Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [117,3,Mod(29,117)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(117, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1, 2]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("117.29");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 117.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 | 113.13 | ||
Character | 117.113 | ||
Dual form | 117.3.k.a.29.14 |
-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 .
0.376029i | 0.188014i | 0.995572 | + | 0.0940072i | ||||||
−0.995572 | + | 0.0940072i | ||||||||
−2.92720 | + | 0.656887i | −0.975733 | + | 0.218962i | |||||
3.85860 | 0.964651 | |||||||||
0.994641 | + | 0.574256i | 0.198928 | + | 0.114851i | 0.596155 | − | 0.802869i | ||
−0.397227 | + | 0.917720i | ||||||||
−0.247009 | − | 1.10071i | −0.0411681 | − | 0.183452i | |||||
−2.57212 | + | 4.45503i | −0.367445 | + | 0.636434i | −0.989165 | − | 0.146806i | ||
0.621720 | + | 0.783239i | ||||||||
2.95506i | 0.369383i | |||||||||
8.13700 | − | 3.84568i | 0.904111 | − | 0.427298i | |||||
−0.215937 | + | 0.374014i | −0.0215937 | + | 0.0374014i | |||||
15.0728i | 1.37025i | 0.728424 | + | 0.685127i | ||||||
−0.728424 | + | 0.685127i | ||||||||
−11.2949 | + | 2.53467i | −0.941242 | + | 0.211222i | |||||
12.9040 | + | 1.57671i | 0.992618 | + | 0.121286i | |||||
−1.67522 | − | 0.967190i | −0.119659 | − | 0.0690850i | |||||
−3.28873 | − | 1.02760i | −0.219249 | − | 0.0685064i | |||||
14.3232 | 0.895201 | |||||||||
−24.4307 | + | 14.1051i | −1.43710 | + | 0.829709i | −0.997647 | − | 0.0685572i | ||
−0.439451 | + | 0.898266i | ||||||||
1.44609 | + | 3.05975i | 0.0803382 | + | 0.169986i | |||||
10.6901 | + | 18.5158i | 0.562638 | + | 0.974518i | 0.997265 | + | 0.0739073i | ||
−0.434627 | + | 0.900611i | ||||||||
3.83792 | + | 2.21583i | 0.191896 | + | 0.110791i | |||||
4.60264 | − | 14.7304i | 0.219173 | − | 0.701446i | |||||
−5.66781 | −0.257628 | |||||||||
12.5928 | − | 7.27045i | 0.547512 | − | 0.316106i | −0.200606 | − | 0.979672i | ||
0.748118 | + | 0.663566i | ||||||||
−1.94114 | − | 8.65006i | −0.0808809 | − | 0.360419i | |||||
−11.8405 | − | 20.5083i | −0.473618 | − | 0.820331i | |||||
−0.592890 | + | 4.85229i | −0.0228035 | + | 0.186627i | |||||
−21.2924 | + | 16.6022i | −0.788609 | + | 0.614895i | |||||
−9.92477 | + | 17.1902i | −0.354456 | + | 0.613936i | |||||
− | 53.9734i | − | 1.86115i | −0.366100 | − | 0.930576i | ||||
0.366100 | − | 0.930576i | ||||||||
0.386406 | − | 1.23666i | 0.0128802 | − | 0.0412220i | |||||
20.6940 | − | 35.8431i | 0.667549 | − | 1.15623i | −0.311039 | − | 0.950397i | ||
0.978588 | − | 0.205831i | ||||||||
17.2062i | 0.537694i | |||||||||
−9.90113 | − | 44.1211i | −0.300034 | − | 1.33700i | |||||
−5.30391 | − | 9.18664i | −0.155997 | − | 0.270195i | |||||
−5.11666 | + | 2.95411i | −0.146190 | + | 0.0844030i | |||||
31.3974 | − | 14.8390i | 0.872151 | − | 0.412193i | |||||
26.5470 | − | 45.9807i | 0.717486 | − | 1.24272i | −0.244507 | − | 0.969647i | ||
0.961993 | − | 0.273074i | ||||||||
−6.96249 | + | 4.01980i | −0.183223 | + | 0.105784i | |||||
−38.8084 | + | 3.86114i | −0.995087 | + | 0.0990035i | |||||
−1.69696 | + | 2.93923i | −0.0424241 | + | 0.0734806i | |||||
−24.9941 | + | 14.4303i | −0.609612 | + | 0.351959i | −0.772813 | − | 0.634633i | ||
0.163202 | + | 0.986593i | ||||||||
5.53904 | + | 1.73073i | 0.131882 | + | 0.0412078i | |||||
−21.0292 | + | 36.4236i | −0.489050 | + | 0.847060i | −0.999921 | − | 0.0125977i | ||
0.510870 | + | 0.859658i | ||||||||
58.1599i | 1.32182i | |||||||||
10.3018 | + | 0.847651i | 0.228929 | + | 0.0188367i | |||||
2.73390 | + | 4.73525i | 0.0594326 | + | 0.102940i | |||||
3.48340 | − | 2.01114i | 0.0741148 | − | 0.0427902i | −0.462485 | − | 0.886627i | ||
0.536599 | + | 0.843837i | ||||||||
−41.9269 | + | 9.40874i | −0.873478 | + | 0.196015i | |||||
11.2684 | + | 19.5175i | 0.229968 | + | 0.398317i | |||||
7.71171 | − | 4.45236i | 0.154234 | − | 0.0890471i | |||||
62.2480 | − | 57.3365i | 1.22055 | − | 1.12425i | |||||
49.7915 | + | 6.08391i | 0.957529 | + | 0.116998i | |||||
12.6540i | 0.238755i | 0.992849 | + | 0.119378i | ||||||
−0.992849 | + | 0.119378i | ||||||||
−6.24290 | − | 8.00658i | −0.115609 | − | 0.148270i | |||||
−8.65564 | + | 14.9920i | −0.157375 | + | 0.272582i | |||||
−13.1649 | − | 7.60076i | −0.235088 | − | 0.135728i | |||||
−43.4549 | − | 47.1774i | −0.762368 | − | 0.827673i | |||||
20.2956 | 0.349923 | |||||||||
− | 22.0040i | − | 0.372948i | −0.982460 | − | 0.186474i | ||||
0.982460 | − | 0.186474i | ||||||||
−12.6899 | − | 3.96508i | −0.211499 | − | 0.0660847i | |||||
−5.17426 | + | 8.96208i | −0.0848239 | + | 0.146919i | −0.905316 | − | 0.424738i | ||
0.820492 | + | 0.571658i | ||||||||
13.4780 | + | 7.78155i | 0.217388 | + | 0.125509i | |||||
−3.79666 | + | 46.1421i | −0.0602644 | + | 0.732415i | |||||
50.8229 | 0.794107 | |||||||||
11.9294 | + | 8.97848i | 0.183530 | + | 0.138130i | |||||
16.5908 | − | 3.72311i | 0.251376 | − | 0.0564108i | |||||
−37.0115 | − | 64.1058i | −0.552410 | − | 0.956802i | −0.998100 | − | 0.0616149i | ||
0.445690 | − | 0.895187i | ||||||||
−94.2683 | + | 54.4258i | −1.38630 | + | 0.800379i | |||||
−32.0857 | + | 29.5541i | −0.465011 | + | 0.428320i | |||||
