Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [72,4,Mod(25,72)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(72, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([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("72.25");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 72.i (of order , degree , minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | |
Analytic rank: | |
Dimension: | |
Relative dimension: | over |
Coefficient field: | 8.0.5206055409.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
|
Coefficient ring: | |
Coefficient ring index: | |
Twist minimal: | yes |
Sato-Tate group: |
Embedding invariants
Embedding label | 25.4 | ||
Root | of defining polynomial | ||
Character | 72.25 | ||
Dual form | 72.4.i.a.49.4 |
-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 | |||||||||
3.96518 | + | 3.35817i | 0.763100 | + | 0.646281i | |||||
0 | 0 | |||||||||
4.00813 | + | 6.94228i | 0.358498 | + | 0.620937i | 0.987710 | − | 0.156297i | ||
−0.629212 | + | 0.777234i | ||||||||
0 | 0 | |||||||||
−0.468615 | + | 0.811666i | −0.0253028 | + | 0.0438258i | −0.878400 | − | 0.477927i | ||
0.853097 | + | 0.521753i | ||||||||
0 | 0 | |||||||||
4.44536 | + | 26.6315i | 0.164643 | + | 0.986353i | |||||
0 | 0 | |||||||||
−2.66835 | + | 4.62171i | −0.0731397 | + | 0.126682i | −0.900276 | − | 0.435320i | ||
0.827136 | + | 0.562002i | ||||||||
0 | 0 | |||||||||
1.55794 | + | 2.69842i | 0.0332380 | + | 0.0575699i | 0.882166 | − | 0.470939i | ||
−0.848928 | + | 0.528509i | ||||||||
0 | 0 | |||||||||
−7.42041 | + | 40.9874i | −0.127730 | + | 0.705527i | |||||
0 | 0 | |||||||||
132.704 | 1.89327 | 0.946634 | − | 0.322311i | ||||||
0.946634 | + | 0.322311i | ||||||||
0 | 0 | |||||||||
−86.6565 | −1.04634 | −0.523168 | − | 0.852230i | ||||||
−0.523168 | + | 0.852230i | ||||||||
0 | 0 | |||||||||
−4.58386 | + | 1.64471i | −0.0476324 | + | 0.0170907i | |||||
0 | 0 | |||||||||
−20.6212 | − | 35.7170i | −0.186949 | − | 0.323805i | 0.757283 | − | 0.653087i | ||
−0.944231 | + | 0.329282i | ||||||||
0 | 0 | |||||||||
30.3698 | − | 52.6021i | 0.242959 | − | 0.420817i | |||||
0 | 0 | |||||||||
−71.8066 | + | 120.527i | −0.511822 | + | 0.859092i | |||||
0 | 0 | |||||||||
101.397 | − | 175.625i | 0.649275 | − | 1.12458i | −0.334021 | − | 0.942566i | ||
0.983296 | − | 0.182012i | ||||||||
0 | 0 | |||||||||
−159.367 | − | 276.031i | −0.923325 | − | 1.59925i | −0.794233 | − | 0.607614i | ||
−0.129093 | − | 0.991633i | ||||||||
0 | 0 | |||||||||
−26.1010 | + | 9.36517i | −0.137685 | + | 0.0494020i | |||||
0 | 0 | |||||||||
−7.51308 | −0.0362841 | |||||||||
0 | 0 | |||||||||
−363.510 | −1.61515 | −0.807577 | − | 0.589762i | ||||||
−0.807577 | + | 0.589762i | ||||||||
0 | 0 | |||||||||
−2.88427 | + | 15.9316i | −0.0118424 | + | 0.0654126i | |||||
0 | 0 | |||||||||
−4.91729 | − | 8.51700i | −0.0187305 | − | 0.0324423i | 0.856508 | − | 0.516133i | ||
−0.875239 | + | 0.483691i | ||||||||
0 | 0 | |||||||||
181.230 | − | 313.899i | 0.642728 | − | 1.11324i | −0.342094 | − | 0.939666i | ||
0.984821 | − | 0.173571i | ||||||||
0 | 0 | |||||||||
−167.066 | + | 137.604i | −0.553439 | + | 0.455838i | |||||
0 | 0 | |||||||||
37.5880 | − | 65.1043i | 0.116655 | − | 0.202052i | −0.801785 | − | 0.597612i | ||
0.918440 | + | 0.395560i | ||||||||
0 | 0 | |||||||||
171.061 | + | 296.286i | 0.498720 | + | 0.863808i | |||||
0 | 0 | |||||||||
526.197 | + | 445.644i | 1.44475 | + | 1.22358i | |||||
0 | 0 | |||||||||
403.981 | 1.04700 | 0.523501 | − | 0.852025i | ||||||
0.523501 | + | 0.852025i | ||||||||
0 | 0 | |||||||||
−42.7803 | −0.104882 | |||||||||
0 | 0 | |||||||||
−343.609 | − | 291.007i | −0.798458 | − | 0.676226i | |||||
0 | 0 | |||||||||
215.351 | + | 372.999i | 0.475192 | + | 0.823057i | 0.999596 | − | 0.0284128i | ||
−0.524404 | + | 0.851469i | ||||||||
0 | 0 | |||||||||
−160.783 | + | 278.484i | −0.337477 | + | 0.584527i | −0.983957 | − | 0.178403i | ||
0.646480 | + | 0.762931i | ||||||||
0 | 0 | |||||||||
−23.6991 | − | 8.87180i | −0.0473937 | − | 0.0177419i | |||||
0 | 0 | |||||||||
−12.4888 | + | 21.6313i | −0.0238315 | + | 0.0412774i | |||||
0 | 0 | |||||||||
363.324 | + | 629.296i | 0.662494 | + | 1.14747i | 0.979958 | + | 0.199203i | ||
−0.317464 | + | 0.948270i | ||||||||
0 | 0 | |||||||||
38.1769 | − | 210.874i | 0.0666081 | − | 0.367917i | |||||
0 | 0 | |||||||||
−829.702 | −1.38687 | −0.693433 | − | 0.720521i | ||||||
−0.693433 | + | 0.720521i | ||||||||
0 | 0 | |||||||||
−160.106 | −0.256699 | −0.128349 | − | 0.991729i | ||||||
−0.128349 | + | 0.991729i | ||||||||
0 | 0 | |||||||||
297.069 | − | 106.590i | 0.457367 | − | 0.164106i | |||||
0 | 0 | |||||||||
−2.50086 | − | 4.33161i | −0.00370129 | − | 0.00641081i | |||||
0 | 0 | |||||||||
462.314 | − | 800.752i | 0.658410 | − | 1.14040i | −0.322617 | − | 0.946530i | ||
0.981027 | − | 0.193870i | ||||||||
0 | 0 | |||||||||
−689.478 | + | 236.773i | −0.945785 | + | 0.324792i | |||||
0 | 0 | |||||||||
−255.843 | + | 443.134i | −0.338343 | + | 0.586027i | −0.984121 | − | 0.177498i | ||
0.645778 | + | 0.763525i | ||||||||
0 | 0 | |||||||||
531.896 | + | 921.271i | 0.678732 | + | 1.17560i | |||||
0 | 0 | |||||||||
991.838 | − | 355.876i | 1.22225 | − | 0.438551i | |||||
0 | 0 | |||||||||
−320.459 | −0.381669 | −0.190835 | − | 0.981622i | ||||||
−0.190835 | + | 0.981622i | ||||||||
0 | 0 | |||||||||
−2.92029 | −0.00336406 | |||||||||
0 | 0 | |||||||||
295.042 | − | 1629.69i | 0.328972 | − | 1.81711i | |||||
0 | 0 | |||||||||
−347.330 | − | 601.594i | −0.375109 | − | 0.649708i | |||||
0 | 0 | |||||||||
300.821 | − | 521.038i | 0.314884 | − | 0.545396i | −0.664529 | − | 0.747263i | ||
0.979413 | + | 0.201867i | ||||||||
0 | 0 | |||||||||
−134.945 | − | 50.5170i | −0.136995 | − | 0.0512843i | |||||
0 | 0 | |||||||||
−438.162 | + | 758.920i | −0.431671 | + | 0.747676i | −0.997017 | − | 0.0771773i | ||
0.565346 | + | 0.824854i | ||||||||
0 | 0 | |||||||||
111.719 | + | 193.502i | 0.106873 | + | 0.185110i | 0.914502 | − | 0.404581i | ||
