Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [336,6,Mod(193,336)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(336, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("336.193");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 336.q (of order , degree , not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | |
Analytic rank: | |
Dimension: | |
Relative dimension: | over |
Coefficient field: | |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
|
Coefficient ring: | |
Coefficient ring index: | |
Twist minimal: | no (minimal twist has level 21) |
Sato-Tate group: |
Embedding invariants
Embedding label | 289.1 | ||
Root | of defining polynomial | ||
Character | 336.289 | ||
Dual form | 336.6.q.e.193.1 |
-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 .
0 | 0 | |||||||||
−4.50000 | − | 7.79423i | −0.288675 | − | 0.500000i | |||||
0 | 0 | |||||||||
−19.3645 | + | 33.5404i | −0.346403 | + | 0.599988i | −0.985608 | − | 0.169049i | ||
0.639204 | + | 0.769037i | ||||||||
0 | 0 | |||||||||
87.5000 | + | 95.6596i | 0.674937 | + | 0.737876i | |||||
0 | 0 | |||||||||
−40.5000 | + | 70.1481i | −0.166667 | + | 0.288675i | |||||
0 | 0 | |||||||||
−288.195 | − | 499.168i | −0.718133 | − | 1.24384i | −0.961739 | − | 0.273968i | ||
0.243606 | − | 0.969874i | ||||||||
0 | 0 | |||||||||
391.491 | 0.642486 | 0.321243 | − | 0.946997i | ||||||
0.321243 | + | 0.946997i | ||||||||
0 | 0 | |||||||||
348.562 | 0.399992 | |||||||||
0 | 0 | |||||||||
664.850 | + | 1151.55i | 0.557958 | + | 0.966412i | 0.997667 | + | 0.0682711i | ||
−0.439709 | + | 0.898140i | ||||||||
0 | 0 | |||||||||
471.237 | − | 816.206i | 0.299471 | − | 0.518699i | −0.676544 | − | 0.736402i | ||
0.976015 | + | 0.217703i | ||||||||
0 | 0 | |||||||||
351.842 | − | 1112.46i | 0.174100 | − | 0.550475i | |||||
0 | 0 | |||||||||
−816.040 | + | 1413.42i | −0.321656 | + | 0.557124i | −0.980830 | − | 0.194866i | ||
0.659174 | + | 0.751991i | ||||||||
0 | 0 | |||||||||
812.530 | + | 1407.34i | 0.260009 | + | 0.450350i | |||||
0 | 0 | |||||||||
729.000 | 0.192450 | |||||||||
0 | 0 | |||||||||
−1463.54 | −0.323155 | −0.161577 | − | 0.986860i | ||||||
−0.161577 | + | 0.986860i | ||||||||
0 | 0 | |||||||||
−1956.21 | − | 3388.25i | −0.365604 | − | 0.633245i | 0.623269 | − | 0.782008i | ||
−0.988873 | + | 0.148763i | ||||||||
0 | 0 | |||||||||
−2593.75 | + | 4492.51i | −0.414614 | + | 0.718133i | |||||
0 | 0 | |||||||||
−4902.85 | + | 1082.38i | −0.676517 | + | 0.149351i | |||||
0 | 0 | |||||||||
8150.17 | − | 14116.5i | 0.978729 | − | 1.69521i | 0.311691 | − | 0.950184i | ||
0.667038 | − | 0.745024i | ||||||||
0 | 0 | |||||||||
−1761.71 | − | 3051.37i | −0.185470 | − | 0.321243i | |||||
0 | 0 | |||||||||
−13103.8 | −1.21741 | −0.608707 | − | 0.793395i | ||||||
−0.608707 | + | 0.793395i | ||||||||
0 | 0 | |||||||||
−14733.5 | −1.21516 | −0.607582 | − | 0.794257i | ||||||
−0.607582 | + | 0.794257i | ||||||||
0 | 0 | |||||||||
−1568.53 | − | 2716.77i | −0.115468 | − | 0.199996i | |||||
0 | 0 | |||||||||
−3407.26 | + | 5901.55i | −0.224989 | + | 0.389692i | −0.956316 | − | 0.292335i | ||
0.731327 | + | 0.682027i | ||||||||
0 | 0 | |||||||||
−1494.50 | + | 16740.4i | −0.0889213 | + | 0.996039i | |||||
0 | 0 | |||||||||
5983.65 | − | 10364.0i | 0.322137 | − | 0.557958i | |||||
0 | 0 | |||||||||
1005.67 | + | 1741.87i | 0.0491775 | + | 0.0851779i | 0.889566 | − | 0.456806i | ||
−0.840389 | + | 0.541984i | ||||||||
0 | 0 | |||||||||
22323.0 | 0.995054 | |||||||||
0 | 0 | |||||||||
−8482.26 | −0.345800 | |||||||||
0 | 0 | |||||||||
25726.6 | + | 44559.7i | 0.962170 | + | 1.66653i | 0.717035 | + | 0.697037i | ||
0.245135 | + | 0.969489i | ||||||||
0 | 0 | |||||||||
−20548.9 | + | 35591.8i | −0.707073 | + | 1.22469i | 0.258865 | + | 0.965913i | ||
−0.965938 | + | 0.258773i | ||||||||
0 | 0 | |||||||||
−10254.1 | + | 2263.74i | −0.325496 | + | 0.0718581i | |||||
0 | 0 | |||||||||
−7581.04 | + | 13130.8i | −0.222559 | + | 0.385484i | |||||
0 | 0 | |||||||||
25289.1 | + | 43802.0i | 0.688250 | + | 1.19208i | 0.972404 | + | 0.233305i | ||
−0.284153 | + | 0.958779i | ||||||||
0 | 0 | |||||||||
14688.7 | 0.371416 | |||||||||
0 | 0 | |||||||||
−39970.6 | −0.941012 | −0.470506 | − | 0.882397i | ||||||
−0.470506 | + | 0.882397i | ||||||||
0 | 0 | |||||||||
27843.3 | + | 48226.0i | 0.611524 | + | 1.05919i | 0.990984 | + | 0.133983i | ||
−0.379459 | + | 0.925208i | ||||||||
0 | 0 | |||||||||
7312.77 | − | 12666.1i | 0.150117 | − | 0.260009i | |||||
0 | 0 | |||||||||
22533.2 | − | 71245.8i | 0.433107 | − | 1.36941i | |||||
0 | 0 | |||||||||
−31575.7 | + | 54690.7i | −0.569226 | + | 0.985929i | 0.427416 | + | 0.904055i | ||
−0.996643 | + | 0.0818739i | ||||||||
0 | 0 | |||||||||
−3280.50 | − | 5681.99i | −0.0555556 | − | 0.0962250i | |||||
0 | 0 | |||||||||
−45572.4 | −0.726116 | −0.363058 | − | 0.931766i | ||||||
−0.363058 | + | 0.931766i | ||||||||
0 | 0 | |||||||||
−51498.1 | −0.773114 | |||||||||
0 | 0 | |||||||||
6585.95 | + | 11407.2i | 0.0932868 | + | 0.161577i | |||||
0 | 0 | |||||||||
−7843.34 | + | 13585.1i | −0.104961 | + | 0.181797i | −0.913722 | − | 0.406340i | ||
0.808762 | + | 0.588137i | ||||||||
0 | 0 | |||||||||
34255.5 | + | 37449.9i | 0.433637 | + | 0.474075i | |||||
0 | 0 | |||||||||
−17605.9 | + | 30494.3i | −0.211082 | + | 0.365604i | |||||
0 | 0 | |||||||||
18250.6 | + | 31610.9i | 0.207476 | + | 0.359358i | |||||
0 | 0 | |||||||||
3128.49 | 0.0337603 | 0.0168801 | − | 0.999858i | ||||||
0.0168801 | + | 0.999858i | ||||||||
0 | 0 | |||||||||
46687.6 | 0.478755 | |||||||||
0 | 0 | |||||||||
84505.5 | + | 146368.i | 0.824292 | + | 1.42772i | 0.902459 | + | 0.430776i | ||
−0.0781663 | + | 0.996940i | ||||||||
0 | 0 | |||||||||
56410.1 | − | 97705.1i | 0.523918 | − | 0.907453i | −0.475694 | − | 0.879611i | ||
0.999612 | − | 0.0278422i | ||||||||
0 | 0 | |||||||||
30499.1 | + | 33343.2i | 0.269969 | + | 0.295144i | |||||
0 | 0 | |||||||||
−11154.7 | + | 19320.6i | −0.0941890 | + | 0.163140i | −0.909270 | − | 0.416207i | ||