−1.11083 | − | 1.92401i | −0.0158690 | − | 0.0274859i | |||||
34.1908 | − | 19.7401i | 0.481561 | − | 0.278029i | −0.239506 | − | 0.970895i | ||
0.721067 | + | 0.692865i | ||||||||
11.3642 | + | 24.0453i | 0.157836 | + | 0.333963i | |||||
−65.2913 | −0.894402 | −0.447201 | − | 0.894434i | ||||||
−0.447201 | + | 0.894434i | ||||||||
17.2901 | + | 9.98243i | 0.233650 | + | 0.134898i | |||||
48.1310 | + | 52.2540i | 0.641747 | + | 0.696720i | |||||
41.2489 | + | 71.4453i | 0.542749 | + | 0.940069i | |||||
−67.1498 | − | 38.7690i | −0.872076 | − | 0.503493i | |||||
−1.45190 | − | 14.5931i | −0.0186141 | − | 0.187091i | |||||
−9.78025 | − | 16.9399i | −0.123801 | − | 0.214429i | 0.797463 | − | 0.603368i | ||
−0.921263 | + | 0.388939i | ||||||||
14.2465 | + | 8.22520i | 0.178081 | + | 0.102815i | |||||
51.4215 | − | 62.5846i | 0.634833 | − | 0.772649i | |||||
−5.42622 | − | 9.39850i | −0.0661735 | − | 0.114616i | |||||
71.7112 | − | 41.4025i | 0.863991 | − | 0.498825i | −0.00135589 | − | 0.999999i | ||
0.865347 | + | 0.501174i | ||||||||
17.7598 | − | 56.8386i | 0.211426 | − | 0.676650i | |||||
−32.3997 | −0.381172 | |||||||||
−13.6963 | − | 7.90758i | −0.159260 | − | 0.0919486i | |||||
35.4544 | + | 157.991i | 0.407522 | + | 1.81599i | |||||
−44.5410 | −0.506148 | |||||||||
134.830 | + | 77.8441i | 1.51494 | + | 0.874653i | 0.999846 | + | 0.0175212i | ||
0.515097 | + | 0.857132i | ||||||||
−0.318741 | + | 3.87377i | −0.00354157 | + | 0.0430419i | |||||
−40.2150 | + | 53.4324i | −0.441923 | + | 0.587169i | |||||
48.5905 | − | 28.0538i | 0.528158 | − | 0.304932i | |||||
−37.0306 | + | 118.513i | −0.398179 | + | 1.27434i | |||||
0.756247 | + | 1.30986i | 0.00804518 | + | 0.0139347i | |||||
24.5555i | 0.258479i | |||||||||
−11.3025 | − | 50.3660i | −0.117735 | − | 0.524646i | |||||
−9.71984 | + | 16.8353i | −0.100205 | + | 0.173559i | −0.911769 | − | 0.410704i | ||
0.811564 | + | 0.584263i | ||||||||
−7.33915 | + | 4.23726i | −0.0748893 | + | 0.0432374i | |||||
57.9651 | + | 122.647i | 0.585507 | + | 1.23886i | |||||
−45.6876 | − | 79.1333i | −0.456876 | − | 0.791333i | |||||
− | 82.8944i | − | 0.820737i | −0.911920 | − | 0.410369i | ||||
0.911920 | − | 0.410369i | ||||||||
21.5602 | + | 23.4071i | 0.211374 | + | 0.229481i | |||||
−38.2718 | + | 66.2886i | −0.371571 | + | 0.643579i | −0.989807 | − | 0.142413i | ||
0.618237 | + | 0.785992i | ||||||||
−4.65929 | + | 38.1322i | −0.0448008 | + | 0.366656i | |||||
13.0370 | − | 12.0083i | 0.124162 | − | 0.114365i | |||||
−4.75828 | −0.0448894 | |||||||||
20.6786 | + | 11.9388i | 0.193258 | + | 0.111578i | 0.593507 | − | 0.804829i | ||
−0.400249 | + | 0.916407i | ||||||||
−82.1591 | + | 64.0612i | −0.760732 | + | 0.593159i | |||||
5.84222 | 0.0535983 | 0.0267992 | − | 0.999641i | ||||||
0.0267992 | + | 0.999641i | ||||||||
−5.63743 | − | 3.25477i | −0.0512494 | − | 0.0295888i | |||||
−47.5042 | + | 152.033i | −0.427965 | + | 1.36967i | |||||
−36.8410 | + | 63.8104i | −0.328937 | + | 0.569736i | |||||
− | 133.419i | − | 1.18070i | −0.807146 | − | 0.590351i | ||||
0.807146 | − | 0.590351i | ||||||||
17.7401 | − | 16.3403i | 0.155615 | − | 0.143336i | |||||
16.7004 | 0.145221 | |||||||||
− | 208.262i | − | 1.79536i | |||||||
111.064 | − | 36.7951i | 0.949262 | − | 0.314488i | |||||
8.27412 | 0.0701197 | |||||||||
− | 145.119i | − | 1.21949i | |||||||
3.03661 | − | 9.71841i | 0.0253051 | − | 0.0809868i | |||||
−106.189 | −0.877596 | |||||||||
−3.37000 | − | 1.94567i | −0.0276230 | − | 0.0159481i | |||||
63.6835 | − | 58.6588i | 0.517752 | − | 0.476900i | |||||
79.8499 | − | 138.304i | 0.643951 | − | 1.11536i | |||||
− | 55.9106i | − | 0.447285i | |||||||
−17.3508 | − | 1.42765i | −0.137705 | − | 0.0113306i | |||||
5.22700 | − | 9.05343i | 0.0411575 | − | 0.0712869i | −0.844713 | − | 0.535220i | ||
0.885870 | + | 0.463933i | ||||||||
87.9356i | 0.686997i | |||||||||
37.6304 | − | 120.433i | 0.291708 | − | 0.933588i | |||||
−3.37617 | + | 4.48581i | −0.0259705 | + | 0.0345063i | |||||
−74.2522 | − | 42.8695i | −0.566811 | − | 0.327248i | 0.189064 | − | 0.981965i | ||
−0.755875 | + | 0.654716i | ||||||||
−38.2045 | − | 170.246i | −0.289428 | − | 1.28974i | |||||
−109.985 | −0.826954 | |||||||||
24.1056 | − | 13.9174i | 0.179893 | − | 0.103861i | |||||
−30.7122 | + | 4.28587i | −0.227498 | + | 0.0317472i | |||||
−41.6813 | − | 72.1942i | −0.306480 | − | 0.530839i | |||||
96.1691 | + | 55.5233i | 0.701964 | + | 0.405279i | 0.808079 | − | 0.589075i | ||
−0.106114 | + | 0.994354i | ||||||||
−11.1132 | − | 12.0652i | −0.0805304 | − | 0.0874287i | |||||
−202.843 | −1.45930 | −0.729652 | − | 0.683818i | ||||||
−0.729652 | + | 0.683818i | ||||||||
−19.7432 | + | 11.3987i | −0.141023 | + | 0.0814194i | |||||
−8.87550 | + | 8.17520i | −0.0629468 | + | 0.0579802i | |||||
7.42285 | + | 12.8567i | 0.0522736 | + | 0.0905405i | |||||
−23.7655 | + | 194.500i | −0.166192 | + | 1.36014i | |||||
116.548 | − | 55.0825i | 0.809361 | − | 0.382518i | |||||
30.9945 | − | 53.6841i | 0.213755 | − | 0.370235i | |||||
− | 24.5514i | − | 0.168161i | |||||||
−45.8058 | − | 49.7296i | −0.311604 | − | 0.338296i | |||||
102.434 | − | 177.421i | 0.692123 | − | 1.19879i | |||||
− | 235.223i | − | 1.57868i | −0.613957 | − | 0.789340i | ||||
0.613957 | − | 0.789340i | ||||||||
