Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [45,3,Mod(7,45)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(45, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([8, 3]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("45.7");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 45.k (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 |
Twist minimal: | yes |
Sato-Tate group: |
Embedding invariants
Embedding label | 22.5 | ||
Character | 45.22 | ||
Dual form | 45.3.k.a.43.5 |
-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 .
0.0492077 | − | 0.183646i | 0.0246039 | − | 0.0918228i | −0.952532 | − | 0.304438i | ||
0.977136 | + | 0.212615i | ||||||||
−2.37796 | + | 1.82902i | −0.792654 | + | 0.609672i | |||||
3.43280 | + | 1.98193i | 0.858199 | + | 0.495482i | |||||
4.90616 | − | 0.964151i | 0.981232 | − | 0.192830i | |||||
0.218877 | + | 0.526704i | 0.0364795 | + | 0.0877840i | |||||
−2.33248 | + | 8.70492i | −0.333211 | + | 1.24356i | 0.572585 | + | 0.819846i | ||
−0.905796 | + | 0.423715i | ||||||||
1.07064 | − | 1.07064i | 0.133831 | − | 0.133831i | |||||
2.30940 | − | 8.69866i | 0.256600 | − | 0.966518i | |||||
0.0643587 | − | 0.948439i | 0.00643587 | − | 0.0948439i | |||||
−7.04110 | − | 12.1955i | −0.640100 | − | 1.10869i | −0.985410 | − | 0.170197i | ||
0.345310 | − | 0.938489i | ||||||||
−11.7880 | + | 1.56570i | −0.982336 | + | 0.130475i | |||||
−3.46845 | − | 12.9444i | −0.266804 | − | 0.995725i | −0.961137 | − | 0.276071i | ||
0.694333 | − | 0.719653i | ||||||||
1.48385 | + | 0.856699i | 0.105989 | + | 0.0611928i | |||||
−9.90321 | + | 11.2662i | −0.660214 | + | 0.751077i | |||||
7.78377 | + | 13.4819i | 0.486486 | + | 0.842618i | |||||
−0.740694 | − | 0.740694i | −0.0435702 | − | 0.0435702i | 0.684986 | − | 0.728556i | ||
−0.728556 | + | 0.684986i | ||||||||
−1.48383 | − | 0.852153i | −0.0824350 | − | 0.0473418i | |||||
7.09073i | 0.373196i | 0.982436 | + | 0.186598i | ||||||
−0.982436 | + | 0.186598i | ||||||||
18.7527 | + | 6.41391i | 0.937637 | + | 0.320696i | |||||
−10.3749 | − | 24.9661i | −0.494043 | − | 1.18886i | |||||
−2.58614 | + | 0.692953i | −0.117552 | + | 0.0314979i | |||||
−5.10441 | − | 19.0499i | −0.221931 | − | 0.828257i | −0.983611 | − | 0.180304i | ||
0.761680 | − | 0.647953i | ||||||||
−0.587726 | + | 4.50418i | −0.0244886 | + | 0.187674i | |||||
23.1408 | − | 9.46056i | 0.925633 | − | 0.378423i | |||||
−2.54786 | −0.0979947 | |||||||||
10.4183 | + | 24.9090i | 0.385863 | + | 0.922556i | |||||
−25.2594 | + | 25.2594i | −0.902123 | + | 0.902123i | |||||
−6.18301 | + | 3.56976i | −0.213207 | + | 0.123095i | −0.602801 | − | 0.797892i | ||
0.389594 | + | 0.920987i | ||||||||
1.58167 | + | 2.37306i | 0.0527222 | + | 0.0791021i | |||||
13.0783 | − | 22.6522i | 0.421879 | − | 0.730716i | −0.574244 | − | 0.818684i | ||
0.996123 | + | 0.0879678i | ||||||||
8.70902 | − | 2.33357i | 0.272157 | − | 0.0729242i | |||||
39.0493 | + | 16.1223i | 1.18331 | + | 0.488553i | |||||
−0.172473 | + | 0.0995774i | −0.00507274 | + | 0.00292875i | |||||
−3.05064 | + | 44.9566i | −0.0871612 | + | 1.28447i | |||||
25.1678 | − | 25.2837i | 0.699106 | − | 0.702324i | |||||
−23.0151 | − | 23.0151i | −0.622031 | − | 0.622031i | 0.324020 | − | 0.946050i | ||
−0.946050 | + | 0.324020i | ||||||||
1.30218 | + | 0.348919i | 0.0342680 | + | 0.00918207i | |||||
31.9234 | + | 24.4375i | 0.818548 | + | 0.626602i | |||||
4.22049 | − | 6.28502i | 0.105512 | − | 0.157125i | |||||
−36.0387 | + | 62.4209i | −0.878993 | + | 1.52246i | −0.0265459 | + | 0.999648i | ||
−0.852447 | + | 0.522813i | ||||||||
−5.09544 | + | 0.676780i | −0.121320 | + | 0.0161138i | |||||
−12.0484 | − | 3.22835i | −0.280195 | − | 0.0750779i | 0.115985 | − | 0.993251i | ||
−0.396180 | + | 0.918173i | ||||||||
− | 55.8198i | − | 1.26863i | |||||||
2.94348 | − | 44.9036i | 0.0654106 | − | 0.997858i | |||||
−3.74961 | −0.0815133 | |||||||||
−13.9048 | + | 51.8935i | −0.295847 | + | 1.10412i | 0.644695 | + | 0.764440i | ||
−0.940542 | + | 0.339677i | ||||||||
−43.1681 | − | 17.8228i | −0.899335 | − | 0.371308i | |||||
−27.9000 | − | 16.1081i | −0.569388 | − | 0.328736i | |||||
−0.598685 | − | 4.71525i | −0.0119737 | − | 0.0943049i | |||||
3.11608 | + | 0.406601i | 0.0610997 | + | 0.00797257i | |||||
13.7484 | − | 51.3098i | 0.264393 | − | 0.986727i | |||||
17.2907 | − | 17.2907i | 0.326240 | − | 0.326240i | −0.524915 | − | 0.851155i | ||
0.851155 | + | 0.524915i | ||||||||
5.08709 | − | 0.687563i | 0.0942054 | − | 0.0127326i | |||||
−46.3031 | − | 53.0446i | −0.841875 | − | 0.964447i | |||||
6.82262 | + | 11.8171i | 0.121833 | + | 0.211020i | |||||
−12.9691 | − | 16.8615i | −0.227527 | − | 0.295816i | |||||
0.351320 | + | 1.31114i | 0.00605724 | + | 0.0226059i | |||||
−27.5407 | − | 15.9006i | −0.466792 | − | 0.269502i | 0.248104 | − | 0.968733i | ||
−0.714896 | + | 0.699231i | ||||||||
−56.3244 | + | 19.0470i | −0.938740 | + | 0.317450i | |||||
40.7317 | + | 70.5494i | 0.667733 | + | 1.15655i | 0.978537 | + | 0.206073i | ||
−0.310804 | + | 0.950474i | ||||||||
−3.51643 | − | 3.51643i | −0.0567166 | − | 0.0567166i | |||||
70.3345 | + | 40.3926i | 1.11642 | + | 0.641152i | |||||
60.5560i | 0.946187i | |||||||||
−29.4971 | − | 60.1633i | −0.453802 | − | 0.925589i | |||||
4.88231 | − | 6.37790i | 0.0739744 | − | 0.0966348i | |||||
64.1404 | − | 17.1864i | 0.957319 | − | 0.256513i | 0.253854 | − | 0.967243i | ||
0.703465 | + | 0.710730i | ||||||||
−1.07465 | − | 4.01065i | −0.0158037 | − | 0.0589802i | |||||
46.9807 | + | 35.9639i | 0.680880 | + | 0.521216i | |||||
8.10597 | + | 2.77245i | 0.115800 | + | 0.0396064i | |||||
−36.3928 | −0.512574 | −0.256287 | − | 0.966601i | ||||||
−0.256287 | + | 0.966601i | ||||||||
−6.84062 | − | 11.7857i | −0.0950086 | − | 0.163691i | |||||
2.90991 | − | 2.90991i | 0.0398617 | − | 0.0398617i | −0.686895 | − | 0.726757i | ||
0.726757 | + | 0.686895i | ||||||||
−5.35915 | + | 3.09411i | −0.0724210 | + | 0.0418123i | |||||
−37.7245 | + | 64.8218i | −0.502993 | + | 0.864291i | |||||
−14.0533 | + | 24.3410i | −0.184912 | + | 0.320277i | |||||
122.584 | − | 32.8464i | 1.59201 | − | 0.426577i | |||||
6.05872 | − | 4.66008i | 0.0776759 | − | 0.0597446i | |||||
−71.8823 | + | 41.5012i | −0.909902 | + | 0.525332i | −0.880400 | − | 0.474232i | ||
−0.0295025 | + | 0.999565i | ||||||||
51.1870 | + | 58.6396i | 0.639838 | + | 0.732995i | |||||
