Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [495,3,Mod(298,495)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(495, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("495.298");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 495.j (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 |
Coefficient field: | |
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 55) |
Sato-Tate group: |
Embedding invariants
Embedding label | 298.1 | ||
Root | of defining polynomial | ||
Character | 495.298 | ||
Dual form | 495.3.j.a.397.1 |
-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of on generators for .
Coefficient data
For each we display the coefficients of the -expansion , the Satake parameters , and the Satake angles .
−2.27868 | + | 2.27868i | −1.13934 | + | 1.13934i | −0.150770 | + | 0.988569i | ||
−0.988569 | + | 0.150770i | ||||||||
0 | 0 | |||||||||
− | 6.38475i | − | 1.59619i | |||||||
−2.55248 | − | 4.29940i | −0.510496 | − | 0.859880i | |||||
0 | 0 | |||||||||
−3.30878 | + | 3.30878i | −0.472684 | + | 0.472684i | −0.902782 | − | 0.430098i | ||
0.430098 | + | 0.902782i | ||||||||
5.43407 | + | 5.43407i | 0.679259 | + | 0.679259i | |||||
0 | 0 | |||||||||
15.6132 | + | 3.98068i | 1.56132 | + | 0.398068i | |||||
−3.31662 | −0.301511 | |||||||||
0 | 0 | |||||||||
7.65935 | + | 7.65935i | 0.589180 | + | 0.589180i | 0.937409 | − | 0.348229i | ||
−0.348229 | + | 0.937409i | ||||||||
− | 15.0793i | − | 1.07709i | |||||||
0 | 0 | |||||||||
0.773991 | 0.0483744 | |||||||||
19.8139 | − | 19.8139i | 1.16552 | − | 1.16552i | 0.182274 | − | 0.983248i | ||
0.983248 | − | 0.182274i | ||||||||
0 | 0 | |||||||||
− | 17.4895i | − | 0.920499i | −0.887789 | − | 0.460250i | ||||
0.887789 | − | 0.460250i | ||||||||
−27.4506 | + | 16.2969i | −1.37253 | + | 0.814846i | |||||
0 | 0 | |||||||||
7.55752 | − | 7.55752i | 0.343524 | − | 0.343524i | |||||
11.7334 | + | 11.7334i | 0.510149 | + | 0.510149i | 0.914572 | − | 0.404423i | ||
−0.404423 | + | 0.914572i | ||||||||
0 | 0 | |||||||||
−11.9697 | + | 21.9483i | −0.478789 | + | 0.877930i | |||||
−34.9064 | −1.34255 | |||||||||
0 | 0 | |||||||||
21.1258 | + | 21.1258i | 0.754491 | + | 0.754491i | |||||
14.2026i | 0.489745i | 0.969555 | + | 0.244873i | ||||||
−0.969555 | + | 0.244873i | ||||||||
0 | 0 | |||||||||
−44.6924 | −1.44169 | −0.720846 | − | 0.693096i | ||||||
−0.720846 | + | 0.693096i | ||||||||
−23.5000 | + | 23.5000i | −0.734374 | + | 0.734374i | |||||
0 | 0 | |||||||||
90.2989i | 2.65585i | |||||||||
22.6714 | + | 5.78020i | 0.647754 | + | 0.165148i | |||||
0 | 0 | |||||||||
−2.84977 | + | 2.84977i | −0.0770207 | + | 0.0770207i | −0.744568 | − | 0.667547i | ||
0.667547 | + | 0.744568i | ||||||||
39.8529 | + | 39.8529i | 1.04876 | + | 1.04876i | |||||
0 | 0 | |||||||||
9.49291 | − | 37.2336i | 0.237323 | − | 0.930840i | |||||
−61.2271 | −1.49334 | −0.746672 | − | 0.665192i | ||||||
−0.746672 | + | 0.665192i | ||||||||
0 | 0 | |||||||||
−10.2480 | − | 10.2480i | −0.238325 | − | 0.238325i | 0.577832 | − | 0.816156i | ||
−0.816156 | + | 0.577832i | ||||||||
21.1758i | 0.481268i | |||||||||
0 | 0 | |||||||||
−53.4734 | −1.16247 | |||||||||
−58.6916 | + | 58.6916i | −1.24876 | + | 1.24876i | −0.292489 | + | 0.956269i | ||
−0.956269 | + | 0.292489i | ||||||||
0 | 0 | |||||||||
27.1039i | 0.553141i | |||||||||
−22.7379 | − | 77.2881i | −0.454758 | − | 1.54576i | |||||
0 | 0 | |||||||||
48.9030 | − | 48.9030i | 0.940442 | − | 0.940442i | |||||
45.5877 | + | 45.5877i | 0.860145 | + | 0.860145i | 0.991355 | − | 0.131210i | ||
−0.131210 | + | 0.991355i | ||||||||
0 | 0 | |||||||||
8.46561 | + | 14.2595i | 0.153920 | + | 0.259264i | |||||
−35.9603 | −0.642149 | |||||||||
0 | 0 | |||||||||
−32.3632 | − | 32.3632i | −0.557986 | − | 0.557986i | |||||
3.71455i | 0.0629584i | 0.999504 | + | 0.0314792i | ||||||
−0.999504 | + | 0.0314792i | ||||||||
0 | 0 | |||||||||
−15.3228 | −0.251193 | −0.125596 | − | 0.992081i | ||||||
−0.125596 | + | 0.992081i | ||||||||
101.840 | − | 101.840i | 1.64258 | − | 1.64258i | |||||
0 | 0 | |||||||||
− | 104.002i | − | 1.62503i | |||||||
13.3803 | − | 52.4809i | 0.205851 | − | 0.807399i | |||||
0 | 0 | |||||||||
−23.6682 | + | 23.6682i | −0.353257 | + | 0.353257i | −0.861320 | − | 0.508063i | ||
0.508063 | + | 0.861320i | ||||||||
−126.507 | − | 126.507i | −1.86039 | − | 1.86039i | |||||
0 | 0 | |||||||||
−64.8320 | + | 38.4896i | −0.926172 | + | 0.549851i | |||||
−66.4871 | −0.936438 | −0.468219 | − | 0.883613i | ||||||
−0.468219 | + | 0.883613i | ||||||||
0 | 0 | |||||||||
93.3093 | + | 93.3093i | 1.27821 | + | 1.27821i | 0.941669 | + | 0.336541i | ||
0.336541 | + | 0.941669i | ||||||||
− | 12.9874i | − | 0.175505i | |||||||
0 | 0 | |||||||||
−111.666 | −1.46929 | |||||||||
10.9740 | − | 10.9740i | 0.142519 | − | 0.142519i | |||||
0 | 0 | |||||||||
− | 57.1583i | − | 0.723523i | −0.932271 | − | 0.361762i | ||||
0.932271 | − | 0.361762i | ||||||||
−1.97559 | − | 3.32770i | −0.0246949 | − | 0.0415962i | |||||
0 | 0 | |||||||||
139.517 | − | 139.517i | 1.70143 | − | 1.70143i | |||||
−45.3490 | − | 45.3490i | −0.546373 | − | 0.546373i | 0.379017 | − | 0.925390i | ||
−0.925390 | + | 0.379017i | ||||||||
0 | 0 | |||||||||
−135.762 | − | 34.6133i | −1.59720 | − | 0.407216i | |||||
46.7036 | 0.543065 | |||||||||
0 | 0 | |||||||||
−18.0228 | − | 18.0228i | −0.204804 | − | 0.204804i | |||||
114.906i | 1.29107i | 0.763729 | + | 0.645537i | ||||||
−0.763729 | + | 0.645537i | ||||||||
0 | 0 | |||||||||
−50.6863 | −0.556992 | |||||||||
74.9150 | − | 74.9150i | 0.814294 | − | 0.814294i | |||||
0 | 0 | |||||||||
− | 267.479i | − | 2.84552i | |||||||
−75.1944 | + | 44.6415i | −0.791519 | + | 0.469911i | |||||
0 | 0 | |||||||||
−31.9248 | + | 31.9248i | −0.329121 | + | 0.329121i | −0.852252 | − | 0.523131i | ||
0.523131 | + | 0.852252i | ||||||||
−61.7610 | − | 61.7610i | −0.630215 | − | 0.630215i | |||||
0 | 0 | |||||||||
140.134 | + | 76.4236i | 1.40134 | + | 0.764236i | |||||
−109.388 | −1.08305 | −0.541523 | − | 0.840686i | ||||||
−0.541523 | + | 0.840686i | ||||||||
0 | 0 | |||||||||
−28.7421 | − | 28.7421i | −0.279050 | − | 0.279050i | 0.553680 | − | 0.832730i | ||
−0.832730 | + | 0.553680i | ||||||||
83.2429i | 0.800412i | |||||||||
0 | 0 | |||||||||
