.647330i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−153353. | − | 88538.3i | −0.552167 | − | 0.318794i | |||||
0 | 0 | |||||||||
140707. | + | 243711.i | 0.502810 | + | 0.870892i | |||||
0 | 0 | |||||||||
− | 91977.0i | − | 0.326205i | |||||||
0 | 0 | |||||||||
− | 337430.i | − | 1.18776i | |||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−25097.3 | + | 43469.7i | −0.0870318 | + | 0.150743i | |||||
0 | 0 | |||||||||
56450.5 | − | 177.461i | 0.194308 | − | 0.000610838i | |||||
0 | 0 | |||||||||
52833.7 | − | 91510.6i | 0.180516 | − | 0.312663i | −0.761540 | − | 0.648118i | ||
0.942056 | + | 0.335454i | ||||||||
0 | 0 | |||||||||
−65188.2 | + | 37636.4i | −0.221090 | + | 0.127646i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
127121.i | 0.424855i | 0.977177 | + | 0.212428i | ||||||
−0.977177 | + | 0.212428i | ||||||||
0 | 0 | |||||||||
−158807. | + | 91687.0i | −0.526895 | + | 0.304203i | |||||
0 | 0 | |||||||||
−157391. | − | 90869.5i | −0.518413 | − | 0.299306i | |||||
0 | 0 | |||||||||
−381938. | + | 600.340i | −1.24894 | + | 0.00196312i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−26407.6 | + | 15246.5i | −0.0851176 | + | 0.0491427i | −0.541955 | − | 0.840408i | ||
0.456837 | + | 0.889550i | ||||||||
0 | 0 | |||||||||
− | 359300.i | − | 1.14983i | |||||||
0 | 0 | |||||||||
−9685.01 | −0.0307733 | |||||||||
0 | 0 | |||||||||
265237. | + | 459404.i | 0.836791 | + | 1.44936i | 0.892564 | + | 0.450921i | ||
−0.0557725 | + | 0.998444i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−145834. | + | 253511.i | −0.453621 | + | 0.788554i | |||||
0 | 0 | |||||||||
−169366. | + | 293351.i | −0.523121 | + | 0.906072i | 0.476517 | + | 0.879165i | ||
−0.999638 | + | 0.0269067i | ||||||||
0 | 0 | |||||||||
53455.6 | + | 92587.8i | 0.163954 | + | 0.283976i | 0.936283 | − | 0.351246i | ||
−0.772330 | + | 0.635222i | ||||||||
0 | 0 | |||||||||
6992.33 | 0.0212967 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
60238.8 | + | 104337.i | 0.180936 | + | 0.313390i | 0.942200 | − | 0.335052i | ||
−0.761264 | + | 0.648443i | ||||||||
0 | 0 | |||||||||
39954.4 | + | 23067.7i | 0.119181 | + | 0.0688093i | |||||
0 | 0 | |||||||||
−53590.0 | − | 92484.6i | −0.158757 | − | 0.273979i | |||||
0 | 0 | |||||||||
41317.9 | + | 23854.9i | 0.121563 | + | 0.0701844i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
525818. | 1.52602 | 0.763008 | − | 0.646389i | ||||||
0.763008 | + | 0.646389i | ||||||||
0 | 0 | |||||||||
−301573. | −0.869283 | |||||||||
0 | 0 | |||||||||
−32366.0 | + | 18686.5i | −0.0926648 | + | 0.0535000i | |||||
0 | 0 | |||||||||
37113.8 | − | 64283.0i | 0.105542 | − | 0.182804i | −0.808417 | − | 0.588610i | ||
0.913960 | + | 0.405805i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−66349.1 | − | 38306.7i | −0.186160 | − | 0.107480i | |||||
0 | 0 | |||||||||
10990.7 | + | 19036.5i | 0.0306318 | + | 0.0530558i | 0.880935 | − | 0.473237i | ||