−70.3333 | − | 40.1774i | −0.868313 | − | 0.496017i | |||||
9.68994 | + | 9.68994i | 0.118170 | + | 0.118170i | |||||
51.3796 | + | 13.7671i | 0.619031 | + | 0.165869i | 0.554687 | − | 0.832059i | ||
0.0643438 | + | 0.997928i | ||||||||
13.8661 | − | 106.266i | 0.165072 | − | 1.26507i | |||||
−4.34811 | − | 2.91982i | −0.0511542 | − | 0.0343509i | |||||
−1.18574 | + | 2.05377i | −0.0137877 | + | 0.0238811i | |||||
8.17381 | − | 19.7976i | 0.0939518 | − | 0.227558i | |||||
−20.5956 | − | 5.51857i | −0.234041 | − | 0.0627111i | |||||
22.5436i | 0.253299i | 0.991948 | + | 0.126650i | ||||||
−0.991948 | + | 0.126650i | ||||||||
−8.10152 | − | 2.75016i | −0.0900168 | − | 0.0305574i | |||||
120.770 | 1.32715 | |||||||||
20.2331 | − | 75.5111i | 0.219925 | − | 0.820773i | |||||
10.3316 | + | 77.7864i | 0.111093 | + | 0.836413i | |||||
8.84580 | + | 5.10712i | 0.0941042 | + | 0.0543311i | |||||
6.83654 | + | 34.7883i | 0.0719636 | + | 0.366192i | |||||
−16.4416 | + | 21.4781i | −0.171266 | + | 0.223730i | |||||
−9.03502 | + | 33.7192i | −0.0931446 | + | 0.347620i | −0.996732 | − | 0.0807843i | ||
0.903587 | + | 0.428405i | ||||||||
−4.33107 | + | 4.33107i | −0.0441946 | + | 0.0441946i | |||||
−122.346 | + | 33.0837i | −1.23581 | + | 0.334179i | |||||
98.1879 | + | 13.3872i | 0.981879 | + | 0.133872i | |||||
−29.7283 | − | 51.4909i | −0.294340 | − | 0.509811i | 0.680491 | − | 0.732756i | ||
−0.974831 | + | 0.222945i | ||||||||
0.228006 | − | 0.552247i | 0.00223535 | − | 0.00541419i | |||||
20.3691 | + | 76.0184i | 0.197758 | + | 0.738043i | 0.991536 | + | 0.129835i | ||
−0.793778 | + | 0.608208i | ||||||||
−17.5723 | − | 10.1454i | −0.168965 | − | 0.0975519i | |||||
−74.9720 | − | 112.485i | −0.714019 | − | 1.07128i | |||||
−2.32453 | − | 4.02620i | −0.0219295 | − | 0.0379830i | |||||
−50.6865 | − | 50.6865i | −0.473706 | − | 0.473706i | 0.429406 | − | 0.903112i | ||
−0.903112 | + | 0.429406i | ||||||||
−13.6039 | + | 106.156i | −0.125962 | + | 0.982925i | |||||
− | 47.8364i | − | 0.438866i | −0.975628 | − | 0.219433i | ||||
0.975628 | − | 0.219433i | ||||||||
−12.0199 | + | 5.89316i | −0.109272 | + | 0.0535742i | |||||
96.8241 | + | 12.6341i | 0.872289 | + | 0.113820i | |||||
−135.514 | + | 36.3109i | −1.20995 | + | 0.324205i | |||||
−45.1005 | − | 168.318i | −0.399120 | − | 1.48954i | −0.814648 | − | 0.579955i | ||
0.415529 | − | 0.909580i | ||||||||
−3.73472 | + | 1.55200i | −0.0327607 | + | 0.0136140i | |||||
−43.4101 | − | 88.5405i | −0.377479 | − | 0.769918i | |||||
−28.3000 | −0.243966 | |||||||||
−120.609 | + | 0.276954i | −1.03085 | + | 0.00236713i | |||||
−4.27530 | + | 4.27530i | −0.0362313 | + | 0.0362313i | |||||
8.17534 | − | 4.72003i | 0.0687003 | − | 0.0396641i | |||||
1.45923 | + | 22.6649i | 0.0121603 | + | 0.188874i | |||||
−38.6542 | + | 66.9510i | −0.319456 | + | 0.553314i | |||||
14.9604 | − | 4.00863i | 0.122626 | − | 0.0328576i | |||||
−28.4701 | − | 214.350i | −0.231464 | − | 1.74268i | |||||
89.7900 | − | 51.8403i | 0.724113 | − | 0.418067i | |||||
104.411 | − | 68.7263i | 0.835289 | − | 0.549810i | |||||
10.8789 | − | 10.9290i | 0.0863407 | − | 0.0867381i | |||||
16.3333 | + | 16.3333i | 0.128608 | + | 0.128608i | 0.768481 | − | 0.639873i | ||
−0.639873 | + | 0.768481i | ||||||||
45.9569 | + | 12.3141i | 0.359038 | + | 0.0962041i | |||||
34.5553 | − | 14.3598i | 0.267870 | − | 0.111316i | |||||
−12.5002 | + | 2.45652i | −0.0961555 | + | 0.0188963i | |||||
−27.6049 | + | 47.8130i | −0.210724 | + | 0.364985i | −0.951941 | − | 0.306280i | ||
0.741217 | + | 0.671265i | ||||||||
102.095 | + | 132.737i | 0.773449 | + | 1.00559i | |||||
−61.7243 | − | 16.5390i | −0.464092 | − | 0.124353i | |||||
− | 12.6248i | − | 0.0942150i | |||||||
75.1300 | + | 112.163i | 0.556518 | + | 0.830835i | |||||
−1.58604 | −0.0116621 | |||||||||
−50.7417 | + | 189.371i | −0.370377 | + | 1.38227i | 0.489606 | + | 0.871944i | ||
−0.859983 | + | 0.510323i | ||||||||
8.91643 | − | 6.85810i | 0.0646118 | − | 0.0496964i | |||||
82.5364 | + | 47.6524i | 0.593787 | + | 0.342823i | 0.766594 | − | 0.642133i | ||
−0.172806 | + | 0.984956i | ||||||||
−99.5729 | + | 148.281i | −0.711235 | + | 1.05915i | |||||
−61.8489 | − | 148.833i | −0.438645 | − | 1.05555i | |||||
−1.79081 | + | 6.68338i | −0.0126113 | + | 0.0470660i | |||||
−133.443 | + | 133.443i | −0.933165 | + | 0.933165i | |||||
135.250 | − | 36.5733i | 0.939237 | − | 0.253981i | |||||
−26.8931 | + | 23.4752i | −0.185469 | + | 0.161898i | |||||
−0.391202 | − | 0.677581i | −0.00267946 | − | 0.00464097i | |||||
95.8070 | − | 12.7252i | 0.651748 | − | 0.0865657i | |||||
−33.3920 | − | 124.621i | −0.225622 | − | 0.842031i | |||||
225.341 | + | 130.101i | 1.51235 | + | 0.873158i | 0.999896 | + | 0.0144460i | ||
0.512458 | + | 0.858712i | ||||||||
10.0479 | + | 10.1177i | 0.0669860 | + | 0.0674511i | |||||
−128.914 | − | 223.285i | −0.853735 | − | 1.47871i | −0.877814 | − | 0.479002i | ||
0.0240792 | − | 0.999710i | ||||||||
7.59165 | + | 7.59165i | 0.0499451 | + | 0.0499451i | |||||
−8.15361 | + | 4.73248i | −0.0532915 | + | 0.0309313i | |||||
− | 24.1284i | − | 0.156678i | |||||||
42.3239 | − | 123.745i | 0.273057 | − | 0.798353i | |||||
61.1532 | + | 147.159i | 0.392008 | + | 0.943325i | |||||
44.8971 | − | 12.0301i | 0.285969 | − | 0.0766251i | −0.112983 | − | 0.993597i | ||
0.398952 | + | 0.916972i | ||||||||
4.08436 | + | 15.2431i | 0.0258504 | + | 0.0964750i | |||||
−9.49166 | + | 72.7416i | −0.0596960 | + | 0.457494i | |||||
40.4779 | − | 19.8457i | 0.252987 | − | 0.124036i | |||||
177.734 | 1.10394 | |||||||||
−10.8393 | + | 10.9394i | −0.0669096 | + | 0.0675270i | |||||
76.8331 | − | 76.8331i | 0.471369 | − | 0.471369i | −0.430989 | − | 0.902357i | ||
0.902357 | + | 0.430989i | ||||||||
−247.427 | + | 142.852i | −1.50870 | + | 0.871050i | |||||
207.126 | + | 41.4489i | 1.25531 | + | 0.251206i | |||||
5.05654 | − | 8.75819i | 0.0304611 | − | 0.0527602i | |||||
−301.256 | + | 80.7212i | −1.80393 | + | 0.483360i | −0.994580 | − | 0.103972i | ||
−0.809346 | + | 0.587333i | ||||||||
−37.8376 | − | 15.6220i | −0.225224 | − | 0.0929881i | |||||
−9.16964 | + | 5.29409i | −0.0542582 | + | 0.0313260i | |||||
−0.750173 | + | 0.654833i | −0.00441278 | + | 0.00385196i | |||||
61.6799 | + | 16.3754i | 0.360701 | + | 0.0957623i | |||||
−34.9612 | − | 34.9612i | −0.203263 | − | 0.203263i | |||||
192.633 | + | 51.6158i | 1.11348 | + | 0.298357i | 0.768244 | − | 0.640157i | ||