−19.6490 | + | 18.0987i | −0.130993 | + | 0.120658i | |||||
133.267 | + | 230.825i | 0.882561 | + | 1.52864i | 0.848483 | + | 0.529222i | ||
0.0340779 | + | 0.999419i | ||||||||
−54.7155 | + | 31.5900i | −0.359970 | + | 0.207829i | |||||
−144.549 | + | 208.725i | −0.944764 | + | 1.36422i | |||||
14.5783 | − | 25.2503i | 0.0946640 | − | 0.163963i | |||||
41.1662 | − | 23.7673i | 0.265588 | − | 0.153338i | |||||
−149.746 | + | 14.8986i | −0.959911 | + | 0.0955038i | |||||
29.0426 | − | 50.3033i | 0.184985 | − | 0.320403i | −0.758587 | − | 0.651572i | ||
0.943571 | + | 0.331169i | ||||||||
6.36989 | − | 3.67766i | 0.0403158 | − | 0.0232763i | |||||
−8.31226 | − | 37.0408i | −0.0522784 | − | 0.232961i | |||||
−9.88076 | + | 17.1140i | −0.0617548 | + | 0.106962i | |||||
74.8017i | 0.464607i | |||||||||
23.5336 | + | 19.3360i | 0.145269 | + | 0.119358i | |||||
−8.10087 | − | 14.0311i | −0.0496986 | − | 0.0860805i | 0.840106 | − | 0.542422i | ||
−0.889805 | + | 0.456342i | ||||||||
−96.4422 | + | 55.6809i | −0.588062 | + | 0.339518i | |||||
15.4887 | − | 49.5704i | 0.0938711 | − | 0.300427i | |||||
15.5685 | + | 26.9655i | 0.0937864 | + | 0.162443i | |||||
−27.0940 | + | 15.6427i | −0.162240 | + | 0.0936691i | −0.578922 | − | 0.815383i | ||
0.416682 | + | 0.909052i | ||||||||
43.5291 | + | 13.6011i | 0.259102 | + | 0.0809589i | |||||
164.028 | + | 40.6919i | 0.970580 | + | 0.240781i | |||||
− | 12.1832i | − | 0.0716659i | |||||||
158.192 | + | 109.553i | 0.925097 | + | 0.640658i | |||||
−81.1432 | + | 140.544i | −0.471763 | + | 0.817117i | |||||
3.74325 | + | 2.16116i | 0.0216373 | + | 0.0124923i | 0.510780 | − | 0.859712i | ||
−0.489142 | + | 0.872204i | ||||||||
−59.4092 | + | 13.3319i | −0.341432 | + | 0.0766201i | |||||
121.820 | 0.696115 | |||||||||
215.891i | 1.22665i | |||||||||
14.4541 | + | 64.4100i | 0.0816617 | + | 0.363898i | |||||
−29.2716 | + | 50.7000i | −0.164447 | + | 0.284831i | |||||
−1.59962 | − | 0.923541i | −0.00893642 | − | 0.00515945i | 0.495525 | − | 0.868594i | ||
−0.504462 | + | 0.863434i | ||||||||
39.7505 | + | 3.27075i | 0.220836 | + | 0.0181708i | |||||
−10.7339 | −0.0593032 | −0.0296516 | − | 0.999560i | ||||||
−0.0296516 | + | 0.999560i | ||||||||
−20.0921 | − | 15.1220i | −0.110396 | − | 0.0830879i | |||||
9.25901 | − | 29.6327i | 0.0505957 | − | 0.161927i | |||||
21.4846 | + | 37.2125i | 0.116764 | + | 0.202242i | |||||
52.8094 | − | 30.4895i | 0.285456 | − | 0.164808i | |||||
−44.5645 | − | 13.9246i | −0.239594 | − | 0.0748634i | |||||
−212.603 | − | 368.239i | −1.13691 | − | 1.96919i | |||||
13.4410 | − | 7.76019i | 0.0714949 | − | 0.0412776i | |||||
−19.1966 | − | 137.561i | −0.101569 | − | 0.727837i | |||||
−9.23357 | −0.0485977 | |||||||||
57.0922 | + | 32.9622i | 0.298912 | + | 0.172577i | 0.641954 | − | 0.766743i | ||
−0.343042 | + | 0.939320i | ||||||||
−148.769 | + | 33.3849i | −0.774837 | + | 0.173880i | |||||
55.9292 | + | 96.8723i | 0.289789 | + | 0.501929i | 0.973759 | − | 0.227581i | ||
−0.683970 | + | 0.729510i | ||||||||
−6.33055 | − | 3.65494i | −0.0326317 | − | 0.0188399i | |||||
−40.8177 | − | 18.4455i | −0.209322 | − | 0.0945924i | |||||
43.4804 | + | 75.3103i | 0.221839 | + | 0.384236i | |||||
10.1710 | + | 5.87226i | 0.0516297 | + | 0.0298084i | 0.525593 | − | 0.850736i | ||
−0.473963 | + | 0.880545i | ||||||||
−46.1189 | + | 21.7966i | −0.232924 | + | 0.110084i | |||||
9.23826 | + | 16.0011i | 0.0464234 | + | 0.0804077i | 0.888303 | − | 0.459257i | ||
−0.841880 | + | 0.539665i | ||||||||
60.6032 | − | 34.9893i | 0.303016 | − | 0.174946i | |||||
150.450 | + | 163.338i | 0.748509 | + | 0.812627i | |||||
31.1707 | 0.154310 | |||||||||
240.453 | + | 138.826i | 1.18450 | + | 0.683871i | |||||
240.190 | − | 221.239i | 1.17740 | − | 1.08450i | |||||
−33.1468 | −0.161692 | |||||||||
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74.5076 | − | 107.587i | 0.359940 | − | 0.519746i | |||||
184.827 | + | 22.5836i | 0.888593 | + | 0.108575i | |||||
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4.51548 | + | 4.90228i | 0.0215023 | + | 0.0233442i | |||||
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48.8268i | 0.230315i | |||||||||
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106.455 | + | 184.385i | 0.490575 | + | 0.849701i | |||||
2.19684i | 0.0100773i | |||||||||
191.121 | − | 42.8890i | 0.872698 | − | 0.195840i | |||||
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50.1696 | 0.221989 | |||||||||
219.554 | + | 126.760i | 0.967200 | + | 0.558413i | 0.898382 | − | 0.439216i | ||
0.0688188 | + | 0.997629i | ||||||||
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119.446 | − | 206.887i | 0.521600 | − | 0.903437i | −0.478085 | − | 0.878314i | ||
0.999684 | − | 0.0251232i | ||||||||
6.27983i | 0.0273036i | |||||||||
222.028 | + | 69.3747i | 0.961159 | + | 0.300323i | |||||
159.495 | 0.687477 | |||||||||
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0.995751 | − | 0.0920912i | ||||||||
13.8360 | + | 41.7631i | 0.0591282 | + | 0.178475i | |||||
4.61964 | 0.0196580 | |||||||||
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39.7563 | + | 43.1619i | 0.167748 | + | 0.182118i | |||||
54.5691 | 0.229282 | |||||||||
67.0524 | + | 38.7127i | 0.280554 | + | 0.161978i | 0.633674 | − | 0.773600i | ||