−0.807629 | + | 0.589691i | ||||||||
0 | 0 | |||||||||
−29.7907 | − | 25.2302i | −0.0276884 | − | 0.0234497i | |||||
0 | 0 | |||||||||
−1265.34 | −1.14322 | −0.571612 | − | 0.820524i | ||||||
−0.571612 | + | 0.820524i | ||||||||
0 | 0 | |||||||||
−213.009 | −0.187180 | −0.0935898 | − | 0.995611i | ||||||
−0.0935898 | + | 0.995611i | ||||||||
0 | 0 | |||||||||
−1441.39 | − | 1220.73i | −1.23252 | − | 1.04384i | |||||
0 | 0 | |||||||||
−806.988 | − | 1397.74i | −0.671814 | − | 1.16362i | −0.977389 | − | 0.211449i | ||
0.305575 | − | 0.952168i | ||||||||
0 | 0 | |||||||||
165.305 | − | 286.317i | 0.134041 | − | 0.232167i | |||||
0 | 0 | |||||||||
−64.9376 | + | 53.4857i | −0.0513118 | + | 0.0422629i | |||||
0 | 0 | |||||||||
−62.1873 | + | 107.712i | −0.0479051 | + | 0.0829740i | |||||
0 | 0 | |||||||||
651.260 | + | 1128.02i | 0.489301 | + | 0.847494i | |||||
0 | 0 | |||||||||
9.10359 | − | 50.2846i | 0.00667352 | − | 0.0368619i | |||||
0 | 0 | |||||||||
1488.94 | 1.06540 | |||||||||
0 | 0 | |||||||||
−1234.19 | −0.862333 | −0.431167 | − | 0.902272i | ||||||
−0.431167 | + | 0.902272i | ||||||||
0 | 0 | |||||||||
1772.74 | − | 636.067i | 1.20993 | − | 0.434129i | |||||
0 | 0 | |||||||||
723.720 | + | 1253.52i | 0.482685 | + | 0.836034i | 0.999802 | − | 0.0198800i | ||
−0.517118 | + | 0.855914i | ||||||||
0 | 0 | |||||||||
40.6086 | − | 70.3361i | 0.0264753 | − | 0.0458565i | |||||
0 | 0 | |||||||||
−1124.54 | − | 15.4133i | −0.716928 | − | 0.00982643i | |||||
0 | 0 | |||||||||
−276.891 | + | 479.589i | −0.172674 | + | 0.299081i | −0.939354 | − | 0.342949i | ||
0.766680 | + | 0.642030i | ||||||||
0 | 0 | |||||||||
794.528 | + | 1376.16i | 0.484827 | + | 0.839745i | 0.999848 | − | 0.0174326i | ||
−0.515021 | + | 0.857178i | ||||||||
0 | 0 | |||||||||
367.675 | − | 131.924i | 0.219601 | − | 0.0787941i | |||||
0 | 0 | |||||||||
−16.6285 | −0.00972406 | |||||||||
0 | 0 | |||||||||
1625.65 | 0.931055 | |||||||||
0 | 0 | |||||||||
−316.692 | + | 1749.28i | −0.177689 | + | 0.981484i | |||||
0 | 0 | |||||||||
606.406 | + | 1050.33i | 0.333414 | + | 0.577490i | 0.983179 | − | 0.182645i | ||
−0.649765 | + | 0.760135i | ||||||||
0 | 0 | |||||||||
−265.929 | + | 460.603i | −0.143318 | + | 0.248234i | −0.928744 | − | 0.370721i | ||
0.785426 | + | 0.618955i | ||||||||
0 | 0 | |||||||||
589.919 | + | 3534.12i | 0.311713 | + | 1.86743i | |||||
0 | 0 | |||||||||
1277.52 | − | 2212.74i | 0.662020 | − | 1.14665i | |||||
0 | 0 | |||||||||
−1081.47 | − | 1873.16i | −0.549749 | − | 0.952194i | −0.998291 | − | 0.0584320i | ||
0.448542 | − | 0.893762i | ||||||||
0 | 0 | |||||||||
1601.86 | + | 1356.64i | 0.798967 | + | 0.676657i | |||||
0 | 0 | |||||||||
38.6537 | 0.0189213 | |||||||||
0 | 0 | |||||||||
−1602.11 | −0.769859 | −0.384930 | − | 0.922946i | ||||||
−0.384930 | + | 0.922946i | ||||||||
0 | 0 | |||||||||
−169.632 | − | 143.664i | −0.0800352 | − | 0.0677830i | |||||
0 | 0 | |||||||||
866.800 | + | 1501.34i | 0.401647 | + | 0.695673i | 0.993925 | − | 0.110061i | ||
−0.592278 | + | 0.805734i | ||||||||
0 | 0 | |||||||||
1093.65 | − | 1894.25i | 0.497790 | − | 0.862198i | |||||
0 | 0 | |||||||||
−385.219 | − | 2307.80i | −0.172272 | − | 1.03206i | |||||
0 | 0 | |||||||||
−937.323 | + | 1623.49i | −0.411927 | + | 0.713478i | −0.995100 | − | 0.0988692i | ||
0.583173 | + | 0.812348i | ||||||||
0 | 0 | |||||||||
28.4635 | + | 49.3003i | 0.0122951 | + | 0.0212957i | |||||
0 | 0 | |||||||||
−398.688 | + | 2202.20i | −0.169307 | + | 0.935182i | |||||
0 | 0 | |||||||||
2058.01 | 0.859344 | 0.429672 | − | 0.902985i | ||||||
0.429672 | + | 0.902985i | ||||||||
0 | 0 | |||||||||
−3938.45 | −1.61736 | −0.808681 | − | 0.588248i | ||||||
−0.808681 | + | 0.588248i | ||||||||
0 | 0 | |||||||||
−1572.73 | + | 564.303i | −0.635297 | + | 0.227948i | |||||
0 | 0 | |||||||||
−1457.00 | − | 2523.59i | −0.579030 | − | 1.00291i | |||||
0 | 0 | |||||||||
−354.101 | + | 613.322i | −0.138473 | + | 0.239842i | |||||
0 | 0 | |||||||||
−64.1781 | − | 114.764i | −0.0246998 | − | 0.0441685i | |||||
0 | 0 | |||||||||
2232.54 | − | 3866.88i | 0.845765 | − | 1.46491i | −0.0391899 | − | 0.999232i | ||
0.884955 | − | 0.465676i | ||||||||
0 | 0 | |||||||||
−2075.02 | − | 3594.03i | −0.773901 | − | 1.34044i | −0.935410 | − | 0.353564i | ||
0.161509 | − | 0.986871i | ||||||||
0 | 0 | |||||||||
−122.162 | + | 43.8323i | −0.0448626 | + | 0.0160969i | |||||
0 | 0 | |||||||||
536.823 | 0.194148 | 0.0970738 | − | 0.995277i | ||||||
0.0970738 | + | 0.995277i | ||||||||
0 | 0 | |||||||||
1953.59 | 0.695911 | 0.347956 | − | 0.937511i | ||||||
0.347956 | + | 0.937511i | ||||||||
0 | 0 | |||||||||
−672.637 | + | 3715.38i | −0.236040 | + | 1.30379i | |||||
0 | 0 | |||||||||
95.0325 | + | 164.601i | 0.0328570 | + | 0.0569100i | |||||
0 | 0 | |||||||||
39.4183 | − | 68.2745i | 0.0134297 | − | 0.0232610i | |||||
0 | 0 | |||||||||
859.530 | − | 707.950i | 0.288606 | − | 0.237710i | |||||
0 | 0 | |||||||||
231.230 | − | 400.501i | 0.0765286 | − | 0.132551i | |||||
0 | 0 | |||||||||
−1613.64 | − | 2794.91i | −0.526482 | − | 0.911894i | −0.999524 | − | 0.0308540i | ||
0.473042 | − | 0.881040i | ||||||||
0 | 0 | |||||||||
−3289.92 | − | 2786.28i | −1.05832 | − | 0.896305i | |||||
0 | 0 | |||||||||
2905.57 | 0.921666 | |||||||||
0 | 0 | |||||||||
298.726 | 0.0934510 | |||||||||
0 | 0 | |||||||||
−634.850 | − | 537.664i | −0.195887 | − | 0.165899i | |||||
0 | 0 | |||||||||
206.745 | + | 358.093i | 0.0629284 | + | 0.108995i | |||||
0 | 0 | |||||||||
−2327.99 | + | 4032.19i | −0.699075 | + | 1.21083i | 0.269713 | + | 0.962941i | ||
−0.968788 | + | 0.247892i | ||||||||
0 | 0 | |||||||||
1535.88 | + | 574.960i | 0.455075 | + | 0.170359i | |||||
0 | 0 | |||||||||
2040.40 | − | 3534.08i | 0.596592 | − | 1.03333i | −0.396728 | − | 0.917936i | ||
0.993320 | − | 0.115391i | ||||||||
0 | 0 | |||||||||
−649.220 | − | 1124.48i | −0.187344 | − | 0.324489i | 0.757020 | − | 0.653391i | ||
−0.944364 | + | 0.328903i | ||||||||
0 | 0 | |||||||||
