Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [176,3,Mod(17,176)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(176, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 9]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("176.17");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 176.n (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 44) |
Sato-Tate group: |
Embedding invariants
Embedding label | 129.2 | ||
Root | of defining polynomial | ||
Character | 176.129 | ||
Dual form | 176.3.n.c.161.2 |
-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 | |||||||||
1.37103 | + | 4.21961i | 0.457011 | + | 1.40654i | 0.868758 | + | 0.495238i | ||
−0.411746 | + | 0.911298i | ||||||||
0 | 0 | |||||||||
−5.30779 | − | 3.85634i | −1.06156 | − | 0.771267i | −0.0871824 | − | 0.996192i | ||
−0.974376 | + | 0.224925i | ||||||||
0 | 0 | |||||||||
−10.9532 | − | 3.55892i | −1.56475 | − | 0.508417i | −0.606676 | − | 0.794950i | ||
−0.958070 | + | 0.286533i | ||||||||
0 | 0 | |||||||||
−8.64421 | + | 6.28038i | −0.960467 | + | 0.697820i | |||||
0 | 0 | |||||||||
−9.32350 | + | 5.83715i | −0.847591 | + | 0.530650i | |||||
0 | 0 | |||||||||
2.97320 | + | 4.09226i | 0.228708 | + | 0.314789i | 0.907913 | − | 0.419159i | ||
−0.679205 | + | 0.733949i | ||||||||
0 | 0 | |||||||||
8.99507 | − | 27.6840i | 0.599671 | − | 1.84560i | |||||
0 | 0 | |||||||||
−5.03681 | + | 6.93258i | −0.296283 | + | 0.407799i | −0.931042 | − | 0.364911i | ||
0.634759 | + | 0.772710i | ||||||||
0 | 0 | |||||||||
10.3045 | − | 3.34815i | 0.542344 | − | 0.176218i | −0.0250177 | − | 0.999687i | ||
0.567362 | + | 0.823469i | ||||||||
0 | 0 | |||||||||
− | 51.0977i | − | 2.43322i | |||||||
0 | 0 | |||||||||
−11.7519 | −0.510954 | −0.255477 | − | 0.966815i | ||||||
−0.255477 | + | 0.966815i | ||||||||
0 | 0 | |||||||||
5.57590 | + | 17.1609i | 0.223036 | + | 0.686434i | |||||
0 | 0 | |||||||||
−6.04753 | − | 4.39379i | −0.223983 | − | 0.162733i | |||||
0 | 0 | |||||||||
19.2505 | + | 6.25487i | 0.663810 | + | 0.215685i | 0.621494 | − | 0.783419i | ||
0.0423166 | + | 0.999104i | ||||||||
0 | 0 | |||||||||
−29.4488 | + | 21.3958i | −0.949961 | + | 0.690187i | −0.950798 | − | 0.309813i | ||
0.000836644 | 1.00000i | |||||||||
0 | 0 | |||||||||
−37.4133 | − | 31.3386i | −1.13374 | − | 0.949654i | |||||
0 | 0 | |||||||||
44.4130 | + | 61.1293i | 1.26894 | + | 1.74655i | |||||
0 | 0 | |||||||||
−11.4023 | + | 35.0927i | −0.308170 | + | 0.948450i | 0.670305 | + | 0.742086i | ||
−0.978475 | + | 0.206365i | ||||||||
0 | 0 | |||||||||
−13.1914 | + | 18.1564i | −0.338241 | + | 0.465548i | |||||
0 | 0 | |||||||||
−40.3205 | + | 13.1009i | −0.983426 | + | 0.319534i | −0.756224 | − | 0.654313i | ||
−0.227202 | + | 0.973848i | ||||||||
0 | 0 | |||||||||
− | 72.4430i | − | 1.68472i | −0.538915 | − | 0.842360i | ||||
0.538915 | − | 0.842360i | ||||||||
0 | 0 | |||||||||
70.1009 | 1.55780 | |||||||||
0 | 0 | |||||||||
3.37433 | + | 10.3851i | 0.0717943 | + | 0.220960i | 0.980515 | − | 0.196445i | ||
−0.908721 | + | 0.417405i | ||||||||
0 | 0 | |||||||||
67.6654 | + | 49.1618i | 1.38093 | + | 1.00330i | |||||
0 | 0 | |||||||||
−36.1584 | − | 11.7486i | −0.708989 | − | 0.230364i | |||||
0 | 0 | |||||||||
−58.4943 | + | 42.4986i | −1.10367 | + | 0.801860i | −0.981654 | − | 0.190668i | ||
−0.122011 | + | 0.992529i | ||||||||
0 | 0 | |||||||||
71.9972 | + | 4.97215i | 1.30904 | + | 0.0904028i | |||||
0 | 0 | |||||||||
28.2557 | + | 38.8907i | 0.495714 | + | 0.682292i | |||||
0 | 0 | |||||||||
−1.38239 | + | 4.25455i | −0.0234303 | + | 0.0721110i | −0.962088 | − | 0.272739i | ||
0.938658 | + | 0.344850i | ||||||||
0 | 0 | |||||||||
63.8606 | − | 87.8965i | 1.04689 | − | 1.44093i | 0.155424 | − | 0.987848i | ||
0.891470 | − | 0.453079i | ||||||||
0 | 0 | |||||||||
117.033 | − | 38.0264i | 1.85767 | − | 0.603594i | |||||
0 | 0 | |||||||||
− | 33.1866i | − | 0.510562i | |||||||
0 | 0 | |||||||||
37.6104 | 0.561349 | 0.280674 | − | 0.959803i | ||||||
0.280674 | + | 0.959803i | ||||||||
0 | 0 | |||||||||
−16.1123 | − | 49.5886i | −0.233512 | − | 0.718675i | |||||
0 | 0 | |||||||||
−43.3875 | − | 31.5228i | −0.611091 | − | 0.443984i | 0.238707 | − | 0.971092i | ||
−0.849798 | + | 0.527108i | ||||||||
0 | 0 | |||||||||
−23.7259 | − | 7.70902i | −0.325013 | − | 0.105603i | 0.141966 | − | 0.989872i | ||
−0.466979 | + | 0.884269i | ||||||||
0 | 0 | |||||||||
−64.7673 | + | 47.0562i | −0.863564 | + | 0.627416i | |||||
0 | 0 | |||||||||
122.896 | − | 30.7541i | 1.59606 | − | 0.399404i | |||||
0 | 0 | |||||||||
41.8941 | + | 57.6623i | 0.530305 | + | 0.729903i | 0.987177 | − | 0.159630i | ||
−0.456872 | + | 0.889533i | ||||||||
0 | 0 | |||||||||
−19.4674 | + | 59.9146i | −0.240339 | + | 0.739686i | |||||
0 | 0 | |||||||||
−6.78240 | + | 9.33518i | −0.0817157 | + | 0.112472i | −0.847918 | − | 0.530127i | ||
0.766202 | + | 0.642600i | ||||||||
0 | 0 | |||||||||
53.4687 | − | 17.3730i | 0.629044 | − | 0.204389i | |||||
0 | 0 | |||||||||
89.8052i | 1.03224i | |||||||||
0 | 0 | |||||||||
−75.6980 | −0.850540 | −0.425270 | − | 0.905067i | ||||||
−0.425270 | + | 0.905067i | ||||||||
0 | 0 | |||||||||
−18.0021 | − | 55.4048i | −0.197826 | − | 0.608844i | |||||
0 | 0 | |||||||||
−130.657 | − | 94.9280i | −1.40492 | − | 1.02073i | |||||
0 | 0 | |||||||||
−67.6059 | − | 21.9665i | −0.711641 | − | 0.231226i | |||||
0 | 0 | |||||||||
−2.41589 | + | 1.75525i | −0.0249061 | + | 0.0180953i | −0.600169 | − | 0.799873i | ||
0.575263 | + | 0.817969i | ||||||||
0 | 0 | |||||||||
43.9347 | − | 109.013i | 0.443785 | − | 1.10114i | |||||
0 | 0 | |||||||||
26.1228 | + | 35.9549i | 0.258641 | + | 0.355989i | 0.918514 | − | 0.395388i | ||
−0.659873 | + | 0.751377i | ||||||||
0 | 0 | |||||||||
−16.6882 | + | 51.3610i | −0.162021 | + | 0.498650i | −0.998804 | − | 0.0488842i | ||
0.836783 | + | 0.547534i | ||||||||
0 | 0 | |||||||||
−197.050 | + | 271.216i | −1.87667 | + | 2.58301i | |||||
0 | 0 | |||||||||
−124.961 | + | 40.6022i | −1.16786 | + | 0.379460i | −0.827843 | − | 0.560960i | ||
−0.340015 | + | 0.940420i | ||||||||
