Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [560,4,Mod(81,560)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(560, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("560.81");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 560.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 35) |
Sato-Tate group: |
Embedding invariants
Embedding label | 81.1 | ||
Root | of defining polynomial | ||
Character | 560.81 | ||
Dual form | 560.4.q.n.401.1 |
-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 | |||||||||
−4.48397 | + | 7.76647i | −0.862941 | + | 1.49466i | 0.00613580 | + | 0.999981i | ||
−0.869077 | + | 0.494677i | ||||||||
0 | 0 | |||||||||
2.50000 | + | 4.33013i | 0.223607 | + | 0.387298i | |||||
0 | 0 | |||||||||
−12.3509 | − | 13.8005i | −0.666887 | − | 0.745159i | |||||
0 | 0 | |||||||||
−26.7120 | − | 46.2666i | −0.989335 | − | 1.71358i | |||||
0 | 0 | |||||||||
11.5560 | − | 20.0155i | 0.316751 | − | 0.548628i | −0.663057 | − | 0.748569i | ||
0.979808 | + | 0.199940i | ||||||||
0 | 0 | |||||||||
61.0473 | 1.30242 | 0.651211 | − | 0.758897i | ||||||
0.651211 | + | 0.758897i | ||||||||
0 | 0 | |||||||||
−44.8397 | −0.771838 | |||||||||
0 | 0 | |||||||||
−0.344154 | + | 0.596093i | −0.00490998 | + | 0.00850434i | −0.868470 | − | 0.495742i | ||
0.863560 | + | 0.504246i | ||||||||
0 | 0 | |||||||||
31.6124 | + | 54.7542i | 0.381704 | + | 0.661130i | 0.991306 | − | 0.131577i | ||
−0.609602 | + | 0.792707i | ||||||||
0 | 0 | |||||||||
162.563 | − | 34.0419i | 1.68924 | − | 0.353740i | |||||
0 | 0 | |||||||||
62.2508 | + | 107.822i | 0.564356 | + | 0.977493i | 0.997109 | + | 0.0759809i | ||
−0.432753 | + | 0.901512i | ||||||||
0 | 0 | |||||||||
−12.5000 | + | 21.6506i | −0.100000 | + | 0.173205i | |||||
0 | 0 | |||||||||
236.970 | 1.68907 | |||||||||
0 | 0 | |||||||||
104.167 | 0.667011 | 0.333506 | − | 0.942748i | ||||||
0.333506 | + | 0.942748i | ||||||||
0 | 0 | |||||||||
140.011 | − | 242.506i | 0.811185 | − | 1.40501i | −0.100850 | − | 0.994902i | ||
0.912035 | − | 0.410112i | ||||||||
0 | 0 | |||||||||
103.633 | + | 179.498i | 0.546674 | + | 0.946868i | |||||
0 | 0 | |||||||||
28.8807 | − | 87.9824i | 0.139478 | − | 0.424907i | |||||
0 | 0 | |||||||||
131.936 | + | 228.519i | 0.586219 | + | 1.01536i | 0.994722 | + | 0.102604i | ||
−0.408504 | + | 0.912757i | ||||||||
0 | 0 | |||||||||
−273.735 | + | 474.122i | −1.12391 | + | 1.94668i | |||||
0 | 0 | |||||||||
−243.366 | −0.927009 | −0.463505 | − | 0.886095i | ||||||
−0.463505 | + | 0.886095i | ||||||||
0 | 0 | |||||||||
−172.541 | −0.611913 | −0.305956 | − | 0.952046i | ||||||
−0.305956 | + | 0.952046i | ||||||||
0 | 0 | |||||||||
133.560 | − | 231.333i | 0.442444 | − | 0.766336i | |||||
0 | 0 | |||||||||
−53.6907 | − | 92.9951i | −0.166630 | − | 0.288611i | 0.770603 | − | 0.637315i | ||
−0.937233 | + | 0.348704i | ||||||||
0 | 0 | |||||||||
−37.9094 | + | 340.899i | −0.110523 | + | 0.993874i | |||||
0 | 0 | |||||||||
−3.08636 | − | 5.34573i | −0.00847405 | − | 0.0146775i | |||||
0 | 0 | |||||||||
−22.4043 | + | 38.8054i | −0.0580654 | + | 0.100572i | −0.893597 | − | 0.448870i | ||
0.835532 | + | 0.549443i | ||||||||
0 | 0 | |||||||||
115.560 | 0.283310 | |||||||||
0 | 0 | |||||||||
−566.996 | −1.31755 | |||||||||
0 | 0 | |||||||||
228.623 | − | 395.986i | 0.504477 | − | 0.873780i | −0.495509 | − | 0.868603i | ||
0.999987 | − | 0.00517746i | ||||||||
0 | 0 | |||||||||
−236.901 | − | 410.324i | −0.497247 | − | 0.861256i | 0.502748 | − | 0.864433i | ||
−0.999995 | + | 0.00317642i | ||||||||
0 | 0 | |||||||||
−308.586 | + | 940.076i | −0.617113 | + | 1.87998i | |||||
0 | 0 | |||||||||
152.618 | + | 264.343i | 0.291230 | + | 0.504426i | |||||
0 | 0 | |||||||||
−114.727 | + | 198.713i | −0.209196 | + | 0.362338i | −0.951461 | − | 0.307768i | ||
0.742266 | + | 0.670106i | ||||||||
0 | 0 | |||||||||
−1116.52 | −1.94802 | |||||||||
0 | 0 | |||||||||
−407.688 | −0.681460 | −0.340730 | − | 0.940161i | ||||||
−0.340730 | + | 0.940161i | ||||||||
0 | 0 | |||||||||
174.238 | − | 301.789i | 0.279356 | − | 0.483859i | −0.691869 | − | 0.722023i | ||
0.971225 | + | 0.238165i | ||||||||
0 | 0 | |||||||||
−112.099 | − | 194.162i | −0.172588 | − | 0.298932i | |||||
0 | 0 | |||||||||
−418.952 | + | 87.7317i | −0.620052 | + | 0.129844i | |||||
0 | 0 | |||||||||
420.068 | + | 727.579i | 0.598244 | + | 1.03619i | 0.993080 | + | 0.117438i | ||
−0.394836 | + | 0.918752i | ||||||||
0 | 0 | |||||||||
−341.342 | + | 591.221i | −0.468233 | + | 0.811003i | |||||
0 | 0 | |||||||||
885.652 | 1.17124 | 0.585620 | − | 0.810586i | ||||||
0.585620 | + | 0.810586i | ||||||||
0 | 0 | |||||||||
−3.44154 | −0.00439162 | |||||||||
0 | 0 | |||||||||
−467.082 | + | 809.010i | −0.575592 | + | 0.996954i | |||||
0 | 0 | |||||||||
428.048 | + | 741.401i | 0.509809 | + | 0.883015i | 0.999935 | + | 0.0113636i | ||
−0.490127 | + | 0.871651i | ||||||||
0 | 0 | |||||||||
−753.991 | − | 842.486i | −0.868569 | − | 0.970511i | |||||
0 | 0 | |||||||||
1255.61 | + | 2174.78i | 1.40001 | + | 2.42489i | |||||
0 | 0 | |||||||||
−158.062 | + | 273.771i | −0.170703 | + | 0.295666i | |||||
0 | 0 | |||||||||
189.436 | 0.198292 | 0.0991459 | − | 0.995073i | ||||||
0.0991459 | + | 0.995073i | ||||||||
0 | 0 | |||||||||
−1234.74 | −1.25349 | |||||||||
0 | 0 | |||||||||
−397.902 | + | 689.186i | −0.392007 | + | 0.678976i | −0.992714 | − | 0.120493i | ||
0.600707 | + | 0.799469i | ||||||||
0 | 0 | |||||||||
970.353 | + | 1680.70i | 0.928269 | + | 1.60781i | 0.786218 | + | 0.617950i | ||
0.142052 | + | 0.989859i | ||||||||
0 | 0 | |||||||||
553.812 | + | 618.812i | 0.514729 | + | 0.575142i | |||||
0 | 0 | |||||||||
244.344 | + | 423.217i | 0.220763 | + | 0.382373i | 0.955040 | − | 0.296477i | ||
−0.734277 | + | 0.678850i | ||||||||
0 | 0 | |||||||||
−815.027 | + | 1411.67i | −0.716197 | + | 1.24049i | 0.246300 | + | 0.969194i | ||
−0.962496 | + | 0.271295i | ||||||||