4.62994 | − | 25.5739i | 0.00131873 | − | 0.00728416i | |||||
0 | 0 | |||||||||
−3073.26 | −0.864103 | −0.432052 | − | 0.901849i | ||||||
−0.432052 | + | 0.901849i | ||||||||
0 | 0 | |||||||||
602.630 | 0.167282 | |||||||||
0 | 0 | |||||||||
4522.22 | − | 1622.60i | 1.23945 | − | 0.444721i | |||||
0 | 0 | |||||||||
1787.76 | + | 3096.49i | 0.483852 | + | 0.838056i | 0.999828 | − | 0.0185469i | ||
−0.515976 | + | 0.856603i | ||||||||
0 | 0 | |||||||||
1358.79 | − | 2353.50i | 0.363185 | − | 0.629055i | −0.625298 | − | 0.780386i | ||
0.988483 | + | 0.151331i | ||||||||
0 | 0 | |||||||||
−3529.03 | − | 1376.53i | −0.931636 | − | 0.363394i | |||||
0 | 0 | |||||||||
−1371.27 | + | 2375.10i | −0.357580 | + | 0.619346i | |||||
0 | 0 | |||||||||
−135.005 | − | 233.836i | −0.0347781 | − | 0.0602374i | |||||
0 | 0 | |||||||||
−2502.59 | + | 897.941i | −0.636928 | + | 0.228533i | |||||
0 | 0 | |||||||||
−4583.36 | −1.15259 | −0.576293 | − | 0.817243i | ||||||
−0.576293 | + | 0.817243i | ||||||||
0 | 0 | |||||||||
220.098 | 0.0546935 | |||||||||
0 | 0 | |||||||||
−984.722 | + | 5439.21i | −0.241826 | + | 1.33575i | |||||
0 | 0 | |||||||||
−2987.71 | − | 5174.87i | −0.725169 | − | 1.25603i | −0.958904 | − | 0.283730i | ||
0.233735 | − | 0.972300i | ||||||||
0 | 0 | |||||||||
170.346 | − | 295.049i | 0.0408680 | − | 0.0707855i | |||||
0 | 0 | |||||||||
5127.91 | + | 1919.65i | 1.21613 | + | 0.455261i | |||||
0 | 0 | |||||||||
−3087.59 | + | 5347.86i | −0.723912 | + | 1.25385i | 0.235509 | + | 0.971872i | ||
−0.959420 | + | 0.281980i | ||||||||
0 | 0 | |||||||||
1619.21 | + | 2804.55i | 0.375348 | + | 0.650121i | |||||
0 | 0 | |||||||||
−1270.68 | − | 1076.16i | −0.291252 | − | 0.246665i | |||||
0 | 0 | |||||||||
6580.02 | 1.49142 | 0.745708 | − | 0.666273i | ||||||
0.745708 | + | 0.666273i | ||||||||
0 | 0 | |||||||||
5817.31 | 1.30397 | 0.651986 | − | 0.758231i | ||||||
0.651986 | + | 0.758231i | ||||||||
0 | 0 | |||||||||
−11.5795 | − | 9.80684i | −0.00256712 | − | 0.00217413i | |||||
0 | 0 | |||||||||
162.074 | + | 280.721i | 0.0355398 | + | 0.0615568i | |||||
0 | 0 | |||||||||
−4325.53 | + | 7492.03i | −0.938252 | + | 1.62510i | −0.169521 | + | 0.985527i | ||
−0.768730 | + | 0.639573i | ||||||||
0 | 0 | |||||||||
6642.69 | − | 5471.23i | 1.42540 | − | 1.17403i | |||||
0 | 0 | |||||||||
−3648.14 | + | 6318.76i | −0.774483 | + | 1.34144i | 0.160602 | + | 0.987019i | ||
−0.935085 | + | 0.354424i | ||||||||
0 | 0 | |||||||||
405.958 | + | 703.140i | 0.0852710 | + | 0.147694i | 0.905507 | − | 0.424332i | ||
−0.820236 | + | 0.572026i | ||||||||
0 | 0 | |||||||||
643.027 | − | 3551.82i | 0.133648 | − | 0.738217i | |||||
0 | 0 | |||||||||
9.21728 | 0.00189574 | |||||||||
0 | 0 | |||||||||
12697.5 | 2.58446 | |||||||||
0 | 0 | |||||||||
2942.55 | − | 1055.80i | 0.592767 | − | 0.212688i | |||||
0 | 0 | |||||||||
2400.96 | + | 4158.58i | 0.478722 | + | 0.829170i | 0.999702 | − | 0.0243984i | ||
−0.520981 | + | 0.853568i | ||||||||
0 | 0 | |||||||||
−1726.31 | + | 2990.06i | −0.340711 | + | 0.590128i | |||||
0 | 0 | |||||||||
−365.437 | − | 653.478i | −0.0713967 | − | 0.127672i | |||||
0 | 0 | |||||||||
64.2531 | − | 111.290i | 0.0124276 | − | 0.0215252i | |||||
0 | 0 | |||||||||
169.854 | + | 294.196i | 0.0325257 | + | 0.0563361i | |||||
0 | 0 | |||||||||
−4285.98 | + | 1537.83i | −0.812617 | + | 0.291571i | |||||
0 | 0 | |||||||||
−2577.75 | −0.483939 | |||||||||
0 | 0 | |||||||||
−755.147 | −0.140386 | −0.0701930 | − | 0.997533i | ||||||
−0.0701930 | + | 0.997533i | ||||||||
0 | 0 | |||||||||
−206.829 | + | 1142.44i | −0.0380780 | + | 0.210328i | |||||
0 | 0 | |||||||||
−2633.03 | − | 4560.55i | −0.480082 | − | 0.831527i | 0.519657 | − | 0.854375i | ||
−0.999739 | + | 0.0228482i | ||||||||
0 | 0 | |||||||||
−697.053 | + | 1207.33i | −0.125878 | + | 0.218027i | −0.922076 | − | 0.387009i | ||
0.796198 | + | 0.605036i | ||||||||
0 | 0 | |||||||||
−33.3983 | − | 200.085i | −0.00597391 | − | 0.0357889i | |||||
0 | 0 | |||||||||
2558.55 | − | 4431.55i | 0.453321 | − | 0.785175i | −0.545269 | − | 0.838261i | ||
0.998590 | + | 0.0530862i | ||||||||
0 | 0 | |||||||||
541.126 | + | 937.257i | 0.0949756 | + | 0.164503i | |||||
0 | 0 | |||||||||
−5017.30 | − | 4249.23i | −0.872394 | − | 0.738843i | |||||
0 | 0 | |||||||||
−11499.7 | −1.98099 | |||||||||
0 | 0 | |||||||||
189.257 | 0.0323018 | |||||||||
0 | 0 | |||||||||
−844.620 | − | 715.321i | −0.142837 | − | 0.120970i | |||||
0 | 0 | |||||||||
35.2286 | + | 61.0177i | 0.00590339 | + | 0.0102250i | |||||
0 | 0 | |||||||||
121.400 | − | 210.271i | 0.0201593 | − | 0.0349170i | −0.855770 | − | 0.517357i | ||
0.875929 | + | 0.482440i | ||||||||
0 | 0 | |||||||||
−1615.93 | − | 9680.84i | −0.265924 | − | 1.59311i | |||||
0 | 0 | |||||||||
−2912.50 | + | 5044.59i | −0.475005 | + | 0.822733i | |||||
0 | 0 | |||||||||
25.6472 | + | 44.4223i | 0.00414568 | + | 0.00718052i | 0.868091 | − | 0.496405i | ||
−0.863945 | + | 0.503586i | ||||||||
0 | 0 | |||||||||
1494.01 | − | 8252.31i | 0.239361 | − | 1.32214i | |||||
0 | 0 | |||||||||
1700.98 | 0.270127 | |||||||||
0 | 0 | |||||||||
−642.117 | −0.101082 | |||||||||
0 | 0 | |||||||||
1616.96 | − | 580.175i | 0.252332 | − | 0.0905379i | |||||
0 | 0 | |||||||||
430.722 | + | 746.032i | 0.0666350 | + | 0.115415i | 0.897418 | − | 0.441181i | ||
−0.830783 | + | 0.556596i | ||||||||
0 | 0 | |||||||||
−1562.68 | + | 2706.64i | −0.239680 | + | 0.415138i | −0.960623 | − | 0.277857i | ||
0.720942 | + | 0.692995i | ||||||||
0 | 0 | |||||||||
−437.104 | − | 5.99107i | −0.0664697 | − | 0.000911053i | |||||
0 | 0 | |||||||||
4162.36 | − | 7209.43i | 0.627593 | − | 1.08702i | −0.360440 | − | 0.932782i | ||
0.988033 | − | 0.154241i | ||||||||
0 | 0 | |||||||||
−3325.55 | − | 5760.02i | −0.497189 | − | 0.861156i | |||||
0 | 0 | |||||||||
−608.298 | + | 218.261i | −0.0901808 | + | 0.0323573i | |||||
0 | 0 | |||||||||
−5819.46 | −0.855542 | −0.427771 | − | 0.903887i | ||||||
−0.427771 | + | 0.903887i | ||||||||
0 | 0 | |||||||||