−0.850303 | + | 0.526293i | ||||||||
0 | 0 | |||||||||
− | 77418.2i | − | 0.214336i | −0.994241 | − | 0.107168i | ||||
0.994241 | − | 0.107168i | ||||||||
0 | 0 | |||||||||
− | 593710.i | − | 1.63282i | |||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
89931.2 | − | 155765.i | 0.244081 | − | 0.422760i | −0.717792 | − | 0.696257i | ||
0.961873 | + | 0.273498i | ||||||||
0 | 0 | |||||||||
15586.9 | − | 27095.5i | 0.0420266 | − | 0.0730572i | |||||
0 | 0 | |||||||||
−45560.7 | + | 78913.5i | −0.122042 | + | 0.211382i | |||||
0 | 0 | |||||||||
544968. | − | 314637.i | 1.45027 | − | 0.837316i | 0.451777 | − | 0.892131i | ||
0.998497 | + | 0.0548147i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
52877.1i | 0.138899i | 0.997585 | + | 0.0694493i | ||||||
−0.997585 | + | 0.0694493i | ||||||||
0 | 0 | |||||||||
−447040. | + | 258099.i | −1.16672 | + | 0.673603i | −0.952904 | − | 0.303271i | ||
−0.213811 | + | 0.976875i | ||||||||
0 | 0 | |||||||||
−162429. | − | 93778.6i | −0.421193 | − | 0.243176i | |||||
0 | 0 | |||||||||
715.955 | + | 455493.i | 0.00184463 | + | 1.17356i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−14284.4 | + | 8247.09i | −0.0363351 | + | 0.0209781i | |||||
0 | 0 | |||||||||
195651.i | 0.494515i | |||||||||
0 | 0 | |||||||||
193439. | 0.485831 | 0.242915 | − | 0.970047i | ||||||
0.242915 | + | 0.970047i | ||||||||
0 | 0 | |||||||||
7518.31 | + | 13022.1i | 0.0187635 | + | 0.0324993i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−162700. | + | 283862.i | −0.400967 | + | 0.699565i | |||||
0 | 0 | |||||||||
297475. | − | 515242.i | 0.728532 | − | 1.26185i | |||||
0 | 0 | |||||||||
−376563. | − | 652226.i | −0.916477 | − | 1.58738i | −0.804725 | − | 0.593648i | ||
−0.111751 | − | 0.993736i | ||||||||
0 | 0 | |||||||||
−7110.23 | −0.0171974 | −0.00859868 | − | 0.999963i | ||||||
−0.00859868 | + | 0.999963i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
197343. | + | 341808.i | 0.471426 | + | 0.816534i | 0.999466 | − | 0.0326859i | ||
−0.528040 | + | 0.849220i | ||||||||
0 | 0 | |||||||||
−23845.8 | − | 13767.4i | −0.0566137 | − | 0.0326860i | |||||
0 | 0 | |||||||||
−81.5306 | − | 51870.0i | −0.000192380 | − | 0.122392i | |||||
0 | 0 | |||||||||
−200186. | − | 115578.i | −0.469470 | − | 0.271049i | 0.246548 | − | 0.969131i | ||
−0.716018 | + | 0.698082i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
297833. | 0.689989 | |||||||||
0 | 0 | |||||||||
772498. | 1.77880 | 0.889399 | − | 0.457131i | ||||||
0.889399 | + | 0.457131i | ||||||||
0 | 0 | |||||||||
−195287. | + | 112749.i | −0.446962 | + | 0.258053i | −0.706546 | − | 0.707667i | ||
0.259584 | + | 0.965720i | ||||||||
0 | 0 | |||||||||
28066.7 | − | 48612.9i | 0.0638504 | − | 0.110592i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−263753. | − | 152278.i | −0.592851 | − | 0.342282i | |||||
0 | 0 | |||||||||
−43137.7 | − | 74716.6i | −0.0963839 | − | 0.166942i | |||||
0 | 0 | |||||||||