−207.759 | −1.95999 | |||||||||
53.4385 | − | 53.4385i | 0.499425 | − | 0.499425i | −0.411834 | − | 0.911259i | ||
0.911259 | + | 0.411834i | ||||||||
0 | 0 | |||||||||
97.4174i | 0.893738i | 0.894600 | + | 0.446869i | ||||||
−0.894600 | + | 0.446869i | ||||||||
−51.7832 | − | 13.2024i | −0.470757 | − | 0.120022i | |||||
0 | 0 | |||||||||
−2.56097 | + | 2.56097i | −0.0228658 | + | 0.0228658i | |||||
109.416 | + | 109.416i | 0.968280 | + | 0.968280i | 0.999512 | − | 0.0312321i | ||
−0.0312321 | + | 0.999512i | ||||||||
0 | 0 | |||||||||
20.4974 | − | 80.3961i | 0.178238 | − | 0.699096i | |||||
90.6801 | 0.781725 | |||||||||
0 | 0 | |||||||||
−8.46425 | − | 8.46425i | −0.0717310 | − | 0.0717310i | |||||
131.120i | 1.10185i | |||||||||
0 | 0 | |||||||||
11.0000 | 0.0909091 | |||||||||
34.9156 | − | 34.9156i | 0.286194 | − | 0.286194i | |||||
0 | 0 | |||||||||
285.350i | 2.30121i | |||||||||
124.917 | − | 4.55981i | 0.999334 | − | 0.0364785i | |||||
0 | 0 | |||||||||
−3.94652 | + | 3.94652i | −0.0310749 | + | 0.0310749i | −0.722474 | − | 0.691399i | ||
0.691399 | + | 0.722474i | ||||||||
142.987 | + | 142.987i | 1.11708 | + | 1.11708i | |||||
0 | 0 | |||||||||
89.0977 | + | 150.077i | 0.685367 | + | 1.15443i | |||||
165.435 | 1.26286 | 0.631430 | − | 0.775433i | ||||||
0.631430 | + | 0.775433i | ||||||||
0 | 0 | |||||||||
57.8690 | + | 57.8690i | 0.435105 | + | 0.435105i | |||||
− | 107.864i | − | 0.804958i | |||||||
0 | 0 | |||||||||
215.340 | 1.58338 | |||||||||
−47.3215 | + | 47.3215i | −0.345412 | + | 0.345412i | −0.858397 | − | 0.512985i | ||
0.512985 | + | 0.858397i | ||||||||
0 | 0 | |||||||||
157.241i | 1.13123i | 0.824670 | + | 0.565614i | ||||||
−0.824670 | + | 0.565614i | ||||||||
36.9051 | − | 144.751i | 0.263608 | − | 1.03394i | |||||
0 | 0 | |||||||||
151.503 | − | 151.503i | 1.06692 | − | 1.06692i | |||||
−25.4032 | − | 25.4032i | −0.177645 | − | 0.177645i | |||||
0 | 0 | |||||||||
61.0627 | − | 36.2518i | 0.421122 | − | 0.250013i | |||||
−425.244 | −2.91263 | |||||||||
0 | 0 | |||||||||
18.1950 | + | 18.1950i | 0.122939 | + | 0.122939i | |||||
91.9814i | 0.617325i | 0.951172 | + | 0.308663i | ||||||
−0.951172 | + | 0.308663i | ||||||||
0 | 0 | |||||||||
178.745 | 1.18374 | 0.591870 | − | 0.806034i | ||||||
0.591870 | + | 0.806034i | ||||||||
95.0391 | − | 95.0391i | 0.625257 | − | 0.625257i | |||||
0 | 0 | |||||||||
50.0124i | 0.324756i | |||||||||
114.076 | + | 192.151i | 0.735977 | + | 1.23968i | |||||
0 | 0 | |||||||||
−85.3500 | + | 85.3500i | −0.543631 | + | 0.543631i | −0.924591 | − | 0.380961i | ||
0.380961 | + | 0.924591i | ||||||||
130.245 | + | 130.245i | 0.824338 | + | 0.824338i | |||||
0 | 0 | |||||||||
161.019 | + | 41.0527i | 1.00637 | + | 0.256579i | |||||
−77.6468 | −0.482278 | |||||||||
0 | 0 | |||||||||
34.8150 | + | 34.8150i | 0.213589 | + | 0.213589i | 0.805790 | − | 0.592201i | ||
−0.592201 | + | 0.805790i | ||||||||
390.920i | 2.38366i | |||||||||
0 | 0 | |||||||||
206.671 | 1.24501 | |||||||||
8.73842 | − | 8.73842i | 0.0523259 | − | 0.0523259i | −0.680460 | − | 0.732786i | ||
0.732786 | + | 0.680460i | ||||||||
0 | 0 | |||||||||
− | 51.6688i | − | 0.305733i | |||||||
388.231 | − | 230.486i | 2.28371 | − | 1.35580i | |||||
0 | 0 | |||||||||
−65.4306 | + | 65.4306i | −0.380411 | + | 0.380411i | |||||
−40.7527 | − | 40.7527i | −0.235565 | − | 0.235565i | 0.579446 | − | 0.815011i | ||
−0.815011 | + | 0.579446i | ||||||||
0 | 0 | |||||||||
−33.0168 | − | 112.227i | −0.188668 | − | 0.641299i | |||||
−2.56704 | −0.0145854 | |||||||||
0 | 0 | |||||||||
−261.833 | − | 261.833i | −1.47097 | − | 1.47097i | |||||
− | 299.550i | − | 1.67346i | −0.547613 | − | 0.836732i | ||||
0.547613 | − | 0.836732i | ||||||||
0 | 0 | |||||||||
−204.042 | −1.12730 | −0.563651 | − | 0.826013i | ||||||
−0.563651 | + | 0.826013i | ||||||||
115.498 | − | 115.498i | 0.634602 | − | 0.634602i | |||||
0 | 0 | |||||||||
127.521i | 0.693047i | |||||||||
19.5263 | + | 4.97833i | 0.105547 | + | 0.0269099i | |||||
0 | 0 | |||||||||
−65.7152 | + | 65.7152i | −0.351418 | + | 0.351418i | |||||
374.731 | + | 374.731i | 1.99325 | + | 1.99325i | |||||
0 | 0 | |||||||||
69.6200 | − | 273.067i | 0.366421 | − | 1.43720i | |||||
−68.1555 | −0.356835 | −0.178418 | − | 0.983955i | ||||||
−0.178418 | + | 0.983955i | ||||||||
0 | 0 | |||||||||
56.3440 | + | 56.3440i | 0.291938 | + | 0.291938i | 0.837845 | − | 0.545908i | ||
−0.545908 | + | 0.837845i | ||||||||
− | 145.493i | − | 0.749962i | |||||||
0 | 0 | |||||||||
173.051 | 0.882916 | |||||||||
−61.2935 | + | 61.2935i | −0.311134 | + | 0.311134i | −0.845349 | − | 0.534215i | ||
0.534215 | + | 0.845349i | ||||||||
0 | 0 | |||||||||
291.772i | 1.46619i | 0.680125 | + | 0.733096i | ||||||
−0.680125 | + | 0.733096i | ||||||||
−184.313 | + | 54.2241i | −0.921563 | + | 0.271120i | |||||
0 | 0 | |||||||||
249.259 | − | 249.259i | 1.23396 | − | 1.23396i | |||||
−46.9934 | − | 46.9934i | −0.231494 | − | 0.231494i | |||||
0 | 0 | |||||||||
156.281 | + | 263.240i | 0.762346 | + | 1.28410i | |||||
130.988 | 0.635864 | |||||||||
0 | 0 | |||||||||
5.92826 | + | 5.92826i | 0.0285013 | + | 0.0285013i | |||||
58.0061i | 0.277541i | |||||||||
0 | 0 | |||||||||
−93.8771 | −0.444915 | −0.222458 | − | 0.974942i | ||||||
−0.222458 | + | 0.974942i | ||||||||
291.066 | − | 291.066i | 1.37295 | − | 1.37295i | |||||
0 | 0 | |||||||||
243.538i | 1.13803i | |||||||||
−17.9024 | + | 70.2178i | −0.0832670 | + | 0.326594i | |||||
0 | 0 | |||||||||
147.878 | − | 147.878i | 0.681464 | − | 0.681464i | |||||
−221.983 | − | 221.983i | −1.01827 | − | 1.01827i | |||||
0 | 0 | |||||||||
91.0433 | − | 54.0508i | 0.413833 | − | 0.245685i | |||||
303.523 | 1.37341 | |||||||||
0 | 0 | |||||||||
−158.088 | − | 158.088i | −0.708915 | − | 0.708915i | 0.257392 | − | 0.966307i | ||
−0.966307 | + | 0.257392i | ||||||||
− | 155.513i | − | 0.694253i | |||||||
0 | 0 | |||||||||
−498.646 | −2.20640 | |||||||||
−158.917 | + | 158.917i | −0.700076 | + | 0.700076i | −0.964427 | − | 0.264351i | ||
0.264351 | + | 0.964427i | ||||||||
0 | 0 | |||||||||
43.6426i | 0.190579i | 0.995450 | + | 0.0952895i | ||||||
−0.995450 | + | 0.0952895i | ||||||||
136.490 | + | 229.904i | 0.593434 | + | 0.999582i | |||||
0 | 0 | |||||||||
−77.1780 | + | 77.1780i | −0.332664 | + | 0.332664i | |||||