0 | 0 | |||||||||
−2366.38 | −2.02349 | |||||||||
0 | 0 | |||||||||
345.925 | 0.287981 | 0.143991 | − | 0.989579i | ||||||
0.143991 | + | 0.989579i | ||||||||
0 | 0 | |||||||||
−311.254 | + | 539.108i | −0.252388 | + | 0.437148i | |||||
0 | 0 | |||||||||
−1630.70 | − | 2824.45i | −1.28853 | − | 2.23180i | |||||
0 | 0 | |||||||||
12.4770 | − | 2.61278i | 0.00961149 | − | 0.00201272i | |||||
0 | 0 | |||||||||
398.419 | + | 690.082i | 0.299338 | + | 0.518469i | |||||
0 | 0 | |||||||||
1091.25 | − | 1890.09i | 0.799954 | − | 1.38556i | |||||
0 | 0 | |||||||||
−125.000 | −0.0894427 | |||||||||
0 | 0 | |||||||||
1665.24 | 1.16351 | 0.581757 | − | 0.813362i | ||||||
0.581757 | + | 0.813362i | ||||||||
0 | 0 | |||||||||
773.669 | − | 1340.03i | 0.528045 | − | 0.914601i | |||||
0 | 0 | |||||||||
338.374 | + | 586.080i | 0.225678 | + | 0.390886i | 0.956523 | − | 0.291658i | ||
−0.730844 | + | 0.682544i | ||||||||
0 | 0 | |||||||||
365.195 | − | 1112.53i | 0.238094 | − | 0.725329i | |||||
0 | 0 | |||||||||
592.425 | + | 1026.11i | 0.377687 | + | 0.654174i | |||||
0 | 0 | |||||||||
517.117 | − | 895.673i | 0.322484 | − | 0.558558i | −0.658516 | − | 0.752567i | ||
0.981000 | + | 0.194008i | ||||||||
0 | 0 | |||||||||
−435.826 | −0.265944 | −0.132972 | − | 0.991120i | ||||||
−0.132972 | + | 0.991120i | ||||||||
0 | 0 | |||||||||
962.992 | 0.575167 | |||||||||
0 | 0 | |||||||||
705.462 | − | 1221.90i | 0.412543 | − | 0.714546i | |||||
0 | 0 | |||||||||
260.418 | + | 451.056i | 0.149148 | + | 0.258332i | |||||
0 | 0 | |||||||||
−2477.59 | − | 1823.00i | −1.39013 | − | 1.02285i | |||||
0 | 0 | |||||||||
−1059.97 | − | 1835.93i | −0.582795 | − | 1.00943i | −0.995146 | − | 0.0984057i | ||
0.412351 | − | 0.911025i | ||||||||
0 | 0 | |||||||||
−1200.20 | + | 2078.81i | −0.646827 | + | 1.12034i | 0.337050 | + | 0.941487i | ||
−0.983876 | + | 0.178850i | ||||||||
0 | 0 | |||||||||
36.7723 | 0.0194305 | |||||||||
0 | 0 | |||||||||
1400.11 | 0.725546 | |||||||||
0 | 0 | |||||||||
253.094 | − | 438.372i | 0.128657 | − | 0.222840i | −0.794500 | − | 0.607265i | ||
0.923156 | + | 0.384425i | ||||||||
0 | 0 | |||||||||
−200.921 | − | 348.005i | −0.100214 | − | 0.173576i | |||||
0 | 0 | |||||||||
719.140 | − | 2190.79i | 0.352026 | − | 1.07241i | |||||
0 | 0 | |||||||||
1300.47 | + | 2252.49i | 0.624913 | + | 1.08238i | 0.988558 | + | 0.150844i | ||
−0.363644 | + | 0.931538i | ||||||||
0 | 0 | |||||||||
−518.167 | + | 897.491i | −0.244480 | + | 0.423452i | |||||
0 | 0 | |||||||||
−546.077 | −0.253034 | −0.126517 | − | 0.991964i | ||||||
−0.126517 | + | 0.991964i | ||||||||
0 | 0 | |||||||||
1529.78 | 0.696303 | |||||||||
0 | 0 | |||||||||
1688.86 | − | 2925.19i | 0.755266 | − | 1.30816i | |||||
0 | 0 | |||||||||
1510.16 | + | 2615.67i | 0.663673 | + | 1.14951i | 0.979643 | + | 0.200746i | ||
−0.315971 | + | 0.948769i | ||||||||
0 | 0 | |||||||||
453.177 | − | 94.8987i | 0.195754 | − | 0.0409924i | |||||
0 | 0 | |||||||||
2050.28 | + | 3551.18i | 0.870668 | + | 1.50804i | |||||
0 | 0 | |||||||||
999.583 | − | 1731.33i | 0.417387 | − | 0.722936i | −0.578288 | − | 0.815832i | ||
0.995676 | + | 0.0928961i | ||||||||
0 | 0 | |||||||||
−681.145 | −0.279719 | −0.139859 | − | 0.990171i | ||||||
−0.139859 | + | 0.990171i | ||||||||
0 | 0 | |||||||||
4249.03 | 1.71638 | |||||||||
0 | 0 | |||||||||
−659.678 | + | 1142.60i | −0.262165 | + | 0.454083i | |||||
0 | 0 | |||||||||
7.95408 | + | 13.7769i | 0.00311048 | + | 0.00538751i | |||||
0 | 0 | |||||||||
−2926.80 | − | 3270.31i | −1.12642 | − | 1.25862i | |||||
0 | 0 | |||||||||
−806.381 | − | 1396.69i | −0.305485 | − | 0.529116i | 0.671884 | − | 0.740656i | ||
−0.977369 | + | 0.211541i | ||||||||
0 | 0 | |||||||||
−404.461 | + | 700.547i | −0.150848 | + | 0.261277i | −0.931540 | − | 0.363640i | ||
0.780691 | + | 0.624917i | ||||||||
0 | 0 | |||||||||
−2737.35 | −1.00526 | |||||||||
0 | 0 | |||||||||
3704.23 | 1.33967 | 0.669836 | − | 0.742509i | ||||||
0.669836 | + | 0.742509i | ||||||||
0 | 0 | |||||||||
−183.964 | + | 318.635i | −0.0655319 | + | 0.113505i | −0.896930 | − | 0.442173i | ||
0.831398 | + | 0.555678i | ||||||||
0 | 0 | |||||||||
−1028.87 | − | 1782.05i | −0.361047 | − | 0.625353i | |||||
0 | 0 | |||||||||
−1286.56 | − | 1437.56i | −0.444821 | − | 0.497029i | |||||
0 | 0 | |||||||||
−608.415 | − | 1053.81i | −0.207286 | − | 0.359029i | |||||
0 | 0 | |||||||||
3325.69 | − | 5760.27i | 1.11667 | − | 1.93414i | |||||
0 | 0 | |||||||||
1461.25 | 0.483620 | |||||||||
0 | 0 | |||||||||
1073.36 | 0.350205 | 0.175102 | − | 0.984550i | ||||||
0.175102 | + | 0.984550i | ||||||||
0 | 0 | |||||||||
1828.06 | − | 3166.30i | 0.588060 | − | 1.01855i | |||||
0 | 0 | |||||||||
−431.352 | − | 747.124i | −0.136828 | − | 0.236993i | |||||
0 | 0 | |||||||||
−5075.98 | + | 1062.95i | −1.58793 | + | 0.332524i | |||||
0 | 0 | |||||||||
1562.55 | + | 2706.42i | 0.482135 | + | 0.835083i | |||||
0 | 0 | |||||||||
−21.0097 | + | 36.3899i | −0.00639487 | + | 0.0110762i | |||||
0 | 0 | |||||||||
1725.16 | 0.518050 | 0.259025 | − | 0.965871i | ||||||
0.259025 | + | 0.965871i | ||||||||
0 | 0 | |||||||||
1335.60 | 0.395734 | |||||||||
0 | 0 | |||||||||
−1808.49 | + | 3132.40i | −0.528784 | + | 0.915880i | 0.470653 | + | 0.882318i | ||
−0.999437 | + | 0.0335619i | ||||||||
0 | 0 | |||||||||
−730.893 | − | 1265.94i | −0.210912 | − | 0.365309i | 0.741089 | − | 0.671407i | ||
−0.952000 | + | 0.306098i | ||||||||
0 | 0 | |||||||||
1197.20 | − | 3647.17i | 0.340997 | − | 1.03881i | |||||
0 | 0 | |||||||||
−1067.66 | − | 1849.24i | −0.300192 | − | 0.519947i | 0.675988 | − | 0.736913i | ||
−0.976179 | + | 0.216966i | ||||||||
0 | 0 | |||||||||
268.454 | − | 464.976i | 0.0745191 | − | 0.129071i | |||||
0 | 0 | |||||||||
−7534.29 | −2.06500 | |||||||||
0 | 0 | |||||||||
−5952.35 | −1.61099 | −0.805493 | − | 0.592605i | ||||||
−0.805493 | + | 0.592605i | ||||||||
0 | 0 | |||||||||