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47.8848 | − | 82.9389i | 0.198692 | − | 0.344145i | −0.749412 | − | 0.662103i | ||
0.948105 | + | 0.317959i | ||||||||
− | 39.9302i | − | 0.165001i | |||||||
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25.8839i | 0.105649i | |||||||||
22.0574 | + | 23.9469i | 0.0896642 | + | 0.0973450i | |||||
108.752 | + | 255.784i | 0.440290 | + | 1.03556i | |||||
105.919 | + | 61.1521i | 0.427091 | + | 0.246581i | |||||
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21.0240 | 0.0840961 | |||||||||
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109.586 | + | 189.808i | 0.433146 | + | 0.750231i | |||||
3.40435 | + | 1.96550i | 0.0134030 | + | 0.00773820i | |||||
94.8403 | − | 21.2829i | 0.371923 | − | 0.0834624i | |||||
170.225 | 0.664942 | |||||||||
336.324 | − | 194.177i | 1.30865 | − | 0.755552i | 0.326783 | − | 0.945100i | ||
0.981872 | + | 0.189548i | ||||||||
45.2863 | + | 14.1501i | 0.175528 | + | 0.0548454i | |||||
136.564 | + | 236.535i | 0.527273 | + | 0.913264i | |||||
46.0309 | + | 34.6444i | 0.177042 | + | 0.133248i | |||||
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16.1202 | − | 27.9210i | 0.0615275 | − | 0.106569i | |||||
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0.952986 | − | 0.303014i | ||||||||
130.381 | − | 29.2584i | 0.493866 | − | 0.110827i | |||||
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0.220784 | + | 0.975323i | ||||||||
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0.630439 | + | 0.776239i | ||||||||
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82.6182 | − | 182.824i | 0.302631 | − | 0.669685i | |||||
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309.117 | − | 178.469i | 1.12406 | − | 0.648977i | |||||
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160.981 | − | 278.828i | 0.581159 | − | 1.00660i | −0.414183 | − | 0.910194i | ||
0.995342 | − | 0.0964039i | ||||||||
− | 76.2750i | − | 0.274370i | |||||||
30.5461 | − | 371.238i | 0.109484 | − | 1.33060i | |||||
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0.00846154 | − | 0.999964i | ||||||||
131.929 | − | 76.1692i | 0.464538 | − | 0.268201i | |||||
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− | 148.466i | − | 0.517303i | |||||||
66.1695 | + | 140.007i | 0.229755 | + | 0.486135i | |||||
253.405 | − | 438.911i | 0.876835 | − | 1.51872i | |||||
20.1868 | + | 11.6548i | 0.0696096 | + | 0.0401891i | |||||
17.3931 | − | 55.6650i | 0.0597700 | − | 0.191289i | |||||
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548.637i | 1.87248i | 0.351360 | + | 0.936240i | ||||||
−0.351360 | + | 0.936240i | ||||||||
18.6998 | − | 17.2243i | 0.0636046 | − | 0.0585861i | |||||
12.6359 | − | 21.8860i | 0.0428336 | − | 0.0741899i | |||||
135.876 | + | 78.4479i | 0.459040 | + | 0.265027i | |||||
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88.4508 | 0.296815 | |||||||||
173.961 | − | 73.9629i | 0.581810 | − | 0.247367i | |||||
185.718 | + | 201.627i | 0.619062 | + | 0.672091i | |||||
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54.4523 | + | 242.649i | 0.179711 | + | 0.800821i | |||||
153.117 | + | 265.206i | 0.503674 | + | 0.872390i | |||||
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78.3446 | 0.255194 | 0.127597 | − | 0.991826i | ||||||
0.127597 | + | 0.991826i | ||||||||
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68.4850 | − | 219.180i | 0.221634 | − | 0.709322i | |||||
8.93720 | + | 15.4797i | 0.0288297 | + | 0.0499345i | |||||
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117.824 | + | 204.077i | 0.376435 | + | 0.652004i | 0.990541 | − | 0.137220i | ||
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18.9155 | + | 10.9209i | 0.0602404 | + | 0.0347798i | |||||
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107.908 | − | 62.3008i | 0.340404 | − | 0.196532i | −0.320047 | − | 0.947402i | ||
0.660451 | + | 0.750869i | ||||||||
13.9284 | − | 3.12565i | 0.0438001 | − | 0.00982909i | |||||
813.530 | 2.55025 | |||||||||
50.5505 | + | 29.1853i | 0.157970 | + | 0.0912042i | |||||
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198.415 | − | 241.489i | 0.612392 | − | 0.745337i | |||||
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5.27611 | − | 3.04616i | 0.0161844 | − | 0.00934406i | |||||
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20.6915i | 0.0628922i | |||||||||
18.6399 | + | 5.82421i | 0.0564846 | + | 0.0176491i | |||||
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276.705 | − | 159.756i | 0.833449 | − | 0.481192i | |||||
39.1856 | − | 476.236i | 0.117674 | − | 1.43014i | |||||
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− | 85.0163i | − | 0.253780i | |||||||
65.9246 | − | 210.986i | 0.196204 | − | 0.627935i | |||||
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87.6415 | + | 390.545i | 0.258530 | + | 1.15205i | |||||
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540.255 | + | 311.916i | 1.58433 | + | 0.914711i | |||||
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0.969242 | − | 0.246110i | ||||||||
136.805 | + | 609.624i | 0.393116 | + | 1.75179i | |||||
134.718 | 0.386010 | 0.193005 | − | 0.981198i | ||||||
0.193005 | + | 0.981198i | ||||||||