0 | 0 | |||||||||
− | 6.96523i | − | 0.0639012i | −0.999489 | − | 0.0319506i | ||||
0.999489 | − | 0.0319506i | ||||||||
0 | 0 | |||||||||
−163.710 | −1.47487 | |||||||||
0 | 0 | |||||||||
16.8926 | + | 51.9900i | 0.149492 | + | 0.460089i | 0.997561 | − | 0.0697966i | ||
−0.848069 | + | 0.529885i | ||||||||
0 | 0 | |||||||||
62.3768 | + | 45.3194i | 0.542407 | + | 0.394082i | |||||
0 | 0 | |||||||||
−51.4020 | − | 16.7015i | −0.439333 | − | 0.142748i | |||||
0 | 0 | |||||||||
79.8418 | − | 58.0085i | 0.670940 | − | 0.487466i | |||||
0 | 0 | |||||||||
52.8553 | − | 108.845i | 0.436820 | − | 0.899549i | |||||
0 | 0 | |||||||||
−110.561 | − | 152.175i | −0.898874 | − | 1.23719i | |||||
0 | 0 | |||||||||
−14.1026 | + | 43.4033i | −0.112821 | + | 0.347226i | |||||
0 | 0 | |||||||||
4.79238 | − | 6.59615i | 0.0377353 | − | 0.0519382i | −0.789732 | − | 0.613451i | ||
0.827468 | + | 0.561513i | ||||||||
0 | 0 | |||||||||
305.681 | − | 99.3218i | 2.36962 | − | 0.769936i | |||||
0 | 0 | |||||||||
− | 162.483i | − | 1.24033i | −0.784473 | − | 0.620163i | ||||
0.784473 | − | 0.620163i | ||||||||
0 | 0 | |||||||||
−124.784 | −0.938223 | |||||||||
0 | 0 | |||||||||
15.1551 | + | 46.6427i | 0.112260 | + | 0.345501i | |||||
0 | 0 | |||||||||
−190.008 | − | 138.049i | −1.38692 | − | 1.00766i | −0.996195 | − | 0.0871507i | ||
−0.390726 | − | 0.920507i | ||||||||
0 | 0 | |||||||||
225.896 | + | 73.3980i | 1.62515 | + | 0.528043i | 0.973149 | − | 0.230175i | ||
0.652001 | + | 0.758218i | ||||||||
0 | 0 | |||||||||
−39.1949 | + | 28.4767i | −0.277978 | + | 0.201963i | |||||
0 | 0 | |||||||||
−51.6078 | − | 20.7992i | −0.360894 | − | 0.145449i | |||||
0 | 0 | |||||||||
−78.0568 | − | 107.436i | −0.538323 | − | 0.740937i | |||||
0 | 0 | |||||||||
−114.672 | + | 352.924i | −0.780081 | + | 2.40084i | |||||
0 | 0 | |||||||||
96.3895 | − | 132.669i | 0.646909 | − | 0.890394i | −0.352051 | − | 0.935981i | ||
0.998960 | + | 0.0455865i | ||||||||
0 | 0 | |||||||||
41.8105 | − | 13.5851i | 0.276891 | − | 0.0899673i | −0.167280 | − | 0.985909i | ||
0.444171 | + | 0.895942i | ||||||||
0 | 0 | |||||||||
− | 91.5598i | − | 0.598430i | |||||||
0 | 0 | |||||||||
238.817 | 1.54076 | |||||||||
0 | 0 | |||||||||
2.48642 | + | 7.65241i | 0.0158371 | + | 0.0487414i | 0.958663 | − | 0.284545i | ||
−0.942826 | + | 0.333286i | ||||||||
0 | 0 | |||||||||
−259.525 | − | 188.556i | −1.63223 | − | 1.18589i | |||||
0 | 0 | |||||||||
128.722 | + | 41.8242i | 0.799513 | + | 0.259777i | |||||
0 | 0 | |||||||||
−102.128 | + | 74.2001i | −0.626550 | + | 0.455216i | −0.855203 | − | 0.518292i | ||
0.228653 | + | 0.973508i | ||||||||
0 | 0 | |||||||||
77.7301 | + | 310.617i | 0.471091 | + | 1.88253i | |||||
0 | 0 | |||||||||
−124.601 | − | 171.498i | −0.746112 | − | 1.02694i | −0.998244 | − | 0.0592423i | ||
0.252131 | − | 0.967693i | ||||||||
0 | 0 | |||||||||
44.3172 | − | 136.394i | 0.262232 | − | 0.807067i | |||||
0 | 0 | |||||||||
−68.0469 | + | 93.6585i | −0.397935 | + | 0.547710i | |||||
0 | 0 | |||||||||
−239.490 | + | 77.8150i | −1.38434 | + | 0.449798i | −0.904092 | − | 0.427338i | ||
−0.480243 | + | 0.877136i | ||||||||
0 | 0 | |||||||||
− | 207.811i | − | 1.18749i | |||||||
0 | 0 | |||||||||
−19.8478 | −0.112135 | |||||||||
0 | 0 | |||||||||
68.5335 | + | 210.924i | 0.382869 | + | 1.17835i | 0.938015 | + | 0.346596i | ||
−0.555146 | + | 0.831753i | ||||||||
0 | 0 | |||||||||
1.59618 | + | 1.15970i | 0.00881869 | + | 0.00640716i | 0.592186 | − | 0.805801i | ||
−0.583367 | + | 0.812209i | ||||||||
0 | 0 | |||||||||
458.444 | + | 148.957i | 2.50516 | + | 0.813975i | |||||
0 | 0 | |||||||||
195.850 | − | 142.293i | 1.05865 | − | 0.769154i | |||||
0 | 0 | |||||||||
6.49420 | − | 94.0366i | 0.0347283 | − | 0.502869i | |||||
0 | 0 | |||||||||
50.6029 | + | 69.6488i | 0.267740 | + | 0.368512i | |||||
0 | 0 | |||||||||
6.42642 | − | 19.7785i | 0.0336462 | − | 0.103552i | −0.932823 | − | 0.360335i | ||
0.966469 | + | 0.256783i | ||||||||
0 | 0 | |||||||||
−109.830 | + | 151.168i | −0.569068 | + | 0.783255i | −0.992444 | − | 0.122699i | ||
0.423376 | + | 0.905954i | ||||||||
0 | 0 | |||||||||
140.034 | − | 45.4999i | 0.718124 | − | 0.233333i | |||||
0 | 0 | |||||||||
325.621i | 1.65290i | 0.563011 | + | 0.826449i | ||||||
−0.563011 | + | 0.826449i | ||||||||
0 | 0 | |||||||||
76.6068 | 0.384959 | 0.192479 | − | 0.981301i | ||||||
0.192479 | + | 0.981301i | ||||||||
0 | 0 | |||||||||
51.5651 | + | 158.701i | 0.256543 | + | 0.789557i | |||||
0 | 0 | |||||||||
−188.594 | − | 137.022i | −0.929037 | − | 0.674985i | |||||
0 | 0 | |||||||||
264.534 | + | 85.9524i | 1.29041 | + | 0.419280i | |||||
0 | 0 | |||||||||
101.586 | − | 73.8066i | 0.490754 | − | 0.356554i | |||||
0 | 0 | |||||||||
−76.5307 | + | 91.3656i | −0.366175 | + | 0.437156i | |||||
0 | 0 | |||||||||
134.868 | + | 185.630i | 0.639186 | + | 0.879764i | 0.998572 | − | 0.0534249i | ||
−0.359386 | + | 0.933189i | ||||||||
0 | 0 | |||||||||
73.5284 | − | 226.297i | 0.345204 | − | 1.06243i | |||||
0 | 0 | |||||||||
−279.365 | + | 384.512i | −1.29937 | + | 1.78843i | |||||
0 | 0 | |||||||||
398.705 | − | 129.547i | 1.83735 | − | 0.596991i | |||||
0 | 0 | |||||||||
− | 110.683i | − | 0.505404i | |||||||
0 | 0 | |||||||||
−43.3454 | −0.196133 | |||||||||
0 | 0 | |||||||||
−105.098 | − | 323.459i | −0.471293 | − | 1.45049i | −0.850893 | − | 0.525339i | ||
0.379600 | − | 0.925151i | ||||||||
0 | 0 | |||||||||
−155.976 | − | 113.323i | −0.693227 | − | 0.503659i | |||||
0 | 0 | |||||||||
176.746 | + | 57.4282i | 0.778616 | + | 0.252988i | 0.671249 | − | 0.741232i | ||
0.107367 | + | 0.994219i | ||||||||
0 | 0 | |||||||||
−120.106 | + | 87.2618i | −0.524479 | + | 0.381056i | −0.818288 | − | 0.574808i | ||
0.293810 | + | 0.955864i | ||||||||
0 | 0 | |||||||||
298.265 | + | 476.409i | 1.29119 | + | 2.06238i | |||||
0 | 0 | |||||||||
47.8872 | + | 65.9111i | 0.205525 | + | 0.282880i | 0.899319 | − | 0.437292i | ||
−0.693795 | + | 0.720173i | ||||||||
0 | 0 | |||||||||
22.1383 | − | 68.1347i | 0.0942056 | − | 0.289935i | |||||
0 | 0 | |||||||||