1923.78 | − | 3332.08i | 0.514197 | − | 0.890615i | −0.485668 | − | 0.874144i | ||
0.999864 | − | 0.0164713i | ||||||||
0 | 0 | |||||||||
137.960 | + | 238.954i | 0.0364203 | + | 0.0630819i | |||||
0 | 0 | |||||||||
−1570.91 | + | 688.094i | −0.409639 | + | 0.179432i | |||||
0 | 0 | |||||||||
1929.85 | + | 3342.60i | 0.497139 | + | 0.861071i | |||||
0 | 0 | |||||||||
−3971.24 | + | 6878.39i | −1.01071 | + | 1.75060i | |||||
0 | 0 | |||||||||
1731.69 | 0.435470 | 0.217735 | − | 0.976008i | ||||||
0.217735 | + | 0.976008i | ||||||||
0 | 0 | |||||||||
2877.47 | 0.715041 | |||||||||
0 | 0 | |||||||||
15.4318 | − | 26.7287i | 0.00378971 | − | 0.00656397i | |||||
0 | 0 | |||||||||
2027.21 | + | 3511.24i | 0.492039 | + | 0.852237i | 0.999958 | − | 0.00916808i | ||
−0.507919 | + | 0.861405i | ||||||||
0 | 0 | |||||||||
1524.16 | − | 4643.21i | 0.365663 | − | 1.11396i | |||||
0 | 0 | |||||||||
−2782.51 | − | 4819.46i | −0.659898 | − | 1.14298i | |||||
0 | 0 | |||||||||
−3167.91 | + | 5486.98i | −0.742744 | + | 1.28647i | 0.208498 | + | 0.978023i | ||
−0.951242 | + | 0.308447i | ||||||||
0 | 0 | |||||||||
−224.043 | −0.0519353 | |||||||||
0 | 0 | |||||||||
−7677.42 | −1.75974 | |||||||||
0 | 0 | |||||||||
660.817 | − | 1144.57i | 0.149780 | − | 0.259426i | −0.781366 | − | 0.624073i | ||
0.931146 | + | 0.364647i | ||||||||
0 | 0 | |||||||||
−1168.00 | − | 2023.04i | −0.261812 | − | 0.453471i | 0.704912 | − | 0.709295i | ||
−0.966723 | + | 0.255824i | ||||||||
0 | 0 | |||||||||
9924.02 | − | 2078.16i | 2.20011 | − | 0.460719i | |||||
0 | 0 | |||||||||
288.899 | + | 500.388i | 0.0633501 | + | 0.109726i | |||||
0 | 0 | |||||||||
3542.61 | − | 6135.99i | 0.768430 | − | 1.33096i | −0.169984 | − | 0.985447i | ||
0.938414 | − | 0.345513i | ||||||||
0 | 0 | |||||||||
−14959.9 | −3.21013 | |||||||||
0 | 0 | |||||||||
2123.17 | 0.450738 | 0.225369 | − | 0.974273i | ||||||
0.225369 | + | 0.974273i | ||||||||
0 | 0 | |||||||||
2945.82 | − | 5102.30i | 0.618765 | − | 1.07173i | −0.370946 | − | 0.928654i | ||
0.989711 | − | 0.143078i | ||||||||
0 | 0 | |||||||||
−1417.49 | − | 2455.16i | −0.294613 | − | 0.510286i | |||||
0 | 0 | |||||||||
3005.79 | + | 3358.58i | 0.618210 | + | 0.690769i | |||||
0 | 0 | |||||||||
2456.26 | + | 4254.37i | 0.499952 | + | 0.865942i | |||||
0 | 0 | |||||||||
−849.426 | + | 1471.25i | −0.171114 | + | 0.296378i | |||||
0 | 0 | |||||||||
−8137.75 | −1.62257 | −0.811284 | − | 0.584652i | ||||||
−0.811284 | + | 0.584652i | ||||||||
0 | 0 | |||||||||
2286.23 | 0.451218 | |||||||||
0 | 0 | |||||||||
2738.42 | − | 4743.08i | 0.535014 | − | 0.926671i | |||||
0 | 0 | |||||||||
3800.25 | + | 6582.22i | 0.735030 | + | 1.27311i | |||||
0 | 0 | |||||||||
2131.04 | + | 2381.16i | 0.408077 | + | 0.455972i | |||||
0 | 0 | |||||||||
−3568.36 | − | 6180.58i | −0.676558 | − | 1.17183i | |||||
0 | 0 | |||||||||
1184.50 | − | 2051.62i | 0.222375 | − | 0.385166i | |||||
0 | 0 | |||||||||
4797.24 | 0.891833 | 0.445917 | − | 0.895075i | ||||||
0.445917 | + | 0.895075i | ||||||||
0 | 0 | |||||||||
−17404.1 | −3.20417 | |||||||||
0 | 0 | |||||||||
2594.76 | − | 4494.26i | 0.473105 | − | 0.819442i | −0.526421 | − | 0.850224i | ||
0.999526 | + | 0.0307823i | ||||||||
0 | 0 | |||||||||
1122.62 | + | 1944.44i | 0.202729 | + | 0.351138i | 0.949407 | − | 0.314049i | ||
−0.746678 | + | 0.665186i | ||||||||
0 | 0 | |||||||||
−4842.11 | + | 1013.98i | −0.866102 | + | 0.181368i | |||||
0 | 0 | |||||||||
4871.13 | + | 8437.05i | 0.863060 | + | 1.49486i | 0.868961 | + | 0.494881i | ||
−0.00590040 | + | 0.999983i | ||||||||
0 | 0 | |||||||||
1203.75 | − | 2084.96i | 0.211276 | − | 0.365941i | |||||
0 | 0 | |||||||||
−4382.53 | −0.762022 | |||||||||
0 | 0 | |||||||||
−43.5181 | −0.00749663 | |||||||||
0 | 0 | |||||||||
−763.092 | + | 1321.71i | −0.130242 | + | 0.225586i | |||||
0 | 0 | |||||||||
−7309.12 | − | 12659.8i | −1.23607 | − | 2.14094i | |||||
0 | 0 | |||||||||
−620.252 | + | 1889.54i | −0.103938 | + | 0.316637i | |||||
0 | 0 | |||||||||
5665.38 | + | 9812.73i | 0.940778 | + | 1.62948i | 0.763992 | + | 0.645226i | ||
0.176786 | + | 0.984249i | ||||||||
0 | 0 | |||||||||
7048.54 | − | 12208.4i | 1.15993 | − | 2.00906i | |||||
0 | 0 | |||||||||
−1147.27 | −0.187110 | |||||||||
0 | 0 | |||||||||
3637.35 | 0.587950 | 0.293975 | − | 0.955813i | ||||||
0.293975 | + | 0.955813i | ||||||||
0 | 0 | |||||||||
−1551.12 | + | 2686.61i | −0.248511 | + | 0.430433i | |||||
0 | 0 | |||||||||
−3235.93 | − | 5604.79i | −0.513887 | − | 0.890078i | |||||
0 | 0 | |||||||||
5172.80 | − | 3687.24i | 0.814300 | − | 0.580444i | |||||
0 | 0 | |||||||||
−2791.31 | − | 4834.69i | −0.435591 | − | 0.754467i | |||||
0 | 0 | |||||||||
−2015.06 | + | 3490.19i | −0.311741 | + | 0.539951i | −0.978739 | − | 0.205108i | ||
0.666998 | + | 0.745059i | ||||||||
0 | 0 | |||||||||
2887.69 | 0.442906 | 0.221453 | − | 0.975171i | ||||||
0.221453 | + | 0.975171i | ||||||||
0 | 0 | |||||||||
14466.4 | 2.19988 | |||||||||
0 | 0 | |||||||||
262.459 | − | 454.592i | 0.0395731 | − | 0.0685425i | −0.845561 | − | 0.533880i | ||
0.885134 | + | 0.465337i | ||||||||
0 | 0 | |||||||||
−1019.22 | − | 1765.34i | −0.152379 | − | 0.263928i | |||||
0 | 0 | |||||||||
−35.6545 | + | 108.618i | −0.00528582 | + | 0.0161027i | |||||
0 | 0 | |||||||||
−1642.66 | − | 2845.17i | −0.241493 | − | 0.418279i | 0.719646 | − | 0.694341i | ||
−0.961140 | + | 0.276062i | ||||||||
0 | 0 | |||||||||
1430.82 | − | 2478.25i | 0.208605 | − | 0.361314i | |||||
0 | 0 | |||||||||
−7146.00 | −1.03324 | |||||||||
0 | 0 | |||||||||
1742.38 | 0.249864 | |||||||||
0 | 0 | |||||||||
4526.98 | − | 7840.95i | 0.643886 | − | 1.11524i | −0.340671 | − | 0.940182i | ||
0.984558 | − | 0.175061i | ||||||||
0 | 0 | |||||||||
6500.80 | + | 11259.7i | 0.917122 | + | 1.58850i | |||||
0 | 0 | |||||||||
812.249 | − | 170.091i | 0.113665 | − | 0.0238024i | |||||
0 | 0 | |||||||||