0.345240 | + | 0.938514i | ||||||||
−3.23353 | − | 2.47528i | −0.0185835 | − | 0.0142257i | |||||
28.3780 | + | 223.506i | 0.162160 | + | 1.27718i | |||||
109.613 | − | 189.855i | 0.622799 | − | 1.07872i | |||||
94.5733 | − | 12.5613i | 0.534312 | − | 0.0709677i | |||||
4.14004 | + | 1.10932i | 0.0232587 | + | 0.00623214i | |||||
− | 254.120i | − | 1.41967i | −0.704370 | − | 0.709833i | ||||
0.704370 | − | 0.709833i | ||||||||
99.1001 | − | 148.311i | 0.550556 | − | 0.823952i | |||||
−236.998 | −1.30938 | −0.654691 | − | 0.755896i | ||||||
−0.654691 | + | 0.755896i | ||||||||
5.94283 | − | 22.1789i | 0.0326529 | − | 0.121862i | |||||
−225.894 | − | 93.2648i | −1.23440 | − | 0.509644i | |||||
−25.8607 | − | 14.9307i | −0.140547 | − | 0.0811450i | |||||
−135.106 | − | 90.7259i | −0.730303 | − | 0.490410i | |||||
14.7935 | + | 1.93033i | 0.0795351 | + | 0.0103781i | |||||
−3.81787 | + | 14.2485i | −0.0204164 | + | 0.0761950i | |||||
−150.582 | + | 150.582i | −0.800966 | + | 0.800966i | |||||
−241.131 | + | 32.5909i | −1.27583 | + | 0.172439i | |||||
6.72513 | + | 0.456350i | 0.0353954 | + | 0.00240184i | |||||
27.2962 | + | 47.2784i | 0.142912 | + | 0.247531i | 0.928592 | − | 0.371102i | ||
−0.785680 | + | 0.618633i | ||||||||
−110.758 | − | 144.000i | −0.576864 | − | 0.749999i | |||||
51.8234 | + | 193.408i | 0.268515 | + | 1.00211i | 0.960063 | + | 0.279782i | ||
−0.691548 | + | 0.722330i | ||||||||
5.74779 | + | 3.31849i | 0.0296278 | + | 0.0171056i | |||||
180.183 | + | 89.1153i | 0.924014 | + | 0.457001i | |||||
−63.8500 | − | 110.591i | −0.325765 | − | 0.564242i | |||||
18.5367 | + | 18.5367i | 0.0940948 | + | 0.0940948i | 0.752587 | − | 0.658492i | ||
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0.0553320 | + | 24.0962i | 0.000279454 | + | 0.121698i | |||||
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0.855507 | − | 0.517792i | ||||||||
14.6467 | − | 34.9045i | 0.0732335 | − | 0.174522i | |||||
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9.89103 | + | 7.57163i | 0.0484854 | + | 0.0371158i | |||||
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14.9628 | 0.0726348 | |||||||||
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147.518 | − | 147.518i | 0.709219 | − | 0.709219i | |||||
86.4753 | − | 49.9266i | 0.413758 | − | 0.238883i | |||||
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121.373 | − | 210.225i | 0.575230 | − | 0.996327i | −0.420787 | − | 0.907159i | ||
0.996017 | − | 0.0891675i | ||||||||
93.6244 | − | 25.0866i | 0.441625 | − | 0.118333i | |||||
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166.681 | + | 166.681i | 0.768115 | + | 0.768115i | |||||
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198.758 | + | 53.2572i | 0.891293 | + | 0.238821i | 0.675273 | − | 0.737568i | ||
0.216020 | + | 0.976389i | ||||||||
81.2544i | 0.362743i | |||||||||
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0.987113 | − | 0.160022i | ||||||||
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0.400351 | + | 0.916362i | ||||||||
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332.123 | + | 191.751i | 1.38963 | + | 0.802306i | 0.993274 | − | 0.115790i | ||
0.396360 | + | 0.918095i | ||||||||
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162.944 | + | 282.226i | 0.676114 | + | 1.17106i | 0.976142 | + | 0.217134i | ||
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10.3932 | + | 10.3932i | 0.0429470 | + | 0.0429470i | |||||
240.735 | − | 33.1004i | 0.990679 | − | 0.136216i | |||||
322.909i | 1.32340i | |||||||||
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428.941 | 1.70893 | 0.854465 | − | 0.519509i | ||||||
0.854465 | + | 0.519509i | ||||||||
161.389 | + | 278.057i | 0.640433 | + | 1.10340i | |||||
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3.80325 | − | 2.19581i | 0.0149734 | − | 0.00864492i | |||||
15.6800 | − | 1.00953i | 0.0614903 | − | 0.00395893i | |||||
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355.861 | − | 95.3527i | 1.38467 | − | 0.371022i | 0.511857 | − | 0.859070i | ||
0.872817 | + | 0.488048i | ||||||||
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254.027 | − | 146.663i | 0.980800 | − | 0.566265i | |||||
17.9815 | − | 264.990i | 0.0691597 | − | 1.01919i | |||||
16.7731 | + | 62.0279i | 0.0642647 | + | 0.237655i | |||||
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59.0691 | − | 24.5467i | 0.223747 | − | 0.0929800i | |||||
68.1601 | − | 101.502i | 0.257208 | − | 0.383026i | |||||
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254.243 | + | 68.1242i | 0.948668 | + | 0.254195i | |||||
146.927i | 0.546197i | 0.961986 | + | 0.273099i | ||||||
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24.2952 | − | 8.27802i | 0.0899822 | − | 0.0306593i | |||||
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32.2802 | + | 18.6370i | 0.117811 | + | 0.0680182i | |||||
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89.9973 | + | 216.569i | 0.326077 | + | 0.784671i | |||||
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12.8126 | − | 12.8126i | 0.0460885 | − | 0.0460885i | |||||
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44.8664 | + | 51.3987i | 0.160237 | + | 0.183567i | |||||
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0.495032 | − | 0.868875i | ||||||||
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2.98777 | + | 6.09395i | 0.0103027 | + | 0.0210136i | |||||
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15.7563 | − | 4.22190i | 0.0539600 | − | 0.0144586i | |||||
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2.37752 | − | 18.2207i | 0.00808682 | − | 0.0619752i | |||||
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230.423 | − | 302.444i | 0.775833 | − | 1.01833i | |||||
34.9809 | − | 34.9809i | 0.117386 | − | 0.117386i | |||||
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56.2051 | − | 97.3500i | 0.186728 | − | 0.323422i | |||||
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164.871 | + | 68.0699i | 0.544127 | + | 0.224653i | |||||
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267.857 | + | 306.855i | 0.878218 | + | 1.00608i | |||||
0.467880 | + | 1.73025i | 0.00152902 | + | 0.00565441i | |||||
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485.907 | + | 130.198i | 1.57762 | + | 0.422722i | |||||
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0.733850 | + | 0.679311i | ||||||||