−231.736 | − | 231.736i | −0.994574 | − | 0.994574i | 0.00541090 | − | 0.999985i | ||
−0.999985 | + | 0.00541090i | ||||||||
0 | 0 | |||||||||
402.148 | + | 102.530i | 1.71127 | + | 0.436297i | |||||
23.7164 | 0.100493 | |||||||||
0 | 0 | |||||||||
−298.780 | − | 298.780i | −1.25538 | − | 1.25538i | |||||
− | 203.850i | − | 0.852930i | −0.904504 | − | 0.426465i | ||||
0.904504 | − | 0.426465i | ||||||||
0 | 0 | |||||||||
96.8670 | 0.401938 | 0.200969 | − | 0.979598i | ||||||
0.200969 | + | 0.979598i | ||||||||
−25.0655 | + | 25.0655i | −0.103576 | + | 0.103576i | |||||
0 | 0 | |||||||||
97.8320i | 0.400951i | |||||||||
116.531 | − | 69.1821i | 0.475635 | − | 0.282376i | |||||
0 | 0 | |||||||||
133.958 | − | 133.958i | 0.542340 | − | 0.542340i | |||||
−242.862 | − | 242.862i | −0.979282 | − | 0.979282i | |||||
0 | 0 | |||||||||
−274.255 | + | 295.036i | −1.09702 | + | 1.18014i | |||||
165.654 | 0.659978 | 0.329989 | − | 0.943985i | ||||||
0.329989 | + | 0.943985i | ||||||||
0 | 0 | |||||||||
−38.9154 | − | 38.9154i | −0.153816 | − | 0.153816i | |||||
− | 17.9857i | − | 0.0708098i | |||||||
0 | 0 | |||||||||
−235.634 | −0.920445 | |||||||||
−168.525 | + | 168.525i | −0.655740 | + | 0.655740i | −0.954369 | − | 0.298629i | ||
0.298629 | + | 0.954369i | ||||||||
0 | 0 | |||||||||
− | 18.8585i | − | 0.0728128i | |||||||
−335.077 | − | 85.4298i | −1.28876 | − | 0.328576i | |||||
0 | 0 | |||||||||
−376.972 | + | 376.972i | −1.43883 | + | 1.43883i | |||||
50.7899 | + | 50.7899i | 0.193117 | + | 0.193117i | 0.797042 | − | 0.603924i | ||
−0.603924 | + | 0.797042i | ||||||||
0 | 0 | |||||||||
79.6382 | − | 312.361i | 0.300522 | − | 1.17872i | |||||
−263.729 | −0.991464 | |||||||||
0 | 0 | |||||||||
151.115 | + | 151.115i | 0.563864 | + | 0.563864i | |||||
256.648i | 0.954081i | 0.878881 | + | 0.477041i | ||||||
−0.878881 | + | 0.477041i | ||||||||
0 | 0 | |||||||||
−215.163 | −0.793958 | −0.396979 | − | 0.917828i | ||||||
−0.396979 | + | 0.917828i | ||||||||
15.3358 | − | 15.3358i | 0.0563815 | − | 0.0563815i | |||||
0 | 0 | |||||||||
− | 215.661i | − | 0.787083i | |||||||
39.6991 | − | 72.7941i | 0.144360 | − | 0.264706i | |||||
0 | 0 | |||||||||
73.9418 | − | 73.9418i | 0.266938 | − | 0.266938i | −0.560927 | − | 0.827865i | ||
0.827865 | + | 0.560927i | ||||||||
−358.301 | − | 358.301i | −1.28885 | − | 1.28885i | |||||
0 | 0 | |||||||||
91.7880 | + | 154.608i | 0.327814 | + | 0.552171i | |||||
−190.836 | −0.679133 | −0.339566 | − | 0.940582i | ||||||
−0.339566 | + | 0.940582i | ||||||||
0 | 0 | |||||||||
−87.1090 | − | 87.1090i | −0.307806 | − | 0.307806i | 0.536252 | − | 0.844058i | ||
−0.844058 | + | 0.536252i | ||||||||
424.503i | 1.49473i | |||||||||
0 | 0 | |||||||||
115.771 | 0.404795 | |||||||||
202.587 | − | 202.587i | 0.705879 | − | 0.705879i | |||||
0 | 0 | |||||||||
− | 496.179i | − | 1.71688i | |||||||
−56.5360 | + | 221.749i | −0.194952 | + | 0.764650i | |||||
0 | 0 | |||||||||
595.756 | − | 595.756i | 2.04026 | − | 2.04026i | |||||
317.484 | + | 317.484i | 1.08356 | + | 1.08356i | 0.996174 | + | 0.0873871i | ||
0.0873871 | + | 0.996174i | ||||||||
0 | 0 | |||||||||
15.9703 | − | 9.48129i | 0.0541367 | − | 0.0321400i | |||||
−30.9717 | −0.104634 | |||||||||
0 | 0 | |||||||||
−209.596 | − | 209.596i | −0.703343 | − | 0.703343i | |||||
179.741i | 0.601140i | |||||||||
0 | 0 | |||||||||
67.8166 | 0.225304 | |||||||||
−407.302 | + | 407.302i | −1.34868 | + | 1.34868i | |||||
0 | 0 | |||||||||
− | 13.5367i | − | 0.0445286i | |||||||
39.1110 | + | 65.8787i | 0.128233 | + | 0.215996i | |||||
0 | 0 | |||||||||
−263.140 | + | 263.140i | −0.857132 | + | 0.857132i | −0.990999 | − | 0.133867i | ||
0.133867 | + | 0.990999i | ||||||||
−70.0662 | − | 70.0662i | −0.227488 | − | 0.227488i | |||||
0 | 0 | |||||||||
−697.793 | − | 177.906i | −2.25095 | − | 0.573891i | |||||
−301.613 | −0.969816 | −0.484908 | − | 0.874565i | ||||||
−0.484908 | + | 0.874565i | ||||||||
0 | 0 | |||||||||
98.0189 | + | 98.0189i | 0.313159 | + | 0.313159i | 0.846132 | − | 0.532973i | ||
−0.532973 | + | 0.846132i | ||||||||
− | 388.971i | − | 1.23876i | |||||||
0 | 0 | |||||||||
−364.941 | −1.15488 | |||||||||
−232.617 | + | 232.617i | −0.733806 | + | 0.733806i | −0.971372 | − | 0.237565i | ||
0.237565 | + | 0.971372i | ||||||||
0 | 0 | |||||||||
− | 47.1047i | − | 0.147664i | |||||||
−447.145 | + | 265.462i | −1.39733 | + | 0.829569i | |||||
0 | 0 | |||||||||
176.932 | − | 176.932i | 0.549479 | − | 0.549479i | |||||
−346.535 | − | 346.535i | −1.07286 | − | 1.07286i | |||||
0 | 0 | |||||||||
−259.789 | + | 76.4291i | −0.799352 | + | 0.235166i | |||||
−158.664 | −0.486701 | |||||||||
0 | 0 | |||||||||
−332.713 | − | 332.713i | −1.01437 | − | 1.01437i | |||||
− | 388.396i | − | 1.18053i | |||||||
0 | 0 | |||||||||
124.210 | 0.375256 | 0.187628 | − | 0.982240i | ||||||
0.187628 | + | 0.982240i | ||||||||
−289.542 | + | 289.542i | −0.872113 | + | 0.872113i | |||||
0 | 0 | |||||||||
39.8241i | 0.119234i | |||||||||
162.172 | + | 41.3466i | 0.484095 | + | 0.123423i | |||||
0 | 0 | |||||||||
248.427 | − | 248.427i | 0.737171 | − | 0.737171i | −0.234858 | − | 0.972030i | ||
0.972030 | + | 0.234858i | ||||||||
117.737 | + | 117.737i | 0.348333 | + | 0.348333i | |||||
0 | 0 | |||||||||
−220.997 | + | 866.808i | −0.649992 | + | 2.54943i | |||||
148.228 | 0.434686 | |||||||||
0 | 0 | |||||||||
−251.811 | − | 251.811i | −0.734144 | − | 0.734144i | |||||
− | 111.376i | − | 0.323768i | |||||||
0 | 0 | |||||||||
185.724 | 0.536776 | |||||||||
−194.711 | + | 194.711i | −0.561127 | + | 0.561127i | −0.929628 | − | 0.368501i | ||
0.368501 | + | 0.929628i | ||||||||
0 | 0 | |||||||||
− | 23.5545i | − | 0.0674914i | −0.999430 | − | 0.0337457i | ||||
0.999430 | − | 0.0337457i | ||||||||
330.965 | + | 180.495i | 0.945613 | + | 0.515700i | |||||
0 | 0 | |||||||||
77.9406 | − | 77.9406i | 0.221422 | − | 0.221422i | |||||
60.4688 | + | 60.4688i | 0.171300 | + | 0.171300i | 0.787550 | − | 0.616251i | ||
−0.616251 | + | 0.787550i | ||||||||
0 | 0 | |||||||||
169.707 | + | 285.855i | 0.478047 | + | 0.805224i | |||||
733.643 | 2.06080 | |||||||||
0 | 0 | |||||||||
682.578 | + | 682.578i | 1.90664 | + | 1.90664i | |||||
− | 502.684i | − | 1.40024i | −0.714028 | − | 0.700118i | ||||