54895.8i | 0.121925i | |||||||||
0 | 0 | |||||||||
59564.6i | 0.131510i | 0.997836 | + | 0.0657549i | ||||||
−0.997836 | + | 0.0657549i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
396715. | − | 687131.i | 0.865569 | − | 1.49921i | −0.000912440 | − | 1.00000i | ||
0.866481 | − | 0.499210i | ||||||||
0 | 0 | |||||||||
−245222. | − | 423199.i | −0.531888 | − | 0.917921i | |||||
0 | 0 | |||||||||
6811.56 | − | 11798.0i | 0.0146876 | − | 0.0254397i | |||||
0 | 0 | |||||||||
−80201.3 | + | 46304.3i | −0.171925 | + | 0.0992612i | −0.583493 | − | 0.812118i | ||
0.411568 | + | 0.911379i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
− | 11348.4i | − | 0.0240447i | |||||||
0 | 0 | |||||||||
−239474. | + | 138261.i | −0.504453 | + | 0.291246i | |||||
0 | 0 | |||||||||
−162273. | − | 93688.2i | −0.339852 | − | 0.196213i | 0.320355 | − | 0.947298i | ||
−0.660206 | + | 0.751084i | ||||||||
0 | 0 | |||||||||
45362.9 | + | 78286.5i | 0.0944571 | + | 0.163012i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
562921. | − | 325003.i | 1.15873 | − | 0.668993i | |||||
0 | 0 | |||||||||
13881.4i | 0.0284105i | |||||||||
0 | 0 | |||||||||
326056. | 0.663522 | 0.331761 | − | 0.943363i | ||||||
0.331761 | + | 0.943363i | ||||||||
0 | 0 | |||||||||
166603. | + | 288564.i | 0.337110 | + | 0.583891i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
33132.0 | + | 19059.4i | 0.0662841 | + | 0.0381303i | |||||
0 | 0 | |||||||||
32372.6 | − | 56070.9i | 0.0643998 | − | 0.111544i | −0.832028 | − | 0.554734i | ||
0.896428 | + | 0.443190i | ||||||||
0 | 0 | |||||||||
−306086. | − | 530157.i | −0.605487 | − | 1.04873i | |||||
0 | 0 | |||||||||
−505371. | −0.994102 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
69432.6 | + | 120261.i | 0.135060 | + | 0.233930i | |||||
0 | 0 | |||||||||
616355. | + | 355853.i | 1.19227 | + | 0.688355i | 0.958820 | − | 0.284014i | ||
0.233446 | + | 0.972370i | ||||||||
0 | 0 | |||||||||
134882. | − | 212.011i | 0.259468 | − | 0.000407838i | |||||
0 | 0 | |||||||||
83744.0 | + | 48349.6i | 0.160205 | + | 0.0924946i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
763134. | 1.44388 | 0.721941 | − | 0.691954i | ||||||
0.721941 | + | 0.691954i | ||||||||
0 | 0 | |||||||||
−436942. | −0.822183 | |||||||||
0 | 0 | |||||||||
599404. | − | 346066.i | 1.12172 | − | 0.647626i | |||||
0 | 0 | |||||||||
10304.6 | − | 17848.0i | 0.0191788 | − | 0.0332187i | −0.856277 | − | 0.516517i | ||
0.875456 | + | 0.483299i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−153924. | − | 88868.0i | −0.283381 | − | 0.163610i | |||||
0 | 0 | |||||||||
−393194. | − | 681032.i | −0.719976 | − | 1.24703i | −0.961009 | − | 0.276518i | ||
0.241033 | − | 0.970517i | ||||||||
0 | 0 | |||||||||
− | 95598.6i | − | 0.174107i | |||||||
0 | 0 | |||||||||
740479.i | 1.34133i | 0.741761 | + | 0.670664i | ||||||
−0.741761 | + | 0.670664i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