650.350 | 0.0948170 | |||||||||
0 | 0 | |||||||||
−1205.70 | + | 6659.83i | −0.174334 | + | 0.962949i | |||||
0 | 0 | |||||||||
−641.725 | − | 1111.50i | −0.0920259 | − | 0.159393i | |||||
0 | 0 | |||||||||
3129.64 | − | 5420.69i | 0.445138 | − | 0.771002i | −0.552924 | − | 0.833232i | ||
0.998062 | + | 0.0622299i | ||||||||
0 | 0 | |||||||||
204.962 | − | 168.816i | 0.0289157 | − | 0.0238163i | |||||
0 | 0 | |||||||||
−189.312 | + | 327.898i | −0.0264921 | + | 0.0458857i | |||||
0 | 0 | |||||||||
−240.335 | − | 416.273i | −0.0333622 | − | 0.0577850i | 0.848862 | − | 0.528614i | ||
−0.882224 | + | 0.470829i | ||||||||
0 | 0 | |||||||||
5903.91 | + | 5000.11i | 0.813004 | + | 0.688545i | |||||
0 | 0 | |||||||||
631.881 | 0.0863224 | |||||||||
0 | 0 | |||||||||
7321.57 | 0.992305 | 0.496152 | − | 0.868235i | ||||||
0.496152 | + | 0.868235i | ||||||||
0 | 0 | |||||||||
−4893.77 | − | 4144.61i | −0.658046 | − | 0.557309i | |||||
0 | 0 | |||||||||
−1323.45 | − | 2292.28i | −0.176567 | − | 0.305823i | 0.764135 | − | 0.645056i | ||
−0.940702 | + | 0.339233i | ||||||||
0 | 0 | |||||||||
20.0475 | − | 34.7233i | 0.00265381 | − | 0.00459653i | |||||
0 | 0 | |||||||||
9165.25 | + | 3431.03i | 1.20387 | + | 0.450670i | |||||
0 | 0 | |||||||||
−2430.72 | + | 4210.12i | −0.316818 | + | 0.548745i | −0.979822 | − | 0.199871i | ||
0.663004 | + | 0.748616i | ||||||||
0 | 0 | |||||||||
−2736.53 | − | 4739.80i | −0.353944 | − | 0.613049i | |||||
0 | 0 | |||||||||
−1339.85 | + | 7400.81i | −0.171976 | + | 0.949927i | |||||
0 | 0 | |||||||||
7412.06 | 0.944155 | |||||||||
0 | 0 | |||||||||
−7253.21 | −0.916948 | −0.458474 | − | 0.888708i | ||||||
−0.458474 | + | 0.888708i | ||||||||
0 | 0 | |||||||||
397.221 | − | 142.525i | 0.0498394 | − | 0.0178826i | |||||
0 | 0 | |||||||||
1150.69 | + | 1993.05i | 0.143298 | + | 0.248200i | 0.928737 | − | 0.370740i | ||
−0.785438 | + | 0.618940i | ||||||||
0 | 0 | |||||||||
496.566 | − | 860.078i | 0.0613789 | − | 0.106311i | |||||
0 | 0 | |||||||||
−4407.26 | − | 3837.53i | −0.540737 | − | 0.470835i | |||||
0 | 0 | |||||||||
969.971 | − | 1680.04i | 0.118132 | − | 0.204611i | |||||
0 | 0 | |||||||||
902.216 | + | 1562.68i | 0.109075 | + | 0.188924i | 0.915396 | − | 0.402555i | ||
−0.806321 | + | 0.591479i | ||||||||
0 | 0 | |||||||||
−2708.47 | + | 971.811i | −0.325058 | + | 0.116632i | |||||
0 | 0 | |||||||||
−403.667 | −0.0480948 | |||||||||
0 | 0 | |||||||||
−4101.81 | −0.485181 | |||||||||
0 | 0 | |||||||||
−1470.94 | + | 8124.90i | −0.172739 | + | 0.954143i | |||||
0 | 0 | |||||||||
3738.18 | + | 6474.71i | 0.435852 | + | 0.754917i | 0.997365 | − | 0.0725506i | ||
−0.561513 | + | 0.827468i | ||||||||
0 | 0 | |||||||||
−6443.01 | + | 11159.6i | −0.745875 | + | 1.29189i | 0.203910 | + | 0.978990i | ||
−0.949785 | + | 0.312903i | ||||||||
0 | 0 | |||||||||
1900.92 | + | 711.614i | 0.218501 | + | 0.0817963i | |||||
0 | 0 | |||||||||
4030.21 | − | 6980.53i | 0.459986 | − | 0.796718i | |||||
0 | 0 | |||||||||
−150.690 | − | 261.003i | −0.0170783 | − | 0.0295804i | |||||
0 | 0 | |||||||||
−65.9349 | − | 55.8412i | −0.00742043 | − | 0.00628447i | |||||
0 | 0 | |||||||||
13065.8 | 1.46022 | 0.730110 | − | 0.683329i | ||||||
0.730110 | + | 0.683329i | ||||||||
0 | 0 | |||||||||
−6190.38 | −0.687046 | −0.343523 | − | 0.939144i | ||||||
−0.343523 | + | 0.939144i | ||||||||
0 | 0 | |||||||||
6446.01 | + | 5459.22i | 0.710488 | + | 0.601723i | |||||
0 | 0 | |||||||||
1786.96 | + | 3095.11i | 0.195611 | + | 0.338808i | |||||
0 | 0 | |||||||||
7271.78 | − | 12595.1i | 0.790576 | − | 1.36932i | −0.135034 | − | 0.990841i | ||
0.925610 | − | 0.378478i | ||||||||
0 | 0 | |||||||||
−7130.13 | + | 5872.71i | −0.769909 | + | 0.634133i | |||||
0 | 0 | |||||||||
426.857 | − | 739.339i | 0.0457802 | − | 0.0792935i | −0.842227 | − | 0.539123i | ||
0.888007 | + | 0.459829i | ||||||||
0 | 0 | |||||||||
−1284.44 | − | 2224.71i | −0.136828 | − | 0.236992i | |||||
0 | 0 | |||||||||
−1122.66 | + | 6201.15i | −0.118792 | + | 0.656162i | |||||
0 | 0 | |||||||||
6187.67 | 0.650366 | 0.325183 | − | 0.945651i | ||||||
0.325183 | + | 0.945651i | ||||||||
0 | 0 | |||||||||
52.4842 | 0.00547979 | |||||||||
0 | 0 | |||||||||
−2601.24 | + | 933.339i | −0.269795 | + | 0.0968037i | |||||
0 | 0 | |||||||||
−11.7049 | − | 20.2735i | −0.00120601 | − | 0.00208887i | |||||
0 | 0 | |||||||||
−2389.06 | + | 4137.98i | −0.244542 | + | 0.423559i | −0.962003 | − | 0.273040i | ||
0.717461 | + | 0.696599i | ||||||||
0 | 0 | |||||||||
−9529.06 | + | 15994.5i | −0.969016 | + | 1.62649i | |||||
0 | 0 | |||||||||
4544.60 | − | 7871.47i | 0.459139 | − | 0.795252i | −0.539777 | − | 0.841808i | ||
0.998916 | + | 0.0465564i | ||||||||
0 | 0 | |||||||||
3674.11 | + | 6363.74i | 0.368791 | + | 0.638765i | 0.989377 | − | 0.145374i | ||
−0.620586 | + | 0.784139i | ||||||||
0 | 0 | |||||||||
12496.4 | − | 4483.76i | 1.24625 | − | 0.447160i | |||||
0 | 0 | |||||||||
948.436 | 0.0939794 | 0.0469897 | − | 0.998895i | ||||||
0.0469897 | + | 0.998895i | ||||||||
0 | 0 | |||||||||
−681.037 | −0.0670519 | |||||||||
0 | 0 | |||||||||
2002.17 | − | 11059.2i | 0.195871 | − | 1.08191i | |||||
0 | 0 | |||||||||
967.168 | + | 1675.18i | 0.0940178 | + | 0.162844i | |||||
0 | 0 | |||||||||
−2631.74 | + | 4558.31i | −0.254216 | + | 0.440315i | |||||
0 | 0 | |||||||||
1795.84 | + | 10758.6i | 0.172381 | + | 1.03271i | |||||
0 | 0 | |||||||||
−1493.94 | + | 2587.58i | −0.142505 | + | 0.246826i | −0.928439 | − | 0.371484i | ||
0.785934 | + | 0.618310i | ||||||||
0 | 0 | |||||||||
−566.326 | − | 980.905i | −0.0536845 | − | 0.0929843i | |||||
0 | 0 | |||||||||
153.269 | + | 129.806i | 0.0144389 | + | 0.0122285i | |||||
0 | 0 | |||||||||
4822.92 | 0.451542 | |||||||||
0 | 0 | |||||||||
−19555.8 | −1.81963 | −0.909814 | − | 0.415017i | ||||||
−0.909814 | + | 0.415017i | ||||||||
0 | 0 | |||||||||
−6352.66 | − | 5380.16i | −0.587479 | − | 0.497545i | |||||
0 | 0 | |||||||||
−429.064 | − | 743.160i | −0.0394366 | − | 0.0683062i | 0.845633 | − | 0.533764i | ||