2604.55 | + | 4511.22i | 0.361551 | + | 0.626225i | 0.988216 | − | 0.153064i | ||
−0.626665 | + | 0.779289i | ||||||||
0 | 0 | |||||||||
560.497 | − | 970.809i | 0.0771838 | − | 0.133686i | |||||
0 | 0 | |||||||||
6359.12 | 0.868730 | |||||||||
0 | 0 | |||||||||
−3200.68 | −0.433794 | −0.216897 | − | 0.976194i | ||||||
−0.216897 | + | 0.976194i | ||||||||
0 | 0 | |||||||||
−7466.90 | + | 12933.1i | −1.00404 | + | 1.73906i | |||||
0 | 0 | |||||||||
−1101.40 | − | 1907.69i | −0.146943 | − | 0.254513i | 0.783153 | − | 0.621829i | ||
−0.930096 | + | 0.367316i | ||||||||
0 | 0 | |||||||||
−1427.27 | − | 1594.79i | −0.188936 | − | 0.211111i | |||||
0 | 0 | |||||||||
4608.92 | + | 7982.89i | 0.605387 | + | 1.04856i | |||||
0 | 0 | |||||||||
3120.79 | − | 5405.38i | 0.406762 | − | 0.704533i | −0.587762 | − | 0.809034i | ||
0.994525 | + | 0.104500i | ||||||||
0 | 0 | |||||||||
−85.6955 | −0.0110839 | |||||||||
0 | 0 | |||||||||
−6069.04 | −0.778988 | |||||||||
0 | 0 | |||||||||
−2100.34 | + | 3637.89i | −0.267543 | + | 0.463398i | |||||
0 | 0 | |||||||||
−5203.58 | − | 9012.87i | −0.657834 | − | 1.13940i | −0.981175 | − | 0.193120i | ||
0.323341 | − | 0.946283i | ||||||||
0 | 0 | |||||||||
7002.92 | + | 7824.84i | 0.878658 | + | 0.981785i | |||||
0 | 0 | |||||||||
7486.63 | + | 12967.2i | 0.932330 | + | 1.61484i | 0.779327 | + | 0.626618i | ||
0.153003 | + | 0.988226i | ||||||||
0 | 0 | |||||||||
8547.30 | − | 14804.4i | 1.05651 | − | 1.82992i | |||||
0 | 0 | |||||||||
−3413.42 | −0.418800 | |||||||||
0 | 0 | |||||||||
6098.58 | 0.742741 | |||||||||
0 | 0 | |||||||||
3529.55 | − | 6113.36i | 0.426711 | − | 0.739086i | −0.569867 | − | 0.821737i | ||
0.996579 | + | 0.0826512i | ||||||||
0 | 0 | |||||||||
4637.48 | + | 8032.35i | 0.556569 | + | 0.964006i | |||||
0 | 0 | |||||||||
−8288.52 | + | 1735.68i | −0.987534 | + | 0.206797i | |||||
0 | 0 | |||||||||
2214.13 | + | 3834.99i | 0.261897 | + | 0.453619i | |||||
0 | 0 | |||||||||
1954.23 | − | 3384.83i | 0.229494 | − | 0.397496i | |||||
0 | 0 | |||||||||
−928.543 | −0.108263 | −0.0541316 | − | 0.998534i | ||||||
−0.0541316 | + | 0.998534i | ||||||||
0 | 0 | |||||||||
7105.06 | 0.822517 | 0.411258 | − | 0.911519i | ||||||
0.411258 | + | 0.911519i | ||||||||
0 | 0 | |||||||||
−2868.38 | + | 4968.18i | −0.329705 | + | 0.571066i | |||||
0 | 0 | |||||||||
−8.60386 | − | 14.9023i | −0.000981996 | − | 0.00170087i | |||||
0 | 0 | |||||||||
−2736.75 | + | 8337.24i | −0.310165 | + | 0.944888i | |||||
0 | 0 | |||||||||
6326.54 | + | 10957.9i | 0.712001 | + | 1.23322i | |||||
0 | 0 | |||||||||
−2159.64 | + | 3740.60i | −0.241360 | + | 0.418047i | −0.961102 | − | 0.276194i | ||
0.719742 | + | 0.694241i | ||||||||
0 | 0 | |||||||||
4600.60 | 0.510602 | 0.255301 | − | 0.966862i | ||||||
0.255301 | + | 0.966862i | ||||||||
0 | 0 | |||||||||
−4670.82 | −0.514825 | |||||||||
0 | 0 | |||||||||
−3935.79 | + | 6816.99i | −0.430834 | + | 0.746226i | |||||
0 | 0 | |||||||||
961.868 | + | 1666.00i | 0.104573 | + | 0.181125i | 0.913564 | − | 0.406696i | ||
−0.808991 | + | 0.587821i | ||||||||
0 | 0 | |||||||||
16784.9 | − | 7352.16i | 1.81242 | − | 0.793884i | |||||
0 | 0 | |||||||||
−2267.44 | − | 3927.32i | −0.243181 | − | 0.421202i | 0.718438 | − | 0.695591i | ||
−0.961619 | + | 0.274390i | ||||||||
0 | 0 | |||||||||
−2140.24 | + | 3707.00i | −0.227993 | + | 0.394896i | |||||
0 | 0 | |||||||||
19011.6 | 2.01167 | |||||||||
0 | 0 | |||||||||
−17431.9 | −1.83221 | −0.916105 | − | 0.400937i | ||||||
−0.916105 | + | 0.400937i | ||||||||
0 | 0 | |||||||||
−2812.33 | + | 4871.10i | −0.293631 | + | 0.508583i | |||||
0 | 0 | |||||||||
−10763.3 | − | 18642.6i | −1.11635 | − | 1.93357i | |||||
0 | 0 | |||||||||
1763.09 | − | 5371.09i | 0.181660 | − | 0.553408i | |||||
0 | 0 | |||||||||
981.162 | + | 1699.42i | 0.100431 | + | 0.173951i | 0.911862 | − | 0.410496i | ||
−0.811431 | + | 0.584448i | ||||||||
0 | 0 | |||||||||
−81.5542 | + | 141.256i | −0.00829330 | + | 0.0143644i | |||||
0 | 0 | |||||||||
14344.4 | 1.44920 | 0.724602 | − | 0.689167i | ||||||
0.724602 | + | 0.689167i | ||||||||
0 | 0 | |||||||||
−11657.8 | −1.17016 | −0.585081 | − | 0.810975i | ||||||
−0.585081 | + | 0.810975i | ||||||||
0 | 0 | |||||||||
−6278.06 | + | 10873.9i | −0.626103 | + | 1.08444i | |||||
0 | 0 | |||||||||
−8256.88 | − | 14301.3i | −0.818164 | − | 1.41710i | −0.907033 | − | 0.421059i | ||
0.0888691 | − | 0.996043i | ||||||||
0 | 0 | |||||||||
4159.33 | − | 870.995i | 0.409509 | − | 0.0857544i | |||||
0 | 0 | |||||||||
2269.73 | + | 3931.30i | 0.222046 | + | 0.384596i | |||||
0 | 0 | |||||||||
−1993.88 | + | 3453.50i | −0.193824 | + | 0.335713i | |||||
0 | 0 | |||||||||
−1580.62 | −0.152681 | |||||||||
0 | 0 | |||||||||
2393.86 | 0.229785 | |||||||||
0 | 0 | |||||||||
−7810.03 | + | 13527.4i | −0.744988 | + | 1.29036i | 0.205212 | + | 0.978718i | ||
−0.950200 | + | 0.311640i | ||||||||
0 | 0 | |||||||||
8054.32 | + | 13950.5i | 0.763504 | + | 1.32243i | |||||
0 | 0 | |||||||||
13790.1 | + | 15408.6i | 1.29911 | + | 1.45159i | |||||
0 | 0 | |||||||||
473.590 | + | 820.282i | 0.0443394 | + | 0.0767981i | |||||
0 | 0 | |||||||||
950.691 | − | 1646.65i | 0.0884598 | − | 0.153217i | −0.818400 | − | 0.574648i | ||
0.906860 | + | 0.421431i | ||||||||
0 | 0 | |||||||||
−23325.1 | −2.15705 | |||||||||
0 | 0 | |||||||||
15964.1 | 1.46731 | 0.733654 | − | 0.679524i | ||||||
0.733654 | + | 0.679524i | ||||||||
0 | 0 | |||||||||
−35.8495 | + | 62.0932i | −0.00327501 | + | 0.00567249i | |||||
0 | 0 | |||||||||
−3086.84 | − | 5346.56i | −0.280289 | − | 0.485475i | |||||
0 | 0 | |||||||||
5035.33 | + | 5626.31i | 0.454457 | + | 0.507796i | |||||
0 | 0 | |||||||||
−3424.59 | − | 5931.56i | −0.307226 | − | 0.532130i | 0.670529 | − | 0.741884i | ||
−0.977754 | + | 0.209753i | ||||||||
0 | 0 | |||||||||
2448.59 | − | 4241.09i | 0.218354 | − | 0.378199i | |||||
0 | 0 | |||||||||
766.190 | 0.0679179 | 0.0339590 | − | 0.999423i | ||||||