85661.3 | − | 148370.i | 0.153512 | − | 0.265891i | |||||
0 | 0 | |||||||||
−1144.42 | − | 728086.i | −0.00203997 | − | 1.29783i | |||||
0 | 0 | |||||||||
247292. | − | 428322.i | 0.438460 | − | 0.759436i | −0.559111 | − | 0.829093i | ||
0.997571 | + | 0.0696574i | ||||||||
0 | 0 | |||||||||
−78545.5 | + | 45348.3i | −0.138526 | + | 0.0799780i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
139399.i | 0.243258i | 0.992576 | + | 0.121629i | ||||||
−0.992576 | + | 0.121629i | ||||||||
0 | 0 | |||||||||
−23937.5 | + | 13820.3i | −0.0415524 | + | 0.0239903i | |||||
0 | 0 | |||||||||
−207340. | − | 119708.i | −0.358025 | − | 0.206706i | 0.310189 | − | 0.950675i | ||
−0.668214 | + | 0.743969i | ||||||||
0 | 0 | |||||||||
67354.1 | − | 117085.i | 0.115695 | − | 0.201119i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
138208. | − | 79794.1i | 0.234931 | − | 0.135638i | |||||
0 | 0 | |||||||||
− | 98701.5i | − | 0.166906i | −0.996512 | − | 0.0834528i | ||||
0.996512 | − | 0.0834528i | ||||||||
0 | 0 | |||||||||
−110051. | −0.185134 | |||||||||
0 | 0 | |||||||||
−293248. | − | 507921.i | −0.490769 | − | 0.850036i | 0.509175 | − | 0.860663i | ||
−0.999944 | + | 0.0106268i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−49587.5 | + | 28733.4i | −0.0821354 | + | 0.0475932i | |||||
0 | 0 | |||||||||
553500. | − | 958690.i | 0.912100 | − | 1.57980i | |||||
0 | 0 | |||||||||
−89053.6 | − | 154245.i | −0.145999 | − | 0.252877i | |||||
0 | 0 | |||||||||
101775. | 0.166003 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
74787.4 | + | 129536.i | 0.120748 | + | 0.209141i | 0.920063 | − | 0.391771i | ||
−0.799315 | + | 0.600912i | ||||||||
0 | 0 | |||||||||
−30226.8 | − | 17451.4i | −0.0485554 | − | 0.0280335i | |||||
0 | 0 | |||||||||
265606. | − | 153905.i | 0.424507 | − | 0.245980i | |||||
0 | 0 | |||||||||
−275544. | − | 159085.i | −0.438171 | − | 0.252978i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
241092. | 0.379547 | 0.189774 | − | 0.981828i | ||||||
0.189774 | + | 0.981828i | ||||||||
0 | 0 | |||||||||
−175531. | −0.274954 | |||||||||
0 | 0 | |||||||||
−632256. | + | 365033.i | −0.985436 | + | 0.568941i | |||||
0 | 0 | |||||||||
44580.4 | − | 77215.6i | 0.0691374 | − | 0.119750i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
63291.3 | + | 36541.3i | 0.0971845 | + | 0.0561095i | |||||
0 | 0 | |||||||||
100933. | + | 174820.i | 0.154218 | + | 0.267113i | 0.932774 | − | 0.360462i | ||
−0.778556 | + | 0.627575i | ||||||||
0 | 0 | |||||||||
− | 1.16747e6i | − | 1.77503i | −0.460779 | − | 0.887515i | ||||
0.460779 | − | 0.887515i | ||||||||
0 | 0 | |||||||||
− | 130389.i | − | 0.197270i | |||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
589373. | − | 1.02082e6i | 0.882970 | − | 1.52935i | |||||
0 | 0 | |||||||||
−524410. | + | 824.281i | −0.781814 | + | 0.00122887i | |||||
0 | 0 | |||||||||
324585. | − | 562198.i | 0.481551 | − | 0.834071i | −0.518225 | − | 0.855245i | ||