45.8079i | 0.130880i | |||||||||
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−259.345 | −0.736777 | |||||||||
126.976i | 0.359705i | 0.983694 | + | 0.179853i | ||||||
−0.983694 | + | 0.179853i | ||||||||
−24.2200 | + | 5.43517i | −0.0684181 | + | 0.0153536i | |||||
45.3435 | 0.127728 | |||||||||
520.255 | + | 300.370i | 1.46139 | + | 0.843735i | |||||
95.3270 | + | 424.793i | 0.267023 | + | 1.18990i | |||||
0.347278 | − | 0.601503i | 0.000970051 | − | 0.00168018i | |||||
− | 443.856i | − | 1.23637i | −0.786034 | − | 0.618184i | ||||
0.786034 | − | 0.618184i | ||||||||
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− | 4.03625i | − | 0.0111499i | |||||||
310.837 | − | 69.7543i | 0.856300 | − | 0.192161i | |||||
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−64.9414 | − | 37.4939i | −0.177922 | − | 0.102723i | |||||
11.1428 | + | 3.48166i | 0.0304447 | + | 0.00951272i | |||||
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−0.158274 | + | 0.987395i | ||||||||
180.369 | − | 104.136i | 0.490134 | − | 0.282979i | |||||
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11.4649 | + | 19.8579i | 0.0309863 | + | 0.0536699i | |||||
−56.3741 | − | 32.5476i | −0.151952 | − | 0.0877294i | |||||
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210.987 | 0.565649 | 0.282825 | − | 0.959172i | ||||||
0.282825 | + | 0.959172i | ||||||||
138.468 | − | 79.9447i | 0.370236 | − | 0.213756i | |||||
36.7270 | + | 163.662i | 0.0979386 | + | 0.436431i | |||||
5.94304 | + | 10.2936i | 0.0158060 | + | 0.0273767i | |||||
85.1006 | − | 696.474i | 0.225731 | − | 1.84741i | |||||
51.7270 | − | 7.21848i | 0.136844 | − | 0.0190965i | |||||
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−0.999991 | + | 0.00421947i | ||||||||
94.7498i | 0.249342i | |||||||||
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0.943445 | − | 0.331530i | ||||||||
−57.7638 | − | 257.405i | −0.150427 | − | 0.670326i | |||||
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0.0762879 | + | 0.997086i | ||||||||
6.93605 | − | 15.3486i | 0.0177847 | − | 0.0393555i | |||||
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−57.6755 | + | 33.2990i | −0.147131 | + | 0.0849463i | |||||
245.512 | + | 76.7124i | 0.624711 | + | 0.195197i | |||||
−2.20814 | + | 3.82461i | −0.00560441 | + | 0.00970713i | |||||
− | 22.4655i | − | 0.0568746i | |||||||
223.664 | + | 473.247i | 0.564809 | + | 1.19507i | |||||
−124.854 | − | 216.254i | −0.314494 | − | 0.544720i | 0.664835 | − | 0.746990i | ||
−0.979330 | + | 0.202269i | ||||||||
−6.01689 | + | 3.47385i | −0.0151178 | + | 0.00872828i | |||||
321.948 | − | 72.2477i | 0.806887 | − | 0.181072i | |||||
−169.594 | − | 293.745i | −0.423984 | − | 0.734361i | |||||
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−0.251731 | + | 0.967797i | ||||||||
−61.4198 | + | 56.5736i | −0.152786 | + | 0.140730i | |||||
323.550 | − | 429.892i | 0.802854 | − | 1.06673i | |||||
− | 319.857i | − | 0.791724i | |||||||
87.0855 | − | 32.7201i | 0.215026 | − | 0.0807903i | |||||
−52.2025 | + | 90.4174i | −0.128578 | + | 0.222703i | |||||
693.058 | + | 400.137i | 1.70284 | + | 0.983138i | |||||
169.433 | + | 183.947i | 0.415277 | + | 0.450850i | |||||
−740.437 | −1.81036 | −0.905179 | − | 0.425030i | ||||||
−0.905179 | + | 0.425030i | ||||||||
− | 12.4642i | − | 0.0304004i | |||||||
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−147.676 | + | 255.782i | −0.358436 | + | 0.620829i | |||||
98.0284 | + | 56.5967i | 0.237357 | + | 0.137038i | |||||
40.4560 | + | 28.0170i | 0.0977198 | + | 0.0676740i | |||||
95.1026 | 0.229163 | |||||||||
−27.1292 | + | 222.029i | −0.0652145 | + | 0.533724i | |||||
593.763 | − | 133.245i | 1.42389 | − | 0.319533i | |||||
−60.5896 | − | 104.944i | −0.144951 | − | 0.251063i | |||||
387.326 | − | 223.623i | 0.924405 | − | 0.533705i | 0.0393673 | − | 0.999225i | ||
0.885038 | + | 0.465519i | ||||||||
50.3045 | − | 46.3354i | 0.119773 | − | 0.110322i | |||||
−159.450 | − | 276.175i | −0.378741 | − | 0.655999i | 0.612138 | − | 0.790751i | ||
−0.990879 | + | 0.134752i | ||||||||
8.52618 | − | 4.92259i | 0.0202042 | − | 0.0116649i | |||||
20.6102 | − | 29.7607i | 0.0487238 | − | 0.0703562i | |||||
−37.3934 | −0.0881920 | |||||||||
578.541 | + | 334.021i | 1.36127 | + | 0.785931i | |||||
−30.1736 | − | 32.7583i | −0.0708300 | − | 0.0768974i | |||||
−26.6176 | − | 46.1030i | −0.0623362 | − | 0.107970i | |||||
79.7906 | + | 46.0671i | 0.186427 | + | 0.107634i | |||||
−58.1981 | − | 584.951i | −0.135660 | − | 1.36352i | |||||
−9.08195 | − | 15.7304i | −0.0211208 | − | 0.0365823i | |||||
101.578 | + | 58.6459i | 0.235679 | + | 0.136069i | 0.613189 | − | 0.789936i | ||
−0.377510 | + | 0.926005i | ||||||||
−304.976 | + | 237.796i | −0.705964 | + | 0.550455i | |||||
211.520 | + | 366.363i | 0.488498 | + | 0.846104i | 0.999912 | − | 0.0132303i | ||
−0.511414 | + | 0.859334i | ||||||||
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22.5428 | 0.0517037 | |||||||||
269.237 | + | 155.444i | 0.616103 | + | 0.355707i | |||||
16.1275 | + | 71.8670i | 0.0368208 | + | 0.164080i | |||||
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166.749 | + | 115.479i | 0.378117 | + | 0.261858i | |||||
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33.2832 | − | 19.2161i | 0.0751314 | − | 0.0433771i | −0.461964 | − | 0.886899i | ||