0.714028 | − | 0.700118i | ||||||||
0 | 0 | |||||||||
55.1177 | 0.152681 | |||||||||
464.945 | − | 464.945i | 1.28438 | − | 1.28438i | |||||
0 | 0 | |||||||||
323.619i | 0.889063i | |||||||||
163.004 | − | 639.344i | 0.446587 | − | 1.75163i | |||||
0 | 0 | |||||||||
−402.334 | + | 402.334i | −1.09628 | + | 1.09628i | −0.101437 | + | 0.994842i | ||
−0.994842 | + | 0.101437i | ||||||||
9.08157 | + | 9.08157i | 0.0246782 | + | 0.0246782i | |||||
0 | 0 | |||||||||
−55.8381 | + | 33.1500i | −0.150914 | + | 0.0895947i | |||||
−301.680 | −0.813153 | |||||||||
0 | 0 | |||||||||
−129.594 | − | 129.594i | −0.347437 | − | 0.347437i | 0.511717 | − | 0.859154i | ||
−0.859154 | + | 0.511717i | ||||||||
− | 299.487i | − | 0.800769i | |||||||
0 | 0 | |||||||||
−637.869 | −1.69646 | |||||||||
−108.783 | + | 108.783i | −0.288548 | + | 0.288548i | |||||
0 | 0 | |||||||||
− | 308.983i | − | 0.815260i | −0.913147 | − | 0.407630i | ||||
0.913147 | − | 0.407630i | ||||||||
285.025 | + | 480.097i | 0.750066 | + | 1.26341i | |||||
0 | 0 | |||||||||
155.305 | − | 155.305i | 0.406556 | − | 0.406556i | |||||
137.024 | + | 137.024i | 0.357765 | + | 0.357765i | 0.862989 | − | 0.505223i | ||
−0.505223 | + | 0.862989i | ||||||||
0 | 0 | |||||||||
−75.1925 | − | 19.1707i | −0.195305 | − | 0.0497941i | |||||
−256.780 | −0.665232 | |||||||||
0 | 0 | |||||||||
203.832 | + | 203.832i | 0.525339 | + | 0.525339i | |||||
219.114i | 0.563275i | 0.959521 | + | 0.281637i | ||||||
−0.959521 | + | 0.281637i | ||||||||
0 | 0 | |||||||||
464.970 | 1.18918 | |||||||||
−147.284 | + | 147.284i | −0.375726 | + | 0.375726i | |||||
0 | 0 | |||||||||
− | 279.336i | − | 0.708975i | |||||||
−245.747 | + | 145.895i | −0.622143 | + | 0.369355i | |||||
0 | 0 | |||||||||
447.147 | − | 447.147i | 1.12631 | − | 1.12631i | 0.135542 | − | 0.990772i | ||
0.990772 | − | 0.135542i | ||||||||
−664.855 | − | 664.855i | −1.67049 | − | 1.67049i | |||||
0 | 0 | |||||||||
−9.26445 | + | 16.9878i | −0.0231611 | + | 0.0424694i | |||||
697.196 | 1.73864 | 0.869321 | − | 0.494247i | ||||||
0.869321 | + | 0.494247i | ||||||||
0 | 0 | |||||||||
−342.315 | − | 342.315i | −0.849416 | − | 0.849416i | |||||
698.412i | 1.72874i | |||||||||
0 | 0 | |||||||||
214.166 | 0.527501 | |||||||||
9.45161 | − | 9.45161i | 0.0232226 | − | 0.0232226i | |||||
0 | 0 | |||||||||
37.7115i | 0.0922043i | 0.998937 | + | 0.0461021i | ||||||
−0.998937 | + | 0.0461021i | ||||||||
−955.953 | − | 243.725i | −2.33159 | − | 0.594452i | |||||
0 | 0 | |||||||||
−183.511 | + | 183.511i | −0.445415 | + | 0.445415i | |||||
−12.2906 | − | 12.2906i | −0.0297594 | − | 0.0297594i | |||||
0 | 0 | |||||||||
−79.2212 | + | 310.726i | −0.190894 | + | 0.748736i | |||||
−359.989 | −0.865357 | |||||||||
0 | 0 | |||||||||
−132.177 | − | 132.177i | −0.316213 | − | 0.316213i | |||||
− | 486.001i | − | 1.15991i | −0.814650 | − | 0.579953i | ||||
0.814650 | − | 0.579953i | ||||||||
0 | 0 | |||||||||
−388.904 | −0.923762 | −0.461881 | − | 0.886942i | ||||||
−0.461881 | + | 0.886942i | ||||||||
213.916 | − | 213.916i | 0.506909 | − | 0.506909i | |||||
0 | 0 | |||||||||
495.453i | 1.16852i | |||||||||
197.714 | + | 672.046i | 0.465208 | + | 1.58129i | |||||
0 | 0 | |||||||||
50.6997 | − | 50.6997i | 0.118735 | − | 0.118735i | |||||
−341.191 | − | 341.191i | −0.797175 | − | 0.797175i | |||||
0 | 0 | |||||||||
−119.210 | − | 200.797i | −0.277232 | − | 0.466971i | |||||
−504.929 | −1.17153 | −0.585764 | − | 0.810482i | ||||||
−0.585764 | + | 0.810482i | ||||||||
0 | 0 | |||||||||
150.370 | + | 150.370i | 0.347274 | + | 0.347274i | 0.859093 | − | 0.511819i | ||
−0.511819 | + | 0.859093i | ||||||||
673.931i | 1.55284i | |||||||||
0 | 0 | |||||||||
621.985 | 1.42657 | |||||||||
205.212 | − | 205.212i | 0.469592 | − | 0.469592i | |||||
0 | 0 | |||||||||
210.919i | 0.480454i | 0.970717 | + | 0.240227i | ||||||
−0.970717 | + | 0.240227i | ||||||||
−31.4844 | + | 123.490i | −0.0715555 | + | 0.280659i | |||||
0 | 0 | |||||||||
−691.630 | + | 691.630i | −1.56477 | + | 1.56477i | |||||
442.849 | + | 442.849i | 0.999660 | + | 0.999660i | 1.00000 | 0.000339697i | |||
−0.000339697 | 1.00000i | |||||||||
0 | 0 | |||||||||
494.026 | − | 293.294i | 1.11017 | − | 0.659088i | |||||
720.463 | 1.61539 | |||||||||
0 | 0 | |||||||||
344.119 | + | 344.119i | 0.768123 | + | 0.768123i | |||||
− | 641.685i | − | 1.42914i | −0.699563 | − | 0.714571i | ||||
0.699563 | − | 0.714571i | ||||||||
0 | 0 | |||||||||
203.067 | 0.450260 | |||||||||
698.591 | − | 698.591i | 1.54556 | − | 1.54556i | |||||
0 | 0 | |||||||||
− | 724.243i | − | 1.59525i | |||||||
129.376 | + | 217.921i | 0.284342 | + | 0.478946i | |||||
0 | 0 | |||||||||
−103.709 | + | 103.709i | −0.226934 | + | 0.226934i | −0.811411 | − | 0.584477i | ||
0.584477 | + | 0.811411i | ||||||||
−99.4474 | − | 99.4474i | −0.217134 | − | 0.217134i | |||||
0 | 0 | |||||||||
−513.309 | − | 130.871i | −1.11589 | − | 0.284502i | |||||
800.040 | 1.73544 | 0.867722 | − | 0.497050i | ||||||
0.867722 | + | 0.497050i | ||||||||
0 | 0 | |||||||||
252.447 | + | 252.447i | 0.545242 | + | 0.545242i | 0.925061 | − | 0.379819i | ||
−0.379819 | + | 0.925061i | ||||||||
10.9927i | 0.0236911i | |||||||||
0 | 0 | |||||||||
1056.10 | 2.26631 | |||||||||
−80.1036 | + | 80.1036i | −0.171528 | + | 0.171528i | −0.787650 | − | 0.616122i | ||
0.616122 | + | 0.787650i | ||||||||
0 | 0 | |||||||||
− | 156.626i | − | 0.333957i | |||||||
−1150.00 | + | 682.733i | −2.44680 | + | 1.45262i | |||||
0 | 0 | |||||||||
−20.1851 | + | 20.1851i | −0.0427651 | + | 0.0427651i | |||||
33.9886 | + | 33.9886i | 0.0718576 | + | 0.0718576i | |||||
0 | 0 | |||||||||
383.864 | + | 209.344i | 0.808134 | + | 0.440725i | |||||
837.166 | 1.75875 | |||||||||
0 | 0 | |||||||||
464.509 | + | 464.509i | 0.971776 | + | 0.971776i | |||||
− | 411.116i | − | 0.858280i | −0.903238 | − | 0.429140i | ||||
0.903238 | − | 0.429140i | ||||||||
0 | 0 | |||||||||
−43.6547 | −0.0907582 | |||||||||
−220.729 | + | 220.729i | −0.457944 | + | 0.457944i | |||||
0 | 0 | |||||||||
− | 70.2322i | − | 0.145108i | |||||||
218.745 | + | 55.7702i | 0.451020 | + | 0.114990i | |||||
0 | 0 | |||||||||
−212.163 | + | 212.163i | −0.435652 | + | 0.435652i | −0.890546 | − | 0.454894i | ||
0.454894 | + | 0.890546i | ||||||||