−185.874 | + | 255.834i | −0.784279 | + | 1.07947i | |||||
0 | 0 | |||||||||
−191.525 | + | 62.2303i | −0.801360 | + | 0.260378i | −0.680934 | − | 0.732345i | ||
−0.120426 | + | 0.992722i | ||||||||
0 | 0 | |||||||||
− | 381.337i | − | 1.58231i | −0.611616 | − | 0.791155i | ||||
0.611616 | − | 0.791155i | ||||||||
0 | 0 | |||||||||
−346.783 | −1.42709 | |||||||||
0 | 0 | |||||||||
−169.569 | − | 521.881i | −0.692120 | − | 2.13013i | |||||
0 | 0 | |||||||||
44.3390 | + | 32.2141i | 0.179510 | + | 0.130422i | |||||
0 | 0 | |||||||||
−48.6897 | − | 15.8202i | −0.195541 | − | 0.0635351i | |||||
0 | 0 | |||||||||
84.0788 | − | 61.0868i | 0.334975 | − | 0.243374i | −0.407563 | − | 0.913177i | ||
0.742539 | + | 0.669803i | ||||||||
0 | 0 | |||||||||
109.569 | − | 68.5978i | 0.433080 | − | 0.271138i | |||||
0 | 0 | |||||||||
146.615 | + | 201.798i | 0.574960 | + | 0.791365i | |||||
0 | 0 | |||||||||
−49.5999 | + | 152.653i | −0.192996 | + | 0.593980i | 0.806998 | + | 0.590554i | ||
−0.999994 | + | 0.00342612i | ||||||||
0 | 0 | |||||||||
249.784 | − | 343.798i | 0.964416 | − | 1.32740i | |||||
0 | 0 | |||||||||
−205.688 | + | 66.8321i | −0.788077 | + | 0.256062i | |||||
0 | 0 | |||||||||
203.520i | 0.773840i | 0.922113 | + | 0.386920i | ||||||
−0.922113 | + | 0.386920i | ||||||||
0 | 0 | |||||||||
474.364 | 1.79005 | |||||||||
0 | 0 | |||||||||
−103.785 | − | 319.416i | −0.388706 | − | 1.19631i | |||||
0 | 0 | |||||||||
−182.799 | − | 132.812i | −0.679552 | − | 0.493723i | 0.193657 | − | 0.981069i | ||
−0.873209 | + | 0.487346i | ||||||||
0 | 0 | |||||||||
−276.556 | − | 89.8585i | −1.02050 | − | 0.331581i | −0.249474 | − | 0.968382i | ||
−0.771029 | + | 0.636800i | ||||||||
0 | 0 | |||||||||
209.105 | − | 151.924i | 0.765953 | − | 0.556498i | |||||
0 | 0 | |||||||||
−152.157 | − | 127.452i | −0.553300 | − | 0.463461i | |||||
0 | 0 | |||||||||
112.068 | + | 154.248i | 0.404577 | + | 0.556853i | 0.961885 | − | 0.273453i | ||
−0.557308 | + | 0.830306i | ||||||||
0 | 0 | |||||||||
120.188 | − | 369.899i | 0.430780 | − | 1.32580i | |||||
0 | 0 | |||||||||
12.7725 | − | 17.5799i | 0.0454538 | − | 0.0625618i | −0.785685 | − | 0.618627i | ||
0.831139 | + | 0.556065i | ||||||||
0 | 0 | |||||||||
−52.2884 | + | 16.9895i | −0.184765 | + | 0.0600337i | −0.399938 | − | 0.916542i | ||
0.215173 | + | 0.976576i | ||||||||
0 | 0 | |||||||||
− | 315.387i | − | 1.10662i | |||||||
0 | 0 | |||||||||
488.264 | 1.70127 | |||||||||
0 | 0 | |||||||||
66.6147 | + | 205.019i | 0.230501 | + | 0.709409i | |||||
0 | 0 | |||||||||
−10.7187 | − | 7.78761i | −0.0368341 | − | 0.0267615i | |||||
0 | 0 | |||||||||
417.197 | + | 135.556i | 1.42388 | + | 0.462647i | 0.916833 | − | 0.399271i | ||
0.507048 | + | 0.861918i | ||||||||
0 | 0 | |||||||||
23.7444 | − | 17.2513i | 0.0804895 | − | 0.0584790i | |||||
0 | 0 | |||||||||
82.0314 | + | 5.66512i | 0.276200 | + | 0.0190745i | |||||
0 | 0 | |||||||||
−34.9409 | − | 48.0920i | −0.116859 | − | 0.160843i | |||||
0 | 0 | |||||||||
−257.819 | + | 793.484i | −0.856540 | + | 2.63616i | |||||
0 | 0 | |||||||||
−115.900 | + | 159.523i | −0.382510 | + | 0.526480i | |||||
0 | 0 | |||||||||
−677.917 | + | 220.269i | −2.22268 | + | 0.722192i | |||||
0 | 0 | |||||||||
232.888i | 0.758594i | 0.925275 | + | 0.379297i | ||||||
−0.925275 | + | 0.379297i | ||||||||
0 | 0 | |||||||||
−239.603 | −0.775415 | |||||||||
0 | 0 | |||||||||
47.0093 | + | 144.680i | 0.151155 | + | 0.465208i | 0.997751 | − | 0.0670284i | ||
−0.846596 | + | 0.532236i | ||||||||
0 | 0 | |||||||||
−81.4642 | − | 59.1872i | −0.260269 | − | 0.189097i | 0.449997 | − | 0.893030i | ||
−0.710266 | + | 0.703934i | ||||||||
0 | 0 | |||||||||
−767.831 | − | 249.483i | −2.43756 | − | 0.792011i | |||||
0 | 0 | |||||||||
−270.287 | + | 196.375i | −0.852639 | + | 0.619478i | −0.925872 | − | 0.377836i | ||
0.0732335 | + | 0.997315i | ||||||||
0 | 0 | |||||||||
−215.993 | + | 54.0509i | −0.677093 | + | 0.169438i | |||||
0 | 0 | |||||||||
−342.651 | − | 471.619i | −1.06745 | − | 1.46922i | |||||
0 | 0 | |||||||||
−28.6907 | + | 88.3010i | −0.0888258 | + | 0.273378i | |||||
0 | 0 | |||||||||
−53.6484 | + | 73.8408i | −0.165072 | + | 0.227202i | |||||
0 | 0 | |||||||||
29.3905 | − | 9.54956i | 0.0898793 | − | 0.0292036i | |||||
0 | 0 | |||||||||
− | 125.760i | − | 0.382248i | |||||||
0 | 0 | |||||||||
−168.614 | −0.509409 | −0.254705 | − | 0.967019i | ||||||
−0.254705 | + | 0.967019i | ||||||||
0 | 0 | |||||||||
−121.832 | − | 374.959i | −0.365860 | − | 1.12600i | |||||
0 | 0 | |||||||||
−199.628 | − | 145.038i | −0.595905 | − | 0.432950i | |||||
0 | 0 | |||||||||
−497.959 | − | 161.797i | −1.47762 | − | 0.480108i | −0.544220 | − | 0.838942i | ||
−0.933401 | + | 0.358834i | ||||||||
0 | 0 | |||||||||
−196.217 | + | 142.560i | −0.578812 | + | 0.420531i | |||||
0 | 0 | |||||||||
149.675 | − | 371.381i | 0.438930 | − | 1.08909i | |||||
0 | 0 | |||||||||
−234.487 | − | 322.744i | −0.683636 | − | 0.940945i | |||||
0 | 0 | |||||||||
−105.709 | + | 325.340i | −0.306404 | + | 0.943015i | |||||
0 | 0 | |||||||||
−281.084 | + | 386.879i | −0.810040 | + | 1.11493i | 0.181277 | + | 0.983432i | ||
−0.991317 | + | 0.131493i | ||||||||
0 | 0 | |||||||||
−9.13440 | + | 2.96795i | −0.0261731 | + | 0.00850415i | −0.322074 | − | 0.946714i | ||
0.295901 | + | 0.955219i | ||||||||
0 | 0 | |||||||||
− | 37.8117i | − | 0.107726i | |||||||
0 | 0 | |||||||||
691.089 | 1.95776 | 0.978880 | − | 0.204436i | ||||||
0.978880 | + | 0.204436i | ||||||||
0 | 0 | |||||||||
108.729 | + | 334.633i | 0.306279 | + | 0.942629i | |||||
0 | 0 | |||||||||
354.239 | + | 257.370i | 0.992266 | + | 0.720923i | |||||
0 | 0 | |||||||||
−43.9277 | − | 14.2730i | −0.122361 | − | 0.0397576i | 0.247196 | − | 0.968965i | ||
−0.369558 | + | 0.929208i | ||||||||
0 | 0 | |||||||||
−197.082 | + | 143.188i | −0.545933 | + | 0.396644i | |||||
0 | 0 | |||||||||
531.751 | + | 73.7978i | 1.46488 | + | 0.203300i | |||||
0 | 0 | |||||||||
96.2037 | + | 132.413i | 0.263572 | + | 0.362775i | |||||
0 | 0 | |||||||||
−140.965 | + | 433.846i | −0.384101 | + | 1.18214i | 0.553030 | + | 0.833162i | ||