0.537095 | + | 0.843522i | ||||||||
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89.4049 | + | 154.854i | 0.200910 | + | 0.347986i | |||||
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154.515 | + | 688.546i | 0.345672 | + | 1.54037i | |||||
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45.6278 | − | 65.8856i | 0.101395 | − | 0.146412i | |||||
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139.412 | − | 128.412i | 0.305728 | − | 0.281605i | |||||
259.602 | 0.568058 | 0.284029 | − | 0.958816i | ||||||
0.284029 | + | 0.958816i | ||||||||
77.7955 | + | 44.9153i | 0.169859 | + | 0.0980683i | |||||
286.014 | − | 705.933i | 0.623125 | − | 1.53798i | |||||
64.4402 | 0.140087 | |||||||||
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16.1371 | 0.0346290 | |||||||||
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0.964372 | − | 0.264550i | ||||||||
428.550 | − | 141.977i | 0.915706 | − | 0.303371i | |||||
380.791 | 0.811921 | |||||||||
1.73712i | 0.00369599i | |||||||||
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65.0230 | 0.137761 | |||||||||
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253.152 | − | 438.472i | 0.532952 | − | 0.923099i | |||||
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48.6633 | + | 102.966i | 0.102020 | + | 0.215861i | |||||
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820.294i | 1.71251i | 0.516550 | + | 0.856257i | ||||||
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17.6810 | − | 56.5866i | 0.0368354 | − | 0.117889i | |||||
415.061 | − | 551.479i | 0.862913 | − | 1.14653i | |||||
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0.190976 | − | 0.981595i | ||||||||
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32.9297 | + | 35.7505i | 0.0673410 | + | 0.0731095i | |||||
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113.097 | − | 65.2966i | 0.230340 | − | 0.132987i | −0.380389 | − | 0.924827i | ||
0.610729 | + | 0.791840i | ||||||||
245.729 | − | 226.341i | 0.499450 | − | 0.460042i | |||||
761.298 | + | 1318.61i | 1.54421 | + | 2.67466i | |||||
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296.405 | − | 513.388i | 0.597590 | − | 1.03506i | |||||
203.095i | 0.408642i | |||||||||
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0.851158 | + | 0.524909i | ||||||||
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69.0341 | − | 63.5871i | 0.137793 | − | 0.126920i | |||||
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0.224455 | + | 0.974484i | ||||||||
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47.6026 | − | 82.4502i | 0.0942627 | − | 0.163268i | |||||
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20.1689 | − | 34.9336i | 0.0397026 | − | 0.0687669i | |||||
538.032 | − | 310.633i | 1.05704 | − | 0.610280i | 0.132425 | − | 0.991193i | ||
0.924611 | + | 0.380913i | ||||||||
8.00300 | + | 35.6627i | 0.0156921 | + | 0.0699269i | |||||
167.937 | − | 290.875i | 0.328644 | − | 0.569227i | |||||
415.752i | 0.812016i | |||||||||
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73.0161 | + | 126.468i | 0.142055 | + | 0.246046i | |||||
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145.201 | − | 464.703i | 0.281397 | − | 0.900587i | |||||
30.3135 | + | 52.5045i | 0.0586334 | + | 0.101556i | |||||
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166.583i | 0.319738i | 0.987138 | + | 0.159869i | ||||||
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165.145 | − | 78.0502i | 0.316370 | − | 0.149522i | |||||
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0.812966 | + | 0.582311i | ||||||||
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59.9334 | 0.113942 | |||||||||
1167.56i | 2.21548i | |||||||||
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52.3798 | − | 167.637i | 0.0980895 | − | 0.313927i | |||||
13.7119 | + | 23.7497i | 0.0256297 | + | 0.0443919i | |||||
189.436 | − | 109.371i | 0.353426 | − | 0.204051i | |||||
5.28907 | + | 1.65262i | 0.00984929 | + | 0.00307750i | |||||
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638.732 | 1.18065 | 0.590325 | − | 0.807166i | ||||||
0.590325 | + | 0.807166i | ||||||||
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31.4202 | − | 7.05095i | 0.0578641 | − | 0.0129852i | |||||
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5.81091 | + | 3.35493i | 0.0106622 | + | 0.00615583i | |||||
68.7471 | + | 31.0668i | 0.125911 | + | 0.0568990i | |||||
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371.078 | + | 214.242i | 0.677150 | + | 0.390953i | |||||
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67.1094 | + | 116.237i | 0.122017 | + | 0.211340i | |||||
999.363 | − | 576.982i | 1.81373 | − | 1.04715i | |||||
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100.624 | 0.181960 | |||||||||
104.847 | + | 60.5336i | 0.189255 | + | 0.109266i | |||||
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139.596 | + | 11.4862i | 0.250172 | + | 0.0205846i | |||||
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864.221 | + | 938.252i | 1.54050 | + | 1.67246i | |||||
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0.744443 | − | 0.667685i | ||||||||