−0.885070 | + | 0.465458i | ||||||||
0 | 0 | |||||||||
13455.9 | − | 23306.2i | 1.22925 | − | 2.12913i | |||||
0 | 0 | |||||||||
−190.174 | − | 1139.30i | −0.0172680 | − | 0.103450i | |||||
0 | 0 | |||||||||
388.811 | − | 673.440i | 0.0350917 | − | 0.0607806i | |||||
0 | 0 | |||||||||
−1844.70 | − | 3195.12i | −0.165491 | − | 0.286640i | 0.771338 | − | 0.636425i | ||
−0.936830 | + | 0.349786i | ||||||||
0 | 0 | |||||||||
−1604.74 | + | 8863.96i | −0.143103 | + | 0.790444i | |||||
0 | 0 | |||||||||
9034.08 | 0.800814 | 0.400407 | − | 0.916337i | ||||||
0.400407 | + | 0.916337i | ||||||||
0 | 0 | |||||||||
−7024.84 | −0.619013 | |||||||||
0 | 0 | |||||||||
10697.7 | − | 3838.40i | 0.937086 | − | 0.336231i | |||||
0 | 0 | |||||||||
3145.21 | + | 5447.66i | 0.273888 | + | 0.474387i | 0.969854 | − | 0.243687i | ||
−0.695966 | + | 0.718075i | ||||||||
0 | 0 | |||||||||
75.0281 | − | 129.953i | 0.00649520 | − | 0.0112500i | |||||
0 | 0 | |||||||||
6222.51 | − | 10444.5i | 0.535537 | − | 0.898898i | |||||
0 | 0 | |||||||||
−895.565 | + | 1551.16i | −0.0766278 | + | 0.132723i | |||||
0 | 0 | |||||||||
200.595 | + | 347.442i | 0.0170642 | + | 0.0295560i | |||||
0 | 0 | |||||||||
−9168.62 | + | 3289.75i | −0.775449 | + | 0.278235i | |||||
0 | 0 | |||||||||
−13010.4 | −1.09404 | −0.547019 | − | 0.837120i | ||||||
−0.547019 | + | 0.837120i | ||||||||
0 | 0 | |||||||||
1108.69 | 0.0926956 | 0.0463478 | − | 0.998925i | ||||||
0.0463478 | + | 0.998925i | ||||||||
0 | 0 | |||||||||
−52.6957 | + | 291.070i | −0.00438063 | + | 0.0241968i | |||||
0 | 0 | |||||||||
−21148.7 | − | 36630.5i | −1.74810 | − | 3.02780i | |||||
0 | 0 | |||||||||
5233.03 | − | 9063.88i | 0.430100 | − | 0.744956i | |||||
0 | 0 | |||||||||
−8976.22 | + | 7393.25i | −0.733588 | + | 0.604218i | |||||
0 | 0 | |||||||||
15.3217 | − | 26.5379i | 0.00124513 | − | 0.00215663i | |||||
0 | 0 | |||||||||
−5071.64 | − | 8784.34i | −0.409843 | − | 0.709869i | |||||
0 | 0 | |||||||||
8160.37 | + | 6911.14i | 0.655765 | + | 0.555377i | |||||
0 | 0 | |||||||||
−1825.80 | −0.145905 | |||||||||
0 | 0 | |||||||||
−38.8964 | −0.00309110 | −0.00154555 | − | 0.999999i | ||||||
−0.00154555 | + | 0.999999i | ||||||||
0 | 0 | |||||||||
−15616.7 | − | 13226.0i | −1.23421 | − | 1.04527i | |||||
0 | 0 | |||||||||
−853.768 | − | 1478.77i | −0.0671035 | − | 0.116227i | |||||
0 | 0 | |||||||||
−5014.91 | + | 8686.08i | −0.391997 | + | 0.678958i | −0.992713 | − | 0.120504i | ||
0.600716 | + | 0.799462i | ||||||||
0 | 0 | |||||||||
−8131.18 | − | 3043.93i | −0.632114 | − | 0.236633i | |||||
0 | 0 | |||||||||
−8786.73 | + | 15219.1i | −0.679359 | + | 1.17669i | |||||
0 | 0 | |||||||||
433.295 | + | 750.489i | 0.0333193 | + | 0.0577107i | |||||
0 | 0 | |||||||||
2697.40 | − | 14899.3i | 0.206303 | − | 1.13953i | |||||
0 | 0 | |||||||||
−7355.74 | −0.559556 | −0.279778 | − | 0.960065i | ||||||
−0.279778 | + | 0.960065i | ||||||||
0 | 0 | |||||||||
1129.38 | 0.0854519 | |||||||||
0 | 0 | |||||||||
−3463.72 | + | 1242.80i | −0.260674 | + | 0.0935312i | |||||
0 | 0 | |||||||||
10729.9 | + | 18584.8i | 0.803220 | + | 1.39122i | 0.917486 | + | 0.397767i | ||
−0.114267 | + | 0.993450i | ||||||||
0 | 0 | |||||||||
6469.02 | − | 11204.7i | 0.481688 | − | 0.834308i | |||||
0 | 0 | |||||||||
130.919 | − | 670.581i | 0.00969678 | − | 0.0496680i | |||||
0 | 0 | |||||||||
728.962 | − | 1262.60i | 0.0537077 | − | 0.0930245i | −0.837922 | − | 0.545791i | ||
0.891629 | + | 0.452766i | ||||||||
0 | 0 | |||||||||
11200.0 | + | 19399.0i | 0.820853 | + | 1.42176i | 0.905048 | + | 0.425310i | ||
−0.0841950 | + | 0.996449i | ||||||||
0 | 0 | |||||||||
21838.1 | − | 7835.62i | 1.59215 | − | 0.571270i | |||||
0 | 0 | |||||||||
−2505.05 | −0.181683 | |||||||||
0 | 0 | |||||||||
−12833.5 | −0.925936 | −0.462968 | − | 0.886375i | ||||||
−0.462968 | + | 0.886375i | ||||||||
0 | 0 | |||||||||
3841.56 | − | 21219.3i | 0.275734 | − | 1.52304i | |||||
0 | 0 | |||||||||
−239.784 | − | 415.319i | −0.0171221 | − | 0.0296563i | |||||
0 | 0 | |||||||||
−1077.96 | + | 1867.08i | −0.0765774 | + | 0.132636i | |||||
0 | 0 | |||||||||
−631.591 | − | 236.438i | −0.0446377 | − | 0.0167102i | |||||
0 | 0 | |||||||||
10377.4 | − | 17974.2i | 0.729677 | − | 1.26384i | −0.227343 | − | 0.973815i | ||
0.957020 | − | 0.290023i | ||||||||
0 | 0 | |||||||||
13810.2 | + | 23919.9i | 0.966108 | + | 1.67335i | |||||
0 | 0 | |||||||||
2128.60 | + | 1802.75i | 0.148154 | + | 0.125474i | |||||
0 | 0 | |||||||||
113.272 | 0.00784406 | 0.00392203 | − | 0.999992i | ||||||
0.00392203 | + | 0.999992i | ||||||||
0 | 0 | |||||||||
−997.019 | −0.0686955 | |||||||||
0 | 0 | |||||||||
7746.34 | + | 6560.49i | 0.531050 | + | 0.449754i | |||||
0 | 0 | |||||||||
5581.01 | + | 9666.59i | 0.380691 | + | 0.659376i | 0.991161 | − | 0.132663i | ||
−0.610470 | + | 0.792039i | ||||||||
0 | 0 | |||||||||
939.910 | − | 1627.97i | 0.0637932 | − | 0.110493i | −0.832365 | − | 0.554228i | ||
0.896158 | + | 0.443735i | ||||||||
0 | 0 | |||||||||
−15144.0 | + | 12473.3i | −1.02274 | + | 0.842376i | |||||
0 | 0 | |||||||||
−5220.67 | + | 9042.46i | −0.350827 | + | 0.607650i | |||||
0 | 0 | |||||||||
10662.2 | + | 18467.4i | 0.712956 | + | 1.23488i | 0.963743 | + | 0.266834i | ||
−0.250787 | + | 0.968042i | ||||||||
0 | 0 | |||||||||
−175.938 | + | 971.810i | −0.0117067 | + | 0.0646629i | |||||
0 | 0 | |||||||||
234.239 | 0.0155095 | |||||||||
0 | 0 | |||||||||
26096.2 | 1.71944 | 0.859720 | − | 0.510765i | ||||||
0.859720 | + | 0.510765i | ||||||||
0 | 0 | |||||||||
385.578 | − | 138.347i | 0.0252813 | − | 0.00907107i | |||||
0 | 0 | |||||||||
9590.63 | + | 16611.5i | 0.625777 | + | 1.08388i | 0.988390 | + | 0.151937i | ||
−0.362614 | + | 0.931940i | ||||||||
0 | 0 | |||||||||
1681.58 | − | 2912.58i | 0.109190 | − | 0.189122i | −0.806253 | − | 0.591571i | ||
0.915442 | + | 0.402450i | ||||||||
0 | 0 | |||||||||
5785.61 | + | 79.2993i | 0.373862 | + | 0.00512427i | |||||
0 | 0 | |||||||||