60.3424 | − | 8.01473i | 0.193405 | − | 0.0256882i | |||||
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− | 8.83713i | − | 0.0281437i | |||||||
384.017 | + | 130.359i | 1.21910 | + | 0.413839i | |||||
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12.8916 | + | 5.32255i | 0.0405397 | + | 0.0167376i | |||||
87.0704 | + | 50.2701i | 0.272948 | + | 0.157587i | |||||
58.3851 | + | 297.097i | 0.182453 | + | 0.928429i | |||||
213.237 | + | 27.8241i | 0.664290 | + | 0.0866796i | |||||
8.74588 | − | 32.6401i | 0.0271611 | − | 0.101367i | |||||
5.25206 | − | 5.25206i | 0.0162603 | − | 0.0162603i | |||||
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87.4936 | + | 113.753i | 0.267565 | + | 0.347869i | |||||
28.2459 | + | 105.415i | 0.0861156 | + | 0.321388i | |||||
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17.8041 | − | 35.9983i | 0.0539519 | − | 0.109086i | |||||
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−0.993142 | + | 0.116913i | ||||||||
149.090 | + | 149.090i | 0.449067 | + | 0.449067i | |||||
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59.2964i | 0.177534i | |||||||||
298.113 | − | 146.160i | 0.889889 | − | 0.436299i | |||||
255.834 | − | 334.204i | 0.761412 | − | 0.994654i | |||||
140.831 | − | 37.7355i | 0.417895 | − | 0.111975i | −0.0437433 | − | 0.999043i | ||
0.461639 | + | 0.887068i | ||||||||
0.521020 | + | 1.94447i | 0.00154148 | + | 0.00575288i | |||||
415.103 | + | 317.763i | 1.22449 | + | 0.937354i | |||||
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6.04239 | − | 10.5214i | 0.0176678 | − | 0.0307645i | |||||
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265.170 | + | 131.148i | 0.768607 | + | 0.380140i | |||||
18.9580 | − | 32.8363i | 0.0547920 | − | 0.0949025i | |||||
9.77990 | − | 2.62052i | 0.0281842 | − | 0.00755192i | −0.244699 | − | 0.969599i | ||
0.272884 | + | 0.962047i | ||||||||
67.2964 | − | 51.7612i | 0.193380 | − | 0.148739i | |||||
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0.359080 | + | 0.933307i | ||||||||
42.4423 | + | 5.78670i | 0.121264 | + | 0.0165334i | |||||
286.297 | − | 221.255i | 0.815662 | − | 0.630355i | |||||
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2.34691 | − | 17.9861i | 0.00662968 | − | 0.0508082i | |||||
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279.063i | 0.777333i | 0.921378 | + | 0.388667i | ||||||
−0.921378 | + | 0.388667i | ||||||||
−44.9244 | − | 51.2272i | −0.124790 | − | 0.142298i | |||||
310.722 | 0.860724 | |||||||||
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414.580 | + | 239.358i | 1.13896 | + | 0.657576i | |||||
11.4709 | − | 17.0821i | 0.0314271 | − | 0.0468001i | |||||
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46.2339 | − | 172.547i | 0.125978 | − | 0.470156i | −0.873895 | − | 0.486115i | ||
0.999873 | + | 0.0159593i | ||||||||
217.097 | − | 217.097i | 0.589938 | − | 0.589938i | |||||
459.750 | + | 457.643i | 1.24594 | + | 1.24023i | |||||
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110.184 | + | 190.844i | 0.296992 | + | 0.514406i | |||||
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2.42880 | + | 1.40227i | 0.00649412 | + | 0.00374938i | |||||
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40.6724 | + | 70.4466i | 0.108171 | + | 0.187358i | |||||
67.6540 | + | 67.6540i | 0.179453 | + | 0.179453i | |||||
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10.3793i | 0.0273860i | 0.999906 | + | 0.0136930i | ||||||
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−45.4793 | + | 132.971i | −0.119682 | + | 0.349923i | |||||
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10.0257 | − | 2.68637i | 0.0262452 | − | 0.00703238i | |||||
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569.750 | − | 279.340i | 1.47987 | − | 0.725558i | |||||
38.0686 | 0.0986233 | |||||||||
−55.9068 | + | 97.3490i | −0.144462 | + | 0.251548i | |||||
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635.357 | − | 366.824i | 1.63331 | − | 0.942991i | 0.650245 | − | 0.759724i | ||
0.983063 | − | 0.183267i | ||||||||
25.2320 | − | 28.7046i | 0.0646975 | − | 0.0736016i | |||||
−10.3294 | + | 17.8910i | −0.0264178 | + | 0.0457570i | |||||
−47.1170 | + | 12.6250i | −0.120196 | + | 0.0322065i | |||||
−21.8075 | − | 164.187i | −0.0554898 | − | 0.417779i | |||||
4.31633 | − | 2.49203i | 0.0109552 | − | 0.00632496i | |||||
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151.257 | + | 151.257i | 0.381000 | + | 0.381000i | 0.871462 | − | 0.490463i | ||
−0.490463 | + | 0.871462i | ||||||||
−37.8459 | − | 10.1408i | −0.0950903 | − | 0.0254794i | |||||
177.028 | − | 73.5656i | 0.443679 | − | 0.184375i | |||||
307.669 | + | 238.343i | 0.769173 | + | 0.595858i | |||||
−3.27254 | + | 5.66821i | −0.00816096 | + | 0.0141352i | −0.870077 | − | 0.492916i | ||
0.861916 | + | 0.507051i | ||||||||
23.0910 | + | 30.0213i | 0.0574402 | + | 0.0746799i | |||||
−338.581 | − | 90.7225i | −0.840151 | − | 0.225118i | |||||
− | 235.677i | − | 0.583360i | |||||||
−383.804 | − | 129.305i | −0.947663 | − | 0.319271i | |||||
−12.2328 | −0.0301302 | |||||||||
−118.630 | + | 442.734i | −0.291475 | + | 1.08780i | |||||
3.77154 | − | 2.90089i | 0.00924397 | − | 0.00711003i | |||||
−639.259 | − | 369.076i | −1.56298 | − | 0.902387i | −0.996953 | − | 0.0779993i | ||
−0.566026 | − | 0.824387i | ||||||||
56.8830 | + | 38.1978i | 0.138739 | + | 0.0931655i | |||||
−225.700 | − | 543.123i | −0.549148 | − | 1.32147i | |||||
−80.7400 | + | 301.326i | −0.195971 | + | 0.731373i | |||||
202.652 | − | 202.652i | 0.490683 | − | 0.490683i | |||||
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265.350 | + | 18.0060i | 0.639398 | + | 0.0433879i | |||||
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307.338 | + | 235.268i | 0.692202 | + | 0.529884i | |||||
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0.819416 | − | 0.573199i | ||||||||
−42.3989 | − | 5.68165i | −0.0942198 | − | 0.0126259i | |||||
1015.01 | 2.25057 | |||||||||
178.772 | − | 667.186i | 0.395513 | − | 1.47607i | |||||
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0.916560 | − | 0.399897i | ||||||||
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0.0488707 | + | 0.998805i | ||||||||
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598.424i | 1.27596i | |||||||||