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76.6169 | − | 132.704i | 0.135605 | − | 0.234875i | |||||
158.839 | − | 91.7056i | 0.280634 | − | 0.162024i | |||||
146.555 | + | 390.059i | 0.258474 | + | 0.687935i | |||||
58.3332 | + | 101.036i | 0.102699 | + | 0.177880i | |||||
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0.882011 | − | 0.471228i | ||||||||
27.0285 | − | 6.06541i | 0.0474184 | − | 0.0106411i | |||||
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0.817940 | + | 0.575303i | ||||||||
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55.8275 | 0.0972605 | |||||||||
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413.545 | − | 195.448i | 0.717961 | − | 0.339320i | |||||
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165.043 | + | 95.2877i | 0.285542 | + | 0.164858i | |||||
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119.596 | − | 207.146i | 0.206199 | − | 0.357148i | |||||
425.968i | 0.733164i | |||||||||
20.9317 | + | 6.54029i | 0.0359651 | + | 0.0112376i | |||||
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− | 192.940i | − | 0.330377i | |||||||
131.598 | + | 27.1811i | 0.224954 | + | 0.0464634i | |||||
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0.895602 | − | 0.444855i | ||||||||
−176.746 | − | 191.887i | −0.300589 | − | 0.326338i | |||||
884.886 | 1.50235 | |||||||||
8.22978 | + | 4.75147i | 0.0139488 | + | 0.00805333i | |||||
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380.238 | − | 658.592i | 0.642294 | − | 1.11249i | |||||
624.635i | 1.05335i | 0.850068 | + | 0.526674i | ||||||
−0.850068 | + | 0.526674i | ||||||||
120.681 | − | 94.0979i | 0.203167 | − | 0.158414i | |||||
83.3357 | − | 144.342i | 0.140060 | − | 0.242591i | |||||
− | 907.633i | − | 1.52287i | |||||||
−37.5532 | − | 40.7700i | −0.0629032 | − | 0.0682915i | |||||
27.8122 | + | 65.4144i | 0.0465087 | + | 0.109389i | |||||
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−0.839802 | + | 0.542893i | ||||||||
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563.710 | 0.937953 | 0.468977 | − | 0.883211i | ||||||
0.468977 | + | 0.883211i | ||||||||
70.4571 | − | 40.6784i | 0.117038 | − | 0.0675721i | |||||
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514.223 | + | 890.661i | 0.851363 | + | 1.47460i | |||||
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201.365 | 0.331739 | 0.165869 | − | 0.986148i | ||||||
0.165869 | + | 0.986148i | ||||||||
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−2.23463 | − | 3.87049i | −0.00366332 | − | 0.00634506i | |||||
48.1208 | − | 20.4595i | 0.0787575 | − | 0.0334852i | |||||
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−0.999780 | + | 0.0209752i | ||||||||
29.4598i | 0.0479802i | |||||||||
97.0274 | − | 21.7737i | 0.157768 | − | 0.0354044i | |||||
114.565 | − | 198.432i | 0.185982 | − | 0.322130i | |||||
64.1839i | 0.104026i | 0.998646 | + | 0.0520129i | ||||||
−0.998646 | + | 0.0520129i | ||||||||
82.4182 | + | 25.7523i | 0.133363 | + | 0.0416704i | |||||
3.79581 | + | 6.57454i | 0.00613217 | + | 0.0106212i | 0.869075 | − | 0.494680i | ||
−0.862943 | + | 0.505301i | ||||||||
158.844 | − | 91.7086i | 0.256200 | − | 0.147917i | |||||
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84.8491 | − | 146.963i | 0.136413 | − | 0.236275i | |||||
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−76.7389 | + | 44.3052i | −0.122586 | + | 0.0707752i | |||||
711.095 | − | 654.987i | 1.13412 | − | 1.04464i | |||||
112.064 | − | 194.100i | 0.178446 | − | 0.309077i | |||||
1497.79i | 2.38122i | |||||||||
−16.4380 | − | 11.3838i | −0.0260920 | − | 0.0180695i | |||||
423.578 | + | 733.658i | 0.671280 | + | 1.16269i | 0.977541 | + | 0.210743i | ||
−0.306262 | + | 0.951947i | ||||||||
50.0584 | − | 28.9012i | 0.0792064 | − | 0.0457298i | |||||
53.2144 | + | 57.7728i | 0.0840669 | + | 0.0912682i | |||||
23.4269 | + | 40.5766i | 0.0369509 | + | 0.0640009i | |||||
10.3980 | − | 6.00327i | 0.0163748 | − | 0.00945398i | |||||
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114.635 | + | 269.622i | 0.179960 | + | 0.423268i | |||||
305.911i | 0.479484i | |||||||||
202.297 | − | 292.112i | 0.316583 | − | 0.457139i | |||||
−50.4976 | + | 87.4644i | −0.0789025 | + | 0.136663i | |||||
928.289 | + | 535.948i | 1.44819 | + | 0.836112i | 0.998374 | − | 0.0570099i | ||
0.449815 | + | 0.893122i | ||||||||
8.03340 | − | 25.7102i | 0.0125131 | − | 0.0400471i | |||||
411.550 | 0.640047 | 0.320023 | − | 0.947410i | ||||||
0.320023 | + | 0.947410i | ||||||||
288.630i | 0.448183i | |||||||||
106.588 | − | 98.1780i | 0.165253 | − | 0.152214i | |||||
113.399 | − | 196.413i | 0.175540 | − | 0.304044i | |||||
872.018 | + | 503.460i | 1.34779 | + | 0.778145i | 0.987936 | − | 0.154865i | ||
0.359851 | + | 0.933010i | ||||||||
184.941 | + | 151.954i | 0.285403 | + | 0.234496i | |||||
331.661 | 0.511034 | |||||||||
106.532 | − | 45.2942i | 0.163896 | − | 0.0696834i | |||||
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−31.2580 | − | 54.1405i | −0.0479418 | − | 0.0830376i | |||||
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−0.999364 | + | 0.0356698i | ||||||||
−1.44308 | − | 6.43060i | −0.00220654 | − | 0.00983272i | |||||
−49.2362 | − | 85.2796i | −0.0751698 | − | 0.130198i | |||||