−83.2650 | − | 83.2650i | −0.170625 | − | 0.170625i | |||||
0 | 0 | |||||||||
−107.892 | + | 423.179i | −0.220187 | + | 0.863631i | |||||
−113.699 | −0.231566 | −0.115783 | − | 0.993275i | ||||||
−0.115783 | + | 0.993275i | ||||||||
0 | 0 | |||||||||
281.409 | + | 281.409i | 0.570809 | + | 0.570809i | |||||
610.495i | 1.23582i | |||||||||
0 | 0 | |||||||||
−34.5915 | −0.0697410 | |||||||||
219.991 | − | 219.991i | 0.442639 | − | 0.442639i | |||||
0 | 0 | |||||||||
− | 343.023i | − | 0.687421i | −0.939076 | − | 0.343711i | ||||
0.939076 | − | 0.343711i | ||||||||
−29.1133 | − | 797.562i | −0.0582265 | − | 1.59512i | |||||
0 | 0 | |||||||||
−377.473 | + | 377.473i | −0.751939 | + | 0.751939i | |||||
625.342 | + | 625.342i | 1.24323 | + | 1.24323i | 0.958655 | + | 0.284571i | ||
0.284571 | + | 0.958655i | ||||||||
0 | 0 | |||||||||
279.209 | + | 470.301i | 0.552890 | + | 0.931290i | |||||
177.351 | 0.350497 | |||||||||
0 | 0 | |||||||||
25.1975 | + | 25.1975i | 0.0496014 | + | 0.0496014i | |||||
106.269i | 0.208780i | 0.994536 | + | 0.104390i | ||||||
−0.994536 | + | 0.104390i | ||||||||
0 | 0 | |||||||||
−617.481 | −1.20838 | |||||||||
−35.0124 | + | 35.0124i | −0.0683837 | + | 0.0683837i | |||||
0 | 0 | |||||||||
− | 768.029i | − | 1.49422i | |||||||
−50.2103 | + | 196.937i | −0.0974957 | + | 0.382403i | |||||
0 | 0 | |||||||||
194.658 | − | 194.658i | 0.376515 | − | 0.376515i | |||||
42.9725 | + | 42.9725i | 0.0829585 | + | 0.0829585i | |||||
0 | 0 | |||||||||
357.895 | − | 212.476i | 0.688259 | − | 0.408607i | |||||
−483.272 | −0.927586 | −0.463793 | − | 0.885944i | ||||||
−0.463793 | + | 0.885944i | ||||||||
0 | 0 | |||||||||
−224.917 | − | 224.917i | −0.430052 | − | 0.430052i | 0.458594 | − | 0.888646i | ||
−0.888646 | + | 0.458594i | ||||||||
− | 1056.26i | − | 2.01576i | |||||||
0 | 0 | |||||||||
−231.468 | −0.440052 | |||||||||
−885.530 | + | 885.530i | −1.68032 | + | 1.68032i | |||||
0 | 0 | |||||||||
− | 253.653i | − | 0.479495i | |||||||
530.301 | + | 893.241i | 1.00057 | + | 1.68536i | |||||
0 | 0 | |||||||||
369.479 | − | 369.479i | 0.694509 | − | 0.694509i | |||||
−468.960 | − | 468.960i | −0.879849 | − | 0.879849i | |||||
0 | 0 | |||||||||
−366.154 | − | 93.3530i | −0.684400 | − | 0.174492i | |||||
−257.229 | −0.479906 | |||||||||
0 | 0 | |||||||||
−584.818 | − | 584.818i | −1.08702 | − | 1.08702i | |||||
− | 89.8934i | − | 0.166778i | |||||||
0 | 0 | |||||||||
507.591 | 0.938246 | 0.469123 | − | 0.883133i | ||||||
0.469123 | + | 0.883133i | ||||||||
490.286 | − | 490.286i | 0.904587 | − | 0.904587i | |||||
0 | 0 | |||||||||
931.251i | 1.71186i | |||||||||
418.837 | − | 248.656i | 0.768507 | − | 0.456249i | |||||
0 | 0 | |||||||||
−224.439 | + | 224.439i | −0.410309 | + | 0.410309i | −0.881846 | − | 0.471537i | ||
0.471537 | + | 0.881846i | ||||||||
302.136 | + | 302.136i | 0.551342 | + | 0.551342i | |||||
0 | 0 | |||||||||
75.4130 | + | 256.336i | 0.137115 | + | 0.466065i | |||||
248.396 | 0.450810 | |||||||||
0 | 0 | |||||||||
189.125 | + | 189.125i | 0.341997 | + | 0.341997i | |||||
336.979i | 0.608265i | |||||||||
0 | 0 | |||||||||
1003.94 | 1.80565 | |||||||||
−40.3442 | + | 40.3442i | −0.0724312 | + | 0.0724312i | −0.742394 | − | 0.669963i | ||
0.669963 | + | 0.742394i | ||||||||
0 | 0 | |||||||||
− | 156.985i | − | 0.280832i | |||||||
17.5475 | + | 4.47382i | 0.0313347 | + | 0.00798896i | |||||
0 | 0 | |||||||||
434.854 | − | 434.854i | 0.773762 | − | 0.773762i | |||||
75.8838 | + | 75.8838i | 0.134785 | + | 0.134785i | 0.771280 | − | 0.636496i | ||
−0.636496 | + | 0.771280i | ||||||||
0 | 0 | |||||||||
191.141 | − | 749.703i | 0.338302 | − | 1.32691i | |||||
396.987 | 0.701390 | |||||||||
0 | 0 | |||||||||
−361.295 | − | 361.295i | −0.636084 | − | 0.636084i | |||||
− | 940.148i | − | 1.65228i | −0.563464 | − | 0.826141i | ||||
0.563464 | − | 0.826141i | ||||||||
0 | 0 | |||||||||
−77.9393 | −0.136496 | −0.0682481 | − | 0.997668i | ||||||
−0.0682481 | + | 0.997668i | ||||||||
−162.193 | + | 162.193i | −0.283554 | + | 0.283554i | |||||
0 | 0 | |||||||||
923.263i | 1.60847i | |||||||||
−397.974 | + | 117.083i | −0.692129 | + | 0.203622i | |||||
0 | 0 | |||||||||
−500.861 | + | 500.861i | −0.868043 | + | 0.868043i | −0.992256 | − | 0.124213i | ||
0.124213 | + | 0.992256i | ||||||||
1130.63 | + | 1130.63i | 1.95611 | + | 1.95611i | |||||
0 | 0 | |||||||||
−231.459 | − | 389.870i | −0.399067 | − | 0.672190i | |||||
300.100 | 0.516523 | |||||||||
0 | 0 | |||||||||
−151.197 | − | 151.197i | −0.259343 | − | 0.259343i | |||||
1014.10i | 1.73647i | |||||||||
0 | 0 | |||||||||
−1446.89 | −2.46909 | |||||||||
101.416 | − | 101.416i | 0.172771 | − | 0.172771i | −0.615425 | − | 0.788196i | ||
0.788196 | + | 0.615425i | ||||||||
0 | 0 | |||||||||
781.648i | 1.32708i | |||||||||
−14.7864 | + | 57.9960i | −0.0250617 | + | 0.0982984i | |||||
0 | 0 | |||||||||
−2.20569 | + | 2.20569i | −0.00372583 | + | 0.00372583i | |||||
−597.297 | − | 597.297i | −1.00725 | − | 1.00725i | −0.999974 | − | 0.00727231i | ||
−0.00727231 | − | 0.999974i | ||||||||
0 | 0 | |||||||||
563.736 | − | 334.680i | 0.947456 | − | 0.562487i | |||||
587.278 | 0.985366 | |||||||||
0 | 0 | |||||||||
−409.572 | − | 409.572i | −0.684902 | − | 0.684902i | |||||
347.771i | 0.580585i | 0.956938 | + | 0.290293i | ||||||
−0.956938 | + | 0.290293i | ||||||||
0 | 0 | |||||||||
−192.174 | −0.319757 | −0.159878 | − | 0.987137i | ||||||
−0.159878 | + | 0.987137i | ||||||||
−154.532 | + | 154.532i | −0.256698 | + | 0.256698i | |||||
0 | 0 | |||||||||
− | 1141.24i | − | 1.88947i | |||||||
−28.0773 | − | 47.2934i | −0.0464087 | − | 0.0781709i | |||||
0 | 0 | |||||||||
−74.3868 | + | 74.3868i | −0.122548 | + | 0.122548i | −0.765721 | − | 0.643173i | ||
0.643173 | + | 0.765721i | ||||||||
411.002 | + | 411.002i | 0.675991 | + | 0.675991i | |||||
0 | 0 | |||||||||
−239.238 | − | 60.9950i | −0.392193 | − | 0.0999918i | |||||
−899.079 | −1.47149 | |||||||||
0 | 0 | |||||||||
599.202 | + | 599.202i | 0.977491 | + | 0.977491i | 0.999752 | − | 0.0222612i | ||
−0.0222612 | + | 0.999752i | ||||||||
− | 1199.22i | − | 1.95313i | |||||||
0 | 0 | |||||||||
119.267 | 0.193615 | |||||||||
95.9908 | − | 95.9908i | 0.155577 | − | 0.155577i | −0.625027 | − | 0.780603i | ||