0.0339590 | + | 0.999423i | ||||||||
0 | 0 | |||||||||
−3979.02 | −0.350621 | |||||||||
0 | 0 | |||||||||
−6859.49 | + | 11881.0i | −0.600869 | + | 1.04074i | |||||
0 | 0 | |||||||||
−6802.36 | − | 11782.0i | −0.592356 | − | 1.02599i | −0.993914 | − | 0.110157i | ||
0.401558 | − | 0.915834i | ||||||||
0 | 0 | |||||||||
−6316.84 | + | 1322.79i | −0.546850 | + | 0.114515i | |||||
0 | 0 | |||||||||
7491.18 | + | 12975.1i | 0.644724 | + | 1.11669i | |||||
0 | 0 | |||||||||
−4851.76 | + | 8403.50i | −0.415135 | + | 0.719034i | |||||
0 | 0 | |||||||||
−2481.80 | −0.211120 | |||||||||
0 | 0 | |||||||||
−27086.1 | −2.29084 | |||||||||
0 | 0 | |||||||||
−9214.16 | + | 15959.4i | −0.774817 | + | 1.34202i | 0.160080 | + | 0.987104i | ||
−0.934897 | + | 0.354919i | ||||||||
0 | 0 | |||||||||
2170.06 | + | 3758.66i | 0.181435 | + | 0.314254i | 0.942369 | − | 0.334575i | ||
−0.760935 | + | 0.648828i | ||||||||
0 | 0 | |||||||||
−1295.01 | + | 3945.11i | −0.107655 | + | 0.327959i | |||||
0 | 0 | |||||||||
96.3708 | + | 166.919i | 0.00796581 | + | 0.0137972i | |||||
0 | 0 | |||||||||
−1666.82 | + | 2887.03i | −0.136996 | + | 0.237283i | |||||
0 | 0 | |||||||||
−24427.9 | −1.99639 | |||||||||
0 | 0 | |||||||||
−14856.8 | −1.20736 | |||||||||
0 | 0 | |||||||||
−1221.72 | + | 2116.08i | −0.0987282 | + | 0.171002i | |||||
0 | 0 | |||||||||
8964.21 | + | 15526.5i | 0.720362 | + | 1.24770i | |||||
0 | 0 | |||||||||
6385.19 | + | 4698.19i | 0.510259 | + | 0.375446i | |||||
0 | 0 | |||||||||
−6308.12 | − | 10926.0i | −0.501308 | − | 0.868290i | −0.999999 | − | 0.00151060i | ||
0.498691 | − | 0.866780i | ||||||||
0 | 0 | |||||||||
3054.24 | − | 5290.09i | 0.241381 | − | 0.418084i | |||||
0 | 0 | |||||||||
−8150.27 | −0.640586 | |||||||||
0 | 0 | |||||||||
−20677.8 | −1.61630 | −0.808151 | − | 0.588975i | ||||||
−0.808151 | + | 0.588975i | ||||||||
0 | 0 | |||||||||
−12656.2 | + | 21921.2i | −0.983887 | + | 1.70414i | |||||
0 | 0 | |||||||||
3292.96 | + | 5703.58i | 0.254601 | + | 0.440981i | |||||
0 | 0 | |||||||||
4852.75 | − | 14783.4i | 0.373164 | − | 1.13681i | |||||
0 | 0 | |||||||||
−5915.96 | − | 10246.7i | −0.452466 | − | 0.783694i | |||||
0 | 0 | |||||||||
507.586 | − | 879.164i | 0.0386124 | − | 0.0668786i | −0.846073 | − | 0.533066i | ||
0.884686 | + | 0.466188i | ||||||||
0 | 0 | |||||||||
−10533.2 | −0.796969 | |||||||||
0 | 0 | |||||||||
−142.664 | −0.0107366 | |||||||||
0 | 0 | |||||||||
2648.32 | − | 4587.03i | 0.198248 | − | 0.343375i | −0.749713 | − | 0.661763i | ||
0.947960 | + | 0.318388i | ||||||||
0 | 0 | |||||||||
864.812 | + | 1497.90i | 0.0643945 | + | 0.111535i | |||||
0 | 0 | |||||||||
12375.0 | − | 2591.43i | 0.916584 | − | 0.191940i | |||||
0 | 0 | |||||||||
−7370.61 | − | 12766.3i | −0.543044 | − | 0.940580i | −0.998727 | − | 0.0504381i | ||
0.455683 | − | 0.890142i | ||||||||
0 | 0 | |||||||||
6830.70 | − | 11831.1i | 0.500624 | − | 0.867105i | −0.499376 | − | 0.866385i | ||
1.00000 | 0.000720144i | |||||||||
0 | 0 | |||||||||
14463.2 | 1.05446 | |||||||||
0 | 0 | |||||||||
−3112.54 | −0.225742 | |||||||||
0 | 0 | |||||||||
−539.307 | + | 934.107i | −0.0389110 | + | 0.0673958i | −0.884825 | − | 0.465923i | ||
0.845914 | + | 0.533319i | ||||||||
0 | 0 | |||||||||
−3627.18 | − | 6282.46i | −0.260346 | − | 0.450933i | |||||
0 | 0 | |||||||||
−10938.6 | − | 12222.5i | −0.781085 | − | 0.872760i | |||||
0 | 0 | |||||||||
517.807 | + | 896.868i | 0.0367845 | + | 0.0637126i | |||||
0 | 0 | |||||||||
8153.50 | − | 14122.3i | 0.576249 | − | 0.998092i | |||||
0 | 0 | |||||||||
−3863.36 | −0.271649 | −0.135824 | − | 0.990733i | ||||||
−0.135824 | + | 0.990733i | ||||||||
0 | 0 | |||||||||
17704.3 | 1.23853 | |||||||||
0 | 0 | |||||||||
−16609.7 | + | 28768.8i | −1.15606 | + | 2.00235i | |||||
0 | 0 | |||||||||
4720.41 | + | 8175.98i | 0.326887 | + | 0.566185i | 0.981892 | − | 0.189439i | ||
−0.655006 | + | 0.755624i | ||||||||
0 | 0 | |||||||||
42.5062 | + | 47.4951i | 0.00292872 | + | 0.00327246i | |||||
0 | 0 | |||||||||
−1649.78 | − | 2857.50i | −0.113100 | − | 0.195896i | |||||
0 | 0 | |||||||||
−10684.5 | + | 18506.0i | −0.728807 | + | 1.26233i | 0.228581 | + | 0.973525i | ||
−0.957388 | + | 0.288806i | ||||||||
0 | 0 | |||||||||
5801.37 | 0.393748 | 0.196874 | − | 0.980429i | ||||||
0.196874 | + | 0.980429i | ||||||||
0 | 0 | |||||||||
12258.4 | 0.827859 | |||||||||
0 | 0 | |||||||||
−1992.09 | + | 3450.41i | −0.133868 | + | 0.231866i | |||||
0 | 0 | |||||||||
13370.0 | + | 23157.5i | 0.894023 | + | 1.54849i | 0.835009 | + | 0.550236i | ||
0.0590141 | + | 0.998257i | ||||||||
0 | 0 | |||||||||
16933.7 | − | 3546.04i | 1.12674 | − | 0.235949i | |||||
0 | 0 | |||||||||
−3277.68 | − | 5677.10i | −0.217022 | − | 0.375894i | |||||
0 | 0 | |||||||||
4169.87 | − | 7222.43i | 0.274746 | − | 0.475875i | −0.695325 | − | 0.718696i | ||
0.970071 | + | 0.242821i | ||||||||
0 | 0 | |||||||||
10912.5 | 0.715501 | |||||||||
0 | 0 | |||||||||
−26639.2 | −1.73818 | −0.869088 | − | 0.494658i | ||||||
−0.869088 | + | 0.494658i | ||||||||
0 | 0 | |||||||||
13930.2 | − | 24127.7i | 0.904523 | − | 1.56668i | 0.0829678 | − | 0.996552i | ||
0.821556 | − | 0.570128i | ||||||||
0 | 0 | |||||||||
14751.6 | + | 25550.5i | 0.953237 | + | 1.65105i | |||||
0 | 0 | |||||||||
4944.94 | − | 15064.3i | 0.318001 | − | 0.968760i | |||||
0 | 0 | |||||||||
−312.500 | − | 541.266i | −0.0200000 | − | 0.0346410i | |||||
0 | 0 | |||||||||
−6552.19 | + | 11348.7i | −0.417335 | + | 0.722846i | |||||
0 | 0 | |||||||||
−181.625 | −0.0115133 | |||||||||
0 | 0 | |||||||||
10886.7 | 0.686833 | 0.343417 | − | 0.939183i | ||||||
0.343417 | + | 0.939183i | ||||||||
0 | 0 | |||||||||
−4812.92 | + | 8336.23i | −0.302206 | + | 0.523437i | |||||
0 | 0 | |||||||||
4163.11 | + | 7210.71i | 0.260170 | + | 0.450627i | |||||
0 | 0 | |||||||||
−2314.27 | + | 20811.0i | −0.143948 | + | 1.29444i | |||||
0 | 0 | |||||||||