0.815081 | + | 0.579347i | ||||||||
0 | 0 | |||||||||
41909.8 | + | 72589.8i | 0.337869 | + | 0.585207i | 0.984032 | − | 0.177993i | ||
−0.646162 | + | 0.763200i | ||||||||
0 | 0 | |||||||||
−146703. | −1.13014 | |||||||||
0 | 0 | |||||||||
−40928.4 | −0.301529 | −0.150764 | − | 0.988570i | ||||||
−0.150764 | + | 0.988570i | ||||||||
0 | 0 | |||||||||
−31604.4 | − | 54740.5i | −0.222845 | − | 0.385980i | |||||
0 | 0 | |||||||||
−15855.4 | + | 27462.3i | −0.107081 | + | 0.185470i | |||||
0 | 0 | |||||||||
−51982.8 | + | 164360.i | −0.336505 | + | 1.06397i | |||||
0 | 0 | |||||||||
−85587.1 | + | 148241.i | −0.531429 | + | 0.920462i | |||||
0 | 0 | |||||||||
58967.2 | + | 102134.i | 0.351437 | + | 0.608707i | |||||
0 | 0 | |||||||||
−183965. | −1.05308 | |||||||||
0 | 0 | |||||||||
−83270.1 | −0.458120 | −0.229060 | − | 0.973412i | ||||||
−0.229060 | + | 0.973412i | ||||||||
0 | 0 | |||||||||
66300.7 | + | 114836.i | 0.350788 | + | 0.607582i | |||||
0 | 0 | |||||||||
−83437.4 | + | 144518.i | −0.424798 | + | 0.735772i | −0.996402 | − | 0.0847580i | ||
0.571603 | + | 0.820530i | ||||||||
0 | 0 | |||||||||
119311. | − | 26339.7i | 0.584860 | − | 0.129117i | |||||
0 | 0 | |||||||||
−14116.7 | + | 24450.9i | −0.0666653 | + | 0.115468i | |||||
0 | 0 | |||||||||
−19111.9 | − | 33102.9i | −0.0869969 | − | 0.150683i | 0.819244 | − | 0.573446i | ||
−0.906240 | + | 0.422763i | ||||||||
0 | 0 | |||||||||
−106263. | −0.466492 | −0.233246 | − | 0.972418i | ||||||
−0.233246 | + | 0.972418i | ||||||||
0 | 0 | |||||||||
61330.7 | 0.259795 | |||||||||
0 | 0 | |||||||||
−112826. | − | 195420.i | −0.461390 | − | 0.799151i | |||||
0 | 0 | |||||||||
28340.8 | − | 49087.8i | 0.111942 | − | 0.193889i | |||||
0 | 0 | |||||||||
137204. | − | 63683.4i | 0.523689 | − | 0.243071i | |||||
0 | 0 | |||||||||
−96277.8 | + | 166758.i | −0.355271 | + | 0.615348i | −0.987164 | − | 0.159708i | ||
0.631893 | + | 0.775056i | ||||||||
0 | 0 | |||||||||
70849.3 | + | 122715.i | 0.252868 | + | 0.437980i | 0.964314 | − | 0.264761i | ||
−0.711447 | + | 0.702740i | ||||||||
0 | 0 | |||||||||
−107706. | −0.371972 | |||||||||
0 | 0 | |||||||||
151524. | 0.506586 | |||||||||
0 | 0 | |||||||||
−282885. | − | 489972.i | −0.915928 | − | 1.58643i | −0.805536 | − | 0.592546i | ||
−0.110392 | − | 0.993888i | ||||||||
0 | 0 | |||||||||
9051.04 | − | 15676.9i | 0.0283926 | − | 0.0491775i | |||||
0 | 0 | |||||||||
−206611. | + | 45612.4i | −0.628186 | + | 0.138682i | |||||
0 | 0 | |||||||||
−215101. | + | 372565.i | −0.634121 | + | 1.09833i | 0.352579 | + | 0.935782i | ||
−0.986701 | + | 0.162549i | ||||||||
0 | 0 | |||||||||
−100454. | − | 173991.i | −0.287247 | − | 0.497527i | |||||
0 | 0 | |||||||||
240265. | 0.666653 | 0.333327 | − | 0.942811i | ||||||
0.333327 | + | 0.942811i | ||||||||
0 | 0 | |||||||||
−218028. | −0.587212 | |||||||||
0 | 0 | |||||||||
38170.2 | + | 66112.7i | 0.0998238 | + | 0.172900i | |||||
0 | 0 | |||||||||
89650.1 | − | 155279.i | 0.227738 | − | 0.394454i | −0.729399 | − | 0.684088i | ||
0.957137 | + | 0.289634i | ||||||||
0 | 0 | |||||||||
−63529.4 | + | 200869.i | −0.156812 | + | 0.495812i | |||||
0 | 0 | |||||||||
231539. | − | 401037.i | 0.555509 | − | 0.962170i | |||||
0 | 0 | |||||||||
−287780. | − | 498449.i | −0.671317 | − | 1.16275i | −0.977531 | − | 0.210792i | ||
0.306214 | − | 0.951963i | ||||||||
0 | 0 | |||||||||
581006. | 1.31821 | 0.659105 | − | 0.752051i | ||||||
0.659105 | + | 0.752051i | ||||||||
0 | 0 | |||||||||
369880. | 0.816458 | |||||||||
0 | 0 | |||||||||
315648. | + | 546719.i | 0.678070 | + | 1.17445i | |||||
0 | 0 | |||||||||
383213. | − | 663744.i | 0.801376 | − | 1.38802i | |||||
0 | 0 | |||||||||
63787.5 | + | 69735.8i | 0.129892 | + | 0.142004i | |||||
0 | 0 | |||||||||
−330280. | + | 572062.i | −0.655087 | + | 1.13464i | 0.326785 | + | 0.945099i | ||
−0.981872 | + | 0.189545i | ||||||||
0 | 0 | |||||||||
278655. | + | 482645.i | 0.538485 | + | 0.932684i | 0.998986 | + | 0.0450243i | ||
−0.460501 | + | 0.887659i | ||||||||
0 | 0 | |||||||||
136459. | 0.256989 | |||||||||
0 | 0 | |||||||||
−761400. | −1.39781 | −0.698904 | − | 0.715216i | ||||||
−0.698904 | + | 0.715216i | ||||||||
0 | 0 | |||||||||
−67929.9 | − | 117658.i | −0.121598 | − | 0.210615i | 0.798800 | − | 0.601597i | ||
−0.920398 | + | 0.390982i | ||||||||
0 | 0 | |||||||||
227602. | − | 394218.i | 0.397361 | − | 0.688250i | |||||
0 | 0 | |||||||||
−128060. | − | 140002.i | −0.218109 | − | 0.238448i | |||||
0 | 0 | |||||||||
253750. | − | 439507.i | 0.421716 | − | 0.730434i | |||||
0 | 0 | |||||||||
−66099.2 | − | 114487.i | −0.107219 | − | 0.185708i | |||||
0 | 0 | |||||||||
−543232. | −0.860240 | |||||||||
0 | 0 | |||||||||
991157. | 1.53263 | 0.766313 | − | 0.642467i | ||||||
0.766313 | + | 0.642467i | ||||||||
0 | 0 | |||||||||
179868. | + | 311540.i | 0.271647 | + | 0.470506i | |||||
0 | 0 | |||||||||
285307. | − | 494167.i | 0.420937 | − | 0.729084i | |||||
0 | 0 | |||||||||
152951. | − | 483602.i | 0.220496 | − | 0.697170i | |||||
0 | 0 | |||||||||
250590. | − | 434034.i | 0.353064 | − | 0.611524i | |||||
0 | 0 | |||||||||
260283. | + | 450823.i | 0.358480 | + | 0.620906i | |||||
0 | 0 | |||||||||
−543344. | −0.731666 | −0.365833 | − | 0.930681i | ||||||
−0.365833 | + | 0.930681i | ||||||||
0 | 0 | |||||||||
−131630. | −0.173340 | |||||||||
0 | 0 | |||||||||
8.16704 | + | 14.1457i | 1.05196e−5 | + | 1.82205e-5i | 0.866031 | − | 0.499991i | ||
−0.866020 | + | 0.500009i | ||||||||
0 | 0 | |||||||||
38689.5 | − | 67012.2i | 0.0487534 | − | 0.0844433i | −0.840619 | − | 0.541627i | ||
0.889372 | + | 0.457184i | ||||||||
0 | 0 | |||||||||
−656705. | + | 144978.i | −0.809731 | + | 0.178760i | |||||
0 | 0 | |||||||||
51828.6 | − | 89769.9i | 0.0625432 | − | 0.108328i | −0.833058 | − | 0.553185i | ||
0.895602 | + | 0.444857i | ||||||||
0 | 0 | |||||||||
−131960. | − | 228561.i | −0.155874 | − | 0.269981i | |||||
0 | 0 | |||||||||