0.780603 | + | 0.625027i | ||||||||
0 | 0 | |||||||||
349.611i | 0.564800i | 0.959297 | + | 0.282400i | ||||||
−0.959297 | + | 0.282400i | ||||||||
1226.83 | − | 728.349i | 1.97876 | − | 1.17476i | |||||
0 | 0 | |||||||||
687.279 | − | 687.279i | 1.10495 | − | 1.10495i | |||||
−380.198 | − | 380.198i | −0.610270 | − | 0.610270i | |||||
0 | 0 | |||||||||
−338.452 | − | 525.429i | −0.541523 | − | 0.840686i | |||||
−446.707 | −0.713590 | |||||||||
0 | 0 | |||||||||
544.938 | + | 544.938i | 0.867736 | + | 0.867736i | |||||
112.930i | 0.179539i | |||||||||
0 | 0 | |||||||||
249.068 | 0.394720 | 0.197360 | − | 0.980331i | ||||||
0.197360 | + | 0.980331i | ||||||||
310.602 | − | 310.602i | 0.491460 | − | 0.491460i | |||||
0 | 0 | |||||||||
− | 1060.12i | − | 1.67211i | |||||||
27.0411 | + | 6.89426i | 0.0425843 | + | 0.0108571i | |||||
0 | 0 | |||||||||
−207.598 | + | 207.598i | −0.325900 | + | 0.325900i | |||||
107.337 | + | 107.337i | 0.168239 | + | 0.168239i | |||||
0 | 0 | |||||||||
249.787 | − | 979.727i | 0.390292 | − | 1.53082i | |||||
−1112.98 | −1.73632 | −0.868159 | − | 0.496287i | ||||||
−0.868159 | + | 0.496287i | ||||||||
0 | 0 | |||||||||
−396.093 | − | 396.093i | −0.616008 | − | 0.616008i | 0.328497 | − | 0.944505i | ||
−0.944505 | + | 0.328497i | ||||||||
495.755i | 0.769806i | |||||||||
0 | 0 | |||||||||
1579.28 | 2.44471 | |||||||||
−190.770 | + | 190.770i | −0.294854 | + | 0.294854i | −0.838994 | − | 0.544140i | ||
0.544140 | + | 0.838994i | ||||||||
0 | 0 | |||||||||
− | 12.3198i | − | 0.0189827i | |||||||
417.819 | − | 766.134i | 0.642799 | − | 1.17867i | |||||
0 | 0 | |||||||||
222.285 | − | 222.285i | 0.340928 | − | 0.340928i | |||||
−41.7823 | − | 41.7823i | −0.0639851 | − | 0.0639851i | 0.674390 | − | 0.738375i | ||
−0.738375 | + | 0.674390i | ||||||||
0 | 0 | |||||||||
−422.268 | − | 711.270i | −0.644684 | − | 1.08591i | |||||
−47.3892 | −0.0722397 | |||||||||
0 | 0 | |||||||||
885.029 | + | 885.029i | 1.34503 | + | 1.34503i | |||||
− | 690.184i | − | 1.04732i | −0.851927 | − | 0.523660i | ||||
0.851927 | − | 0.523660i | ||||||||
0 | 0 | |||||||||
−658.583 | −0.996344 | −0.498172 | − | 0.867078i | ||||||
−0.498172 | + | 0.867078i | ||||||||
−283.034 | + | 283.034i | −0.427544 | + | 0.427544i | |||||
0 | 0 | |||||||||
− | 492.859i | − | 0.742258i | |||||||
101.093 | − | 396.511i | 0.152019 | − | 0.596257i | |||||
0 | 0 | |||||||||
−166.645 | + | 166.645i | −0.249843 | + | 0.249843i | |||||
−55.7926 | − | 55.7926i | −0.0835219 | − | 0.0835219i | |||||
0 | 0 | |||||||||
−463.753 | + | 275.322i | −0.692168 | + | 0.410928i | |||||
50.8198 | 0.0757375 | |||||||||
0 | 0 | |||||||||
−901.911 | − | 901.911i | −1.34014 | − | 1.34014i | −0.895920 | − | 0.444216i | ||
−0.444216 | − | 0.895920i | ||||||||
1132.17i | 1.67978i | |||||||||
0 | 0 | |||||||||
−329.893 | −0.488007 | |||||||||
485.397 | − | 485.397i | 0.716982 | − | 0.716982i | −0.251004 | − | 0.967986i | ||
0.967986 | + | 0.251004i | ||||||||
0 | 0 | |||||||||
− | 211.264i | − | 0.311141i | |||||||
−549.651 | − | 925.833i | −0.808310 | − | 1.36152i | |||||
0 | 0 | |||||||||
−337.764 | + | 337.764i | −0.495255 | + | 0.495255i | |||||
−713.724 | − | 713.724i | −1.04498 | − | 1.04498i | −0.998939 | − | 0.0460448i | ||
−0.0460448 | − | 0.998939i | ||||||||
0 | 0 | |||||||||
324.241 | + | 82.6670i | 0.473345 | + | 0.120682i | |||||
1147.59 | 1.67288 | |||||||||
0 | 0 | |||||||||
−7.93183 | − | 7.93183i | −0.0115288 | − | 0.0115288i | |||||
698.344i | 1.01356i | |||||||||
0 | 0 | |||||||||
−1319.75 | −1.90991 | −0.954954 | − | 0.296754i | ||||||
−0.954954 | + | 0.296754i | ||||||||
−260.195 | + | 260.195i | −0.376005 | + | 0.376005i | |||||
0 | 0 | |||||||||
− | 887.368i | − | 1.27863i | |||||||
676.041 | − | 401.353i | 0.972721 | − | 0.577487i | |||||
0 | 0 | |||||||||
−1213.15 | + | 1213.15i | −1.74053 | + | 1.74053i | |||||
53.6731 | + | 53.6731i | 0.0768955 | + | 0.0768955i | |||||
0 | 0 | |||||||||
−716.543 | + | 210.804i | −1.02363 | + | 0.301149i | |||||
1276.93 | 1.82159 | 0.910795 | − | 0.412859i | ||||||
0.910795 | + | 0.412859i | ||||||||
0 | 0 | |||||||||
49.8410 | + | 49.8410i | 0.0708975 | + | 0.0708975i | |||||
344.935i | 0.489964i | |||||||||
0 | 0 | |||||||||
−275.578 | −0.390337 | |||||||||
361.940 | − | 361.940i | 0.511938 | − | 0.511938i | |||||
0 | 0 | |||||||||
746.781i | 1.05329i | 0.850086 | + | 0.526644i | ||||||
−0.850086 | + | 0.526644i | ||||||||
−1038.08 | − | 264.664i | −1.46208 | − | 0.372766i | |||||
0 | 0 | |||||||||
−624.405 | + | 624.405i | −0.876974 | + | 0.876974i | |||||
−524.396 | − | 524.396i | −0.735478 | − | 0.735478i | |||||
0 | 0 | |||||||||
−44.3774 | + | 174.060i | −0.0620663 | + | 0.243440i | |||||
−1912.55 | −2.67116 | |||||||||
0 | 0 | |||||||||
1145.46 | + | 1145.46i | 1.59534 | + | 1.59534i | |||||
135.949i | 0.189080i | 0.995521 | + | 0.0945402i | ||||||
−0.995521 | + | 0.0945402i | ||||||||
0 | 0 | |||||||||
190.203 | 0.263804 | |||||||||
−125.596 | + | 125.596i | −0.173955 | + | 0.173955i | |||||
0 | 0 | |||||||||
1302.75i | 1.79938i | |||||||||
−311.723 | − | 170.001i | −0.429962 | − | 0.234484i | |||||
0 | 0 | |||||||||
192.127 | − | 192.127i | 0.264273 | − | 0.264273i | −0.562514 | − | 0.826788i | ||
0.826788 | + | 0.562514i | ||||||||
−275.433 | − | 275.433i | −0.378342 | − | 0.378342i | |||||
0 | 0 | |||||||||
1085.43 | + | 1828.29i | 1.48688 | + | 2.50451i | |||||
−406.103 | −0.555545 | |||||||||
0 | 0 | |||||||||
−288.677 | − | 288.677i | −0.393830 | − | 0.393830i | 0.482220 | − | 0.876050i | ||
−0.876050 | + | 0.482220i | ||||||||
− | 1833.58i | − | 2.49807i | |||||||
0 | 0 | |||||||||
−551.471 | −0.749281 | |||||||||
78.4985 | − | 78.4985i | 0.106511 | − | 0.106511i | |||||
0 | 0 | |||||||||
− | 135.495i | − | 0.183349i | −0.995789 | − | 0.0916746i | ||||
0.995789 | − | 0.0916746i | ||||||||
31.7854 | − | 124.670i | 0.0429532 | − | 0.168473i | |||||
0 | 0 | |||||||||
687.431 | − | 687.431i | 0.926457 | − | 0.926457i | |||||
350.021 | + | 350.021i | 0.471091 | + | 0.471091i | 0.902268 | − | 0.431177i | ||
−0.431177 | + | 0.902268i | ||||||||
0 | 0 | |||||||||
395.465 | − | 234.781i | 0.530826 | − | 0.315142i | |||||
590.605 | 0.791696 | |||||||||
0 | 0 | |||||||||
419.575 | + | 419.575i | 0.560929 | + | 0.560929i | |||||