0.999776 | + | 0.0211734i | ||||||||
0 | 0 | |||||||||
−425193. | + | 245486.i | −0.627750 | + | 0.362432i | −0.779880 | − | 0.625929i | ||
0.152130 | + | 0.988360i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
709017.i | 1.03668i | 0.855174 | + | 0.518341i | ||||||
−0.855174 | + | 0.518341i | ||||||||
0 | 0 | |||||||||
−534645. | + | 308677.i | −0.777958 | + | 0.449154i | −0.835706 | − | 0.549177i | ||
0.0577480 | + | 0.998331i | ||||||||
0 | 0 | |||||||||
−12269.3 | − | 7083.68i | −0.0177671 | − | 0.0102579i | |||||
0 | 0 | |||||||||
−630262. | + | 1981.33i | −0.908304 | + | 0.00285540i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
146256. | − | 84441.0i | 0.208768 | − | 0.120532i | |||||
0 | 0 | |||||||||
493961.i | 0.701728i | 0.936426 | + | 0.350864i | ||||||
−0.936426 | + | 0.350864i | ||||||||
0 | 0 | |||||||||
−542019. | −0.766342 | |||||||||
0 | 0 | |||||||||
−50363.7 | − | 87232.4i | −0.0708699 | − | 0.122750i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−690322. | + | 1085.07i | −0.962243 | + | 0.00151248i | |||||
0 | 0 | |||||||||
17724.8 | − | 30700.2i | 0.0245904 | − | 0.0425918i | |||||
0 | 0 | |||||||||
279190. | + | 483571.i | 0.385514 | + | 0.667730i | |||||
0 | 0 | |||||||||
505142. | 0.694249 | 0.347124 | − | 0.937819i | ||||||
0.347124 | + | 0.937819i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
560018. | + | 969980.i | 0.762501 | + | 1.32069i | 0.941557 | + | 0.336852i | ||
−0.179056 | + | 0.983839i | ||||||||
0 | 0 | |||||||||
605141. | + | 349379.i | 0.820107 | + | 0.473489i | 0.850453 | − | 0.526050i | ||
−0.0303463 | + | 0.999539i | ||||||||
0 | 0 | |||||||||
165043. | + | 94941.9i | 0.222633 | + | 0.128071i | |||||
0 | 0 | |||||||||
−830576. | − | 479533.i | −1.11521 | − | 0.643868i | −0.175038 | − | 0.984562i | ||
−0.940175 | + | 0.340693i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−22933.1 | −0.0305088 | |||||||||
0 | 0 | |||||||||
−183263. | −0.242681 | |||||||||
0 | 0 | |||||||||
892127. | − | 515069.i | 1.17595 | − | 0.678937i | |||||
0 | 0 | |||||||||
391976. | − | 678923.i | 0.514318 | − | 0.890824i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−863326. | − | 498442.i | −1.12247 | − | 0.648060i | −0.180442 | − | 0.983586i | ||
−0.942031 | + | 0.335526i | ||||||||
0 | 0 | |||||||||
102372. | + | 177314.i | 0.132497 | + | 0.229491i | |||||
0 | 0 | |||||||||
− | 494568.i | − | 0.637198i | −0.947890 | − | 0.318599i | ||||
0.947890 | − | 0.318599i | ||||||||
0 | 0 | |||||||||
887278.i | 1.13799i | 0.822341 | + | 0.568995i | ||||||
−0.822341 | + | 0.568995i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
312960. | − | 542062.i | 0.397779 | − | 0.688973i | −0.595673 | − | 0.803227i | ||
0.993452 | + | 0.114254i | ||||||||
0 | 0 | |||||||||
−545008. | + | 315804.i | −0.689604 | + | 0.399589i | |||||
0 | 0 | |||||||||
−70165.8 | + | 121531.i | −0.0883833 | + | 0.153084i | |||||