568362. | 0.657286 | |||||||||
0 | 0 | |||||||||
−689109. | −0.780356 | −0.390178 | − | 0.920739i | ||||||
−0.390178 | + | 0.920739i | ||||||||
0 | 0 | |||||||||
−110148. | − | 190782.i | −0.122161 | − | 0.211590i | 0.798458 | − | 0.602050i | ||
−0.920620 | + | 0.390460i | ||||||||
0 | 0 | |||||||||
−29524.5 | + | 51137.9i | −0.0320750 | + | 0.0555556i | |||||
0 | 0 | |||||||||
−532539. | − | 374297.i | −0.566809 | − | 0.398383i | |||||
0 | 0 | |||||||||
184485. | − | 319537.i | 0.192406 | − | 0.333257i | |||||
0 | 0 | |||||||||
205076. | + | 355201.i | 0.209612 | + | 0.363058i | |||||
0 | 0 | |||||||||
−1.43641e6 | −1.43912 | −0.719558 | − | 0.694433i | ||||||
−0.719558 | + | 0.694433i | ||||||||
0 | 0 | |||||||||
940714. | 0.923966 | |||||||||
0 | 0 | |||||||||
231741. | + | 401388.i | 0.223179 | + | 0.386557i | |||||
0 | 0 | |||||||||
454598. | − | 787388.i | 0.429334 | − | 0.743628i | −0.567480 | − | 0.823387i | ||
0.996814 | + | 0.0797589i | ||||||||
0 | 0 | |||||||||
2.06352e6 | − | 455553.i | 1.91143 | − | 0.421977i | |||||
0 | 0 | |||||||||
59273.5 | − | 102665.i | 0.0538592 | − | 0.0932868i | |||||
0 | 0 | |||||||||
374528. | + | 648702.i | 0.333884 | + | 0.578304i | 0.983270 | − | 0.182155i | ||
−0.649386 | + | 0.760459i | ||||||||
0 | 0 | |||||||||
−77897.4 | −0.0681410 | |||||||||
0 | 0 | |||||||||
141180. | 0.121198 | |||||||||
0 | 0 | |||||||||
−334972. | − | 580189.i | −0.282246 | − | 0.488865i | 0.689691 | − | 0.724104i | ||
−0.971938 | + | 0.235238i | ||||||||
0 | 0 | |||||||||
270330. | − | 468225.i | 0.223599 | − | 0.387285i | −0.732299 | − | 0.680983i | ||
0.955898 | + | 0.293698i | ||||||||
0 | 0 | |||||||||
137743. | − | 435519.i | 0.111857 | − | 0.353672i | |||||
0 | 0 | |||||||||
468334. | − | 811178.i | 0.373443 | − | 0.646821i | |||||
0 | 0 | |||||||||
200955. | + | 348064.i | 0.157362 | + | 0.272558i | 0.933916 | − | 0.357491i | ||
−0.776555 | + | 0.630050i | ||||||||
0 | 0 | |||||||||
316906. | 0.243736 | |||||||||
0 | 0 | |||||||||
−429139. | −0.324214 | −0.162107 | − | 0.986773i | ||||||
−0.162107 | + | 0.986773i | ||||||||
0 | 0 | |||||||||
−170463. | − | 295251.i | −0.126522 | − | 0.219142i | 0.795805 | − | 0.605553i | ||
−0.922327 | + | 0.386411i | ||||||||
0 | 0 | |||||||||
164255. | − | 284498.i | 0.119786 | − | 0.207476i | |||||
0 | 0 | |||||||||
−1.14658e6 | − | 1.25351e6i | −0.821678 | − | 0.898301i | |||||
0 | 0 | |||||||||
−174123. | + | 301590.i | −0.122634 | + | 0.212409i | |||||
0 | 0 | |||||||||
−14078.2 | − | 24384.2i | −0.00974575 | − | 0.0168801i | |||||
0 | 0 | |||||||||
−388847. | −0.264612 | −0.132306 | − | 0.991209i | ||||||
−0.132306 | + | 0.991209i | ||||||||
0 | 0 | |||||||||
−1.99273e6 | −1.33319 | |||||||||
0 | 0 | |||||||||
−210094. | − | 363894.i | −0.138205 | − | 0.239378i | |||||
0 | 0 | |||||||||
−319472. | + | 553342.i | −0.206659 | + | 0.357945i | |||||
0 | 0 | |||||||||
−1.28918e6 | − | 1.40940e6i | −0.820158 | − | 0.896640i | |||||
0 | 0 | |||||||||
760549. | − | 1.31731e6i | 0.475905 | − | 0.824292i | |||||
0 | 0 | |||||||||
−795840. | − | 1.37844e6i | −0.489865 | − | 0.848471i | |||||
0 | 0 | |||||||||
2.35747e6 | 1.42758 | 0.713789 | − | 0.700361i | ||||||
0.713789 | + | 0.700361i | ||||||||
0 | 0 | |||||||||
−1.01538e6 | −0.604969 | |||||||||
0 | 0 | |||||||||
−718314. | − | 1.24416e6i | −0.421127 | − | 0.729414i | 0.574923 | − | 0.818208i | ||
−0.996050 | + | 0.0887939i | ||||||||
0 | 0 | |||||||||
411400. | − | 712566.i | 0.237358 | − | 0.411116i | −0.722598 | − | 0.691269i | ||
0.959955 | + | 0.280153i | ||||||||
0 | 0 | |||||||||
122639. | − | 387762.i | 0.0696388 | − | 0.220186i | |||||
0 | 0 | |||||||||
883467. | − | 1.53021e6i | 0.493790 | − | 0.855269i | −0.506184 | − | 0.862425i | ||
0.999974 | + | 0.00715584i | ||||||||
0 | 0 | |||||||||
421786. | + | 730555.i | 0.232068 | + | 0.401954i | |||||
0 | 0 | |||||||||
200785. | 0.108760 | |||||||||
0 | 0 | |||||||||
1.25321e6 | 0.668370 | |||||||||
0 | 0 | |||||||||
318098. | + | 550962.i | 0.167052 | + | 0.289343i | |||||
0 | 0 | |||||||||
377188. | − | 653309.i | 0.195069 | − | 0.337869i | |||||
0 | 0 | |||||||||
−862675. | + | 190448.i | −0.439397 | + | 0.0970036i | |||||
0 | 0 | |||||||||
−1526.14 | + | 2643.35i | −0.000765638 | + | 0.00132612i | −0.866408 | − | 0.499337i | ||
0.865642 | + | 0.500663i | ||||||||
0 | 0 | |||||||||
660164. | + | 1.14344e6i | 0.326243 | + | 0.565069i | |||||
0 | 0 | |||||||||
−1.95885e6 | −0.953649 | |||||||||
0 | 0 | |||||||||
2.02939e6 | 0.973398 | 0.486699 | − | 0.873570i | ||||||
0.486699 | + | 0.873570i | ||||||||
0 | 0 | |||||||||
184178. | + | 319006.i | 0.0870439 | + | 0.150764i | |||||
0 | 0 | |||||||||
−1.12754e6 | + | 1.95295e6i | −0.525104 | + | 0.909507i | |||||
0 | 0 | |||||||||
−1.73215e6 | + | 1.32182e6i | −0.794969 | + | 0.606650i | |||||
0 | 0 | |||||||||
−284440. | + | 492665.i | −0.128660 | + | 0.222845i | |||||
0 | 0 | |||||||||
1.89109e6 | + | 3.27547e6i | 0.843119 | + | 1.46033i | 0.887245 | + | 0.461299i | ||
−0.0441252 | + | 0.999026i | ||||||||
0 | 0 | |||||||||
291147. | 0.127953 | 0.0639763 | − | 0.997951i | ||||||
0.0639763 | + | 0.997951i | ||||||||
0 | 0 | |||||||||
285397. | 0.123646 | |||||||||
0 | 0 | |||||||||
−192538. | − | 333486.i | −0.0822394 | − | 0.142443i | 0.821972 | − | 0.569528i | ||
−0.904212 | + | 0.427085i | ||||||||
0 | 0 | |||||||||
774013. | − | 1.34063e6i | 0.325970 | − | 0.564596i | |||||
0 | 0 | |||||||||
1.51498e6 | − | 334456.i | 0.629126 | − | 0.138889i | |||||
0 | 0 | |||||||||
−1.61507e6 | + | 2.79738e6i | −0.661385 | + | 1.14555i | 0.318866 | + | 0.947800i | ||
−0.980252 | + | 0.197753i | ||||||||
0 | 0 | |||||||||
793921. | + | 1.37511e6i | 0.320634 | + | 0.555354i | |||||
0 | 0 | |||||||||
1.54057e6 | 0.613641 | |||||||||
0 | 0 | |||||||||
−2.15669e6 | −0.847336 | |||||||||
0 | 0 | |||||||||
−239779. | − | 415310.i | −0.0929280 | − | 0.160956i | 0.815814 | − | 0.578314i | ||
−0.908742 | + | 0.417358i | ||||||||
0 | 0 | |||||||||