353.633i | 0.472140i | |||||||||
0 | 0 | |||||||||
1143.86 | 1.52311 | 0.761556 | − | 0.648099i | ||||||
0.761556 | + | 0.648099i | ||||||||
−45.4268 | + | 45.4268i | −0.0604080 | + | 0.0604080i | |||||
0 | 0 | |||||||||
− | 495.761i | − | 0.657509i | |||||||
−456.242 | − | 768.495i | −0.604294 | − | 1.01787i | |||||
0 | 0 | |||||||||
−99.4207 | + | 99.4207i | −0.131335 | + | 0.131335i | −0.769719 | − | 0.638383i | ||
0.638383 | + | 0.769719i | ||||||||
704.074 | + | 704.074i | 0.928857 | + | 0.928857i | |||||
0 | 0 | |||||||||
−651.197 | − | 166.026i | −0.856838 | − | 0.218456i | |||||
782.950 | 1.02884 | 0.514421 | − | 0.857537i | ||||||
0.514421 | + | 0.857537i | ||||||||
0 | 0 | |||||||||
−322.333 | − | 322.333i | −0.422455 | − | 0.422455i | |||||
435.156i | 0.569576i | |||||||||
0 | 0 | |||||||||
−624.467 | −0.815231 | |||||||||
−28.4510 | + | 28.4510i | −0.0370939 | + | 0.0370939i | |||||
0 | 0 | |||||||||
− | 1060.55i | − | 1.37913i | −0.724224 | − | 0.689565i | ||||
0.724224 | − | 0.689565i | ||||||||
215.023 | − | 127.656i | 0.279251 | − | 0.165786i | |||||
0 | 0 | |||||||||
359.742 | − | 359.742i | 0.465987 | − | 0.465987i | |||||
599.585 | + | 599.585i | 0.775660 | + | 0.775660i | 0.979090 | − | 0.203429i | ||
−0.203429 | + | 0.979090i | ||||||||
0 | 0 | |||||||||
534.956 | − | 980.921i | 0.690265 | − | 1.26570i | |||||
−346.963 | −0.447117 | |||||||||
0 | 0 | |||||||||
−499.290 | − | 499.290i | −0.641761 | − | 0.641761i | |||||
1070.83i | 1.37462i | |||||||||
0 | 0 | |||||||||
220.513 | 0.282347 | |||||||||
−1059.52 | + | 1059.52i | −1.35488 | + | 1.35488i | |||||
0 | 0 | |||||||||
20.9782i | 0.0267579i | |||||||||
584.808 | + | 149.100i | 0.744979 | + | 0.189936i | |||||
0 | 0 | |||||||||
−10.9757 | + | 10.9757i | −0.0139462 | + | 0.0139462i | −0.714046 | − | 0.700099i | ||
0.700099 | + | 0.714046i | ||||||||
391.343 | + | 391.343i | 0.496628 | + | 0.496628i | |||||
0 | 0 | |||||||||
227.529 | − | 892.426i | 0.288011 | − | 1.12965i | |||||
−724.066 | −0.915380 | |||||||||
0 | 0 | |||||||||
−117.362 | − | 117.362i | −0.147998 | − | 0.147998i | |||||
2037.81i | 2.56651i | |||||||||
0 | 0 | |||||||||
1862.89 | 2.34032 | |||||||||
−291.068 | + | 291.068i | −0.365205 | + | 0.365205i | −0.865725 | − | 0.500520i | ||
0.500520 | + | 0.865725i | ||||||||
0 | 0 | |||||||||
2325.82i | 2.91091i | |||||||||
−234.495 | − | 797.071i | −0.293119 | − | 0.996339i | |||||
0 | 0 | |||||||||
−1588.68 | + | 1588.68i | −1.98090 | + | 1.98090i | |||||
−309.472 | − | 309.472i | −0.385395 | − | 0.385395i | |||||
0 | 0 | |||||||||
198.192 | + | 333.835i | 0.246201 | + | 0.414702i | |||||
1560.05 | 1.93555 | |||||||||
0 | 0 | |||||||||
−594.420 | − | 594.420i | −0.735669 | − | 0.735669i | |||||
934.080i | 1.15461i | 0.816528 | + | 0.577305i | ||||||
−0.816528 | + | 0.577305i | ||||||||
0 | 0 | |||||||||
247.443 | 0.305109 | 0.152554 | − | 0.988295i | ||||||
0.152554 | + | 0.988295i | ||||||||
−300.041 | + | 300.041i | −0.369508 | + | 0.369508i | |||||
0 | 0 | |||||||||
43.0743i | 0.0529169i | |||||||||
60.8192 | − | 238.548i | 0.0746248 | − | 0.292697i | |||||
0 | 0 | |||||||||
−179.232 | + | 179.232i | −0.219378 | + | 0.219378i | |||||
−85.9325 | − | 85.9325i | −0.105052 | − | 0.105052i | |||||
0 | 0 | |||||||||
1680.72 | − | 997.814i | 2.04966 | − | 1.21685i | |||||
958.912 | 1.16798 | 0.583990 | − | 0.811761i | ||||||
0.583990 | + | 0.811761i | ||||||||
0 | 0 | |||||||||
−841.533 | − | 841.533i | −1.02252 | − | 1.02252i | −0.999741 | − | 0.0227782i | ||
−0.0227782 | − | 0.999741i | ||||||||
− | 312.373i | − | 0.379094i | |||||||
0 | 0 | |||||||||
56.0128 | 0.0678121 | |||||||||
−501.948 | + | 501.948i | −0.606951 | + | 0.606951i | −0.942148 | − | 0.335197i | ||
0.335197 | + | 0.942148i | ||||||||
0 | 0 | |||||||||
− | 219.411i | − | 0.264670i | −0.991205 | − | 0.132335i | ||||
0.991205 | − | 0.132335i | ||||||||
−527.524 | − | 888.563i | −0.635571 | − | 1.07056i | |||||
0 | 0 | |||||||||
796.585 | − | 796.585i | 0.957434 | − | 0.957434i | |||||
537.033 | + | 537.033i | 0.644697 | + | 0.644697i | |||||
0 | 0 | |||||||||
−59.8746 | − | 15.2654i | −0.0717061 | − | 0.0182819i | |||||
370.354 | 0.443007 | |||||||||
0 | 0 | |||||||||
1107.44 | + | 1107.44i | 1.32153 | + | 1.32153i | |||||
1101.77i | 1.31320i | 0.754241 | + | 0.656598i | ||||||
−0.754241 | + | 0.656598i | ||||||||
0 | 0 | |||||||||
639.286 | 0.760150 | |||||||||
886.187 | − | 886.187i | 1.05248 | − | 1.05248i | |||||
0 | 0 | |||||||||
599.381i | 0.710168i | |||||||||
−222.145 | + | 131.884i | −0.262894 | + | 0.156075i | |||||
0 | 0 | |||||||||
−36.3966 | + | 36.3966i | −0.0429712 | + | 0.0429712i | |||||
35.2845 | + | 35.2845i | 0.0416090 | + | 0.0416090i | |||||
0 | 0 | |||||||||
−1981.90 | − | 1080.85i | −2.33165 | − | 1.27159i | |||||
−66.8751 | −0.0785841 | |||||||||
0 | 0 | |||||||||
1045.69 | + | 1045.69i | 1.22589 | + | 1.22589i | 0.965504 | + | 0.260387i | ||
0.260387 | + | 0.965504i | ||||||||
231.057i | 0.270558i | |||||||||
0 | 0 | |||||||||
580.777 | 0.678478 | |||||||||
1006.72 | − | 1006.72i | 1.17471 | − | 1.17471i | 0.193632 | − | 0.981074i | ||
0.981074 | − | 0.193632i | ||||||||
0 | 0 | |||||||||
1366.58i | 1.59090i | 0.606021 | + | 0.795448i | ||||||
−0.606021 | + | 0.795448i | ||||||||
448.323 | + | 114.302i | 0.521305 | + | 0.132910i | |||||
0 | 0 | |||||||||
1150.57 | − | 1150.57i | 1.33477 | − | 1.33477i | |||||
−947.174 | − | 947.174i | −1.09754 | − | 1.09754i | −0.994698 | − | 0.102838i | ||
−0.102838 | − | 0.994698i | ||||||||
0 | 0 | |||||||||
−71.1918 | + | 279.232i | −0.0823027 | + | 0.322812i | |||||
−685.288 | −0.791325 | |||||||||
0 | 0 | |||||||||
−944.161 | − | 944.161i | −1.08774 | − | 1.08774i | |||||
189.573i | 0.218150i | |||||||||
0 | 0 | |||||||||
−362.566 | −0.416264 | |||||||||
−529.373 | + | 529.373i | −0.607079 | + | 0.607079i | |||||
0 | 0 | |||||||||
935.223i | 1.07005i | |||||||||
−398.235 | + | 428.410i | −0.455126 | + | 0.489612i | |||||
0 | 0 | |||||||||
−87.0484 | + | 87.0484i | −0.0992570 | + | 0.0992570i | −0.754992 | − | 0.655735i | ||
0.655735 | + | 0.754992i | ||||||||
−480.617 | − | 480.617i | −0.547400 | − | 0.547400i | |||||
0 | 0 | |||||||||
6.55231 | + | 11.0367i | 0.00744580 | + | 0.0125417i | |||||