150.172 | − | 260.105i | 0.00965731 | − | 0.0167270i | |||||
0 | 0 | |||||||||
2171.62 | + | 3761.36i | 0.138984 | + | 0.240727i | |||||
0 | 0 | |||||||||
2261.82 | − | 811.553i | 0.144064 | − | 0.0516911i | |||||
0 | 0 | |||||||||
−48239.4 | −3.05792 | |||||||||
0 | 0 | |||||||||
1485.04 | 0.0936900 | 0.0468450 | − | 0.998902i | ||||||
0.0468450 | + | 0.998902i | ||||||||
0 | 0 | |||||||||
2987.40 | − | 16501.2i | 0.187581 | − | 1.03612i | |||||
0 | 0 | |||||||||
−4946.78 | − | 8568.07i | −0.309145 | − | 0.535454i | |||||
0 | 0 | |||||||||
−533.004 | + | 923.189i | −0.0331529 | + | 0.0574224i | |||||
0 | 0 | |||||||||
−3688.32 | − | 22096.2i | −0.228338 | − | 1.36794i | |||||
0 | 0 | |||||||||
−8208.10 | + | 14216.8i | −0.505773 | + | 0.876024i | 0.494205 | + | 0.869345i | ||
−0.999978 | + | 0.00667861i | ||||||||
0 | 0 | |||||||||
10200.0 | + | 17666.9i | 0.625580 | + | 1.08354i | 0.988428 | + | 0.151688i | ||
−0.362848 | + | 0.931848i | ||||||||
0 | 0 | |||||||||
11521.1 | + | 9757.40i | 0.703323 | + | 0.595655i | |||||
0 | 0 | |||||||||
25011.7 | 1.51980 | 0.759900 | − | 0.650040i | ||||||
0.759900 | + | 0.650040i | ||||||||
0 | 0 | |||||||||
−2298.53 | −0.139022 | |||||||||
0 | 0 | |||||||||
1184.51 | + | 1003.17i | 0.0713125 | + | 0.0603956i | |||||
0 | 0 | |||||||||
−3763.77 | − | 6519.03i | −0.225555 | − | 0.390673i | 0.730931 | − | 0.682452i | ||
−0.956486 | + | 0.291779i | ||||||||
0 | 0 | |||||||||
−5801.52 | + | 10048.5i | −0.346083 | + | 0.599433i | |||||
0 | 0 | |||||||||
−711.729 | − | 4263.87i | −0.0422636 | − | 0.253195i | |||||
0 | 0 | |||||||||
−14984.0 | + | 25953.0i | −0.885725 | + | 1.53412i | −0.0408452 | + | 0.999165i | ||
−0.844880 | + | 0.534956i | ||||||||
0 | 0 | |||||||||
−6153.81 | − | 10658.7i | −0.362111 | − | 0.627195i | 0.626197 | − | 0.779665i | ||
−0.988308 | + | 0.152470i | ||||||||
0 | 0 | |||||||||
−382.756 | + | 2114.19i | −0.0224208 | + | 0.123844i | |||||
0 | 0 | |||||||||
651.057 | 0.0379653 | |||||||||
0 | 0 | |||||||||
−8363.73 | −0.485525 | |||||||||
0 | 0 | |||||||||
−22771.7 | + | 8170.60i | −1.31600 | + | 0.472188i | |||||
0 | 0 | |||||||||
−858.047 | − | 1486.18i | −0.0493659 | − | 0.0855043i | |||||
0 | 0 | |||||||||
−1385.42 | + | 2399.61i | −0.0793521 | + | 0.137442i | −0.902971 | − | 0.429702i | ||
0.823618 | + | 0.567144i | ||||||||
0 | 0 | |||||||||
4159.23 | + | 7437.57i | 0.237168 | + | 0.424107i | |||||
0 | 0 | |||||||||
11232.5 | − | 19455.2i | 0.637666 | − | 1.10447i | −0.348278 | − | 0.937391i | ||
0.985944 | − | 0.167078i | ||||||||
0 | 0 | |||||||||
281.939 | + | 488.333i | 0.0159349 | + | 0.0276001i | |||||
0 | 0 | |||||||||
19958.6 | − | 7161.26i | 1.12308 | − | 0.402966i | |||||
0 | 0 | |||||||||
−7924.28 | −0.443945 | −0.221972 | − | 0.975053i | ||||||
−0.221972 | + | 0.975053i | ||||||||
0 | 0 | |||||||||
−4439.25 | −0.247613 | |||||||||
0 | 0 | |||||||||
1201.93 | − | 6638.97i | 0.0667488 | − | 0.368694i | |||||
0 | 0 | |||||||||
629.377 | + | 1090.11i | 0.0348002 | + | 0.0602757i | |||||
0 | 0 | |||||||||
11390.2 | − | 19728.4i | 0.627067 | − | 1.08611i | −0.361070 | − | 0.932539i | ||
0.988137 | − | 0.153573i | ||||||||
0 | 0 | |||||||||
104.240 | − | 85.8572i | 0.00571394 | − | 0.00470627i | |||||
0 | 0 | |||||||||
−6369.14 | + | 11031.7i | −0.347619 | + | 0.602094i | |||||
0 | 0 | |||||||||
−652.547 | − | 1130.24i | −0.0354619 | − | 0.0614219i | |||||
0 | 0 | |||||||||
−12186.0 | − | 10320.5i | −0.659397 | − | 0.558453i | |||||
0 | 0 | |||||||||
−13999.0 | −0.754256 | −0.377128 | − | 0.926161i | ||||||
−0.377128 | + | 0.926161i | ||||||||
0 | 0 | |||||||||
31500.5 | 1.68999 | |||||||||
0 | 0 | |||||||||
2389.54 | + | 2023.73i | 0.127653 | + | 0.108111i | |||||
0 | 0 | |||||||||
−410.659 | − | 711.283i | −0.0218450 | − | 0.0378367i | |||||
0 | 0 | |||||||||
4513.32 | − | 7817.30i | 0.239071 | − | 0.414083i | −0.721377 | − | 0.692543i | ||
0.960448 | + | 0.278459i | ||||||||
0 | 0 | |||||||||
23380.4 | + | 8752.51i | 1.23324 | + | 0.461666i | |||||
0 | 0 | |||||||||
−6572.67 | + | 11384.2i | −0.345229 | + | 0.597954i | |||||
0 | 0 | |||||||||
−66.6490 | − | 115.439i | −0.00348606 | − | 0.00603803i | |||||
0 | 0 | |||||||||
−3309.76 | + | 18281.8i | −0.172392 | + | 0.952225i | |||||
0 | 0 | |||||||||
18206.9 | 0.944371 | 0.472186 | − | 0.881499i | ||||||
0.472186 | + | 0.881499i | ||||||||
0 | 0 | |||||||||
−209.412 | −0.0108168 | |||||||||
0 | 0 | |||||||||
13291.3 | − | 4768.99i | 0.683692 | − | 0.245312i | |||||
0 | 0 | |||||||||
−6158.83 | − | 10667.4i | −0.315494 | − | 0.546452i | |||||
0 | 0 | |||||||||
−5167.05 | + | 8949.60i | −0.263598 | + | 0.456564i | −0.967195 | − | 0.254034i | ||
0.703598 | + | 0.710599i | ||||||||
0 | 0 | |||||||||
−9370.62 | − | 17309.3i | −0.476077 | − | 0.879404i | |||||
0 | 0 | |||||||||
24050.0 | − | 41655.8i | 1.21686 | − | 2.10766i | |||||
0 | 0 | |||||||||
−11176.3 | − | 19358.0i | −0.563176 | − | 0.975449i | −0.997217 | − | 0.0745557i | ||
0.434041 | − | 0.900893i | ||||||||
0 | 0 | |||||||||
−13413.3 | + | 4812.77i | −0.673141 | + | 0.241526i | |||||
0 | 0 | |||||||||
−3877.90 | −0.193818 | |||||||||
0 | 0 | |||||||||
−22423.2 | −1.11617 | −0.558086 | − | 0.829783i | ||||||
−0.558086 | + | 0.829783i | ||||||||
0 | 0 | |||||||||
249.941 | − | 1380.57i | 0.0123911 | − | 0.0684435i | |||||
0 | 0 | |||||||||
−5827.69 | − | 10093.9i | −0.287749 | − | 0.498395i | 0.685523 | − | 0.728051i | ||
−0.973272 | + | 0.229655i | ||||||||
0 | 0 | |||||||||
−4861.10 | + | 8419.68i | −0.239056 | + | 0.414058i | |||||
0 | 0 | |||||||||
−12938.7 | − | 4843.62i | −0.633736 | − | 0.237240i | |||||
0 | 0 | |||||||||
592.957 | − | 1027.03i | 0.0289268 | − | 0.0501027i | |||||
0 | 0 | |||||||||
−1319.06 | − | 2284.68i | −0.0640923 | − | 0.111011i | 0.832199 | − | 0.554478i | ||
−0.896291 | + | 0.443466i | ||||||||
0 | 0 | |||||||||
−18173.9 | − | 15391.7i | −0.879539 | − | 0.744895i | |||||
0 | 0 | |||||||||
−4263.51 | −0.205517 | |||||||||
0 | 0 | |||||||||