530705. | − | 919208.i | 0.202902 | − | 0.351437i | |||||
0 | 0 | |||||||||
−78630.6 | + | 248616.i | −0.0296590 | + | 0.0937766i | |||||
0 | 0 | |||||||||
−436333. | + | 755751.i | −0.162385 | + | 0.281259i | −0.935724 | − | 0.352734i | ||
0.773339 | + | 0.633993i | ||||||||
0 | 0 | |||||||||
827844. | + | 1.43387e6i | 0.303998 | + | 0.526540i | |||||
0 | 0 | |||||||||
−572965. | −0.207622 | |||||||||
0 | 0 | |||||||||
2.43493e6 | 0.870742 | 0.435371 | − | 0.900251i | ||||||
0.435371 | + | 0.900251i | ||||||||
0 | 0 | |||||||||
374715. | + | 649026.i | 0.132248 | + | 0.229060i | |||||
0 | 0 | |||||||||
−1.80584e6 | + | 3.12781e6i | −0.629047 | + | 1.08954i | 0.358696 | + | 0.933454i | ||
−0.987743 | + | 0.156087i | ||||||||
0 | 0 | |||||||||
1.95327e6 | + | 2.13541e6i | 0.671598 | + | 0.734226i | |||||
0 | 0 | |||||||||
596707. | − | 1.03353e6i | 0.202527 | − | 0.350788i | |||||
0 | 0 | |||||||||
87616.2 | + | 151756.i | 0.0293569 | + | 0.0508477i | 0.880331 | − | 0.474361i | ||
−0.850974 | + | 0.525208i | ||||||||
0 | 0 | |||||||||
−2.17018e6 | −0.717882 | |||||||||
0 | 0 | |||||||||
1.50187e6 | 0.490515 | |||||||||
0 | 0 | |||||||||
−1.22290e6 | − | 2.11812e6i | −0.394364 | − | 0.683058i | |||||
0 | 0 | |||||||||
−942577. | + | 1.63259e6i | −0.300152 | + | 0.519878i | −0.976170 | − | 0.217007i | ||
0.676019 | + | 0.736885i | ||||||||
0 | 0 | |||||||||
−742198. | − | 811409.i | −0.233393 | − | 0.255157i | |||||
0 | 0 | |||||||||
−669915. | + | 1.16033e6i | −0.208046 | + | 0.360346i | −0.951099 | − | 0.308887i | ||
0.743053 | + | 0.669232i | ||||||||
0 | 0 | |||||||||
−765839. | − | 1.32647e6i | −0.234895 | − | 0.406851i | |||||
0 | 0 | |||||||||
254101. | 0.0769785 | |||||||||
0 | 0 | |||||||||
−9.39535e6 | −2.81143 | |||||||||
0 | 0 | |||||||||
−3.29314e6 | − | 5.70388e6i | −0.973423 | − | 1.68602i | −0.685043 | − | 0.728503i | ||
−0.288381 | − | 0.957516i | ||||||||
0 | 0 | |||||||||
−172008. | + | 297926.i | −0.0502277 | + | 0.0869969i | |||||
0 | 0 | |||||||||
−2.01149e6 | + | 6.35996e6i | −0.580286 | + | 1.83476i | |||||
0 | 0 | |||||||||
882487. | − | 1.52851e6i | 0.251529 | − | 0.435661i | |||||
0 | 0 | |||||||||
478182. | + | 828236.i | 0.134665 | + | 0.233246i | |||||
0 | 0 | |||||||||
6.96869e6 | 1.93917 | 0.969585 | − | 0.244754i | ||||||
0.969585 | + | 0.244754i | ||||||||
0 | 0 | |||||||||
3.84041e6 | 1.05602 | 0.528010 | − | 0.849238i | ||||||
0.528010 | + | 0.849238i | ||||||||
0 | 0 | |||||||||
−275988. | − | 478025.i | −0.0749962 | − | 0.129897i | |||||
0 | 0 | |||||||||
−1.08042e6 | + | 1.87134e6i | −0.290149 | + | 0.502552i | |||||
0 | 0 | |||||||||
−5.20272e6 | + | 1.14858e6i | −1.38090 | + | 0.304854i | |||||
0 | 0 | |||||||||
−1.01543e6 | + | 1.75878e6i | −0.266384 | + | 0.461390i | |||||
0 | 0 | |||||||||
1.51818e6 | + | 2.62957e6i | 0.393668 | + | 0.681854i | 0.992930 | − | 0.118699i | ||
−0.599262 | + | 0.800553i | ||||||||
0 | 0 | |||||||||
−941529. | −0.241332 | −0.120666 | − | 0.992693i | ||||||
−0.120666 | + | 0.992693i | ||||||||
0 | 0 | |||||||||
−510135. | −0.129259 | |||||||||
0 | 0 | |||||||||
769096. | + | 1.33211e6i | 0.192653 | + | 0.333686i | |||||
0 | 0 | |||||||||
670546. | − | 1.16142e6i | 0.166061 | − | 0.287626i | −0.770971 | − | 0.636871i | ||
0.937031 | + | 0.349245i | ||||||||
0 | 0 | |||||||||
−1.11378e6 | − | 782823.i | −0.272711 | − | 0.191676i | |||||
0 | 0 | |||||||||
−386171. | + | 668867.i | −0.0934910 | + | 0.161931i | −0.908978 | − | 0.416844i | ||
0.815487 | + | 0.578776i | ||||||||
0 | 0 | |||||||||
−303765. | − | 526137.i | −0.0727174 | − | 0.125950i | |||||
0 | 0 | |||||||||
1.73300e6 | 0.410232 | |||||||||
0 | 0 | |||||||||
2.25684e6 | 0.528304 | 0.264152 | − | 0.964481i | ||||||
0.264152 | + | 0.964481i | ||||||||
0 | 0 | |||||||||
3.77646e6 | + | 6.54101e6i | 0.874265 | + | 1.51427i | |||||
0 | 0 | |||||||||
637644. | − | 1.10443e6i | 0.145993 | − | 0.252868i | |||||
0 | 0 | |||||||||
−1.91942e6 | + | 423742.i | −0.434653 | + | 0.0959561i | |||||
0 | 0 | |||||||||
−2.14235e6 | + | 3.71066e6i | −0.479844 | + | 0.831114i | −0.999733 | − | 0.0231196i | ||
0.519889 | + | 0.854234i | ||||||||
0 | 0 | |||||||||
484676. | + | 839483.i | 0.107379 | + | 0.185986i | |||||
0 | 0 | |||||||||
−3.10462e6 | −0.680387 | −0.340193 | − | 0.940355i | ||||||
−0.340193 | + | 0.940355i | ||||||||
0 | 0 | |||||||||
3.53386e6 | 0.766121 | 0.383060 | − | 0.923723i | ||||||
0.383060 | + | 0.923723i | ||||||||
0 | 0 | |||||||||
−681859. | − | 1.18102e6i | −0.146239 | − | 0.253293i | |||||
0 | 0 | |||||||||
1.36230e6 | − | 2.35957e6i | 0.289054 | − | 0.500657i | −0.684530 | − | 0.728985i | ||
0.973584 | + | 0.228328i | ||||||||
0 | 0 | |||||||||
−1.97728e6 | + | 6.25182e6i | −0.415085 | + | 1.31242i | |||||
0 | 0 | |||||||||
−2.54597e6 | + | 4.40975e6i | −0.528812 | + | 0.915928i | |||||
0 | 0 | |||||||||
4.24612e6 | + | 7.35449e6i | 0.872649 | + | 1.51147i | |||||
0 | 0 | |||||||||
1.53158e6 | 0.311461 | |||||||||
0 | 0 | |||||||||
−162919. | −0.0327850 | |||||||||
0 | 0 | |||||||||
489342. | + | 847566.i | 0.0974482 | + | 0.168785i | 0.910628 | − | 0.413228i | ||
−0.813180 | + | 0.582013i | ||||||||
0 | 0 | |||||||||
3.19072e6 | − | 5.52649e6i | 0.628819 | − | 1.08915i | |||||
0 | 0 | |||||||||
1.28526e6 | + | 1.40512e6i | 0.250682 | + | 0.274059i | |||||
0 | 0 | |||||||||
−60581.8 | + | 104931.i | −0.0116947 | + | 0.0202558i | |||||
0 | 0 | |||||||||
1.96372e6 | + | 3.40126e6i | 0.375195 | + | 0.649857i | 0.990356 | − | 0.138544i | ||
−0.615161 | + | 0.788401i | ||||||||
0 | 0 | |||||||||
3.87181e6 | 0.732220 | |||||||||
0 | 0 | |||||||||
−2.63241e6 | −0.492777 | −0.246388 | − | 0.969171i | ||||||
−0.246388 | + | 0.969171i | ||||||||
0 | 0 | |||||||||
−973037. | − | 1.68535e6i | −0.180307 | − | 0.312301i | |||||
0 | 0 | |||||||||
−904083. | + | 1.56592e6i | −0.165842 | + | 0.287247i | |||||
0 | 0 | |||||||||
−3.49743e6 | − | 3.82357e6i | −0.635123 | − | 0.694350i | |||||
0 | 0 | |||||||||