−868.490 | −0.985800 | −0.492900 | − | 0.870086i | ||||||
−0.492900 | + | 0.870086i | ||||||||
0 | 0 | |||||||||
608.328 | + | 608.328i | 0.688934 | + | 0.688934i | 0.961996 | − | 0.273063i | ||
−0.273063 | + | 0.961996i | ||||||||
− | 1937.92i | − | 2.19221i | |||||||
0 | 0 | |||||||||
−2018.22 | −2.27790 | |||||||||
−495.738 | + | 495.738i | −0.558892 | + | 0.558892i | −0.928992 | − | 0.370100i | ||
0.370100 | + | 0.928992i | ||||||||
0 | 0 | |||||||||
− | 26.1163i | − | 0.0293772i | |||||||
−457.402 | + | 1794.05i | −0.513935 | + | 2.01578i | |||||
0 | 0 | |||||||||
−1009.35 | + | 1009.35i | −1.13156 | + | 1.13156i | |||||
1026.49 | + | 1026.49i | 1.14948 | + | 1.14948i | |||||
0 | 0 | |||||||||
−1287.89 | + | 764.595i | −1.43898 | + | 0.854296i | |||||
−946.224 | −1.05605 | |||||||||
0 | 0 | |||||||||
1462.19 | + | 1462.19i | 1.62828 | + | 1.62828i | |||||
− | 634.749i | − | 0.706061i | |||||||
0 | 0 | |||||||||
1806.54 | 2.00504 | |||||||||
−462.725 | + | 462.725i | −0.512999 | + | 0.512999i | |||||
0 | 0 | |||||||||
1189.14i | 1.31543i | |||||||||
520.812 | + | 877.257i | 0.575483 | + | 0.969345i | |||||
0 | 0 | |||||||||
163.744 | − | 163.744i | 0.180534 | − | 0.180534i | −0.611055 | − | 0.791588i | ||
0.791588 | + | 0.611055i | ||||||||
1014.65 | + | 1014.65i | 1.11745 | + | 1.11745i | |||||
0 | 0 | |||||||||
−791.376 | − | 201.766i | −0.869644 | − | 0.221720i | |||||
−1750.93 | −1.92199 | −0.960995 | − | 0.276566i | ||||||
−0.960995 | + | 0.276566i | ||||||||
0 | 0 | |||||||||
150.405 | + | 150.405i | 0.164738 | + | 0.164738i | |||||
− | 472.638i | − | 0.517109i | |||||||
0 | 0 | |||||||||
278.647 | 0.304200 | |||||||||
−547.388 | + | 547.388i | −0.596933 | + | 0.596933i | |||||
0 | 0 | |||||||||
− | 1637.39i | − | 1.78170i | −0.454293 | − | 0.890852i | ||||
0.454293 | − | 0.890852i | ||||||||
548.263 | − | 325.494i | 0.595938 | − | 0.353797i | |||||
0 | 0 | |||||||||
−1823.03 | + | 1823.03i | −1.97726 | + | 1.97726i | |||||
−509.247 | − | 509.247i | −0.551731 | − | 0.551731i | |||||
0 | 0 | |||||||||
−28.4365 | − | 96.6583i | −0.0307422 | − | 0.104495i | |||||
−1150.49 | −1.24243 | |||||||||
0 | 0 | |||||||||
−333.761 | − | 333.761i | −0.359656 | − | 0.359656i | |||||
− | 1639.43i | − | 1.76473i | −0.470568 | − | 0.882364i | ||||
0.470568 | − | 0.882364i | ||||||||
0 | 0 | |||||||||
474.033 | 0.509166 | |||||||||
−1479.57 | + | 1479.57i | −1.58753 | + | 1.58753i | |||||
0 | 0 | |||||||||
− | 365.061i | − | 0.390857i | |||||||
450.273 | + | 114.799i | 0.481575 | + | 0.122780i | |||||
0 | 0 | |||||||||
−141.600 | + | 141.600i | −0.151121 | + | 0.151121i | −0.778618 | − | 0.627498i | ||
0.627498 | + | 0.778618i | ||||||||
356.900 | + | 356.900i | 0.380491 | + | 0.380491i | |||||
0 | 0 | |||||||||
654.627 | − | 2567.61i | 0.696412 | − | 2.73150i | |||||
−1074.74 | −1.14212 | −0.571062 | − | 0.820907i | ||||||
−0.571062 | + | 0.820907i | ||||||||
0 | 0 | |||||||||
−718.405 | − | 718.405i | −0.761829 | − | 0.761829i | |||||
2.87502i | 0.00304558i | |||||||||
0 | 0 | |||||||||
−154.898 | −0.163740 | |||||||||
1127.43 | − | 1127.43i | 1.19053 | − | 1.19053i | 0.213609 | − | 0.976919i | ||
0.976919 | − | 0.213609i | ||||||||
0 | 0 | |||||||||
1429.38i | 1.50619i | |||||||||
−1351.73 | + | 397.674i | −1.42287 | + | 0.418604i | |||||
0 | 0 | |||||||||
−712.514 | + | 712.514i | −0.748439 | + | 0.748439i | |||||
−99.4706 | − | 99.4706i | −0.104376 | − | 0.104376i | 0.652990 | − | 0.757366i | ||
−0.757366 | + | 0.652990i | ||||||||
0 | 0 | |||||||||
173.965 | + | 293.028i | 0.182163 | + | 0.306836i | |||||
−1301.53 | −1.36144 | |||||||||
0 | 0 | |||||||||
936.801 | + | 936.801i | 0.977871 | + | 0.977871i | |||||
− | 313.153i | − | 0.326541i | |||||||
0 | 0 | |||||||||
1036.41 | 1.07847 | |||||||||
99.4750 | − | 99.4750i | 0.103404 | − | 0.103404i | |||||
0 | 0 | |||||||||
− | 618.472i | − | 0.641568i | |||||||
98.4287 | − | 386.062i | 0.101999 | − | 0.400065i | |||||
0 | 0 | |||||||||
1260.15 | − | 1260.15i | 1.30315 | − | 1.30315i | 0.376896 | − | 0.926256i | ||
0.926256 | − | 0.376896i | ||||||||
59.7748 | + | 59.7748i | 0.0617508 | + | 0.0617508i | |||||
0 | 0 | |||||||||
−625.531 | + | 371.367i | −0.644878 | + | 0.382852i | |||||
−1148.23 | −1.18252 | −0.591261 | − | 0.806481i | ||||||
−0.591261 | + | 0.806481i | ||||||||
0 | 0 | |||||||||
−520.275 | − | 520.275i | −0.534713 | − | 0.534713i | |||||
− | 966.900i | − | 0.992711i | |||||||
0 | 0 | |||||||||
−11.8597 | −0.0121513 | |||||||||
−145.709 | + | 145.709i | −0.149139 | + | 0.149139i | −0.777733 | − | 0.628594i | ||
0.628594 | + | 0.777733i | ||||||||
0 | 0 | |||||||||
− | 381.099i | − | 0.389274i | |||||||
−441.710 | − | 744.018i | −0.450725 | − | 0.759202i | |||||
0 | 0 | |||||||||
259.083 | − | 259.083i | 0.263832 | − | 0.263832i | |||||
562.675 | + | 562.675i | 0.572406 | + | 0.572406i | 0.932800 | − | 0.360394i | ||
−0.360394 | + | 0.932800i | ||||||||
0 | 0 | |||||||||
419.975 | + | 107.075i | 0.426371 | + | 0.108706i | |||||
−1282.48 | −1.30069 | |||||||||
0 | 0 | |||||||||
−855.288 | − | 855.288i | −0.865676 | − | 0.865676i | |||||
− | 240.487i | − | 0.243162i | |||||||
0 | 0 | |||||||||
−1445.80 | −1.45893 | −0.729464 | − | 0.684019i | ||||||
−0.729464 | + | 0.684019i | ||||||||
1050.27 | − | 1050.27i | 1.05874 | − | 1.05874i | |||||
0 | 0 | |||||||||
1002.58i | 1.00863i | |||||||||
1254.45 | − | 744.742i | 1.26075 | − | 0.748484i | |||||
0 | 0 | |||||||||
273.932 | − | 273.932i | 0.274757 | − | 0.274757i | −0.556255 | − | 0.831012i | ||
0.831012 | + | 0.556255i | ||||||||
781.639 | + | 781.639i | 0.783206 | + | 0.783206i | |||||
0 | 0 |
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 495.3.j.a.298.1 | 20 | ||
3.2 | odd | 2 | 55.3.f.a.23.10 | yes | 20 | ||
5.2 | odd | 4 | inner | 495.3.j.a.397.1 | 20 | ||
15.2 | even | 4 | 55.3.f.a.12.10 | ✓ | 20 | ||
15.8 | even | 4 | 275.3.f.b.232.1 | 20 | |||
15.14 | odd | 2 | 275.3.f.b.243.1 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
55.3.f.a.12.10 | ✓ | 20 | 15.2 | even | 4 | ||
55.3.f.a.23.10 | yes | 20 | 3.2 | odd | 2 | ||
275.3.f.b.232.1 | 20 | 15.8 | even | 4 | |||
275.3.f.b.243.1 | 20 | 15.14 | odd | 2 | |||
495.3.j.a.298.1 | 20 | 1.1 | even | 1 | trivial | ||
495.3.j.a.397.1 | 20 | 5.2 | odd | 4 | inner |