−0.937131 | + | 0.348979i | ||||||||
0 | 0 | |||||||||
266.260 | − | 366.475i | 0.721571 | − | 0.993157i | |||||
0 | 0 | |||||||||
791.950 | − | 257.320i | 2.13464 | − | 0.693585i | |||||
0 | 0 | |||||||||
− | 99.8021i | − | 0.267566i | −0.991011 | − | 0.133783i | ||||
0.991011 | − | 0.133783i | ||||||||
0 | 0 | |||||||||
−202.480 | −0.539947 | |||||||||
0 | 0 | |||||||||
31.6391 | + | 97.3751i | 0.0839233 | + | 0.258289i | |||||
0 | 0 | |||||||||
313.281 | + | 227.612i | 0.826600 | + | 0.600560i | 0.918595 | − | 0.395199i | ||
−0.0919953 | + | 0.995759i | ||||||||
0 | 0 | |||||||||
34.4037 | + | 11.1784i | 0.0902984 | + | 0.0293397i | |||||
0 | 0 | |||||||||
490.495 | − | 356.366i | 1.28067 | − | 0.930458i | 0.281093 | − | 0.959681i | ||
0.999573 | + | 0.0292222i | ||||||||
0 | 0 | |||||||||
−770.906 | − | 310.693i | −2.00235 | − | 0.806996i | |||||
0 | 0 | |||||||||
454.970 | + | 626.212i | 1.17563 | + | 1.61812i | |||||
0 | 0 | |||||||||
179.028 | − | 550.992i | 0.460226 | − | 1.41643i | −0.404662 | − | 0.914466i | ||
0.864888 | − | 0.501964i | ||||||||
0 | 0 | |||||||||
59.1923 | − | 81.4712i | 0.151387 | − | 0.208366i | |||||
0 | 0 | |||||||||
685.614 | − | 222.769i | 1.74456 | − | 0.566843i | |||||
0 | 0 | |||||||||
− | 467.617i | − | 1.18384i | |||||||
0 | 0 | |||||||||
−163.072 | −0.410761 | −0.205381 | − | 0.978682i | ||||||
−0.205381 | + | 0.978682i | ||||||||
0 | 0 | |||||||||
−171.083 | − | 526.538i | −0.428778 | − | 1.31964i | |||||
0 | 0 | |||||||||
604.368 | + | 439.099i | 1.50715 | + | 1.09501i | 0.967422 | + | 0.253171i | ||
0.539730 | + | 0.841838i | ||||||||
0 | 0 | |||||||||
−175.114 | − | 56.8981i | −0.434527 | − | 0.141186i | |||||
0 | 0 | |||||||||
334.380 | − | 242.941i | 0.825629 | − | 0.599855i | |||||
0 | 0 | |||||||||
−98.5319 | − | 393.743i | −0.242093 | − | 0.967428i | |||||
0 | 0 | |||||||||
−71.6699 | − | 98.6451i | −0.175232 | − | 0.241186i | 0.712363 | − | 0.701812i | ||
−0.887595 | + | 0.460625i | ||||||||
0 | 0 | |||||||||
322.005 | − | 991.030i | 0.783468 | − | 2.41127i | |||||
0 | 0 | |||||||||
30.2832 | − | 41.6812i | 0.0733249 | − | 0.100923i | |||||
0 | 0 | |||||||||
71.9992 | − | 23.3940i | 0.173492 | − | 0.0563710i | |||||
0 | 0 | |||||||||
1053.82i | 2.52715i | |||||||||
0 | 0 | |||||||||
−330.708 | −0.789279 | −0.394640 | − | 0.918836i | ||||||
−0.394640 | + | 0.918836i | ||||||||
0 | 0 | |||||||||
197.794 | + | 608.747i | 0.469819 | + | 1.44595i | 0.852819 | + | 0.522206i | ||
−0.383000 | + | 0.923748i | ||||||||
0 | 0 | |||||||||
−94.3910 | − | 68.5791i | −0.223147 | − | 0.162126i | |||||
0 | 0 | |||||||||
−147.054 | − | 47.7807i | −0.346009 | − | 0.112425i | |||||
0 | 0 | |||||||||
−1012.30 | + | 735.476i | −2.37072 | + | 1.72243i | |||||
0 | 0 | |||||||||
17.0083 | − | 246.281i | 0.0396463 | − | 0.574082i | |||||
0 | 0 | |||||||||
85.8703 | + | 118.190i | 0.199235 | + | 0.274223i | 0.896931 | − | 0.442170i | ||
−0.697696 | + | 0.716394i | ||||||||
0 | 0 | |||||||||
28.3924 | − | 87.3827i | 0.0655713 | − | 0.201808i | −0.912903 | − | 0.408177i | ||
0.978474 | + | 0.206369i | ||||||||
0 | 0 | |||||||||
346.319 | − | 476.667i | 0.796136 | − | 1.09579i | |||||
0 | 0 | |||||||||
−121.098 | + | 39.3472i | −0.277112 | + | 0.0900393i | |||||
0 | 0 | |||||||||
358.371i | 0.816335i | 0.912907 | + | 0.408168i | ||||||
−0.912907 | + | 0.408168i | ||||||||
0 | 0 | |||||||||
−893.668 | −2.02646 | |||||||||
0 | 0 | |||||||||
253.799 | + | 781.114i | 0.572910 | + | 1.76324i | 0.643186 | + | 0.765710i | ||
−0.0702760 | + | 0.997528i | ||||||||
0 | 0 | |||||||||
401.790 | + | 291.917i | 0.902898 | + | 0.655994i | |||||
0 | 0 | |||||||||
691.963 | + | 224.833i | 1.54802 | + | 0.502981i | |||||
0 | 0 | |||||||||
−131.173 | + | 95.3029i | −0.292145 | + | 0.212256i | −0.724197 | − | 0.689593i | ||
0.432052 | + | 0.901849i | ||||||||
0 | 0 | |||||||||
299.456 | − | 357.503i | 0.663982 | − | 0.792690i | |||||
0 | 0 | |||||||||
114.647 | + | 157.798i | 0.253084 | + | 0.348341i | |||||
0 | 0 | |||||||||
−118.108 | + | 363.500i | −0.259578 | + | 0.798900i | |||||
0 | 0 | |||||||||
213.638 | − | 294.048i | 0.467479 | − | 0.643430i | −0.508559 | − | 0.861027i | ||
0.976039 | + | 0.217597i | ||||||||
0 | 0 | |||||||||
60.9206 | − | 19.7943i | 0.132725 | − | 0.0431249i | |||||
0 | 0 | |||||||||
− | 487.885i | − | 1.05832i | −0.848523 | − | 0.529159i | ||||
0.848523 | − | 0.529159i | ||||||||
0 | 0 | |||||||||
−367.635 | −0.794028 | −0.397014 | − | 0.917812i | ||||||
−0.397014 | + | 0.917812i | ||||||||
0 | 0 | |||||||||
327.427 | + | 1007.72i | 0.704144 | + | 2.16713i | |||||
0 | 0 | |||||||||
333.686 | + | 242.437i | 0.714531 | + | 0.519137i | 0.884632 | − | 0.466289i | ||
−0.170101 | + | 0.985427i | ||||||||
0 | 0 | |||||||||
−411.955 | − | 133.852i | −0.878368 | − | 0.285399i | |||||
0 | 0 | |||||||||
−28.8812 | + | 20.9834i | −0.0613189 | + | 0.0445508i | |||||
0 | 0 | |||||||||
422.861 | + | 675.422i | 0.893998 | + | 1.42795i | |||||
0 | 0 | |||||||||
114.914 | + | 158.166i | 0.241924 | + | 0.332980i | |||||
0 | 0 | |||||||||
238.729 | − | 734.733i | 0.500481 | − | 1.54032i | |||||
0 | 0 | |||||||||
312.503 | − | 430.123i | 0.652407 | − | 0.897961i | −0.346794 | − | 0.937941i | ||
0.999200 | + | 0.0399806i | ||||||||
0 | 0 | |||||||||
−177.510 | + | 57.6764i | −0.369043 | + | 0.119909i | |||||
0 | 0 | |||||||||
600.497i | 1.24326i | |||||||||
0 | 0 | |||||||||
19.5919 | 0.0403956 | |||||||||
0 | 0 | |||||||||
198.833 | + | 611.946i | 0.408282 | + | 1.25656i | 0.918124 | + | 0.396294i | ||
−0.509842 | + | 0.860268i | ||||||||
0 | 0 | |||||||||
−453.116 | − | 329.208i | −0.926618 | − | 0.673227i | |||||
0 | 0 | |||||||||
−713.624 | − | 231.871i | −1.45341 | − | 0.472241i | −0.527360 | − | 0.849642i | ||
−0.926050 | + | 0.377401i | ||||||||
0 | 0 | |||||||||
−140.324 | + | 101.951i | −0.284632 | + | 0.206797i | |||||
0 | 0 | |||||||||
−653.586 | + | 409.190i | −1.32038 | + | 0.826646i | |||||
0 | 0 | |||||||||
363.045 | + | 499.689i | 0.730474 | + | 1.00541i | |||||
0 | 0 | |||||||||