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326.960 | + | 326.960i | 0.671376 | + | 0.671376i | 0.958033 | − | 0.286657i | ||
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119.142 | + | 31.9241i | 0.244144 | + | 0.0654183i | |||||
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407.193 | 0.820953 | |||||||||
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3.99460 | + | 30.0751i | 0.00802129 | + | 0.0603918i | |||||
353.578 | + | 204.138i | 0.708573 | + | 0.409095i | 0.810532 | − | 0.585694i | ||
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494.633 | − | 28.9882i | 0.989266 | − | 0.0579764i | |||||
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21.1072 | − | 78.7732i | 0.0420463 | − | 0.156919i | |||||
555.921 | − | 555.921i | 1.10521 | − | 1.10521i | 0.111440 | − | 0.993771i | ||
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12.2165 | − | 0.0280527i | 0.0234033 | − | 5.37408e-5i | |||||
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464.790 | + | 604.288i | 0.865531 | + | 1.12530i | |||||
26.9825 | + | 7.22994i | 0.0501534 | + | 0.0134386i | |||||
453.674i | 0.841696i | |||||||||
35.6076 | + | 533.934i | 0.0659400 | + | 0.988767i | |||||
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707.751 | − | 191.384i | 1.28916 | − | 0.348605i | |||||
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88.8042 | − | 11.7950i | 0.160877 | − | 0.0213678i | |||||
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26.1382 | + | 15.0909i | 0.0471809 | + | 0.0272399i | |||||
487.216 | − | 31.3684i | 0.877866 | − | 0.0565196i | |||||
188.887 | + | 327.162i | 0.339725 | + | 0.588421i | |||||
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167.156i | 0.299028i | |||||||||
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82.6612 | − | 633.493i | 0.146562 | − | 1.12322i | |||||
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513.792 | − | 518.533i | 0.906159 | − | 0.914521i | |||||
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526.756 | + | 139.848i | 0.914506 | + | 0.242792i | |||||
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41.2824 | 0.0704478 | |||||||||
213.739 | − | 797.684i | 0.364120 | − | 1.35892i | −0.504489 | − | 0.863418i | ||
0.868609 | − | 0.495498i | ||||||||
354.106 | + | 146.200i | 0.602222 | + | 0.248639i | |||||
160.621 | + | 92.7344i | 0.272701 | + | 0.157444i | |||||
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131.143 | − | 489.432i | 0.221525 | − | 0.826743i | |||||
329.014 | − | 329.014i | 0.554829 | − | 0.554829i | −0.373002 | − | 0.927831i | ||
0.927831 | + | 0.373002i | ||||||||
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35.5587 | − | 31.0395i | 0.0597625 | − | 0.0521672i | |||||
515.699 | + | 893.218i | 0.865267 | + | 1.49869i | |||||
376.926 | + | 490.053i | 0.631366 | + | 0.820860i | |||||
13.0053 | + | 48.5366i | 0.0217480 | + | 0.0811648i | |||||
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29.0116 | + | 109.791i | 0.0483526 | + | 0.182984i | |||||
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− | 1021.99i | − | 1.69204i | |||||||
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20.6137 | − | 26.9282i | 0.0340159 | − | 0.0444360i | |||||
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16.5468 | + | 61.7533i | 0.0272151 | + | 0.101568i | |||||
153.271 | + | 117.330i | 0.251677 | + | 0.192660i | |||||
69.5332 | − | 34.0911i | 0.113989 | − | 0.0558870i | |||||
719.960 | 1.17833 | |||||||||
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0.0836213 | + | 0.996498i | ||||||||
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96.0775 | − | 166.411i | 0.155970 | − | 0.270148i | |||||
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384.591 | − | 222.044i | 0.621311 | − | 0.358714i | −0.156068 | − | 0.987746i | ||
0.777379 | + | 0.629032i | ||||||||
390.542 | − | 340.908i | 0.629907 | − | 0.549852i | |||||
421.335 | − | 325.614i | 0.678479 | − | 0.524338i | |||||
18.5115 | + | 18.5115i | 0.0297613 | + | 0.0297613i | |||||
−196.241 | − | 52.5825i | −0.314993 | − | 0.0844021i | |||||
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445.995 | − | 437.850i | 0.713593 | − | 0.700561i | |||||
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177.965 | + | 47.6857i | 0.283384 | + | 0.0759326i | |||||
34.0943i | 0.0542040i | |||||||||
42.8365 | − | 64.1084i | 0.0679945 | − | 0.101759i | |||||
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95.8834 | + | 721.901i | 0.151475 | + | 1.14044i | |||||
72.8343 | + | 42.0509i | 0.114881 | + | 0.0663264i | |||||
95.8813 | + | 64.3858i | 0.150994 | + | 0.101395i | |||||
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237.345 | + | 16.1056i | 0.370851 | + | 0.0251650i | |||||
44.3645 | + | 76.8416i | 0.0692114 | + | 0.119878i | 0.898554 | − | 0.438862i | ||
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15.6027 | − | 37.7909i | 0.0243032 | − | 0.0588643i | |||||
111.166 | + | 414.879i | 0.172887 | + | 0.645224i | 0.996902 | + | 0.0786553i | ||
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610.125 | + | 352.256i | 0.947399 | + | 0.546981i | |||||
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447.832i | 0.690034i | |||||||||
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416.030 | − | 111.475i | 0.638083 | − | 0.170974i | |||||
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407.245 | − | 235.123i | 0.617974 | − | 0.356787i | −0.158106 | − | 0.987422i | ||
0.776080 | + | 0.630635i | ||||||||
628.875 | + | 552.795i | 0.952840 | + | 0.837568i | |||||
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0.996123 | − | 0.0879760i | ||||||||
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14.5381 | + | 53.7630i | 0.0218290 | + | 0.0807252i | |||||
99.5643 | + | 99.5643i | 0.149272 | + | 0.149272i | |||||
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573.592 | − | 993.490i | 0.854832 | − | 1.48061i | |||||
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1217.91 | + | 326.337i | 1.80967 | + | 0.484899i | 0.995418 | − | 0.0956152i | ||
0.814250 | + | 0.580514i | ||||||||
− | 27.7198i | − | 0.0411273i | |||||||
476.742 | + | 477.852i | 0.706284 | + | 0.707929i | |||||
−41.9700 | −0.0620858 | |||||||||
25.8294 | − | 96.3967i | 0.0381528 | − | 0.142388i | −0.944222 | − | 0.329309i | ||
0.982375 | + | 0.186921i | ||||||||
78.7820 | − | 60.5954i | 0.116198 | − | 0.0893738i | |||||