10890.2 | + | 18862.4i | 0.674193 | + | 1.16774i | |||||
0 | 0 | |||||||||
8425.73 | − | 14593.8i | 0.519183 | − | 0.899251i | −0.480568 | − | 0.876957i | ||
0.999751 | − | 0.0222942i | ||||||||
0 | 0 | |||||||||
−4793.72 | −0.294006 | −0.147003 | − | 0.989136i | ||||||
−0.147003 | + | 0.989136i | ||||||||
0 | 0 | |||||||||
7736.69 | 0.472298 | |||||||||
0 | 0 | |||||||||
−13342.3 | + | 23109.5i | −0.810725 | + | 1.40422i | 0.101633 | + | 0.994822i | ||
−0.912358 | + | 0.409394i | ||||||||
0 | 0 | |||||||||
−5283.92 | − | 9152.01i | −0.319587 | − | 0.553541i | |||||
0 | 0 | |||||||||
14505.2 | − | 44188.7i | 0.873278 | − | 2.66036i | |||||
0 | 0 | |||||||||
−8770.94 | − | 15191.7i | −0.525625 | − | 0.910409i | −0.999554 | − | 0.0298466i | ||
0.473929 | − | 0.880563i | ||||||||
0 | 0 | |||||||||
−1691.87 | + | 2930.40i | −0.100926 | + | 0.174810i | |||||
0 | 0 | |||||||||
−18617.0 | −1.10551 | |||||||||
0 | 0 | |||||||||
26285.3 | 1.55377 | 0.776883 | − | 0.629645i | ||||||
0.776883 | + | 0.629645i | ||||||||
0 | 0 | |||||||||
−12522.1 | + | 21689.0i | −0.736845 | + | 1.27625i | 0.217064 | + | 0.976157i | ||
−0.953909 | + | 0.300096i | ||||||||
0 | 0 | |||||||||
−188.414 | − | 326.343i | −0.0110368 | − | 0.0191163i | |||||
0 | 0 | |||||||||
5730.39 | − | 1199.99i | 0.334158 | − | 0.0699753i | |||||
0 | 0 | |||||||||
6484.48 | + | 11231.4i | 0.376432 | + | 0.651999i | |||||
0 | 0 | |||||||||
−7735.57 | + | 13398.4i | −0.447047 | + | 0.774308i | |||||
0 | 0 | |||||||||
−10950.5 | −0.630013 | |||||||||
0 | 0 | |||||||||
20799.4 | 1.19132 | 0.595658 | − | 0.803238i | ||||||
0.595658 | + | 0.803238i | ||||||||
0 | 0 | |||||||||
−2962.12 | + | 5130.55i | −0.168907 | + | 0.292555i | |||||
0 | 0 | |||||||||
−14886.3 | − | 25783.8i | −0.845089 | − | 1.46374i | −0.885543 | − | 0.464556i | ||
0.0404540 | − | 0.999181i | ||||||||
0 | 0 | |||||||||
−2339.71 | − | 2614.32i | −0.132238 | − | 0.147759i | |||||
0 | 0 | |||||||||
−16218.5 | − | 28091.2i | −0.912619 | − | 1.58070i | |||||
0 | 0 | |||||||||
11945.2 | − | 20689.6i | 0.669208 | − | 1.15910i | −0.308918 | − | 0.951089i | ||
0.978126 | − | 0.208014i | ||||||||
0 | 0 | |||||||||
5171.17 | 0.288438 | |||||||||
0 | 0 | |||||||||
13109.2 | 0.728017 | |||||||||
0 | 0 | |||||||||
−1367.72 | + | 2368.97i | −0.0756257 | + | 0.130987i | |||||
0 | 0 | |||||||||
−12648.8 | − | 21908.3i | −0.696356 | − | 1.20612i | −0.969721 | − | 0.244214i | ||
0.273365 | − | 0.961910i | ||||||||
0 | 0 | |||||||||
15250.1 | + | 17040.0i | 0.835937 | + | 0.934049i | |||||
0 | 0 | |||||||||
−1089.56 | − | 1887.18i | −0.0594670 | − | 0.103000i | |||||
0 | 0 | |||||||||
83.7554 | − | 145.069i | 0.00455160 | − | 0.00788360i | |||||
0 | 0 | |||||||||
19149.4 | 1.03619 | |||||||||
0 | 0 | |||||||||
18659.1 | 1.00534 | 0.502670 | − | 0.864478i | ||||||
0.502670 | + | 0.864478i | ||||||||
0 | 0 | |||||||||
−8341.59 | + | 14448.1i | −0.447524 | + | 0.775134i | |||||
0 | 0 | |||||||||
2407.48 | + | 4169.88i | 0.128611 | + | 0.222761i | |||||
0 | 0 | |||||||||
14425.6 | − | 3020.83i | 0.767369 | − | 0.160693i | |||||
0 | 0 | |||||||||
12847.4 | + | 22252.3i | 0.680528 | + | 1.17871i | 0.974820 | + | 0.222993i | ||
−0.294292 | + | 0.955715i | ||||||||
0 | 0 | |||||||||
22441.7 | − | 38870.2i | 1.18373 | − | 2.05028i | |||||
0 | 0 | |||||||||
34863.2 | 1.83119 | |||||||||
0 | 0 | |||||||||
7054.62 | 0.368990 | |||||||||
0 | 0 | |||||||||
26690.2 | − | 46228.8i | 1.39019 | − | 2.40787i | |||||
0 | 0 | |||||||||
−13627.3 | − | 23603.2i | −0.706834 | − | 1.22427i | −0.966025 | − | 0.258447i | ||
0.259191 | − | 0.965826i | ||||||||
0 | 0 | |||||||||
11209.8 | − | 34149.6i | 0.579022 | − | 1.76394i | |||||
0 | 0 | |||||||||
17252.3 | + | 29881.9i | 0.887443 | + | 1.53710i | |||||
0 | 0 | |||||||||
−1302.09 | + | 2255.28i | −0.0667011 | + | 0.115530i | |||||
0 | 0 | |||||||||
13194.3 | 0.673110 | 0.336555 | − | 0.941664i | ||||||
0.336555 | + | 0.941664i | ||||||||
0 | 0 | |||||||||
−20906.9 | −1.06218 | |||||||||
0 | 0 | |||||||||
59.3807 | − | 102.850i | 0.00300448 | − | 0.00520391i | |||||
0 | 0 | |||||||||
−2904.47 | − | 5030.70i | −0.146356 | − | 0.253497i | 0.783522 | − | 0.621364i | ||
−0.929878 | + | 0.367868i | ||||||||
0 | 0 | |||||||||
1699.85 | − | 15285.8i | 0.0853059 | − | 0.767109i | |||||
0 | 0 | |||||||||
2651.56 | + | 4592.64i | 0.132526 | + | 0.229542i | |||||
0 | 0 | |||||||||
6968.34 | − | 12069.5i | 0.346867 | − | 0.600791i | −0.638824 | − | 0.769353i | ||
0.985691 | + | 0.168562i | ||||||||
0 | 0 | |||||||||
−34613.6 | −1.71601 | |||||||||
0 | 0 | |||||||||
−32424.2 | −1.60098 | −0.800489 | − | 0.599347i | ||||||
−0.800489 | + | 0.599347i | ||||||||
0 | 0 | |||||||||
5299.87 | − | 9179.65i | 0.260634 | − | 0.451431i | |||||
0 | 0 | |||||||||
−23657.6 | − | 40976.1i | −1.15875 | − | 2.00701i | |||||
0 | 0 | |||||||||
2822.74 | − | 8599.19i | 0.137704 | − | 0.419503i | |||||
0 | 0 | |||||||||
−17644.2 | − | 30560.6i | −0.857316 | − | 1.48491i | −0.874480 | − | 0.485062i | ||
0.0171639 | − | 0.999853i | ||||||||
0 | 0 | |||||||||
−7764.83 | + | 13449.1i | −0.375785 | + | 0.650879i | |||||
0 | 0 | |||||||||
−12002.0 | −0.578539 | |||||||||
0 | 0 | |||||||||
2079.86 | 0.0998595 | 0.0499298 | − | 0.998753i | ||||||
0.0499298 | + | 0.998753i | ||||||||
0 | 0 | |||||||||
−12902.5 | + | 22347.8i | −0.617038 | + | 1.06874i | |||||
0 | 0 | |||||||||
−6125.72 | − | 10610.1i | −0.291797 | − | 0.505407i | 0.682438 | − | 0.730944i | ||
−0.974235 | + | 0.225537i | ||||||||
0 | 0 | |||||||||
29548.1 | − | 6187.60i | 1.40198 | − | 0.293586i | |||||
0 | 0 | |||||||||
91.9307 | + | 159.229i | 0.00434479 | + | 0.00752539i | |||||
0 | 0 | |||||||||
13956.8 | − | 24173.9i | 0.657042 | − | 1.13803i | |||||
0 | 0 | |||||||||
4335.87 | 0.203323 | 0.101661 | − | 0.994819i | ||||||
0.101661 | + | 0.994819i | ||||||||
0 | 0 | |||||||||
−36359.9 | −1.69840 | |||||||||