−56.8823 | + | 175.066i | −0.113993 | + | 0.350833i | −0.991736 | − | 0.128298i | ||
0.877743 | + | 0.479132i | ||||||||
0 | 0 | |||||||||
552.823 | − | 760.896i | 1.10344 | − | 1.51875i | |||||
0 | 0 | |||||||||
−422.195 | + | 137.180i | −0.839355 | + | 0.272723i | −0.696981 | − | 0.717090i | ||
−0.142374 | + | 0.989813i | ||||||||
0 | 0 | |||||||||
− | 291.580i | − | 0.577385i | |||||||
0 | 0 | |||||||||
636.291 | 1.25501 | |||||||||
0 | 0 | |||||||||
−154.181 | − | 474.520i | −0.302909 | − | 0.932259i | −0.980449 | − | 0.196773i | ||
0.677540 | − | 0.735486i | ||||||||
0 | 0 | |||||||||
232.440 | + | 168.877i | 0.454872 | + | 0.330484i | |||||
0 | 0 | |||||||||
−77.0281 | − | 25.0279i | −0.150152 | − | 0.0487874i | |||||
0 | 0 | |||||||||
286.643 | − | 208.258i | 0.556588 | − | 0.404385i | |||||
0 | 0 | |||||||||
−92.0802 | − | 77.1293i | −0.178105 | − | 0.149186i | |||||
0 | 0 | |||||||||
−656.698 | − | 903.867i | −1.26531 | − | 1.74155i | |||||
0 | 0 | |||||||||
−79.1535 | + | 243.610i | −0.151926 | + | 0.467581i | −0.997836 | − | 0.0657445i | ||
0.845910 | + | 0.533325i | ||||||||
0 | 0 | |||||||||
429.405 | − | 591.025i | 0.821041 | − | 1.13007i | −0.168484 | − | 0.985704i | ||
0.989525 | − | 0.144362i | ||||||||
0 | 0 | |||||||||
876.880 | − | 284.916i | 1.67025 | − | 0.542697i | |||||
0 | 0 | |||||||||
− | 311.923i | − | 0.591884i | |||||||
0 | 0 | |||||||||
−390.892 | −0.738926 | |||||||||
0 | 0 | |||||||||
−14.7706 | − | 45.4591i | −0.0278165 | − | 0.0856104i | |||||
0 | 0 | |||||||||
−173.493 | − | 126.050i | −0.325503 | − | 0.236492i | |||||
0 | 0 | |||||||||
819.842 | + | 266.383i | 1.53242 | + | 0.497912i | |||||
0 | 0 | |||||||||
−796.057 | + | 578.369i | −1.48241 | + | 1.07704i | |||||
0 | 0 | |||||||||
−917.843 | − | 63.3865i | −1.70286 | − | 0.117600i | |||||
0 | 0 | |||||||||
−207.051 | − | 284.981i | −0.382718 | − | 0.526766i | 0.573584 | − | 0.819147i | ||
−0.956302 | + | 0.292380i | ||||||||
0 | 0 | |||||||||
−2.70504 | + | 8.32525i | −0.00498165 | + | 0.0153320i | |||||
0 | 0 | |||||||||
−26.8603 | + | 36.9700i | −0.0492849 | + | 0.0678348i | |||||
0 | 0 | |||||||||
−794.486 | + | 258.144i | −1.45244 | + | 0.471927i | −0.925752 | − | 0.378131i | ||
−0.526690 | + | 0.850058i | ||||||||
0 | 0 | |||||||||
1160.86i | 2.11451i | |||||||||
0 | 0 | |||||||||
219.310 | 0.398021 | |||||||||
0 | 0 | |||||||||
−253.660 | − | 780.686i | −0.458698 | − | 1.41173i | |||||
0 | 0 | |||||||||
868.940 | + | 631.322i | 1.56566 | + | 1.13752i | |||||
0 | 0 | |||||||||
373.525 | + | 121.366i | 0.670601 | + | 0.217891i | 0.624476 | − | 0.781044i | ||
0.0461252 | + | 0.998936i | ||||||||
0 | 0 | |||||||||
296.456 | − | 215.388i | 0.530332 | − | 0.385309i | |||||
0 | 0 | |||||||||
405.701 | − | 101.524i | 0.723175 | − | 0.180970i | |||||
0 | 0 | |||||||||
−228.481 | − | 314.478i | −0.405828 | − | 0.558575i | 0.556366 | − | 0.830937i | ||
−0.962195 | + | 0.272362i | ||||||||
0 | 0 | |||||||||
110.829 | − | 341.096i | 0.196157 | − | 0.603709i | |||||
0 | 0 | |||||||||
426.462 | − | 586.975i | 0.752138 | − | 1.03523i | |||||
0 | 0 | |||||||||
−626.840 | + | 203.673i | −1.10165 | + | 0.357948i | −0.802738 | − | 0.596332i | ||
−0.298914 | + | 0.954280i | ||||||||
0 | 0 | |||||||||
− | 893.667i | − | 1.56509i | −0.622593 | − | 0.782546i | ||||
0.622593 | − | 0.782546i | ||||||||
0 | 0 | |||||||||
92.2683 | 0.161027 | |||||||||
0 | 0 | |||||||||
−65.5276 | − | 201.673i | −0.113961 | − | 0.350736i | |||||
0 | 0 | |||||||||
14.3594 | + | 10.4327i | 0.0248864 | + | 0.0180810i | 0.600159 | − | 0.799881i | ||
−0.575273 | + | 0.817962i | ||||||||
0 | 0 | |||||||||
−788.452 | − | 256.183i | −1.36175 | − | 0.442459i | |||||
0 | 0 | |||||||||
107.512 | − | 78.1123i | 0.185047 | − | 0.134445i | |||||
0 | 0 | |||||||||
297.301 | − | 737.676i | 0.509950 | − | 1.26531i | |||||
0 | 0 | |||||||||
208.424 | + | 286.871i | 0.356281 | + | 0.490378i | |||||
0 | 0 | |||||||||
50.3870 | − | 155.075i | 0.0858382 | − | 0.264183i | −0.898920 | − | 0.438113i | ||
0.984758 | + | 0.173931i | ||||||||
0 | 0 | |||||||||
−231.820 | + | 319.073i | −0.393582 | + | 0.541719i | |||||
0 | 0 | |||||||||
−1373.99 | + | 446.438i | −2.32486 | + | 0.755393i | |||||
0 | 0 | |||||||||
− | 513.367i | − | 0.865711i | −0.901463 | − | 0.432855i | ||||
0.901463 | − | 0.432855i | ||||||||
0 | 0 | |||||||||
−647.484 | −1.08821 | |||||||||
0 | 0 | |||||||||
105.031 | + | 323.251i | 0.175931 | + | 0.541458i | |||||
0 | 0 | |||||||||
749.454 | + | 544.510i | 1.25118 | + | 0.909032i | 0.998290 | − | 0.0584638i | ||
0.252886 | + | 0.967496i | ||||||||
0 | 0 | |||||||||
152.709 | + | 49.6182i | 0.254092 | + | 0.0825594i | 0.433293 | − | 0.901253i | ||
−0.179202 | + | 0.983812i | ||||||||
0 | 0 | |||||||||
−325.112 | + | 236.208i | −0.539157 | + | 0.391721i | |||||
0 | 0 | |||||||||
−700.289 | + | 373.901i | −1.15750 | + | 0.618018i | |||||
0 | 0 | |||||||||
−309.898 | − | 426.539i | −0.510541 | − | 0.702700i | 0.473469 | − | 0.880810i | ||
−0.984010 | + | 0.178111i | ||||||||
0 | 0 | |||||||||
319.609 | − | 983.656i | 0.524810 | − | 1.61520i | |||||
0 | 0 | |||||||||
−32.4661 | + | 44.6858i | −0.0531360 | + | 0.0731355i | |||||
0 | 0 | |||||||||
−630.712 | + | 204.931i | −1.02889 | + | 0.334308i | −0.774353 | − | 0.632754i | ||
−0.254541 | + | 0.967062i | ||||||||
0 | 0 | |||||||||
1234.07i | 2.00662i | |||||||||
0 | 0 | |||||||||
−260.782 | −0.422661 | −0.211331 | − | 0.977415i | ||||||
−0.211331 | + | 0.977415i | ||||||||
0 | 0 | |||||||||
−328.398 | − | 1010.70i | −0.530529 | − | 1.63280i | −0.753115 | − | 0.657889i | ||
0.222586 | − | 0.974913i | ||||||||
0 | 0 | |||||||||
71.0702 | + | 51.6355i | 0.114445 | + | 0.0831490i | |||||
0 | 0 | |||||||||
829.138 | + | 269.403i | 1.33088 | + | 0.432429i | |||||
0 | 0 | |||||||||
607.179 | − | 441.141i | 0.971486 | − | 0.705826i | |||||
0 | 0 | |||||||||
−490.453 | − | 197.664i | −0.782222 | − | 0.315254i | |||||
0 | 0 | |||||||||
−185.851 | − | 255.803i | −0.295471 | − | 0.406681i | |||||
0 | 0 | |||||||||
−161.533 | + | 497.148i | −0.255996 | + | 0.787874i | 0.737636 | + | 0.675199i | ||