−19939.5 | −0.957350 | −0.478675 | − | 0.877992i | ||||||
−0.478675 | + | 0.877992i | ||||||||
0 | 0 | |||||||||
872.730 | + | 739.128i | 0.0417366 | + | 0.0353473i | |||||
0 | 0 | |||||||||
13380.7 | + | 23176.0i | 0.637385 | + | 1.10398i | 0.986005 | + | 0.166719i | ||
−0.348620 | + | 0.937264i | ||||||||
0 | 0 | |||||||||
99.8193 | − | 172.892i | 0.00473618 | − | 0.00820330i | |||||
0 | 0 | |||||||||
−22170.4 | + | 18260.6i | −1.04781 | + | 0.863024i | |||||
0 | 0 | |||||||||
−671.007 | + | 1162.22i | −0.0315888 | + | 0.0547135i | |||||
0 | 0 | |||||||||
−3788.40 | − | 6561.71i | −0.177651 | − | 0.307700i | 0.763425 | − | 0.645897i | ||
−0.941075 | + | 0.338197i | ||||||||
0 | 0 | |||||||||
5531.28 | − | 30552.6i | 0.258371 | − | 1.42714i | |||||
0 | 0 | |||||||||
27041.3 | 1.25823 | 0.629113 | − | 0.777314i | ||||||
0.629113 | + | 0.777314i | ||||||||
0 | 0 | |||||||||
−19359.7 | −0.897319 | |||||||||
0 | 0 | |||||||||
1666.28 | − | 597.870i | 0.0769337 | − | 0.0276042i | |||||
0 | 0 | |||||||||
426.116 | + | 738.054i | 0.0195984 | + | 0.0339455i | |||||
0 | 0 | |||||||||
2213.93 | − | 3834.64i | 0.101435 | − | 0.175691i | |||||
0 | 0 | |||||||||
13886.6 | + | 24832.2i | 0.633802 | + | 1.13337i | |||||
0 | 0 | |||||||||
8669.33 | − | 15015.7i | 0.394168 | − | 0.682719i | |||||
0 | 0 | |||||||||
−16802.1 | − | 29102.2i | −0.761031 | − | 1.31814i | −0.942320 | − | 0.334714i | ||
0.181289 | − | 0.983430i | ||||||||
0 | 0 | |||||||||
−30201.9 | + | 10836.6i | −1.36276 | + | 0.488964i | |||||
0 | 0 | |||||||||
1512.67 | 0.0679953 | |||||||||
0 | 0 | |||||||||
−1001.96 | −0.0448682 | |||||||||
0 | 0 | |||||||||
−2997.71 | + | 16558.1i | −0.133733 | + | 0.738688i | |||||
0 | 0 | |||||||||
−21603.1 | − | 37417.7i | −0.960127 | − | 1.66299i | −0.722172 | − | 0.691714i | ||
−0.237955 | − | 0.971276i | ||||||||
0 | 0 | |||||||||
4988.09 | − | 8639.63i | 0.220859 | − | 0.382538i | |||||
0 | 0 | |||||||||
−1424.55 | − | 8534.30i | −0.0628391 | − | 0.376460i | |||||
0 | 0 | |||||||||
427.218 | − | 739.964i | 0.0187749 | − | 0.0325190i | |||||
0 | 0 | |||||||||
154.929 | + | 268.345i | 0.00678326 | + | 0.0117490i | |||||
0 | 0 | |||||||||
26091.0 | + | 22096.8i | 1.13810 | + | 0.963873i | |||||
0 | 0 | |||||||||
33276.5 | 1.44616 | 0.723078 | − | 0.690766i | ||||||
0.723078 | + | 0.690766i | ||||||||
0 | 0 | |||||||||
21917.4 | 0.948980 | 0.474490 | − | 0.880261i | ||||||
0.474490 | + | 0.880261i | ||||||||
0 | 0 | |||||||||
23066.7 | + | 19535.5i | 0.995061 | + | 0.842732i | |||||
0 | 0 | |||||||||
−6421.47 | − | 11122.3i | −0.275993 | − | 0.478034i | |||||
0 | 0 | |||||||||
−15704.7 | + | 27201.4i | −0.672509 | + | 1.16482i | |||||
0 | 0 | |||||||||
−12.9817 | − | 77.7718i | −0.000553869 | − | 0.00331815i | |||||
0 | 0 | |||||||||
536.732 | − | 929.647i | 0.0228162 | − | 0.0395188i | −0.854392 | − | 0.519629i | ||
0.877208 | + | 0.480110i | ||||||||
0 | 0 | |||||||||
−6229.21 | − | 10789.3i | −0.263835 | − | 0.456976i | 0.703422 | − | 0.710772i | ||
−0.967258 | + | 0.253796i | ||||||||
0 | 0 | |||||||||
−300.055 | + | 1657.38i | −0.0126625 | + | 0.0699427i | |||||
0 | 0 | |||||||||
−902.282 | −0.0379388 | −0.0189694 | − | 0.999820i | ||||||
−0.0189694 | + | 0.999820i | ||||||||
0 | 0 | |||||||||
29605.8 | 1.24035 | 0.620176 | − | 0.784462i | ||||||
0.620176 | + | 0.784462i | ||||||||
0 | 0 | |||||||||
−42311.0 | + | 15181.4i | −1.76625 | + | 0.633740i | |||||
0 | 0 | |||||||||
22700.5 | + | 39318.5i | 0.944210 | + | 1.63542i | |||||
0 | 0 | |||||||||
−6948.49 | + | 12035.1i | −0.287979 | + | 0.498794i | |||||
0 | 0 | |||||||||
44712.8 | + | 612.847i | 1.84648 | + | 0.0253084i | |||||
0 | 0 | |||||||||
−22726.8 | + | 39363.9i | −0.935178 | + | 1.61978i | −0.160863 | + | 0.986977i | ||
−0.774316 | + | 0.632799i | ||||||||
0 | 0 | |||||||||
−8368.28 | − | 14494.3i | −0.343117 | − | 0.594296i | |||||
0 | 0 | |||||||||
−35685.0 | + | 12804.0i | −1.45796 | + | 0.523122i | |||||
0 | 0 | |||||||||
17533.9 | 0.713827 | |||||||||
0 | 0 | |||||||||
−1220.76 | −0.0495229 | |||||||||
0 | 0 | |||||||||
−751.567 | + | 4151.36i | −0.0303813 | + | 0.167814i | |||||
0 | 0 | |||||||||
7496.02 | + | 12983.5i | 0.301951 | + | 0.522995i | |||||
0 | 0 | |||||||||
−2795.92 | + | 4842.68i | −0.112228 | + | 0.194385i | −0.916668 | − | 0.399649i | ||
0.804440 | + | 0.594034i | ||||||||
0 | 0 | |||||||||
14477.4 | − | 11924.2i | 0.579082 | − | 0.476960i | |||||
0 | 0 | |||||||||
20490.8 | − | 35491.1i | 0.816747 | − | 1.41465i | −0.0913204 | − | 0.995822i | ||
0.908067 | − | 0.418825i | ||||||||
0 | 0 | |||||||||
−21149.0 | − | 36631.2i | −0.840040 | − | 1.45499i | −0.889860 | − | 0.456234i | ||
0.0498192 | − | 0.998758i | ||||||||
0 | 0 | |||||||||
36.5482 | + | 30.9532i | 0.00144664 | + | 0.00122518i | |||||
0 | 0 | |||||||||
19236.0 | 0.758749 | 0.379374 | − | 0.925243i | ||||||
0.379374 | + | 0.925243i | ||||||||
0 | 0 | |||||||||
−15027.6 | −0.590700 | |||||||||
0 | 0 | |||||||||
50347.8 | + | 42640.3i | 1.97220 | + | 1.67029i | |||||
0 | 0 | |||||||||
2467.23 | + | 4273.36i | 0.0963118 | + | 0.166817i | |||||
0 | 0 | |||||||||
−1132.07 | + | 1960.80i | −0.0440399 | + | 0.0762794i | |||||
0 | 0 | |||||||||
15213.3 | + | 5695.14i | 0.589796 | + | 0.220792i | |||||
0 | 0 | |||||||||
−697.738 | + | 1208.52i | −0.0269576 | + | 0.0466919i | |||||
0 | 0 | |||||||||
12060.4 | + | 20889.2i | 0.464368 | + | 0.804308i | 0.999173 | − | 0.0406670i | ||
−0.534805 | + | 0.844975i | ||||||||
0 | 0 | |||||||||
−4444.99 | + | 24552.4i | −0.170564 | + | 0.942128i | |||||
0 | 0 | |||||||||
34292.4 | 1.31140 | 0.655698 | − | 0.755023i | ||||||
0.655698 | + | 0.755023i | ||||||||
0 | 0 | |||||||||
−15818.9 | −0.602887 | −0.301444 | − | 0.953484i | ||||||
−0.301444 | + | 0.953484i | ||||||||
0 | 0 | |||||||||
−16886.3 | + | 6058.87i | −0.641384 | + | 0.230132i | |||||
0 | 0 | |||||||||
10381.8 | + | 17981.8i | 0.392995 | + | 0.680688i | 0.992843 | − | 0.119426i | ||
−0.599848 | + | 0.800114i | ||||||||
0 | 0 | |||||||||