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214.318 | + | 515.734i | 0.314711 | + | 0.757319i | |||||
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366.381 | − | 366.381i | 0.536430 | − | 0.536430i | −0.386049 | − | 0.922478i | ||
0.922478 | + | 0.386049i | ||||||||
179.280 | + | 178.458i | 0.262105 | + | 0.260904i | |||||
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14.3787 | + | 24.9047i | 0.0209602 | + | 0.0363042i | |||||
538.114 | − | 71.4727i | 0.783281 | − | 0.104036i | |||||
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37.1332 | − | 42.2437i | 0.0538162 | − | 0.0612228i | |||||
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558.971 | + | 558.971i | 0.807761 | + | 0.807761i | |||||
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450.881 | + | 154.213i | 0.648750 | + | 0.221889i | |||||
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147.235 | 0.210036 | 0.105018 | − | 0.994470i | ||||||
0.105018 | + | 0.994470i | ||||||||
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163.194 | − | 163.194i | 0.232140 | − | 0.232140i | |||||
738.513 | − | 426.381i | 1.04902 | − | 0.605654i | |||||
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517.565 | − | 138.681i | 0.732058 | − | 0.196154i | |||||
349.546 | + | 144.317i | 0.493710 | + | 0.203837i | |||||
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0.584382 | + | 0.811479i | ||||||||
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195.000 | + | 721.122i | 0.274262 | + | 1.01424i | |||||
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503.648 | − | 872.343i | 0.703418 | − | 1.21836i | |||||
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51.2486 | + | 13.7320i | 0.0713769 | + | 0.0191254i | |||||
1075.81i | 1.49626i | 0.663555 | + | 0.748128i | ||||||
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628.297 | − | 309.836i | 0.872635 | − | 0.430328i | |||||
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129.302 | − | 129.302i | 0.177613 | − | 0.177613i | |||||
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0.318918 | − | 0.947782i | ||||||||
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457.776 | − | 154.804i | 0.622824 | − | 0.210618i | |||||
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106.668 | − | 61.9115i | 0.144536 | − | 0.0838910i | |||||
683.603i | 0.925038i | 0.886609 | + | 0.462519i | ||||||
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40.4697 | − | 10.8438i | 0.0545413 | − | 0.0146143i | |||||
204.636 | + | 763.713i | 0.275419 | + | 1.02788i | 0.955560 | + | 0.294797i | ||
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94.3431 | + | 72.2201i | 0.126805 | + | 0.0970700i | |||||
1230.99 | + | 421.032i | 1.65234 | + | 0.565143i | |||||
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238.412 | − | 415.140i | 0.319159 | − | 0.555742i | |||||
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559.447 | − | 322.997i | 0.746925 | − | 0.431238i | |||||
59.0516 | + | 39.9512i | 0.0787355 | + | 0.0532683i | |||||
326.862 | − | 566.142i | 0.435236 | − | 0.753851i | −0.562079 | − | 0.827084i | ||
0.997315 | + | 0.0732329i | ||||||||
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668.868 | + | 668.868i | 0.883577 | + | 0.883577i | 0.993896 | − | 0.110319i | ||
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1.90611 | + | 0.510741i | 0.00251466 | + | 0.000673800i | |||||
107.804 | − | 826.181i | 0.142034 | − | 1.08851i | |||||
44.5654 | + | 29.9264i | 0.0586386 | + | 0.0393768i | |||||
478.705 | − | 829.141i | 0.629047 | − | 1.08954i | −0.358696 | − | 0.933454i | ||
0.987743 | − | 0.156087i | ||||||||
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416.413 | + | 111.577i | 0.545757 | + | 0.146235i | |||||
216.396i | 0.283241i | |||||||||
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435.970 | + | 251.708i | 0.566932 | + | 0.327318i | 0.755923 | − | 0.654661i | ||
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0.432827 | + | 0.901477i | ||||||||
15.1267 | + | 15.0574i | 0.0195435 | + | 0.0194540i | |||||
88.3390 | − | 647.918i | 0.113986 | − | 0.836024i | |||||
26.4279 | + | 45.7745i | 0.0340566 | + | 0.0589878i | |||||
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441.911 | + | 663.024i | 0.566552 | + | 0.850030i | |||||
256.245 | + | 443.830i | 0.328099 | + | 0.568284i | |||||
2.77732 | + | 2.77732i | 0.00355155 | + | 0.00355155i | |||||
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− | 501.526i | − | 0.639701i | |||||||
208.673 | − | 102.309i | 0.265826 | − | 0.130330i | |||||
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26.8943 | + | 100.371i | 0.0341299 | + | 0.127374i | |||||
182.779 | − | 75.9557i | 0.231659 | − | 0.0962683i | |||||
34.7351 | + | 70.8469i | 0.0439685 | + | 0.0896796i | |||||
1570.39 | 1.98532 | |||||||||
−95.5677 | + | 166.409i | −0.120666 | + | 0.210113i | |||||
771.945 | − | 771.945i | 0.973449 | − | 0.973449i | |||||
35.2207 | − | 20.3347i | 0.0443585 | − | 0.0256104i | |||||
23.5663 | + | 366.033i | 0.0296432 | + | 0.460419i | |||||
408.438 | − | 707.435i | 0.513113 | − | 0.888737i | |||||
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0.0858466 | + | 0.996308i | ||||||||
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48.7365 | − | 28.1380i | 0.0609968 | − | 0.0352165i | |||||
179.457 | − | 136.393i | 0.224321 | − | 0.170491i | |||||
196.099 | + | 52.0623i | 0.244818 | + | 0.0649967i | |||||
0.879908 | + | 0.879908i | 0.00109714 | + | 0.00109714i | |||||
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871.992 | − | 171.363i | 1.08322 | − | 0.212873i | |||||
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423.966i | 0.524062i | 0.965060 | + | 0.262031i | ||||||
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66.0092 | − | 246.350i | 0.0812921 | − | 0.303386i | |||||
107.045 | − | 82.3340i | 0.131667 | − | 0.101272i | |||||
75.4686 | + | 43.5718i | 0.0927133 | + | 0.0535281i | |||||
302.877 | − | 451.034i | 0.371628 | − | 0.553416i | |||||
18.7731 | + | 45.1756i | 0.0230063 | + | 0.0553622i | |||||
22.8914 | − | 85.4317i | 0.0280188 | − | 0.104568i | |||||
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278.907 | − | 1050.54i | 0.340546 | − | 1.28271i | |||||
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256.028 | + | 955.510i | 0.311091 | + | 1.16101i | 0.927574 | + | 0.373640i | ||