0 | 0 | |||||||||
−258890. | + | 149470.i | −0.324647 | + | 0.187435i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
− | 160203.i | − | 0.199106i | |||||||
0 | 0 | |||||||||
237491. | − | 137115.i | 0.293851 | − | 0.169655i | |||||
0 | 0 | |||||||||
−461309. | − | 266337.i | −0.568253 | − | 0.328081i | |||||
0 | 0 | |||||||||
175739. | + | 101095.i | 0.215523 | + | 0.123981i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.09835e6 | − | 634131.i | 1.33513 | − | 0.770840i | 0.349052 | − | 0.937103i | ||
0.986081 | + | 0.166263i | ||||||||
0 | 0 | |||||||||
61263.9i | 0.0741442i | |||||||||
0 | 0 | |||||||||
−1.09985e6 | −1.32525 | −0.662625 | − | 0.748951i | ||||||
−0.662625 | + | 0.748951i | ||||||||
0 | 0 | |||||||||
−25644.0 | − | 44416.7i | −0.0307641 | − | 0.0532850i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1904.30 | + | 1.21152e6i | 0.00226463 | + | 1.44076i | |||||
0 | 0 | |||||||||
430660. | − | 745925.i | 0.509922 | − | 0.883211i | −0.490012 | − | 0.871716i | ||
0.999934 | − | 0.0114950i | ||||||||
0 | 0 | |||||||||
44075.3 | + | 76340.6i | 0.0519608 | + | 0.0899987i | |||||
0 | 0 | |||||||||
1.03229e6 | 1.21171 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
108095. | + | 187226.i | 0.125790 | + | 0.217874i | |||||
0 | 0 | |||||||||
326247. | + | 188359.i | 0.378021 | + | 0.218250i | 0.676957 | − | 0.736023i | ||
−0.298936 | + | 0.954273i | ||||||||
0 | 0 | |||||||||
−927884. | + | 539610.i | −1.07052 | + | 0.622560i | |||||
0 | 0 | |||||||||
−62906.7 | − | 36319.2i | −0.0722659 | − | 0.0417227i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
417813. | 0.475885 | 0.237943 | − | 0.971279i | ||||||
0.237943 | + | 0.971279i | ||||||||
0 | 0 | |||||||||
−217103. | −0.246227 | |||||||||
0 | 0 | |||||||||
213031. | − | 122994.i | 0.240582 | − | 0.138900i | −0.374862 | − | 0.927081i | ||
0.615444 | + | 0.788180i | ||||||||
0 | 0 | |||||||||
927546. | − | 1.60656e6i | 1.04307 | − | 1.80665i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.25221e6 | − | 722964.i | −1.39630 | − | 0.806152i | −0.402294 | − | 0.915511i | ||
−0.994002 | + | 0.109359i | ||||||||
0 | 0 | |||||||||
258384. | + | 447533.i | 0.286901 | + | 0.496928i | |||||
0 | 0 | |||||||||
91495.4i | 0.101167i | |||||||||
0 | 0 | |||||||||
907377.i | 0.999084i | 0.866290 | + | 0.499542i | ||||||
−0.866290 | + | 0.499542i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
7499.38 | − | 12989.3i | 0.00818845 | − | 0.0141828i | |||||
0 | 0 | |||||||||
56156.9 | + | 32304.6i | 0.0610612 | + | 0.0351259i | |||||
0 | 0 | |||||||||
−234235. | + | 405707.i | −0.253633 | + | 0.439305i | |||||
0 | 0 | |||||||||
1.01064e6 | − | 583491.i | 1.08979 | − | 0.629189i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
50286.2i | 0.0537770i | 0.999638 | + | 0.0268885i | ||||||
−0.999638 | + | 0.0268885i | ||||||||
0 | 0 | |||||||||
159483. | − | 92077.6i | 0.169851 | − | 0.0980633i | |||||
0 | 0 | |||||||||