−0.993632 | + | 0.112675i | ||||||||
0 | 0 | |||||||||
−598.378 | + | 823.597i | −0.945305 | + | 1.30110i | |||||
0 | 0 | |||||||||
−50.8740 | + | 16.5300i | −0.0801165 | + | 0.0260314i | |||||
0 | 0 | |||||||||
423.072i | 0.664164i | |||||||||
0 | 0 | |||||||||
573.026 | 0.896754 | |||||||||
0 | 0 | |||||||||
−343.291 | − | 1056.54i | −0.535556 | − | 1.64827i | −0.742445 | − | 0.669907i | ||
0.206889 | − | 0.978364i | ||||||||
0 | 0 | |||||||||
−716.585 | − | 520.630i | −1.11444 | − | 0.809689i | −0.131084 | − | 0.991371i | ||
−0.983357 | + | 0.181683i | ||||||||
0 | 0 | |||||||||
−2005.51 | − | 651.630i | −3.10932 | − | 1.01028i | |||||
0 | 0 | |||||||||
−92.5424 | + | 67.2360i | −0.143033 | + | 0.103920i | −0.657001 | − | 0.753890i | ||
0.513968 | + | 0.857810i | ||||||||
0 | 0 | |||||||||
−11.9458 | − | 47.7365i | −0.0184064 | − | 0.0735539i | |||||
0 | 0 | |||||||||
1093.28 | + | 1504.77i | 1.67938 | + | 2.31147i | |||||
0 | 0 | |||||||||
−50.6565 | + | 155.905i | −0.0775750 | + | 0.238751i | −0.982322 | − | 0.187197i | ||
0.904747 | + | 0.425949i | ||||||||
0 | 0 | |||||||||
−626.588 | + | 862.425i | −0.956623 | + | 1.31668i | |||||
0 | 0 | |||||||||
253.507 | − | 82.3695i | 0.385856 | − | 0.125372i | |||||
0 | 0 | |||||||||
116.651i | 0.177012i | 0.996076 | + | 0.0885062i | ||||||
−0.996076 | + | 0.0885062i | ||||||||
0 | 0 | |||||||||
205.962 | 0.311591 | 0.155796 | − | 0.987789i | ||||||
0.155796 | + | 0.987789i | ||||||||
0 | 0 | |||||||||
−59.4280 | − | 182.901i | −0.0896350 | − | 0.275868i | |||||
0 | 0 | |||||||||
662.325 | + | 481.208i | 0.995978 | + | 0.723620i | |||||
0 | 0 | |||||||||
−226.231 | − | 73.5068i | −0.339176 | − | 0.110205i | |||||
0 | 0 | |||||||||
1220.78 | − | 886.947i | 1.82478 | − | 1.32578i | |||||
0 | 0 | |||||||||
−82.3384 | + | 1192.27i | −0.122710 | + | 1.77685i | |||||
0 | 0 | |||||||||
16.4238 | + | 22.6055i | 0.0244039 | + | 0.0335891i | 0.821045 | − | 0.570864i | ||
−0.796641 | + | 0.604453i | ||||||||
0 | 0 | |||||||||
41.6808 | − | 128.280i | 0.0617493 | − | 0.190045i | |||||
0 | 0 | |||||||||
317.546 | − | 437.064i | 0.469049 | − | 0.645590i | −0.507306 | − | 0.861766i | ||
0.976354 | + | 0.216176i | ||||||||
0 | 0 | |||||||||
32.7086 | − | 10.6277i | 0.0481717 | − | 0.0156519i | |||||
0 | 0 | |||||||||
824.534i | 1.21077i | |||||||||
0 | 0 | |||||||||
1117.89 | 1.63674 | 0.818369 | − | 0.574694i | ||||||
0.818369 | + | 0.574694i | ||||||||
0 | 0 | |||||||||
476.161 | + | 1465.47i | 0.695125 | + | 2.13937i | |||||
0 | 0 | |||||||||
−532.880 | − | 387.160i | −0.775662 | − | 0.563551i | |||||
0 | 0 | |||||||||
−347.831 | − | 113.017i | −0.504834 | − | 0.164031i | |||||
0 | 0 | |||||||||
404.704 | − | 294.035i | 0.585679 | − | 0.425521i | −0.255088 | − | 0.966918i | ||
0.840767 | + | 0.541397i | ||||||||
0 | 0 | |||||||||
−869.194 | + | 1037.68i | −1.25425 | + | 1.49737i | |||||
0 | 0 | |||||||||
−915.961 | − | 1260.71i | −1.31793 | − | 1.81397i | |||||
0 | 0 | |||||||||
112.264 | − | 345.512i | 0.161067 | − | 0.495713i | |||||
0 | 0 | |||||||||
−212.464 | + | 292.432i | −0.303954 | + | 0.418357i | |||||
0 | 0 | |||||||||
615.162 | − | 199.878i | 0.877549 | − | 0.285133i | 0.164610 | − | 0.986359i | ||
0.712939 | + | 0.701226i | ||||||||
0 | 0 | |||||||||
399.790i | 0.568691i | |||||||||
0 | 0 | |||||||||
317.854 | 0.450857 | |||||||||
0 | 0 | |||||||||
−158.168 | − | 486.791i | −0.223717 | − | 0.688531i | |||||
0 | 0 | |||||||||
638.569 | + | 463.948i | 0.900662 | + | 0.654369i | 0.938636 | − | 0.344910i | ||
−0.0379740 | + | 0.999279i | ||||||||
0 | 0 | |||||||||
−724.283 | − | 235.334i | −1.01868 | − | 0.330990i | |||||
0 | 0 | |||||||||
346.080 | − | 251.442i | 0.485386 | − | 0.352654i | |||||
0 | 0 | |||||||||
193.715 | + | 309.415i | 0.270930 | + | 0.432748i | |||||
0 | 0 | |||||||||
−525.175 | − | 722.841i | −0.732461 | − | 1.00815i | |||||
0 | 0 | |||||||||
76.5507 | − | 235.599i | 0.106468 | − | 0.327676i | −0.883604 | − | 0.468235i | ||
0.990072 | + | 0.140559i | ||||||||
0 | 0 | |||||||||
365.579 | − | 503.176i | 0.507044 | − | 0.697887i | |||||
0 | 0 | |||||||||
1609.09 | − | 522.825i | 2.22558 | − | 0.723133i | |||||
0 | 0 | |||||||||
365.231i | 0.503768i | |||||||||
0 | 0 | |||||||||
133.030 | 0.182986 | 0.0914928 | − | 0.995806i | ||||||
0.0914928 | + | 0.995806i | ||||||||
0 | 0 | |||||||||
−300.244 | − | 924.057i | −0.411858 | − | 1.26757i | |||||
0 | 0 | |||||||||
502.217 | + | 364.882i | 0.687027 | + | 0.499154i | |||||
0 | 0 | |||||||||
−392.639 | − | 127.576i | −0.535661 | − | 0.174047i | 0.0286800 | − | 0.999589i | ||
−0.564341 | + | 0.825542i | ||||||||
0 | 0 | |||||||||
1969.65 | − | 1431.03i | 2.67979 | − | 1.94698i | |||||
0 | 0 | |||||||||
−350.660 | + | 219.538i | −0.475794 | + | 0.297880i | |||||
0 | 0 | |||||||||
−46.5395 | − | 64.0561i | −0.0629763 | − | 0.0866794i | 0.776367 | − | 0.630281i | ||
−0.839343 | + | 0.543602i | ||||||||
0 | 0 | |||||||||
−75.1408 | + | 231.260i | −0.101405 | + | 0.312091i | |||||
0 | 0 | |||||||||
−302.034 | + | 415.714i | −0.406506 | + | 0.559507i | −0.962362 | − | 0.271771i | ||
0.555856 | + | 0.831279i | ||||||||
0 | 0 | |||||||||
−1023.23 | + | 332.468i | −1.37346 | + | 0.446266i | |||||
0 | 0 | |||||||||
− | 123.291i | − | 0.165049i | |||||||
0 | 0 | |||||||||
1513.22 | 2.02033 | |||||||||
0 | 0 | |||||||||
15.0351 | + | 46.2733i | 0.0200201 | + | 0.0616156i | 0.960567 | − | 0.278047i | ||
−0.940547 | + | 0.339663i | ||||||||
0 | 0 | |||||||||
373.037 | + | 271.027i | 0.495401 | + | 0.359930i | |||||
0 | 0 | |||||||||
−274.310 | − | 89.1288i | −0.363325 | − | 0.118051i | |||||
0 | 0 | |||||||||
165.372 | − | 120.149i | 0.218456 | − | 0.158718i | −0.473175 | − | 0.880968i | ||
0.691632 | + | 0.722250i | ||||||||
0 | 0 | |||||||||
439.679 | + | 368.289i | 0.579287 | + | 0.485229i | |||||
0 | 0 | |||||||||
218.796 | + | 301.147i | 0.287512 | + | 0.395726i | 0.928204 | − | 0.372072i | ||
−0.640692 | + | 0.767798i | ||||||||
0 | 0 | |||||||||
−24.7887 | + | 76.2917i | −0.0324884 | + | 0.0999891i | |||||