0 | 0 | |||||||||
−15199.7 | + | 26326.7i | −0.707240 | + | 1.22498i | 0.258637 | + | 0.965975i | ||
−0.965877 | + | 0.259001i | ||||||||
0 | 0 | |||||||||
3500.28 | + | 6062.66i | 0.162237 | + | 0.281003i | |||||
0 | 0 | |||||||||
29227.0 | + | 32657.4i | 1.34944 | + | 1.50782i | |||||
0 | 0 | |||||||||
−7693.37 | − | 13325.3i | −0.353843 | − | 0.612874i | |||||
0 | 0 | |||||||||
−4711.23 | + | 8160.10i | −0.215853 | + | 0.373868i | |||||
0 | 0 | |||||||||
24684.4 | 1.12663 | |||||||||
0 | 0 | |||||||||
2530.94 | 0.115074 | |||||||||
0 | 0 | |||||||||
17637.1 | − | 30548.4i | 0.798850 | − | 1.38365i | −0.121515 | − | 0.992590i | ||
0.920365 | − | 0.391059i | ||||||||
0 | 0 | |||||||||
−28409.6 | − | 49206.9i | −1.28189 | − | 2.22030i | |||||
0 | 0 | |||||||||
−4272.49 | − | 4773.94i | −0.192051 | − | 0.214592i | |||||
0 | 0 | |||||||||
−14462.2 | − | 25049.2i | −0.647625 | − | 1.12172i | |||||
0 | 0 | |||||||||
1004.60 | − | 1740.02i | 0.0448171 | − | 0.0776255i | |||||
0 | 0 | |||||||||
−27524.0 | −1.22328 | −0.611638 | − | 0.791138i | ||||||
−0.611638 | + | 0.791138i | ||||||||
0 | 0 | |||||||||
73.9116 | 0.00327260 | |||||||||
0 | 0 | |||||||||
22868.1 | − | 39608.7i | 1.00874 | − | 1.74720i | |||||
0 | 0 | |||||||||
−4026.97 | − | 6974.92i | −0.176972 | − | 0.306525i | |||||
0 | 0 | |||||||||
11284.2 | − | 2363.01i | 0.494059 | − | 0.103460i | |||||
0 | 0 | |||||||||
5926.17 | + | 10264.4i | 0.258502 | + | 0.447739i | |||||
0 | 0 | |||||||||
3533.68 | − | 6120.51i | 0.153569 | − | 0.265990i | −0.778968 | − | 0.627064i | ||
0.932537 | + | 0.361074i | ||||||||
0 | 0 | |||||||||
37757.5 | 1.63483 | 0.817413 | − | 0.576052i | ||||||
0.817413 | + | 0.576052i | ||||||||
0 | 0 | |||||||||
20949.1 | 0.903713 | |||||||||
0 | 0 | |||||||||
−6502.36 | + | 11262.4i | −0.279470 | + | 0.484056i | |||||
0 | 0 | |||||||||
−5454.43 | − | 9447.34i | −0.233569 | − | 0.404554i | |||||
0 | 0 | |||||||||
−18838.3 | + | 57389.1i | −0.803742 | + | 2.44852i | |||||
0 | 0 | |||||||||
12653.7 | + | 21916.9i | 0.537902 | + | 0.931673i | 0.999017 | + | 0.0443325i | ||
−0.461115 | + | 0.887340i | ||||||||
0 | 0 | |||||||||
−12742.4 | + | 22070.5i | −0.539699 | + | 0.934786i | 0.459221 | + | 0.888322i | ||
−0.998920 | + | 0.0464643i | ||||||||
0 | 0 | |||||||||
−5181.67 | −0.218670 | |||||||||
0 | 0 | |||||||||
−34985.7 | −1.47107 | −0.735534 | − | 0.677488i | ||||||
−0.735534 | + | 0.677488i | ||||||||
0 | 0 | |||||||||
−1949.04 | + | 3375.84i | −0.0816564 | + | 0.141433i | −0.903962 | − | 0.427614i | ||
0.822305 | + | 0.569047i | ||||||||
0 | 0 | |||||||||
31770.0 | + | 55027.2i | 1.32622 | + | 2.29708i | |||||
0 | 0 | |||||||||
−190.161 | − | 139.919i | −0.00790957 | − | 0.00581983i | |||||
0 | 0 | |||||||||
−1365.19 | − | 2364.58i | −0.0565802 | − | 0.0979997i | |||||
0 | 0 | |||||||||
33178.4 | − | 57466.7i | 1.37015 | − | 2.37317i | |||||
0 | 0 | |||||||||
−22118.8 | −0.910161 | −0.455081 | − | 0.890450i | ||||||
−0.455081 | + | 0.890450i | ||||||||
0 | 0 | |||||||||
−13538.2 | −0.555096 | |||||||||
0 | 0 | |||||||||
−9520.22 | + | 16489.5i | −0.388961 | + | 0.673699i | |||||
0 | 0 | |||||||||
3824.45 | + | 6624.13i | 0.155698 | + | 0.269677i | |||||
0 | 0 | |||||||||
4602.65 | − | 14021.5i | 0.186717 | − | 0.568814i | |||||
0 | 0 | |||||||||
26417.9 | + | 45757.2i | 1.06792 | + | 1.84968i | |||||
0 | 0 | |||||||||
−16426.2 | + | 28451.0i | −0.661672 | + | 1.14605i | |||||
0 | 0 | |||||||||
33152.4 | 1.33074 | 0.665368 | − | 0.746516i | ||||||
0.665368 | + | 0.746516i | ||||||||
0 | 0 | |||||||||
16888.6 | 0.675530 | |||||||||
0 | 0 | |||||||||
5173.12 | − | 8960.11i | 0.206197 | − | 0.357143i | −0.744317 | − | 0.667827i | ||
0.950513 | + | 0.310684i | ||||||||
0 | 0 | |||||||||
−5952.82 | − | 10310.6i | −0.236447 | − | 0.409538i | 0.723245 | − | 0.690591i | ||
−0.959692 | + | 0.281053i | ||||||||
0 | 0 | |||||||||
−39562.2 | + | 8284.63i | −1.56594 | + | 0.327920i | |||||
0 | 0 | |||||||||
15401.2 | + | 26675.6i | 0.607487 | + | 1.05220i | 0.991653 | + | 0.128935i | ||
−0.384166 | + | 0.923264i | ||||||||
0 | 0 | |||||||||
−7550.80 | + | 13078.4i | −0.296803 | + | 0.514079i | |||||
0 | 0 | |||||||||
−44055.3 | −1.72572 | |||||||||
0 | 0 | |||||||||
19417.2 | 0.757977 | |||||||||
0 | 0 | |||||||||
−7003.77 | + | 12130.9i | −0.272461 | + | 0.471917i | |||||
0 | 0 | |||||||||
−5060.22 | − | 8764.56i | −0.196177 | − | 0.339789i | |||||
0 | 0 | |||||||||
1543.87 | + | 1725.07i | 0.0596482 | + | 0.0666490i | |||||
0 | 0 | |||||||||
10846.6 | + | 18786.9i | 0.417634 | + | 0.723363i | 0.995701 | − | 0.0926262i | ||
−0.578067 | + | 0.815989i | ||||||||
0 | 0 | |||||||||
36489.5 | − | 63201.6i | 1.40018 | − | 2.42518i | |||||
0 | 0 | |||||||||
−29963.1 | −1.14584 | −0.572918 | − | 0.819612i | ||||||
−0.572918 | + | 0.819612i | ||||||||
0 | 0 | |||||||||
4090.61 | 0.155900 | 0.0779501 | − | 0.996957i | ||||||
0.0779501 | + | 0.996957i | ||||||||
0 | 0 | |||||||||
−10251.4 | + | 17755.9i | −0.389375 | + | 0.674417i | |||||
0 | 0 | |||||||||
−14409.7 | − | 24958.3i | −0.545468 | − | 0.944778i | −0.998577 | − | 0.0533229i | ||
0.453110 | − | 0.891455i | ||||||||
0 | 0 | |||||||||
−20567.3 | − | 22981.2i | −0.775933 | − | 0.867003i | |||||
0 | 0 | |||||||||
7889.07 | + | 13664.3i | 0.296626 | + | 0.513771i | |||||
0 | 0 | |||||||||
3394.58 | − | 5879.59i | 0.127206 | − | 0.220328i | |||||
0 | 0 | |||||||||
9995.83 | 0.373323 | |||||||||
0 | 0 | |||||||||
−68160.8 | −2.53715 | |||||||||
0 | 0 | |||||||||
14584.5 | − | 25261.2i | 0.541070 | − | 0.937160i | |||||
0 | 0 | |||||||||
−15.4211 | − | 26.7101i | −0.000570200 | − | 0.000987616i | |||||
0 | 0 | |||||||||
−28048.7 | + | 5873.62i | −1.03367 | + | 0.216458i | |||||
0 | 0 | |||||||||
−1702.86 | − | 2949.44i | −0.0625470 | − | 0.108335i | |||||
0 | 0 | |||||||||
−10319.4 | + | 17873.7i | −0.377784 | + | 0.654340i | −0.990739 | − | 0.135777i | ||