1.06272e6 | − | 1.84069e6i | 0.191059 | − | 0.330924i | −0.754542 | − | 0.656251i | ||
0.945601 | + | 0.325327i | ||||||||
0 | 0 | |||||||||
−1.08119e6 | − | 1.87268e6i | −0.192446 | − | 0.333327i | |||||
0 | 0 | |||||||||
−2.60929e6 | −0.459835 | −0.229917 | − | 0.973210i | ||||||
−0.229917 | + | 0.973210i | ||||||||
0 | 0 | |||||||||
−6.54564e6 | −1.14215 | |||||||||
0 | 0 | |||||||||
981124. | + | 1.69936e6i | 0.169513 | + | 0.293606i | |||||
0 | 0 | |||||||||
5.00911e6 | − | 8.67603e6i | 0.856970 | − | 1.48432i | −0.0178348 | − | 0.999841i | ||
0.874805 | − | 0.484475i | ||||||||
0 | 0 | |||||||||
−2.17699e6 | + | 6.88326e6i | −0.368811 | + | 1.16612i | |||||
0 | 0 | |||||||||
343532. | − | 595014.i | 0.0576333 | − | 0.0998238i | |||||
0 | 0 | |||||||||
2.18471e6 | + | 3.78403e6i | 0.362974 | + | 0.628689i | |||||
0 | 0 | |||||||||
3.92782e6 | 0.646287 | |||||||||
0 | 0 | |||||||||
−1.61370e6 | −0.262969 | |||||||||
0 | 0 | |||||||||
2.08970e6 | + | 3.61947e6i | 0.337280 | + | 0.584186i | 0.983920 | − | 0.178609i | ||
−0.646640 | + | 0.762795i | ||||||||
0 | 0 | |||||||||
1.80263e6 | − | 3.12224e6i | 0.288172 | − | 0.499128i | −0.685202 | − | 0.728353i | ||
0.973373 | + | 0.229225i | ||||||||
0 | 0 | |||||||||
1.85150e6 | − | 408746.i | 0.293174 | − | 0.0647225i | |||||
0 | 0 | |||||||||
2.60117e6 | − | 4.50536e6i | 0.407983 | − | 0.706648i | |||||
0 | 0 | |||||||||
1.88633e6 | + | 3.26722e6i | 0.293075 | + | 0.507621i | |||||
0 | 0 | |||||||||
−4.16770e6 | −0.641446 | |||||||||
0 | 0 | |||||||||
−5.13003e6 | −0.782172 | |||||||||
0 | 0 | |||||||||
−432013. | − | 748268.i | −0.0652547 | − | 0.113025i | |||||
0 | 0 | |||||||||
−2.59002e6 | + | 4.48604e6i | −0.387585 | + | 0.671317i | |||||
0 | 0 | |||||||||
8.78699e6 | − | 4.07850e6i | 1.30277 | − | 0.604684i | |||||
0 | 0 | |||||||||
3.34083e6 | − | 5.78648e6i | 0.490751 | − | 0.850005i | −0.509193 | − | 0.860653i | ||
0.999943 | + | 0.0106475i | ||||||||
0 | 0 | |||||||||
−2.61453e6 | − | 4.52850e6i | −0.380534 | − | 0.659105i | |||||
0 | 0 | |||||||||
−3.24625e6 | −0.468156 | |||||||||
0 | 0 | |||||||||
−8.69076e6 | −1.24191 | −0.620954 | − | 0.783847i | ||||||
−0.620954 | + | 0.783847i | ||||||||
0 | 0 | |||||||||
−1.66446e6 | − | 2.88293e6i | −0.235691 | − | 0.408229i | |||||
0 | 0 | |||||||||
−689676. | + | 1.19455e6i | −0.0967756 | + | 0.167620i | |||||
0 | 0 | |||||||||
−7.99456e6 | + | 1.76492e6i | −1.11168 | + | 0.245421i | |||||
0 | 0 | |||||||||
2.84084e6 | − | 4.92047e6i | 0.391484 | − | 0.678070i | |||||
0 | 0 | |||||||||
−3.12371e6 | − | 5.41042e6i | −0.426612 | − | 0.738913i | 0.569958 | − | 0.821674i | ||
−0.996569 | + | 0.0827611i | ||||||||
0 | 0 | |||||||||
−5.76803e6 | −0.780725 | |||||||||
0 | 0 | |||||||||
−6.89783e6 | −0.925349 | |||||||||
0 | 0 | |||||||||
−5.95223e6 | − | 1.03096e7i | −0.791423 | − | 1.37078i | −0.925086 | − | 0.379758i | ||
0.133663 | − | 0.991027i | ||||||||
0 | 0 | |||||||||
792560. | − | 1.37275e6i | 0.104451 | − | 0.180914i | |||||
0 | 0 | |||||||||
256493. | − | 810986.i | 0.0335057 | − | 0.105939i | |||||
0 | 0 | |||||||||
−10707.2 | + | 18545.4i | −0.00138642 | + | 0.00240135i | −0.866718 | − | 0.498799i | ||
0.865331 | + | 0.501200i | ||||||||
0 | 0 | |||||||||
3.55823e6 | + | 6.16304e6i | 0.456714 | + | 0.791051i | 0.998785 | − | 0.0492811i | ||
−0.542071 | + | 0.840333i | ||||||||
0 | 0 | |||||||||
5.94504e6 | 0.756429 | |||||||||
0 | 0 | |||||||||
−2.65223e6 | −0.334534 | |||||||||
0 | 0 | |||||||||
5.33259e6 | + | 9.23632e6i | 0.666805 | + | 1.15494i | 0.978793 | + | 0.204854i | ||
−0.311988 | + | 0.950086i | ||||||||
0 | 0 | |||||||||
2.50790e6 | − | 4.34380e6i | 0.310895 | − | 0.538485i | |||||
0 | 0 | |||||||||
−3.98758e6 | − | 4.35943e6i | −0.490083 | − | 0.535784i | |||||
0 | 0 | |||||||||
579659. | − | 1.00400e6i | 0.0706319 | − | 0.122338i | |||||
0 | 0 | |||||||||
−614065. | − | 1.06359e6i | −0.0741864 | − | 0.128495i | |||||
0 | 0 | |||||||||
1.30101e7 | 1.55843 | 0.779213 | − | 0.626759i | ||||||
0.779213 | + | 0.626759i | ||||||||
0 | 0 | |||||||||
−3.68735e6 | −0.437952 | |||||||||
0 | 0 | |||||||||
3.42630e6 | + | 5.93453e6i | 0.403512 | + | 0.698904i | |||||
0 | 0 | |||||||||
−2.13043e6 | + | 3.69002e6i | −0.248789 | + | 0.430915i | −0.963190 | − | 0.268821i | ||
0.714401 | + | 0.699736i | ||||||||
0 | 0 | |||||||||
−4.50608e6 | − | 4.92628e6i | −0.521803 | − | 0.570462i | |||||
0 | 0 | |||||||||
−611369. | + | 1.05892e6i | −0.0702049 | + | 0.121598i | |||||
0 | 0 | |||||||||
−6.89790e6 | − | 1.19475e7i | −0.785507 | − | 1.36054i | −0.928696 | − | 0.370842i | ||
0.143189 | − | 0.989695i | ||||||||
0 | 0 | |||||||||
4.99695e6 | 0.564311 | 0.282155 | − | 0.959369i | ||||||
0.282155 | + | 0.959369i | ||||||||
0 | 0 | |||||||||
−4.09683e6 | −0.458833 | |||||||||
0 | 0 | |||||||||
−3.31471e6 | − | 5.74125e6i | −0.368177 | − | 0.637702i | |||||
0 | 0 | |||||||||
−1.52473e6 | + | 2.64091e6i | −0.167966 | + | 0.290926i | −0.937705 | − | 0.347434i | ||
0.769739 | + | 0.638359i | ||||||||
0 | 0 | |||||||||
−514937. | + | 1.62814e6i | −0.0562614 | + | 0.177889i | |||||
0 | 0 | |||||||||
−1.33391e6 | + | 2.31040e6i | −0.144552 | + | 0.250372i | |||||
0 | 0 | |||||||||
3.51813e6 | + | 6.09357e6i | 0.378147 | + | 0.654969i | 0.990793 | − | 0.135388i | ||
−0.612646 | + | 0.790357i | ||||||||
0 | 0 | |||||||||
−4.56749e6 | −0.486956 | |||||||||
0 | 0 | |||||||||
1.00066e7 | 1.05822 | 0.529108 | − | 0.848554i | ||||||
0.529108 | + | 0.848554i | ||||||||
0 | 0 | |||||||||
−3.27533e6 | − | 5.67304e6i | −0.343581 | − | 0.595099i | 0.641514 | − | 0.767111i | ||
−0.985095 | + | 0.172012i | ||||||||
0 | 0 | |||||||||
−594893. | + | 1.03038e6i | −0.0619027 | + | 0.107219i | |||||
0 | 0 | |||||||||
−1.98583e6 | + | 438403.i | −0.204985 | + | 0.0452536i | |||||
0 | 0 | |||||||||
1.02325e6 | − | 1.77232e6i | 0.104781 | − | 0.181485i | |||||
0 | 0 | |||||||||
2.44455e6 | + | 4.23408e6i | 0.248330 | + | 0.430120i | |||||
0 | 0 | |||||||||
2.16746e7 | 2.18436 | |||||||||