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103.197 | + | 59.5806i | 0.125239 | + | 0.0723066i | |||||
1056.16 | + | 3.65372i | 1.28019 | + | 0.00442876i | |||||
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− | 325.275i | − | 0.392370i | −0.980567 | − | 0.196185i | ||||
0.980567 | − | 0.196185i | ||||||||
16.3640 | − | 47.8444i | 0.0197157 | − | 0.0576438i | |||||
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783.862 | − | 210.035i | 0.942142 | − | 0.252446i | |||||
8.73421 | + | 32.5965i | 0.0104852 | + | 0.0391315i | |||||
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395.803 | 0.473449 | |||||||||
700.497 | + | 89.7687i | 0.836914 | + | 0.107251i | |||||
36.5387 | − | 36.5387i | 0.0436022 | − | 0.0436022i | |||||
81.4767 | − | 47.0406i | 0.0971116 | − | 0.0560674i | −0.450658 | − | 0.892697i | ||
0.547769 | + | 0.836629i | ||||||||
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37.8296 | − | 10.1364i | 0.0449283 | − | 0.0120385i | |||||
183.535 | + | 75.7757i | 0.217716 | + | 0.0898882i | |||||
833.301 | − | 481.107i | 0.987323 | − | 0.570031i | |||||
−39.8834 | + | 34.8146i | −0.0471993 | + | 0.0412007i | |||||
64.8536 | − | 65.1522i | 0.0766591 | − | 0.0770120i | |||||
−492.644 | − | 492.644i | −0.581633 | − | 0.581633i | |||||
367.698 | + | 98.5244i | 0.433606 | + | 0.116184i | |||||
958.837 | + | 733.994i | 1.12937 | + | 0.864539i | |||||
−3.04911 | + | 3.93600i | −0.00358719 | + | 0.00463058i | |||||
−320.958 | + | 555.915i | −0.377154 | + | 0.653249i | |||||
428.999 | − | 56.9800i | 0.503520 | − | 0.0668779i | |||||
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−0.784856 | + | 0.619678i | ||||||||
139.579i | 0.163442i | |||||||||
318.400 | + | 20.8714i | 0.372397 | + | 0.0244110i | |||||
−108.534 | −0.126793 | |||||||||
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−0.616920 | + | 0.787026i | ||||||||
−99.4922 | − | 41.0773i | −0.115958 | − | 0.0478756i | |||||
507.067 | + | 292.755i | 0.590299 | + | 0.340809i | 0.765216 | − | 0.643774i | ||
−0.174917 | + | 0.984583i | ||||||||
−205.233 | − | 137.818i | −0.238643 | − | 0.160253i | |||||
1932.30 | + | 252.136i | 2.24426 | + | 0.292841i | |||||
−11.7345 | + | 43.7939i | −0.0136132 | + | 0.0508050i | |||||
−550.423 | + | 550.423i | −0.637802 | + | 0.637802i | −0.950013 | − | 0.312211i | ||
0.312211 | + | 0.950013i | ||||||||
148.860 | + | 192.621i | 0.172292 | + | 0.222941i | |||||
994.853 | + | 67.5082i | 1.15012 | + | 0.0780442i | |||||
−10.7144 | − | 18.5579i | −0.0123723 | − | 0.0214294i | |||||
526.579 | + | 684.622i | 0.607357 | + | 0.789644i | |||||
241.833 | + | 902.531i | 0.278609 | + | 1.03978i | |||||
1012.26 | + | 584.429i | 1.16486 | + | 0.672530i | |||||
−18.2507 | − | 9.02650i | −0.0209779 | − | 0.0103753i | |||||
−444.935 | − | 770.650i | −0.510833 | − | 0.884788i | |||||
−51.2158 | − | 51.2158i | −0.0587337 | − | 0.0587337i | |||||
272.446 | + | 156.464i | 0.312080 | + | 0.179225i | |||||
− | 26.5875i | − | 0.0304205i | |||||||
354.720 | + | 1069.19i | 0.405395 | + | 1.22194i | |||||
−29.7460 | + | 38.8581i | −0.0339567 | + | 0.0443585i | |||||
−882.630 | + | 236.500i | −1.00642 | + | 0.269669i | −0.724133 | − | 0.689661i | ||
−0.282287 | + | 0.959330i | ||||||||
15.9166 | + | 59.4017i | 0.0181283 | + | 0.0676557i | |||||
−517.247 | − | 395.955i | −0.588450 | − | 0.450461i | |||||
354.729 | − | 1037.14i | 0.403101 | − | 1.17857i | |||||
−459.689 | −0.521781 | −0.260891 | − | 0.965368i | ||||||
−0.260891 | + | 0.965368i | ||||||||
27.6723 | + | 47.6767i | 0.0313745 | + | 0.0540552i | |||||
107.163 | − | 107.163i | 0.121362 | − | 0.121362i | −0.643817 | − | 0.765179i | ||
0.765179 | + | 0.643817i | ||||||||
−48.1882 | + | 27.8215i | −0.0545116 | + | 0.0314723i | |||||
451.881 | − | 152.811i | 0.510600 | − | 0.172667i | |||||
−71.8119 | + | 124.382i | −0.0810519 | + | 0.140386i | |||||
642.507 | − | 172.159i | 0.724360 | − | 0.194092i | 0.122244 | − | 0.992500i | ||
0.602116 | + | 0.798408i | ||||||||
117.191 | − | 90.1376i | 0.131972 | − | 0.101506i | |||||
−180.277 | + | 104.083i | −0.202786 | + | 0.117078i | |||||
21.3813 | + | 1.45088i | 0.0240239 | + | 0.00163020i | |||||
5.23854 | + | 1140.65i | 0.00587940 | + | 1.28019i | |||||
576.746 | + | 576.746i | 0.646576 | + | 0.646576i | |||||
−367.963 | − | 98.5954i | −0.412053 | − | 0.110409i | |||||
−19.2026 | + | 147.164i | −0.0214794 | + | 0.164613i | |||||
−245.010 | − | 1246.75i | −0.273755 | − | 1.39302i | |||||
−214.387 | + | 371.329i | −0.239271 | + | 0.414430i | |||||
302.582 | − | 732.877i | 0.337327 | − | 0.817031i | |||||
−94.5284 | − | 25.3288i | −0.105266 | − | 0.0282058i | |||||
186.745i | 0.207725i | |||||||||
343.206 | − | 823.187i | 0.381340 | − | 0.914652i | |||||
−25.6142 | −0.0284287 | |||||||||
49.9463 | − | 186.402i | 0.0553728 | − | 0.206654i | |||||
44.4012 | + | 334.295i | 0.0491708 | + | 0.370204i | |||||
−228.495 | − | 131.922i | −0.252760 | − | 0.145931i | |||||
−1162.75 | + | 228.502i | −1.28481 | + | 0.252489i | |||||
89.3891 | − | 116.772i | 0.0986635 | − | 0.128887i | |||||
215.603 | − | 804.640i | 0.237710 | − | 0.887144i | −0.739199 | − | 0.673487i | ||
0.976909 | − | 0.213657i | ||||||||
521.794 | − | 521.794i | 0.574663 | − | 0.574663i | |||||
−516.557 | + | 139.683i | −0.568269 | + | 0.153667i | |||||
7.77262 | − | 114.543i | 0.00854134 | − | 0.125872i | |||||
−38.7954 | − | 67.1955i | −0.0425855 | − | 0.0737602i | 0.843947 | − | 0.536427i | ||
−0.886533 | + | 0.462666i | ||||||||
126.376 | − | 306.093i | 0.138571 | − | 0.335629i | |||||
−193.871 | − | 723.538i | −0.212345 | − | 0.792484i | |||||
−93.8309 | − | 54.1733i | −0.102660 | − | 0.0592706i | |||||
−1198.20 | − | 239.776i | −1.30950 | − | 0.262050i | |||||
−358.623 | − | 621.153i | −0.391510 | − | 0.678115i | |||||
−351.821 | − | 351.821i | −0.383665 | − | 0.383665i | |||||
−4.27725 | − | 3.25871i | −0.00465932 | − | 0.00354979i | |||||
− | 1478.95i | − | 1.60930i | −0.593750 | − | 0.804650i | ||||
0.593750 | − | 0.804650i | ||||||||
−141.272 | − | 48.3187i | −0.153557 | − | 0.0525203i | |||||
921.730 | + | 120.272i | 1.00079 | + | 0.130588i | |||||
−43.8305 | + | 11.7443i | −0.0475385 | + | 0.0127379i | |||||
126.226 | + | 471.083i | 0.136757 | + | 0.510383i | |||||
−1393.60 | + | 579.125i | −1.50823 | + | 0.626758i | |||||
−750.325 | − | 314.853i | −0.811162 | − | 0.340382i | |||||
156.839 | 0.169373 | |||||||||