677500. | + | 391155.i | 0.718573 | + | 0.414868i | 0.814227 | − | 0.580546i | ||
−0.0956544 | + | 0.995415i | ||||||||
0 | 0 | |||||||||
217062. | − | 125776.i | 0.229275 | − | 0.132853i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.10629e6 | + | 638714.i | −1.15899 | + | 0.669141i | −0.951061 | − | 0.309004i | ||
−0.207925 | + | 0.978145i | ||||||||
0 | 0 | |||||||||
218557.i | 0.228033i | |||||||||
0 | 0 | |||||||||
216501. | 0.224968 | |||||||||
0 | 0 | |||||||||
786638. | + | 1.36250e6i | 0.814081 | + | 1.41003i | 0.909986 | + | 0.414639i | ||
−0.0959049 | + | 0.995391i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−25778.6 | − | 44488.2i | −0.0264621 | − | 0.0456679i | |||||
0 | 0 | |||||||||
987661. | − | 1.71068e6i | 1.00975 | − | 1.74894i | |||||
0 | 0 | |||||||||
−162173. | − | 280892.i | −0.165132 | − | 0.286017i | 0.771570 | − | 0.636144i | ||
−0.936702 | + | 0.350127i | ||||||||
0 | 0 | |||||||||
1552.30 | 0.00157427 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
907185. | + | 1.57129e6i | 0.912652 | + | 1.58076i | 0.810303 | + | 0.586012i | ||
0.102350 | + | 0.994748i | ||||||||
0 | 0 | |||||||||
−161597. | − | 93298.2i | −0.161921 | − | 0.0934851i |
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 700.5.o.a.649.3 | 12 | ||
5.2 | odd | 4 | 28.5.h.a.5.2 | ✓ | 6 | ||
5.3 | odd | 4 | 700.5.s.a.201.2 | 6 | |||
5.4 | even | 2 | inner | 700.5.o.a.649.4 | 12 | ||
7.3 | odd | 6 | inner | 700.5.o.a.549.4 | 12 | ||
15.2 | even | 4 | 252.5.z.f.145.1 | 6 | |||
20.7 | even | 4 | 112.5.s.c.33.2 | 6 | |||
35.2 | odd | 12 | 196.5.b.a.97.3 | 6 | |||
35.3 | even | 12 | 700.5.s.a.101.2 | 6 | |||
35.12 | even | 12 | 196.5.b.a.97.4 | 6 | |||
35.17 | even | 12 | 28.5.h.a.17.2 | yes | 6 | ||
35.24 | odd | 6 | inner | 700.5.o.a.549.3 | 12 | ||
35.27 | even | 4 | 196.5.h.c.117.2 | 6 | |||
35.32 | odd | 12 | 196.5.h.c.129.2 | 6 | |||
105.17 | odd | 12 | 252.5.z.f.73.1 | 6 | |||
140.47 | odd | 12 | 784.5.c.e.97.3 | 6 | |||
140.87 | odd | 12 | 112.5.s.c.17.2 | 6 | |||
140.107 | even | 12 | 784.5.c.e.97.4 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
28.5.h.a.5.2 | ✓ | 6 | 5.2 | odd | 4 | ||
28.5.h.a.17.2 | yes | 6 | 35.17 | even | 12 | ||
112.5.s.c.17.2 | 6 | 140.87 | odd | 12 | |||
112.5.s.c.33.2 | 6 | 20.7 | even | 4 | |||
196.5.b.a.97.3 | 6 | 35.2 | odd | 12 | |||
196.5.b.a.97.4 | 6 | 35.12 | even | 12 | |||
196.5.h.c.117.2 | 6 | 35.27 | even | 4 | |||
196.5.h.c.129.2 | 6 | 35.32 | odd | 12 | |||
252.5.z.f.73.1 | 6 | 105.17 | odd | 12 | |||
252.5.z.f.145.1 | 6 | 15.2 | even | 4 | |||
700.5.o.a.549.3 | 12 | 35.24 | odd | 6 | inner | ||
700.5.o.a.549.4 | 12 | 7.3 | odd | 6 | inner | ||
700.5.o.a.649.3 | 12 | 1.1 | even | 1 | trivial | ||
700.5.o.a.649.4 | 12 | 5.4 | even | 2 | inner | ||
700.5.s.a.101.2 | 6 | 35.3 | even | 12 | |||
700.5.s.a.201.2 | 6 | 5.3 | odd | 4 | |||
784.5.c.e.97.3 | 6 | 140.47 | odd | 12 | |||
784.5.c.e.97.4 | 6 | 140.107 | even | 12 |