0 | 0 | |||||||||
−2.22672e6 | −0.222635 | −0.111317 | − | 0.993785i | ||||||
−0.111317 | + | 0.993785i | ||||||||
0 | 0 | |||||||||
−4.46021e6 | − | 7.72531e6i | −0.442431 | − | 0.766313i | |||||
0 | 0 | |||||||||
1.61249e6 | − | 2.79291e6i | 0.158694 | − | 0.274867i | |||||
0 | 0 | |||||||||
−585084. | + | 6.55373e6i | −0.0571307 | + | 0.639941i | |||||
0 | 0 | |||||||||
1.61881e6 | − | 2.80386e6i | 0.156835 | − | 0.271647i | |||||
0 | 0 | |||||||||
7.96698e6 | + | 1.37992e7i | 0.765859 | + | 1.32651i | 0.939791 | + | 0.341749i | ||
−0.173932 | + | 0.984758i | ||||||||
0 | 0 | |||||||||
1.49933e7 | 1.43011 | 0.715056 | − | 0.699067i | ||||||
0.715056 | + | 0.699067i | ||||||||
0 | 0 | |||||||||
−5.13553e6 | −0.486056 | |||||||||
0 | 0 | |||||||||
6.49027e6 | + | 1.12415e7i | 0.609540 | + | 1.05575i | 0.991316 | + | 0.131500i | ||
−0.381776 | + | 0.924255i | ||||||||
0 | 0 | |||||||||
1.48285e7 | − | 2.56838e7i | 1.38193 | − | 2.39357i | |||||
0 | 0 | |||||||||
−4.45758e6 | + | 984079.i | −0.412237 | + | 0.0910075i | |||||
0 | 0 | |||||||||
8.27460e6 | − | 1.43320e7i | 0.759389 | − | 1.31530i | −0.183774 | − | 0.982969i | ||
0.943163 | − | 0.332332i | ||||||||
0 | 0 | |||||||||
−3.23145e6 | − | 5.59704e6i | −0.294303 | − | 0.509748i | |||||
0 | 0 | |||||||||
−4.51062e6 | −0.407683 | |||||||||
0 | 0 | |||||||||
−5.86879e6 | −0.526423 | −0.263212 | − | 0.964738i | ||||||
−0.263212 | + | 0.964738i | ||||||||
0 | 0 | |||||||||
−3.63843e6 | − | 6.30195e6i | −0.323900 | − | 0.561011i | 0.657389 | − | 0.753551i | ||
−0.981289 | + | 0.192540i | ||||||||
0 | 0 | |||||||||
2.34255e6 | − | 4.05741e6i | 0.206969 | − | 0.358480i | |||||
0 | 0 | |||||||||
−1.42696e6 | + | 4.51179e6i | −0.125129 | + | 0.395635i | |||||
0 | 0 | |||||||||
1.19431e6 | − | 2.06861e6i | 0.103945 | − | 0.180038i | |||||
0 | 0 | |||||||||
2.44505e6 | + | 4.23495e6i | 0.211214 | + | 0.365833i | |||||
0 | 0 | |||||||||
2.36884e7 | 2.03109 | |||||||||
0 | 0 | |||||||||
−1.82417e7 | −1.55248 | −0.776241 | − | 0.630437i | ||||||
−0.776241 | + | 0.630437i | ||||||||
0 | 0 | |||||||||
592334. | + | 1.02595e6i | 0.0500388 | + | 0.0866698i | |||||
0 | 0 | |||||||||
3.88203e6 | − | 6.72387e6i | 0.325527 | − | 0.563829i | −0.656092 | − | 0.754681i | ||
0.981619 | + | 0.190852i | ||||||||
0 | 0 | |||||||||
273743. | + | 299270.i | 0.0227860 | + | 0.0249109i | |||||
0 | 0 | |||||||||
73.5034 | − | 127.312i | 6.07351e−6 | − | 1.05196e-5i | |||||
0 | 0 | |||||||||
4.28162e6 | + | 7.41598e6i | 0.351201 | + | 0.608299i | 0.986460 | − | 0.164001i | ||
−0.635259 | + | 0.772299i | ||||||||
0 | 0 | |||||||||
1.48038e6 | 0.120544 | |||||||||
0 | 0 | |||||||||
−696411. | −0.0562955 | |||||||||
0 | 0 | |||||||||
393712. | + | 681928.i | 0.0315959 | + | 0.0547256i | |||||
0 | 0 | |||||||||
8.22547e6 | − | 1.42469e7i | 0.655338 | − | 1.13508i | −0.326471 | − | 0.945207i | ||
0.981809 | − | 0.189872i | ||||||||
0 | 0 | |||||||||
4.08516e6 | + | 4.46611e6i | 0.323129 | + | 0.353262i | |||||
0 | 0 | |||||||||
2.05773e6 | − | 3.56409e6i | 0.161594 | − | 0.279890i | |||||
0 | 0 | |||||||||
−8.71208e6 | − | 1.50898e7i | −0.679266 | − | 1.17652i | |||||
0 | 0 | |||||||||
−932916. | −0.0722187 | |||||||||
0 | 0 | |||||||||
−1.66928e7 | −1.28302 | −0.641512 | − | 0.767113i | ||||||
−0.641512 | + | 0.767113i | ||||||||
0 | 0 | |||||||||
−7.68132e6 | − | 1.33044e7i | −0.586202 | − | 1.01533i | |||||
0 | 0 | |||||||||
−1.18764e6 | + | 2.05705e6i | −0.0899937 | + | 0.155874i | |||||
0 | 0 | |||||||||
−6.60725e6 | + | 2.08909e7i | −0.497132 | + | 1.57184i | |||||
0 | 0 | |||||||||
−2.80890e6 | + | 4.86515e6i | −0.209855 | + | 0.363480i | −0.951669 | − | 0.307126i | ||
0.741813 | + | 0.670606i | ||||||||
0 | 0 | |||||||||
−2.55763e6 | − | 4.42994e6i | −0.189742 | − | 0.328643i | |||||
0 | 0 | |||||||||
6.38537e6 | 0.470395 | |||||||||
0 | 0 | |||||||||
8.73927e6 | 0.639308 | |||||||||
0 | 0 | |||||||||
3.10099e6 | + | 5.37107e6i | 0.225269 | + | 0.390178i | |||||
0 | 0 | |||||||||
5.18592e6 | − | 8.98227e6i | 0.374113 | − | 0.647983i | −0.616081 | − | 0.787683i | ||
0.990194 | + | 0.139700i | ||||||||
0 | 0 | |||||||||
1.42823e7 | − | 3.15303e6i | 1.02320 | − | 0.225887i | |||||
0 | 0 | |||||||||
−991332. | + | 1.71704e6i | −0.0705299 | + | 0.122161i | |||||
0 | 0 | |||||||||
−1.18917e6 | − | 2.05971e6i | −0.0840233 | − | 0.145533i | |||||
0 | 0 | |||||||||
−1.15369e7 | −0.809565 | −0.404783 | − | 0.914413i | ||||||
−0.404783 | + | 0.914413i | ||||||||
0 | 0 | |||||||||
531441. | 0.0370370 | |||||||||
0 | 0 | |||||||||
−9.79557e6 | − | 1.69664e7i | −0.678010 | − | 1.17435i | |||||
0 | 0 | |||||||||
−7.47349e6 | + | 1.29445e7i | −0.513764 | + | 0.889865i | 0.486109 | + | 0.873898i | ||
−0.999873 | + | 0.0159667i | ||||||||
0 | 0 | |||||||||
−520925. | + | 5.83507e6i | −0.0355678 | + | 0.398408i | |||||
0 | 0 | |||||||||
1.45764e7 | − | 2.52470e7i | 0.988510 | − | 1.71215i | |||||
0 | 0 | |||||||||
4.50682e6 | + | 7.80604e6i | 0.303570 | + | 0.525799i | 0.976942 | − | 0.213505i | ||
−0.673372 | + | 0.739304i | ||||||||
0 | 0 | |||||||||
−3.32073e6 | −0.222171 | |||||||||
0 | 0 | |||||||||
2.10239e7 | 1.39714 | 0.698571 | − | 0.715541i | ||||||
0.698571 | + | 0.715541i | ||||||||
0 | 0 | |||||||||
−3.72875e6 | − | 6.45838e6i | −0.246134 | − | 0.426317i | |||||
0 | 0 | |||||||||
1.84568e6 | − | 3.19681e6i | 0.121019 | − | 0.209612i | |||||
0 | 0 | |||||||||
−2.82424e6 | + | 623493.i | −0.183949 | + | 0.0406094i | |||||
0 | 0 | |||||||||
2.02110e6 | − | 3.50064e6i | 0.130764 | − | 0.226489i | −0.793207 | − | 0.608952i | ||
0.923971 | + | 0.382462i | ||||||||
0 | 0 | |||||||||
6.46387e6 | + | 1.11957e7i | 0.415437 | + | 0.719558i | |||||
0 | 0 | |||||||||
−5.48786e6 | −0.350377 | |||||||||
0 | 0 | |||||||||
−1.82059e7 | −1.15471 | −0.577353 | − | 0.816495i | ||||||
−0.577353 | + | 0.816495i | ||||||||
0 | 0 | |||||||||
−4.23321e6 | − | 7.33214e6i | −0.266726 | − | 0.461983i | |||||
0 | 0 | |||||||||