0 | 0 | |||||||||
−353.085 | + | 485.980i | −0.461549 | + | 0.635268i | |||||
0 | 0 | |||||||||
−21.5208 | + | 6.99255i | −0.0280585 | + | 0.00911675i | |||||
0 | 0 | |||||||||
1491.70i | 1.93979i | 0.243531 | + | 0.969893i | ||||||
−0.243531 | + | 0.969893i | ||||||||
0 | 0 | |||||||||
−712.138 | −0.923655 | |||||||||
0 | 0 | |||||||||
−209.903 | − | 646.014i | −0.271543 | − | 0.835723i | −0.990113 | − | 0.140269i | ||
0.718570 | − | 0.695454i | ||||||||
0 | 0 | |||||||||
−531.374 | − | 386.066i | −0.685644 | − | 0.498149i | |||||
0 | 0 | |||||||||
1793.15 | + | 582.631i | 2.30779 | + | 0.749847i | |||||
0 | 0 | |||||||||
−371.620 | + | 269.998i | −0.477047 | + | 0.346595i | |||||
0 | 0 | |||||||||
588.527 | + | 40.6439i | 0.753555 | + | 0.0520408i | |||||
0 | 0 | |||||||||
−88.9355 | − | 122.409i | −0.113583 | − | 0.156334i | |||||
0 | 0 | |||||||||
16.3129 | − | 50.2058i | 0.0207807 | − | 0.0639565i | |||||
0 | 0 | |||||||||
311.831 | − | 429.199i | 0.396228 | − | 0.545361i | −0.563564 | − | 0.826072i | ||
0.959792 | + | 0.280711i | ||||||||
0 | 0 | |||||||||
−858.774 | + | 279.033i | −1.08843 | + | 0.353654i | |||||
0 | 0 | |||||||||
− | 629.577i | − | 0.795926i | |||||||
0 | 0 | |||||||||
549.566 | 0.693022 | |||||||||
0 | 0 | |||||||||
650.370 | + | 2001.63i | 0.818075 | + | 2.51778i | |||||
0 | 0 | |||||||||
−723.680 | − | 525.784i | −0.908005 | − | 0.659704i | 0.0325047 | − | 0.999472i | ||
−0.940509 | + | 0.339768i | ||||||||
0 | 0 | |||||||||
−88.9917 | − | 28.9151i | −0.111379 | − | 0.0361892i | |||||
0 | 0 | |||||||||
654.349 | − | 475.413i | 0.816916 | − | 0.593524i | |||||
0 | 0 | |||||||||
266.207 | − | 66.6168i | 0.331516 | − | 0.0829599i | |||||
0 | 0 | |||||||||
−521.939 | − | 718.388i | −0.648372 | − | 0.892407i | |||||
0 | 0 | |||||||||
309.789 | − | 953.431i | 0.383877 | − | 1.18145i | |||||
0 | 0 | |||||||||
634.298 | − | 873.036i | 0.784052 | − | 1.07915i | −0.210772 | − | 0.977535i | ||
0.994823 | − | 0.101619i | ||||||||
0 | 0 | |||||||||
−1130.95 | + | 367.469i | −1.39452 | + | 0.453106i | −0.907414 | − | 0.420237i | ||
−0.487104 | + | 0.873344i | ||||||||
0 | 0 | |||||||||
− | 1290.16i | − | 1.58691i | |||||||
0 | 0 | |||||||||
828.213 | 1.01621 | |||||||||
0 | 0 | |||||||||
−242.550 | − | 746.491i | −0.296878 | − | 0.913698i | |||||
0 | 0 | |||||||||
503.578 | + | 365.871i | 0.614869 | + | 0.446728i | |||||
0 | 0 | |||||||||
1011.88 | + | 328.781i | 1.23250 | + | 0.400464i | 0.851620 | − | 0.524159i | ||
0.380882 | + | 0.924623i | ||||||||
0 | 0 | |||||||||
832.874 | − | 605.118i | 1.01200 | − | 0.735259i | 0.0473700 | − | 0.998877i | ||
0.964627 | + | 0.263619i | ||||||||
0 | 0 | |||||||||
329.184 | − | 816.786i | 0.399011 | − | 0.990043i | |||||
0 | 0 | |||||||||
654.331 | + | 900.610i | 0.791211 | + | 1.08901i | 0.993956 | + | 0.109776i | ||
−0.202746 | + | 0.979231i | ||||||||
0 | 0 | |||||||||
−399.558 | + | 1229.71i | −0.481976 | + | 1.48337i | 0.354338 | + | 0.935117i | ||
−0.836314 | + | 0.548251i | ||||||||
0 | 0 | |||||||||
−497.218 | + | 684.362i | −0.598337 | + | 0.823540i | |||||
0 | 0 | |||||||||
−681.636 | + | 221.477i | −0.818290 | + | 0.265879i | |||||
0 | 0 | |||||||||
1390.78i | 1.66560i | |||||||||
0 | 0 | |||||||||
272.101 | 0.325091 | |||||||||
0 | 0 | |||||||||
−380.239 | − | 1170.26i | −0.453205 | − | 1.39482i | −0.873229 | − | 0.487309i | ||
0.420024 | − | 0.907513i | ||||||||
0 | 0 | |||||||||
−348.925 | − | 253.509i | −0.414893 | − | 0.301437i | |||||
0 | 0 | |||||||||
91.6917 | + | 29.7924i | 0.108768 | + | 0.0353410i | |||||
0 | 0 | |||||||||
−761.209 | + | 553.051i | −0.900839 | + | 0.654498i | |||||
0 | 0 | |||||||||
−966.307 | + | 1004.10i | −1.14086 | + | 1.18548i | |||||
0 | 0 | |||||||||
−143.378 | − | 197.343i | −0.168879 | − | 0.232442i | |||||
0 | 0 | |||||||||
133.999 | − | 412.407i | 0.157461 | − | 0.484614i | |||||
0 | 0 | |||||||||
−509.204 | + | 700.859i | −0.596956 | + | 0.821640i | −0.995425 | − | 0.0955420i | ||
0.398469 | + | 0.917182i | ||||||||
0 | 0 | |||||||||
722.357 | − | 234.708i | 0.844862 | − | 0.274512i | |||||
0 | 0 | |||||||||
− | 1219.98i | − | 1.42354i | −0.702411 | − | 0.711772i | ||||
0.702411 | − | 0.711772i | ||||||||
0 | 0 | |||||||||
469.893 | 0.547023 | 0.273512 | − | 0.961869i | ||||||
0.273512 | + | 0.961869i | ||||||||
0 | 0 | |||||||||
669.427 | + | 2060.28i | 0.777499 | + | 2.39290i | |||||
0 | 0 | |||||||||
3.42992 | + | 2.49198i | 0.00397442 | + | 0.00288758i | 0.589771 | − | 0.807571i | ||
−0.585796 | + | 0.810458i | ||||||||
0 | 0 | |||||||||
1571.24 | + | 510.528i | 1.81647 | + | 0.590206i | |||||
0 | 0 | |||||||||
−773.769 | + | 562.176i | −0.892467 | + | 0.648415i | |||||
0 | 0 | |||||||||
−727.184 | − | 293.072i | −0.836805 | − | 0.337252i | |||||
0 | 0 | |||||||||
111.823 | + | 153.912i | 0.128385 | + | 0.176707i | |||||
0 | 0 | |||||||||
9.85983 | − | 30.3454i | 0.0112942 | − | 0.0347599i | |||||
0 | 0 | |||||||||
308.938 | − | 425.216i | 0.353071 | − | 0.485961i | |||||
0 | 0 | |||||||||
404.726 | − | 131.503i | 0.461489 | − | 0.149947i | −0.0690394 | − | 0.997614i | ||
0.530529 | + | 0.847667i | ||||||||
0 | 0 | |||||||||
1946.26i | 2.21417i | |||||||||
0 | 0 | |||||||||
−1669.31 | −1.89479 | −0.947396 | − | 0.320064i | ||||||
−0.947396 | + | 0.320064i | ||||||||
0 | 0 | |||||||||
65.8838 | + | 202.770i | 0.0746136 | + | 0.229637i | 0.981407 | − | 0.191938i | ||
−0.906793 | + | 0.421575i | ||||||||
0 | 0 | |||||||||
105.348 | + | 76.5399i | 0.119037 | + | 0.0864857i | |||||
0 | 0 | |||||||||
498.213 | + | 161.879i | 0.561683 | + | 0.182502i | 0.576078 | − | 0.817394i | ||
−0.0143952 | + | 0.999896i | ||||||||
0 | 0 | |||||||||
−75.9672 | + | 55.1934i | −0.0854524 | + | 0.0620848i | |||||
0 | 0 | |||||||||
−168.226 | − | 672.248i | −0.188806 | − | 0.754487i | |||||
0 | 0 | |||||||||
69.5419 | + | 95.7162i | 0.0778744 | + | 0.107185i | |||||
0 | 0 | |||||||||
449.634 | − | 1383.83i | 0.502384 | − | 1.54618i | |||||
0 | 0 | |||||||||
155.024 | − | 213.373i | 0.172825 | − | 0.237874i | |||||
0 | 0 | |||||||||