578.359 | − | 1001.75i | 0.0218195 | − | 0.0377925i | |||||
0 | 0 | |||||||||
745.466 | − | 3818.36i | 0.0280292 | − | 0.143569i | |||||
0 | 0 | |||||||||
−3257.24 | + | 5641.71i | −0.122060 | + | 0.211414i | |||||
0 | 0 | |||||||||
8248.75 | + | 14287.3i | 0.308073 | + | 0.533598i | |||||
0 | 0 | |||||||||
628.505 | − | 225.511i | 0.0233948 | − | 0.00839419i | |||||
0 | 0 | |||||||||
−64637.3 | −2.39797 | |||||||||
0 | 0 | |||||||||
53610.1 | 1.98225 | |||||||||
0 | 0 | |||||||||
−314.458 | + | 1736.94i | −0.0115886 | + | 0.0640108i | |||||
0 | 0 | |||||||||
−15785.8 | − | 27341.8i | −0.579821 | − | 1.00428i | |||||
0 | 0 | |||||||||
6337.77 | − | 10977.3i | 0.232020 | − | 0.401871i | −0.726382 | − | 0.687291i | ||
0.958402 | + | 0.285420i | ||||||||
0 | 0 | |||||||||
−22159.0 | − | 8295.27i | −0.808545 | − | 0.302681i | |||||
0 | 0 | |||||||||
9162.83 | − | 15870.5i | 0.333236 | − | 0.577182i | −0.649908 | − | 0.760013i | ||
0.983144 | + | 0.182831i | ||||||||
0 | 0 | |||||||||
−1365.36 | − | 2364.87i | −0.0494926 | − | 0.0857237i | |||||
0 | 0 | |||||||||
−10221.2 | − | 8656.52i | −0.369294 | − | 0.312760i | |||||
0 | 0 | |||||||||
−1356.58 | −0.0488532 | |||||||||
0 | 0 | |||||||||
2706.30 | 0.0971409 | 0.0485705 | − | 0.998820i | ||||||
0.0485705 | + | 0.998820i | ||||||||
0 | 0 | |||||||||
−2994.30 | − | 2535.91i | −0.107129 | − | 0.0907288i | |||||
0 | 0 | |||||||||
−1292.62 | − | 2238.89i | −0.0460966 | − | 0.0798417i | |||||
0 | 0 | |||||||||
−11039.7 | + | 19121.4i | −0.392416 | + | 0.679684i | |||||
0 | 0 | |||||||||
−4656.64 | + | 3835.43i | −0.164988 | + | 0.135892i | |||||
0 | 0 | |||||||||
−12442.9 | + | 21551.7i | −0.439437 | + | 0.761127i | −0.997646 | − | 0.0685731i | ||
0.558209 | + | 0.829700i | ||||||||
0 | 0 | |||||||||
−14823.5 | − | 25675.1i | −0.521828 | − | 0.903832i | |||||
0 | 0 | |||||||||
4874.64 | − | 26925.6i | 0.171049 | − | 0.944806i | |||||
0 | 0 | |||||||||
−5677.13 | −0.198569 | |||||||||
0 | 0 | |||||||||
−33383.1 | −1.16390 | −0.581952 | − | 0.813223i | ||||||
−0.581952 | + | 0.813223i | ||||||||
0 | 0 | |||||||||
−6818.37 | + | 2446.47i | −0.236964 | + | 0.0850238i | |||||
0 | 0 | |||||||||
14589.7 | + | 25270.1i | 0.505431 | + | 0.875433i | 0.999980 | + | 0.00628300i | ||
−0.494549 | + | 0.869150i | ||||||||
0 | 0 | |||||||||
−202.801 | + | 351.262i | −0.00700330 | + | 0.0121301i | |||||
0 | 0 | |||||||||
539.489 | − | 905.531i | 0.0185710 | − | 0.0311713i | |||||
0 | 0 | |||||||||
19442.0 | − | 33674.6i | 0.667140 | − | 1.15552i | −0.311561 | − | 0.950226i | ||
0.978700 | − | 0.205294i | ||||||||
0 | 0 | |||||||||
−249.435 | − | 432.034i | −0.00853214 | − | 0.0147781i | |||||
0 | 0 | |||||||||
25027.0 | − | 8979.83i | 0.853372 | − | 0.306194i | |||||
0 | 0 | |||||||||
−5321.13 | −0.180869 | −0.0904345 | − | 0.995902i | ||||||
−0.0904345 | + | 0.995902i | ||||||||
0 | 0 | |||||||||
35793.3 | 1.21282 | |||||||||
0 | 0 | |||||||||
−1001.81 | + | 5533.59i | −0.0338389 | + | 0.186913i | |||||
0 | 0 | |||||||||
−259.511 | − | 449.485i | −0.00873830 | − | 0.0151352i | |||||
0 | 0 | |||||||||
−35899.9 | + | 62180.5i | −1.20506 | + | 2.08722i | |||||
0 | 0 | |||||||||
−5624.88 | − | 33697.9i | −0.188224 | − | 1.12762i | |||||
0 | 0 | |||||||||
16633.9 | − | 28810.7i | 0.554884 | − | 0.961087i | |||||
0 | 0 | |||||||||
−24510.2 | − | 42453.0i | −0.815094 | − | 1.41178i | −0.909261 | − | 0.416227i | ||
0.0941669 | − | 0.995556i | ||||||||
0 | 0 | |||||||||
−45598.4 | − | 38618.0i | −1.51170 | − | 1.28028i | |||||
0 | 0 | |||||||||
−11409.6 | −0.377087 | −0.188544 | − | 0.982065i | ||||||
−0.188544 | + | 0.982065i | ||||||||
0 | 0 | |||||||||
−1489.31 | −0.0490700 | |||||||||
0 | 0 | |||||||||
750.439 | + | 635.558i | 0.0246495 | + | 0.0208760i | |||||
0 | 0 | |||||||||
−9228.33 | − | 15983.9i | −0.302191 | − | 0.523410i | 0.674441 | − | 0.738329i | ||
−0.976632 | + | 0.214919i | ||||||||
0 | 0 | |||||||||
855.094 | − | 1481.07i | 0.0279152 | − | 0.0483505i | |||||
0 | 0 | |||||||||
−946.902 | − | 5672.76i | −0.0308178 | − | 0.184625i | |||||
0 | 0 | |||||||||
−17803.6 | + | 30836.8i | −0.577668 | + | 1.00055i | 0.418078 | + | 0.908411i | ||
−0.995746 | + | 0.0921393i | ||||||||
0 | 0 | |||||||||
2151.66 | + | 3726.78i | 0.0696015 | + | 0.120553i | |||||
0 | 0 | |||||||||
−65.2202 | + | 360.250i | −0.00210332 | + | 0.0116179i | |||||
0 | 0 | |||||||||
−14948.7 | −0.480629 | |||||||||
0 | 0 | |||||||||
31299.9 | 1.00330 | 0.501652 | − | 0.865070i | ||||||
0.501652 | + | 0.865070i | ||||||||
0 | 0 | |||||||||
1187.50 | − | 426.080i | 0.0379497 | − | 0.0136166i | |||||
0 | 0 | |||||||||
7830.24 | + | 13562.4i | 0.249483 | + | 0.432117i | |||||
0 | 0 | |||||||||
14389.2 | − | 24922.9i | 0.457083 | − | 0.791691i | −0.541722 | − | 0.840557i | ||
0.998805 | + | 0.0488666i | ||||||||
0 | 0 | |||||||||
26102.4 | − | 43812.9i | 0.826672 | − | 1.38757i |
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 72.4.i.a.25.4 | ✓ | 8 | |
3.2 | odd | 2 | 216.4.i.a.73.1 | 8 | |||
4.3 | odd | 2 | 144.4.i.e.97.1 | 8 | |||
9.2 | odd | 6 | 648.4.a.h.1.4 | 4 | |||
9.4 | even | 3 | inner | 72.4.i.a.49.4 | yes | 8 | |
9.5 | odd | 6 | 216.4.i.a.145.1 | 8 | |||
9.7 | even | 3 | 648.4.a.i.1.1 | 4 | |||
12.11 | even | 2 | 432.4.i.e.289.1 | 8 | |||
36.7 | odd | 6 | 1296.4.a.ba.1.1 | 4 | |||
36.11 | even | 6 | 1296.4.a.y.1.4 | 4 | |||
36.23 | even | 6 | 432.4.i.e.145.1 | 8 | |||
36.31 | odd | 6 | 144.4.i.e.49.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
72.4.i.a.25.4 | ✓ | 8 | 1.1 | even | 1 | trivial | |
72.4.i.a.49.4 | yes | 8 | 9.4 | even | 3 | inner | |
144.4.i.e.49.1 | 8 | 36.31 | odd | 6 | |||
144.4.i.e.97.1 | 8 | 4.3 | odd | 2 | |||
216.4.i.a.73.1 | 8 | 3.2 | odd | 2 | |||
216.4.i.a.145.1 | 8 | 9.5 | odd | 6 | |||
432.4.i.e.145.1 | 8 | 36.23 | even | 6 | |||
432.4.i.e.289.1 | 8 | 12.11 | even | 2 | |||
648.4.a.h.1.4 | 4 | 9.2 | odd | 6 | |||
648.4.a.i.1.1 | 4 | 9.7 | even | 3 | |||
1296.4.a.y.1.4 | 4 | 36.11 | even | 6 | |||
1296.4.a.ba.1.1 | 4 | 36.7 | odd | 6 |