9.45999e6 | − | 1.63852e7i | 0.592146 | − | 1.02563i | −0.401797 | − | 0.915729i | ||
0.993943 | − | 0.109898i | ||||||||
0 | 0 | |||||||||
−3.27681e6 | + | 1.03607e7i | −0.203770 | + | 0.644283i | |||||
0 | 0 | |||||||||
2.08567e6 | − | 3.61249e6i | 0.128852 | − | 0.223179i | |||||
0 | 0 | |||||||||
1.00717e7 | + | 1.74447e7i | 0.618180 | + | 1.07072i | |||||
0 | 0 | |||||||||
−1.12831e7 | −0.688037 | −0.344019 | − | 0.938963i | ||||||
−0.344019 | + | 0.938963i | ||||||||
0 | 0 | |||||||||
−8.18277e6 | −0.495752 | |||||||||
0 | 0 | |||||||||
1.84282e6 | + | 3.19186e6i | 0.110926 | + | 0.192130i | 0.916144 | − | 0.400849i | ||
−0.805218 | + | 0.592979i | ||||||||
0 | 0 | |||||||||
3.17896e6 | − | 5.50611e6i | 0.190121 | − | 0.329299i | |||||
0 | 0 | |||||||||
−1.28365e7 | − | 1.40335e7i | −0.762772 | − | 0.833902i | |||||
0 | 0 | |||||||||
−6.17501e6 | + | 1.06954e7i | −0.364581 | + | 0.631472i | |||||
0 | 0 | |||||||||
1.15193e7 | + | 1.99521e7i | 0.675771 | + | 1.17047i | |||||
0 | 0 | |||||||||
−1.06692e6 | −0.0621912 | |||||||||
0 | 0 | |||||||||
2.19118e7 | 1.26912 | |||||||||
0 | 0 | |||||||||
−7.03741e6 | − | 1.21891e7i | −0.405019 | − | 0.701514i | 0.589304 | − | 0.807911i | ||
−0.994324 | + | 0.106397i | ||||||||
0 | 0 | |||||||||
3.37076e6 | − | 5.83832e6i | 0.192768 | − | 0.333884i | |||||
0 | 0 | |||||||||
−3.58124e6 | − | 3.91519e6i | −0.203513 | − | 0.222491i | |||||
0 | 0 | |||||||||
−8.04472e6 | + | 1.39339e7i | −0.454284 | + | 0.786844i | |||||
0 | 0 | |||||||||
350538. | + | 607150.i | 0.0196706 | + | 0.0340705i | |||||
0 | 0 | |||||||||
−1.75191e7 | −0.976937 | −0.488469 | − | 0.872582i | ||||||
−0.488469 | + | 0.872582i | ||||||||
0 | 0 | |||||||||
−9.06127e6 | −0.502137 | |||||||||
0 | 0 | |||||||||
−635311. | − | 1.10039e6i | −0.0349869 | − | 0.0605990i | |||||
0 | 0 | |||||||||
1.60486e7 | − | 2.77970e7i | 0.878311 | − | 1.52128i | |||||
0 | 0 | |||||||||
2.47106e6 | − | 7.81306e6i | 0.134398 | − | 0.424944i | |||||
0 | 0 | |||||||||
−3.01475e6 | + | 5.22170e6i | −0.162955 | + | 0.282246i | |||||
0 | 0 | |||||||||
−407261. | − | 705396.i | −0.0218777 | − | 0.0378932i | 0.854879 | − | 0.518827i | ||
−0.876757 | + | 0.480934i | ||||||||
0 | 0 | |||||||||
−1.26533e7 | −0.675540 | −0.337770 | − | 0.941229i | ||||||
−0.337770 | + | 0.941229i | ||||||||
0 | 0 | |||||||||
−4.86593e6 | −0.258190 | |||||||||
0 | 0 | |||||||||
−8.33064e6 | − | 1.44291e7i | −0.439324 | − | 0.760931i | |||||
0 | 0 | |||||||||
−6.94297e6 | + | 1.20256e7i | −0.363907 | + | 0.630305i | |||||
0 | 0 | |||||||||
−4.01438e6 | + | 886236.i | −0.209126 | + | 0.0461678i | |||||
0 | 0 | |||||||||
−2.13697e6 | + | 3.70133e6i | −0.110647 | + | 0.191646i | −0.916031 | − | 0.401107i | ||
0.805384 | + | 0.592753i | ||||||||
0 | 0 | |||||||||
8.52317e6 | + | 1.47626e7i | 0.438633 | + | 0.759735i | 0.997584 | − | 0.0694656i | ||
−0.558951 | + | 0.829201i | ||||||||
0 | 0 | |||||||||
−8.43001e6 | −0.431214 | |||||||||
0 | 0 | |||||||||
−2.60828e6 | −0.132614 | −0.0663071 | − | 0.997799i | ||||||
−0.0663071 | + | 0.997799i | ||||||||
0 | 0 | |||||||||
−1.06932e7 | − | 1.85212e7i | −0.540409 | − | 0.936016i | −0.998880 | − | 0.0473066i | ||
0.458471 | − | 0.888709i | ||||||||
0 | 0 | |||||||||
1.80859e6 | − | 3.13257e6i | 0.0908528 | − | 0.157362i | |||||
0 | 0 | |||||||||
−2.02711e7 | + | 9.40887e6i | −1.01220 | + | 0.469813i | |||||
0 | 0 | |||||||||
−4.65263e6 | + | 8.05859e6i | −0.230931 | + | 0.399984i | |||||
0 | 0 | |||||||||
−1.42608e6 | − | 2.47004e6i | −0.0703605 | − | 0.121868i | |||||
0 | 0 | |||||||||
−771393. | −0.0378330 | −0.0189165 | − | 0.999821i | ||||||
−0.0189165 | + | 0.999821i | ||||||||
0 | 0 | |||||||||
−1.83692e7 | −0.895571 | |||||||||
0 | 0 | |||||||||
1.93112e6 | + | 3.34480e6i | 0.0935925 | + | 0.162107i | |||||
0 | 0 | |||||||||
4.22200e6 | − | 7.31272e6i | 0.203412 | − | 0.352320i | |||||
0 | 0 | |||||||||
−2.16696e7 | + | 4.78388e6i | −1.03787 | + | 0.229125i | |||||
0 | 0 | |||||||||
−1.53417e6 | + | 2.65726e6i | −0.0730474 | + | 0.126522i | |||||
0 | 0 | |||||||||
1.33017e7 | + | 2.30393e7i | 0.629628 | + | 1.09055i | |||||
0 | 0 | |||||||||
2.94032e7 | 1.38364 | 0.691818 | − | 0.722072i | ||||||
0.691818 | + | 0.722072i | ||||||||
0 | 0 | |||||||||
−2.95659e6 | −0.138317 | |||||||||
0 | 0 | |||||||||
1.32505e7 | + | 2.29505e7i | 0.616283 | + | 1.06743i | 0.990158 | + | 0.139954i | ||
−0.373875 | + | 0.927479i | ||||||||
0 | 0 | |||||||||
−1.83759e7 | + | 3.18281e7i | −0.849702 | + | 1.47173i | 0.0317727 | + | 0.999495i | ||
−0.881475 | + | 0.472232i | ||||||||
0 | 0 | |||||||||
−4.61048e6 | + | 1.45775e7i | −0.211952 | + | 0.670156i | |||||
0 | 0 | |||||||||
5.90946e6 | − | 1.02355e7i | 0.270098 | − | 0.467823i | −0.698789 | − | 0.715328i | ||
0.968887 | + | 0.247505i | ||||||||
0 | 0 | |||||||||
3.47207e6 | + | 6.01379e6i | 0.157778 | + | 0.273280i | |||||
0 | 0 | |||||||||
3.13421e6 | 0.141606 | |||||||||
0 | 0 | |||||||||
3.63998e7 | 1.63512 | |||||||||
0 | 0 | |||||||||
9.90046e6 | + | 1.71481e7i | 0.442191 | + | 0.765897i | |||||
0 | 0 | |||||||||
−126704. | + | 219458.i | −0.00562671 | + | 0.00974575i | |||||
0 | 0 | |||||||||
−1.60970e7 | − | 1.75980e7i | −0.710762 | − | 0.777042i | |||||
0 | 0 | |||||||||
−3.96754e6 | + | 6.87199e6i | −0.174190 | + | 0.301706i | −0.939881 | − | 0.341503i | ||
0.765691 | + | 0.643209i | ||||||||
0 | 0 | |||||||||
1.74981e6 | + | 3.03077e6i | 0.0763870 | + | 0.132306i | |||||
0 | 0 | |||||||||
4.20152e7 | 1.82375 | 0.911877 | − | 0.410464i | ||||||
0.911877 | + | 0.410464i | ||||||||
0 | 0 | |||||||||
−2.12461e7 | −0.917016 | −0.458508 | − | 0.888690i | ||||||
−0.458508 | + | 0.888690i | ||||||||
0 | 0 | |||||||||
8.96729e6 | + | 1.55318e7i | 0.384860 | + | 0.666597i | |||||
0 | 0 | |||||||||
9.42452e6 | − | 1.63238e7i | 0.402208 | − | 0.696644i | −0.591784 | − | 0.806096i | ||
0.993992 | + | 0.109452i | ||||||||
0 | 0 | |||||||||
−7.28613e6 | − | 7.96558e6i | −0.309202 | − | 0.338036i | |||||
0 | 0 | |||||||||