−700.732 | + | 227.682i | −0.779457 | + | 0.253261i | |||||
0 | 0 | |||||||||
− | 619.574i | − | 0.687651i | |||||||
0 | 0 | |||||||||
−3701.67 | −4.09930 | |||||||||
0 | 0 | |||||||||
−4.00004 | − | 12.3108i | −0.00441993 | − | 0.0136031i | |||||
0 | 0 | |||||||||
705.473 | + | 512.556i | 0.777810 | + | 0.565112i | 0.904321 | − | 0.426853i | ||
−0.126511 | + | 0.991965i | ||||||||
0 | 0 | |||||||||
−451.621 | − | 146.741i | −0.496833 | − | 0.161431i | |||||
0 | 0 | |||||||||
−733.848 | + | 533.172i | −0.805541 | + | 0.585260i | −0.912534 | − | 0.409000i | ||
0.106993 | + | 0.994260i | ||||||||
0 | 0 | |||||||||
8.74487 | − | 126.626i | 0.00957817 | − | 0.138693i | |||||
0 | 0 | |||||||||
−1858.89 | − | 2558.55i | −2.03158 | − | 2.79623i | |||||
0 | 0 | |||||||||
−578.263 | + | 1779.71i | −0.630603 | + | 1.94080i | |||||
0 | 0 | |||||||||
708.097 | − | 974.612i | 0.770508 | − | 1.06051i | −0.225758 | − | 0.974183i | ||
0.996267 | − | 0.0863305i | ||||||||
0 | 0 | |||||||||
−982.698 | + | 319.298i | −1.06699 | + | 0.346686i | |||||
0 | 0 | |||||||||
− | 271.277i | − | 0.293908i | |||||||
0 | 0 | |||||||||
−665.798 | −0.719782 | |||||||||
0 | 0 | |||||||||
−178.310 | − | 548.783i | −0.192352 | − | 0.591999i | |||||
0 | 0 | |||||||||
1387.31 | + | 1007.94i | 1.49334 | + | 1.08497i | 0.972942 | + | 0.231050i | ||
0.520397 | + | 0.853924i | ||||||||
0 | 0 | |||||||||
861.860 | + | 280.035i | 0.925736 | + | 0.300790i | |||||
0 | 0 | |||||||||
−546.040 | + | 396.721i | −0.585252 | + | 0.425210i | |||||
0 | 0 | |||||||||
−397.107 | + | 474.083i | −0.424713 | + | 0.507040i | |||||
0 | 0 | |||||||||
−525.277 | − | 722.982i | −0.560595 | − | 0.771593i | 0.430807 | − | 0.902444i | ||
−0.991402 | + | 0.130851i | ||||||||
0 | 0 | |||||||||
138.057 | − | 424.895i | 0.147025 | − | 0.452497i | |||||
0 | 0 | |||||||||
−856.109 | + | 1178.33i | −0.909786 | + | 1.25221i | 0.0574535 | + | 0.998348i | ||
−0.967240 | + | 0.253865i | ||||||||
0 | 0 | |||||||||
473.843 | − | 153.961i | 0.502485 | − | 0.163267i | |||||
0 | 0 | |||||||||
− | 564.823i | − | 0.597697i | |||||||
0 | 0 | |||||||||
−1026.37 | −1.08381 | −0.541906 | − | 0.840439i | ||||||
−0.541906 | + | 0.840439i | ||||||||
0 | 0 | |||||||||
−38.9946 | − | 120.013i | −0.0410902 | − | 0.126463i | |||||
0 | 0 | |||||||||
−1199.20 | − | 871.267i | −1.26098 | − | 0.916159i | |||||
0 | 0 | |||||||||
73.2826 | + | 23.8110i | 0.0768968 | + | 0.0249853i | 0.347213 | − | 0.937786i | ||
−0.270316 | + | 0.962772i | ||||||||
0 | 0 | |||||||||
−110.383 | + | 80.1977i | −0.115584 | + | 0.0839766i | |||||
0 | 0 | |||||||||
−524.207 | − | 837.299i | −0.547760 | − | 0.874920i | |||||
0 | 0 | |||||||||
1589.90 | + | 2188.31i | 1.65787 | + | 2.28186i | |||||
0 | 0 | |||||||||
112.486 | − | 346.196i | 0.117051 | − | 0.360245i | |||||
0 | 0 | |||||||||
825.190 | − | 1135.78i | 0.856895 | − | 1.17941i | |||||
0 | 0 | |||||||||
1165.91 | − | 378.828i | 1.20820 | − | 0.392567i | |||||
0 | 0 | |||||||||
637.935i | 0.659705i | 0.944032 | + | 0.329853i | ||||||
−0.944032 | + | 0.329853i | ||||||||
0 | 0 | |||||||||
−411.931 | −0.425110 | |||||||||
0 | 0 | |||||||||
−415.360 | − | 1278.35i | −0.427766 | − | 1.31653i | −0.900321 | − | 0.435226i | ||
0.472556 | − | 0.881301i | ||||||||
0 | 0 | |||||||||
−2213.07 | − | 1607.89i | −2.27448 | − | 1.65251i | |||||
0 | 0 | |||||||||
−385.133 | − | 125.137i | −0.395008 | − | 0.128346i | |||||
0 | 0 | |||||||||
−620.481 | + | 450.806i | −0.635088 | + | 0.461418i | −0.858159 | − | 0.513384i | ||
0.223071 | + | 0.974802i | ||||||||
0 | 0 | |||||||||
705.771 | − | 441.861i | 0.720910 | − | 0.451339i | |||||
0 | 0 | |||||||||
43.7443 | + | 60.2089i | 0.0445915 | + | 0.0613750i | |||||
0 | 0 | |||||||||
−198.170 | + | 609.906i | −0.201598 | + | 0.620454i | 0.798238 | + | 0.602342i | ||
−0.999836 | + | 0.0181119i | ||||||||
0 | 0 | |||||||||
1255.70 | − | 1728.33i | 1.27483 | − | 1.75465i | |||||
0 | 0 | |||||||||
530.656 | − | 172.421i | 0.537646 | − | 0.174692i | |||||
0 | 0 | |||||||||
851.345i | 0.860814i | |||||||||
0 | 0 | |||||||||
1547.49 | 1.56154 | 0.780770 | − | 0.624818i | ||||||
0.780770 | + | 0.624818i | ||||||||
0 | 0 | |||||||||
−231.176 | − | 711.487i | −0.232806 | − | 0.716502i | |||||
0 | 0 | |||||||||
−406.613 | − | 295.422i | −0.408656 | − | 0.296906i | |||||
0 | 0 | |||||||||
1848.46 | + | 600.601i | 1.85402 | + | 0.602408i | 0.996059 | + | 0.0886972i | ||
0.857963 | + | 0.513711i | ||||||||
0 | 0 | |||||||||
223.146 | − | 162.125i | 0.223369 | − | 0.162287i |
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 176.3.n.c.129.2 | 8 | ||
4.3 | odd | 2 | 44.3.f.a.41.1 | yes | 8 | ||
11.7 | odd | 10 | inner | 176.3.n.c.161.2 | 8 | ||
12.11 | even | 2 | 396.3.t.a.217.2 | 8 | |||
44.3 | odd | 10 | 484.3.f.d.457.2 | 8 | |||
44.7 | even | 10 | 44.3.f.a.29.1 | ✓ | 8 | ||
44.15 | odd | 10 | 484.3.f.a.161.1 | 8 | |||
44.19 | even | 10 | 484.3.f.e.457.2 | 8 | |||
44.27 | odd | 10 | 484.3.f.e.233.2 | 8 | |||
44.31 | odd | 10 | 484.3.d.c.241.2 | 8 | |||
44.35 | even | 10 | 484.3.d.c.241.1 | 8 | |||
44.39 | even | 10 | 484.3.f.d.233.2 | 8 | |||
44.43 | even | 2 | 484.3.f.a.481.1 | 8 | |||
132.35 | odd | 10 | 4356.3.f.g.1693.1 | 8 | |||
132.95 | odd | 10 | 396.3.t.a.73.2 | 8 | |||
132.119 | even | 10 | 4356.3.f.g.1693.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
44.3.f.a.29.1 | ✓ | 8 | 44.7 | even | 10 | ||
44.3.f.a.41.1 | yes | 8 | 4.3 | odd | 2 | ||
176.3.n.c.129.2 | 8 | 1.1 | even | 1 | trivial | ||
176.3.n.c.161.2 | 8 | 11.7 | odd | 10 | inner | ||
396.3.t.a.73.2 | 8 | 132.95 | odd | 10 | |||
396.3.t.a.217.2 | 8 | 12.11 | even | 2 | |||
484.3.d.c.241.1 | 8 | 44.35 | even | 10 | |||
484.3.d.c.241.2 | 8 | 44.31 | odd | 10 | |||
484.3.f.a.161.1 | 8 | 44.15 | odd | 10 | |||
484.3.f.a.481.1 | 8 | 44.43 | even | 2 | |||
484.3.f.d.233.2 | 8 | 44.39 | even | 10 | |||
484.3.f.d.457.2 | 8 | 44.3 | odd | 10 | |||
484.3.f.e.233.2 | 8 | 44.27 | odd | 10 | |||
484.3.f.e.457.2 | 8 | 44.19 | even | 10 | |||
4356.3.f.g.1693.1 | 8 | 132.35 | odd | 10 | |||
4356.3.f.g.1693.2 | 8 | 132.119 | even | 10 |