708.298 | − | 1.62646i | 0.764076 | − | 0.00175454i | |||||
−45.5177 | + | 45.5177i | −0.0490492 | + | 0.0490492i | |||||
−1381.56 | + | 797.643i | −1.48715 | + | 0.858604i | −0.999893 | − | 0.0146572i | ||
−0.487253 | + | 0.873261i | ||||||||
74.4406 | − | 4.79270i | 0.0800436 | − | 0.00515345i | |||||
114.218 | − | 197.831i | 0.122683 | − | 0.212493i | |||||
−651.014 | + | 174.439i | −0.698513 | + | 0.187166i | |||||
−54.3888 | − | 409.491i | −0.0582946 | − | 0.438897i | |||||
113.927 | − | 65.7757i | 0.121977 | − | 0.0704237i | |||||
−4.99338 | + | 73.5863i | −0.00534051 | + | 0.0787019i | |||||
−128.833 | + | 129.426i | −0.137642 | + | 0.138276i | |||||
−921.265 | − | 921.265i | −0.983207 | − | 0.983207i | 0.0166542 | − | 0.999861i | ||
−0.999861 | + | 0.0166542i | ||||||||
109.898 | + | 29.4471i | 0.117162 | + | 0.0313935i | |||||
18.2824 | − | 7.59741i | 0.0194700 | − | 0.00809096i | |||||
−593.594 | + | 883.961i | −0.631483 | + | 0.940384i | |||||
−618.185 | + | 1070.73i | −0.656945 | + | 1.13786i | 0.324458 | + | 0.945900i | ||
−0.981402 | + | 0.191961i | ||||||||
16.1632 | + | 21.0144i | 0.0171584 | + | 0.0223082i | |||||
1373.07 | + | 367.913i | 1.45607 | + | 0.390152i | |||||
− | 495.068i | − | 0.524436i | |||||||
−1151.61 | + | 392.383i | −1.21863 | + | 0.415221i | |||||
33.3958 | 0.0353021 | |||||||||
418.272 | − | 1561.01i | 0.441681 | − | 1.64838i | −0.282872 | − | 0.959158i | ||
0.724553 | − | 0.689219i | ||||||||
782.372 | − | 601.764i | 0.825287 | − | 0.634772i | |||||
−47.7599 | − | 27.5742i | −0.0503265 | − | 0.0290560i | |||||
33.4345 | − | 4.24511i | 0.0351943 | − | 0.00446854i | |||||
−509.250 | − | 1225.46i | −0.535489 | − | 1.28860i | |||||
3.69940 | − | 13.8064i | 0.00388593 | − | 0.0145025i | |||||
1074.57 | − | 1074.57i | 1.12756 | − | 1.12756i | 0.136988 | − | 0.990573i | ||
0.990573 | − | 0.136988i | ||||||||
−40.3908 | + | 10.9222i | −0.0423384 | + | 0.0114488i | |||||
179.503 | + | 205.638i | 0.187961 | + | 0.215328i | |||||
760.073 | + | 1316.48i | 0.795055 | + | 1.37708i | |||||
−298.995 | + | 39.7127i | −0.312429 | + | 0.0414971i | |||||
8.11362 | + | 30.2804i | 0.00846933 | + | 0.0316080i | |||||
−1530.10 | − | 883.405i | −1.59552 | − | 0.921173i | |||||
−682.233 | − | 599.699i | −0.710660 | − | 0.624686i | |||||
138.418 | + | 239.748i | 0.144036 | + | 0.249477i | |||||
58.6394 | + | 58.6394i | 0.0609557 | + | 0.0609557i | |||||
−557.960 | + | 323.849i | −0.579398 | + | 0.336292i | |||||
1291.77i | 1.34001i | |||||||||
440.729 | + | 898.924i | 0.456713 | + | 0.931527i | |||||
38.9019 | + | 93.6132i | 0.0402711 | + | 0.0969081i | |||||
174.037 | − | 46.6332i | 0.179977 | − | 0.0482246i | −0.167705 | − | 0.985837i | ||
0.347682 | + | 0.937613i | ||||||||
30.2958 | + | 113.066i | 0.0312974 | + | 0.116803i | |||||
−2.88310 | + | 22.0953i | −0.00297533 | + | 0.0228022i | |||||
31.3991 | + | 10.7393i | 0.0323702 | + | 0.0110714i | |||||
−40.8568 | −0.0420770 | −0.0210385 | − | 0.999779i | ||||||
−0.0210385 | + | 0.999779i | ||||||||
891.997 | + | 363.492i | 0.917693 | + | 0.373963i | |||||
−607.325 | + | 607.325i | −0.624178 | + | 0.624178i | |||||
76.1338 | − | 43.9558i | 0.0781661 | − | 0.0451292i | |||||
969.926 | + | 263.491i | 0.994796 | + | 0.270247i | |||||
−634.092 | + | 1098.28i | −0.649685 | + | 1.12529i | |||||
754.152 | − | 202.074i | 0.771906 | − | 0.206832i | 0.148693 | − | 0.988883i | ||
0.623213 | + | 0.782052i | ||||||||
57.2853 | + | 23.6513i | 0.0585739 | + | 0.0241834i | |||||
274.932 | − | 158.732i | 0.280829 | − | 0.162137i | |||||
−419.885 | − | 481.018i | −0.428454 | − | 0.490835i | |||||
−416.113 | − | 110.474i | −0.424172 | − | 0.112613i | |||||
48.9385 | + | 48.9385i | 0.0498355 | + | 0.0498355i | |||||
−496.515 | − | 133.041i | −0.505101 | − | 0.135341i | −0.00273477 | − | 0.999996i | ||
−0.502367 | + | 0.864655i | ||||||||
−259.974 | − | 199.011i | −0.264201 | − | 0.202247i | |||||
108.816 | + | 73.0718i | 0.110473 | + | 0.0741845i | |||||
0.710935 | − | 1.23138i | 0.000721030 | − | 0.00124886i | |||||
1439.84 | − | 191.241i | 1.45881 | − | 0.193760i | |||||
363.824 | + | 97.4863i | 0.368243 | + | 0.0986704i | |||||
245.999i | 0.248735i | |||||||||
23.5039 | + | 118.167i | 0.0237413 | + | 0.119360i | |||||
941.294 | 0.949843 | 0.474922 | − | 0.880028i | ||||||
0.474922 | + | 0.880028i | ||||||||
61.0382 | − | 227.798i | 0.0615304 | − | 0.229635i | |||||
725.690 | + | 299.615i | 0.730805 | + | 0.301727i | |||||
−54.0013 | − | 31.1776i | −0.0543272 | − | 0.0313658i | |||||
−198.693 | − | 1011.07i | −0.199692 | − | 1.01615i | |||||
−627.219 | − | 81.8425i | −0.629738 | − | 0.0821712i | |||||
344.990 | − | 1287.52i | 0.346029 | − | 1.29140i | −0.545377 | − | 0.838191i | ||
0.891406 | − | 0.453206i | ||||||||
54.8879 | − | 54.8879i | 0.0549979 | − | 0.0549979i | |||||
333.505 | − | 813.063i | 0.333839 | − | 0.813877i |
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 45.3.k.a.22.5 | yes | 40 | |
3.2 | odd | 2 | 135.3.l.a.37.6 | 40 | |||
5.2 | odd | 4 | 225.3.o.b.193.5 | 40 | |||
5.3 | odd | 4 | inner | 45.3.k.a.13.6 | yes | 40 | |
5.4 | even | 2 | 225.3.o.b.157.6 | 40 | |||
9.2 | odd | 6 | 135.3.l.a.127.5 | 40 | |||
9.4 | even | 3 | 405.3.g.h.82.5 | 20 | |||
9.5 | odd | 6 | 405.3.g.g.82.6 | 20 | |||
9.7 | even | 3 | inner | 45.3.k.a.7.6 | ✓ | 40 | |
15.8 | even | 4 | 135.3.l.a.118.5 | 40 | |||
45.7 | odd | 12 | 225.3.o.b.43.6 | 40 | |||
45.13 | odd | 12 | 405.3.g.h.163.5 | 20 | |||
45.23 | even | 12 | 405.3.g.g.163.6 | 20 | |||
45.34 | even | 6 | 225.3.o.b.7.5 | 40 | |||
45.38 | even | 12 | 135.3.l.a.73.6 | 40 | |||
45.43 | odd | 12 | inner | 45.3.k.a.43.5 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
45.3.k.a.7.6 | ✓ | 40 | 9.7 | even | 3 | inner | |
45.3.k.a.13.6 | yes | 40 | 5.3 | odd | 4 | inner | |
45.3.k.a.22.5 | yes | 40 | 1.1 | even | 1 | trivial | |
45.3.k.a.43.5 | yes | 40 | 45.43 | odd | 12 | inner | |
135.3.l.a.37.6 | 40 | 3.2 | odd | 2 | |||
135.3.l.a.73.6 | 40 | 45.38 | even | 12 | |||
135.3.l.a.118.5 | 40 | 15.8 | even | 4 | |||
135.3.l.a.127.5 | 40 | 9.2 | odd | 6 | |||
225.3.o.b.7.5 | 40 | 45.34 | even | 6 | |||
225.3.o.b.43.6 | 40 | 45.7 | odd | 12 | |||
225.3.o.b.157.6 | 40 | 5.4 | even | 2 | |||
225.3.o.b.193.5 | 40 | 5.2 | odd | 4 | |||
405.3.g.g.82.6 | 20 | 9.5 | odd | 6 | |||
405.3.g.g.163.6 | 20 | 45.23 | even | 12 | |||
405.3.g.h.82.5 | 20 | 9.4 | even | 3 | |||
405.3.g.h.163.5 | 20 | 45.13 | odd | 12 |