−1.89085e6 | + | 3.27504e6i | −0.0797925 | + | 0.138205i | |||||
0 | 0 | |||||||||
3.21125e6 | + | 5.56205e6i | 0.134755 | + | 0.233403i | |||||
0 | 0 | |||||||||
2.22909e7 | 0.930186 | |||||||||
0 | 0 | |||||||||
5.75050e6 | 0.238630 | |||||||||
0 | 0 | |||||||||
2.86300e6 | + | 4.95886e6i | 0.118147 | + | 0.204636i | |||||
0 | 0 | |||||||||
−1.33724e6 | + | 2.31617e6i | −0.0548780 | + | 0.0950514i | |||||
0 | 0 | |||||||||
−5.18387e6 | + | 1.63905e7i | −0.211561 | + | 0.668917i | |||||
0 | 0 | |||||||||
−1.12509e7 | + | 1.94872e7i | −0.456632 | + | 0.790910i | |||||
0 | 0 | |||||||||
−3.09723e6 | − | 5.36456e6i | −0.125013 | − | 0.216529i | 0.796725 | − | 0.604342i | ||
−0.921738 | + | 0.387813i | ||||||||
0 | 0 | |||||||||
−1.36899e7 | −0.549528 | |||||||||
0 | 0 | |||||||||
2.50171e7 | 0.998712 | 0.499356 | − | 0.866397i | ||||||
0.499356 | + | 0.866397i | ||||||||
0 | 0 | |||||||||
1.31337e7 | + | 2.27483e7i | 0.521448 | + | 0.903174i | |||||
0 | 0 | |||||||||
−7.16256e6 | + | 1.24059e7i | −0.282824 | + | 0.489865i | |||||
0 | 0 | |||||||||
−2.11253e7 | + | 4.66373e6i | −0.829620 | + | 0.183151i | |||||
0 | 0 | |||||||||
7.74961e6 | − | 1.34227e7i | 0.302685 | − | 0.524266i | −0.674058 | − | 0.738678i | ||
0.976743 | + | 0.214412i | ||||||||
0 | 0 | |||||||||
−1.06086e7 | − | 1.83746e7i | −0.412106 | − | 0.713789i | |||||
0 | 0 | |||||||||
−1.56481e7 | −0.604587 | |||||||||
0 | 0 | |||||||||
2.64890e7 | 1.01791 | |||||||||
0 | 0 | |||||||||
4.56921e6 | + | 7.91411e6i | 0.174639 | + | 0.302484i | |||||
0 | 0 | |||||||||
−1.87643e7 | + | 3.25007e7i | −0.713333 | + | 1.23553i | 0.250266 | + | 0.968177i | ||
−0.963599 | + | 0.267352i | ||||||||
0 | 0 | |||||||||
1.29594e7 | + | 9.10852e6i | 0.490015 | + | 0.344408i | |||||
0 | 0 | |||||||||
−6.46483e6 | + | 1.11974e7i | −0.243138 | + | 0.421127i | |||||
0 | 0 | |||||||||
1.48415e7 | + | 2.57062e7i | 0.555198 | + | 0.961632i | |||||
0 | 0 | |||||||||
−1.08298e7 | −0.402969 | −0.201485 | − | 0.979492i | ||||||
−0.201485 | + | 0.979492i | ||||||||
0 | 0 | |||||||||
−7.40520e6 | −0.274077 | |||||||||
0 | 0 | |||||||||
−1.62295e7 | − | 2.81104e7i | −0.597492 | − | 1.03489i | −0.993190 | − | 0.116505i | ||
0.395699 | − | 0.918380i | ||||||||
0 | 0 | |||||||||
1.06932e7 | − | 1.85212e7i | 0.391589 | − | 0.678251i | |||||
0 | 0 | |||||||||
−3.57418e6 | + | 789054.i | −0.130196 | + | 0.0287427i | |||||
0 | 0 | |||||||||
3.76939e6 | − | 6.52877e6i | 0.136583 | − | 0.236568i | −0.789618 | − | 0.613598i | ||
0.926201 | + | 0.377030i | ||||||||
0 | 0 | |||||||||
1.09004e7 | + | 1.88801e7i | 0.392896 | + | 0.680516i | |||||
0 | 0 | |||||||||
−1.59024e7 | −0.570180 | |||||||||
0 | 0 | |||||||||
−3.01356e7 | −1.07485 | −0.537424 | − | 0.843312i | ||||||
−0.537424 | + | 0.843312i | ||||||||
0 | 0 | |||||||||
−1.27914e7 | − | 2.21554e7i | −0.453848 | − | 0.786089i | |||||
0 | 0 | |||||||||
3.79607e6 | − | 6.57499e6i | 0.133985 | − | 0.232068i | |||||
0 | 0 | |||||||||
1.49431e6 | − | 4.72474e6i | 0.0524680 | − | 0.165894i | |||||
0 | 0 | |||||||||
6.66107e6 | − | 1.15373e7i | 0.232667 | − | 0.402992i | |||||
0 | 0 | |||||||||
−903534. | − | 1.56497e6i | −0.0313963 | − | 0.0543800i | |||||
0 | 0 | |||||||||
−2.15841e7 | −0.746132 | |||||||||
0 | 0 | |||||||||
−2.88021e6 | −0.0990509 | −0.0495255 | − | 0.998773i | ||||||
−0.0495255 | + | 0.998773i | ||||||||
0 | 0 | |||||||||
−5.63943e6 | − | 9.76779e6i | −0.192942 | − | 0.334185i | |||||
0 | 0 | |||||||||
−1.37245e7 | + | 2.37715e7i | −0.467142 | + | 0.809113i | −0.999295 | − | 0.0375347i | ||
0.532154 | + | 0.846648i | ||||||||
0 | 0 | |||||||||
−9.29799e6 | − | 1.01650e7i | −0.314852 | − | 0.344213i | |||||
0 | 0 | |||||||||
2.86288e6 | − | 4.95866e6i | 0.0964478 | − | 0.167052i | |||||
0 | 0 | |||||||||
2.94262e7 | + | 5.09676e7i | 0.986274 | + | 1.70828i | 0.636133 | + | 0.771579i | ||
0.350141 | + | 0.936697i | ||||||||
0 | 0 | |||||||||
9.04164e6 | 0.301502 | |||||||||
0 | 0 | |||||||||
−6.78938e6 | −0.225246 | |||||||||
0 | 0 | |||||||||
9.30384e6 | + | 1.61147e7i | 0.307099 | + | 0.531911i | 0.977726 | − | 0.209883i | ||
−0.670627 | + | 0.741794i | ||||||||
0 | 0 | |||||||||
1.47442e7 | − | 2.55376e7i | 0.484205 | − | 0.838668i | |||||
0 | 0 | |||||||||
5.36643e6 | + | 5.86687e6i | 0.175345 | + | 0.191696i | |||||
0 | 0 | |||||||||
1.20231e7 | − | 2.08246e7i | 0.390865 | − | 0.676997i | |||||
0 | 0 | |||||||||
1.23577e7 | + | 2.14041e7i | 0.399718 | + | 0.692331i | 0.993691 | − | 0.112154i | ||
−0.593973 | + | 0.804485i | ||||||||
0 | 0 | |||||||||
27470.5 | 0.000884083 | |||||||||
0 | 0 | |||||||||
5.26172e6 | 0.168488 | |||||||||
0 | 0 | |||||||||
8.97906e6 | + | 1.55522e7i | 0.286084 | + | 0.495511i | 0.972871 | − | 0.231347i | ||
−0.686788 | + | 0.726858i | ||||||||
0 | 0 | |||||||||
5.94147e6 | − | 1.02909e7i | 0.188356 | − | 0.326243i |
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 336.6.q.e.289.1 | 4 | ||
4.3 | odd | 2 | 21.6.e.b.16.1 | yes | 4 | ||
7.4 | even | 3 | inner | 336.6.q.e.193.1 | 4 | ||
12.11 | even | 2 | 63.6.e.c.37.2 | 4 | |||
28.3 | even | 6 | 147.6.e.l.67.1 | 4 | |||
28.11 | odd | 6 | 21.6.e.b.4.1 | ✓ | 4 | ||
28.19 | even | 6 | 147.6.a.k.1.2 | 2 | |||
28.23 | odd | 6 | 147.6.a.i.1.2 | 2 | |||
28.27 | even | 2 | 147.6.e.l.79.1 | 4 | |||
84.11 | even | 6 | 63.6.e.c.46.2 | 4 | |||
84.23 | even | 6 | 441.6.a.t.1.1 | 2 | |||
84.47 | odd | 6 | 441.6.a.s.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.6.e.b.4.1 | ✓ | 4 | 28.11 | odd | 6 | ||
21.6.e.b.16.1 | yes | 4 | 4.3 | odd | 2 | ||
63.6.e.c.37.2 | 4 | 12.11 | even | 2 | |||
63.6.e.c.46.2 | 4 | 84.11 | even | 6 | |||
147.6.a.i.1.2 | 2 | 28.23 | odd | 6 | |||
147.6.a.k.1.2 | 2 | 28.19 | even | 6 | |||
147.6.e.l.67.1 | 4 | 28.3 | even | 6 | |||
147.6.e.l.79.1 | 4 | 28.27 | even | 2 | |||
336.6.q.e.193.1 | 4 | 7.4 | even | 3 | inner | ||
336.6.q.e.289.1 | 4 | 1.1 | even | 1 | trivial | ||
441.6.a.s.1.1 | 2 | 84.47 | odd | 6 | |||
441.6.a.t.1.1 | 2 | 84.23 | even | 6 |