0.612956 | + | 0.790117i | ||||||||
0 | 0 | |||||||||
42515.1 | 1.55130 | |||||||||
0 | 0 | |||||||||
15080.1 | 0.548435 | 0.274218 | − | 0.961668i | ||||||
0.274218 | + | 0.961668i | ||||||||
0 | 0 | |||||||||
10234.6 | − | 17726.8i | 0.370991 | − | 0.642576i | |||||
0 | 0 | |||||||||
10622.6 | + | 18398.8i | 0.383794 | + | 0.664750i | |||||
0 | 0 | |||||||||
3908.99 | − | 11908.4i | 0.140770 | − | 0.428843i | |||||
0 | 0 | |||||||||
−1082.14 | − | 1874.33i | −0.0388429 | − | 0.0672778i | 0.845950 | − | 0.533262i | ||
−0.884793 | + | 0.465984i | ||||||||
0 | 0 | |||||||||
−21510.7 | + | 37257.6i | −0.769600 | + | 1.33299i | |||||
0 | 0 | |||||||||
−24888.3 | −0.887549 | |||||||||
0 | 0 | |||||||||
−6596.78 | −0.234487 | |||||||||
0 | 0 | |||||||||
51840.2 | − | 89789.9i | 1.83674 | − | 3.18132i | |||||
0 | 0 | |||||||||
−6819.56 | − | 11811.8i | −0.240842 | − | 0.417151i | 0.720112 | − | 0.693858i | ||
−0.960954 | + | 0.276707i | ||||||||
0 | 0 | |||||||||
−19864.0 | + | 8700.91i | −0.699267 | + | 0.306295i | |||||
0 | 0 | |||||||||
23269.7 | + | 40304.3i | 0.816523 | + | 1.41426i | |||||
0 | 0 | |||||||||
−39.7704 | + | 68.8843i | −0.00139105 | + | 0.00240937i | |||||
0 | 0 | |||||||||
6568.49 | 0.229011 | 0.114505 | − | 0.993423i | ||||||
0.114505 | + | 0.993423i | ||||||||
0 | 0 | |||||||||
−20135.2 | −0.699774 | |||||||||
0 | 0 | |||||||||
−4727.25 | + | 8187.84i | −0.163766 | + | 0.283652i | −0.936216 | − | 0.351424i | ||
0.772450 | + | 0.635075i | ||||||||
0 | 0 | |||||||||
−15149.7 | − | 26240.1i | −0.523163 | − | 0.906145i | |||||
0 | 0 | |||||||||
6843.87 | − | 20849.2i | 0.235588 | − | 0.717697i | |||||
0 | 0 | |||||||||
17038.4 | + | 29511.3i | 0.584660 | + | 1.01266i | 0.994918 | + | 0.100691i | ||
−0.410258 | + | 0.911969i | ||||||||
0 | 0 | |||||||||
10636.7 | − | 18423.4i | 0.363839 | − | 0.630188i | |||||
0 | 0 | |||||||||
−87368.1 | −2.97908 | |||||||||
0 | 0 | |||||||||
−32862.3 | −1.11702 | −0.558508 | − | 0.829499i | ||||||
−0.558508 | + | 0.829499i | ||||||||
0 | 0 | |||||||||
4031.90 | − | 6983.46i | 0.136617 | − | 0.236628i | |||||
0 | 0 | |||||||||
10795.2 | + | 18697.8i | 0.364638 | + | 0.631572i | |||||
0 | 0 | |||||||||
−18747.6 | + | 3925.90i | −0.631275 | + | 0.132194i | |||||
0 | 0 | |||||||||
−24310.7 | − | 42107.4i | −0.816042 | − | 1.41343i | |||||
0 | 0 | |||||||||
13053.9 | − | 22610.0i | 0.436817 | − | 0.756590i | |||||
0 | 0 | |||||||||
−4044.61 | −0.134923 | |||||||||
0 | 0 | |||||||||
−57597.8 | −1.91543 | −0.957715 | − | 0.287720i | ||||||
−0.957715 | + | 0.287720i | ||||||||
0 | 0 | |||||||||
195.134 | − | 337.982i | 0.00646915 | − | 0.0112049i | |||||
0 | 0 | |||||||||
−14092.8 | − | 24409.5i | −0.465768 | − | 0.806734i | 0.533468 | − | 0.845820i | ||
−0.999236 | + | 0.0390865i | ||||||||
0 | 0 | |||||||||
5382.85 | + | 6014.63i | 0.177355 | + | 0.198171i | |||||
0 | 0 | |||||||||
−6843.37 | − | 11853.1i | −0.224783 | − | 0.389335i | |||||
0 | 0 | |||||||||
−22131.8 | + | 38333.4i | −0.724727 | + | 1.25526i | 0.234359 | + | 0.972150i | ||
−0.959086 | + | 0.283114i | ||||||||
0 | 0 | |||||||||
19786.0 | 0.645929 | |||||||||
0 | 0 | |||||||||
87084.1 | 2.83423 | |||||||||
0 | 0 | |||||||||
73.6999 | − | 127.652i | 0.00239131 | − | 0.00414187i | −0.864827 | − | 0.502070i | ||
0.867219 | + | 0.497928i | ||||||||
0 | 0 | |||||||||
9260.57 | + | 16039.8i | 0.299560 | + | 0.518853i | |||||
0 | 0 | |||||||||
−11893.8 | − | 13289.8i | −0.383571 | − | 0.428591i | |||||
0 | 0 | |||||||||
−10740.8 | − | 18603.6i | −0.345337 | − | 0.598141i | |||||
0 | 0 | |||||||||
6243.42 | − | 10813.9i | 0.200130 | − | 0.346635i | −0.748440 | − | 0.663202i | ||
0.948570 | + | 0.316567i | ||||||||
0 | 0 | |||||||||
−101614. | −3.24734 | |||||||||
0 | 0 | |||||||||
−1839.64 | −0.0586135 | |||||||||
0 | 0 | |||||||||
3310.57 | − | 5734.08i | 0.105162 | − | 0.182147i | −0.808642 | − | 0.588301i | ||
0.913805 | + | 0.406154i | ||||||||
0 | 0 | |||||||||
31264.8 | + | 54152.2i | 0.990164 | + | 1.71501i |
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 560.4.q.n.81.1 | 10 | ||
4.3 | odd | 2 | 35.4.e.c.11.2 | ✓ | 10 | ||
7.2 | even | 3 | inner | 560.4.q.n.401.1 | 10 | ||
12.11 | even | 2 | 315.4.j.g.46.4 | 10 | |||
20.3 | even | 4 | 175.4.k.d.74.3 | 20 | |||
20.7 | even | 4 | 175.4.k.d.74.8 | 20 | |||
20.19 | odd | 2 | 175.4.e.d.151.4 | 10 | |||
28.3 | even | 6 | 245.4.a.n.1.4 | 5 | |||
28.11 | odd | 6 | 245.4.a.m.1.4 | 5 | |||
28.19 | even | 6 | 245.4.e.o.226.2 | 10 | |||
28.23 | odd | 6 | 35.4.e.c.16.2 | yes | 10 | ||
28.27 | even | 2 | 245.4.e.o.116.2 | 10 | |||
84.11 | even | 6 | 2205.4.a.bu.1.2 | 5 | |||
84.23 | even | 6 | 315.4.j.g.226.4 | 10 | |||
84.59 | odd | 6 | 2205.4.a.bt.1.2 | 5 | |||
140.23 | even | 12 | 175.4.k.d.149.8 | 20 | |||
140.39 | odd | 6 | 1225.4.a.bg.1.2 | 5 | |||
140.59 | even | 6 | 1225.4.a.bf.1.2 | 5 | |||
140.79 | odd | 6 | 175.4.e.d.51.4 | 10 | |||
140.107 | even | 12 | 175.4.k.d.149.3 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
35.4.e.c.11.2 | ✓ | 10 | 4.3 | odd | 2 | ||
35.4.e.c.16.2 | yes | 10 | 28.23 | odd | 6 | ||
175.4.e.d.51.4 | 10 | 140.79 | odd | 6 | |||
175.4.e.d.151.4 | 10 | 20.19 | odd | 2 | |||
175.4.k.d.74.3 | 20 | 20.3 | even | 4 | |||
175.4.k.d.74.8 | 20 | 20.7 | even | 4 | |||
175.4.k.d.149.3 | 20 | 140.107 | even | 12 | |||
175.4.k.d.149.8 | 20 | 140.23 | even | 12 | |||
245.4.a.m.1.4 | 5 | 28.11 | odd | 6 | |||
245.4.a.n.1.4 | 5 | 28.3 | even | 6 | |||
245.4.e.o.116.2 | 10 | 28.27 | even | 2 | |||
245.4.e.o.226.2 | 10 | 28.19 | even | 6 | |||
315.4.j.g.46.4 | 10 | 12.11 | even | 2 | |||
315.4.j.g.226.4 | 10 | 84.23 | even | 6 | |||
560.4.q.n.81.1 | 10 | 1.1 | even | 1 | trivial | ||
560.4.q.n.401.1 | 10 | 7.2 | even | 3 | inner | ||
1225.4.a.bf.1.2 | 5 | 140.59 | even | 6 | |||
1225.4.a.bg.1.2 | 5 | 140.39 | odd | 6 | |||
2205.4.a.bt.1.2 | 5 | 84.59 | odd | 6 | |||
2205.4.a.bu.1.2 | 5 | 84.11 | even | 6 |