−357.996 | + | 206.689i | −0.545725 | + | 0.315074i | |||||
−531.275 | + | 251.090i | −0.808638 | + | 0.382176i | |||||
−7.78061 | −0.0118246 | |||||||||
−269.095 | − | 155.362i | −0.408338 | − | 0.235754i | 0.281737 | − | 0.959492i | ||
−0.690076 | + | 0.723737i | ||||||||
59.7649 | − | 191.272i | 0.0905528 | − | 0.289807i | |||||
257.855 | + | 446.618i | 0.390099 | + | 0.675670i | 0.992462 | − | 0.122551i | ||
−0.602364 | + | 0.798222i | ||||||||
−108.957 | − | 62.9065i | −0.164588 | − | 0.0950250i | |||||
893.654 | − | 641.725i | 1.34789 | − | 0.967911i | |||||
122.347 | + | 211.911i | 0.184257 | + | 0.319143i | |||||
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179.079 | + | 14.7349i | 0.268887 | + | 0.0221245i | |||||
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31.9686 | 0.0477143 | |||||||||
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253.454 | + | 79.1939i | 0.377163 | + | 0.117848i | |||||
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592.594 | + | 240.094i | 0.877917 | + | 0.355695i | |||||
632.919 | + | 157.014i | 0.936270 | + | 0.232269i | |||||
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0.508779 | + | 0.860897i | ||||||||
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0.765071 | + | 0.643946i | ||||||||
610.398 | + | 422.720i | 0.892395 | + | 0.618011i | |||||
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14.4437 | + | 8.33907i | 0.0208724 | + | 0.0120507i | |||||
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407.081 | − | 705.086i | 0.584048 | − | 1.01160i | |||||
50.6577i | 0.0725755i | |||||||||
28.1900 | + | 125.619i | 0.0403290 | + | 0.179713i | |||||
470.055 | 0.671508 | |||||||||
775.035i | 1.10561i | 0.833310 | + | 0.552806i | ||||||
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1135.16 | 1.61474 | |||||||||
766.042i | 1.08813i | |||||||||
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369.298 | + | 213.214i | 0.522345 | + | 0.301576i | |||||
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0.562096 | + | 0.827072i | ||||||||
17.0505i | 0.0240147i | |||||||||
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166.903 | 0.232455 | |||||||||
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0.0797184 | + | 0.996817i | ||||||||
147.555 | + | 12.1411i | 0.204937 | + | 0.0168626i | |||||
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0.232462 | − | 0.972605i | ||||||||
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177.736 | − | 707.001i | 0.243808 | − | 0.969823i | |||||
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35.7268 | − | 114.341i | 0.0488072 | − | 0.156203i | |||||
435.712 | − | 754.675i | 0.594422 | − | 1.02957i | −0.399206 | − | 0.916861i | ||
0.993628 | − | 0.112708i | ||||||||
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125.097 | + | 216.674i | 0.169968 | + | 0.294394i | |||||
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0.890664 | + | 0.454662i | ||||||||
203.770 | − | 117.647i | 0.275365 | − | 0.158982i | |||||
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12.2388 | − | 21.1983i | 0.0164944 | − | 0.0285691i | |||||
426.534 | − | 246.260i | 0.574071 | − | 0.331440i | −0.184703 | − | 0.982794i | ||
0.758773 | + | 0.651355i | ||||||||
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135.078 | − | 233.963i | 0.181313 | − | 0.314044i | |||||
79.3373i | 0.106350i | |||||||||
424.293 | − | 612.671i | 0.567997 | − | 0.820175i | |||||
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49.8934 | − | 28.8060i | 0.0663477 | − | 0.0383058i | |||||
930.916 | − | 857.465i | 1.23628 | − | 1.13873i | |||||
261.894 | + | 32.0003i | 0.347340 | + | 0.0424407i | |||||
306.117i | 0.405453i | |||||||||
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0.894295 | + | 0.447478i | ||||||||
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220.296 | + | 127.188i | 0.288346 | + | 0.166477i | |||||
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95.4934 | 0.124665 | |||||||||
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29.0003 | − | 16.7433i | 0.0376627 | − | 0.0217445i | |||||
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215.809 | + | 373.792i | 0.279545 | + | 0.484186i | |||||
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0.486474 | + | 0.873695i | ||||||||
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297.538 | + | 515.351i | 0.380971 | + | 0.659861i | |||||
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896.075 | + | 1149.23i | 1.14441 | + | 1.46772i | |||||
161.400 | + | 279.554i | 0.205868 | + | 0.356574i | |||||
57.7739 | − | 33.3558i | 0.0735974 | − | 0.0424915i | |||||
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39.2460 | + | 22.6587i | 0.0498046 | + | 0.0287547i | |||||
104.698 | + | 466.552i | 0.132697 | + | 0.591321i | |||||
8.44767 | 0.0106933 | |||||||||
594.388 | + | 343.170i | 0.751439 | + | 0.433843i | |||||
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35.6468 | + | 61.7420i | 0.0447824 | + | 0.0775654i | |||||
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0.966297 | − | 0.257429i | ||||||||
27.1672 | + | 121.062i | 0.0340441 | + | 0.151706i | |||||
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352.869 | − | 203.729i | 0.441087 | − | 0.254662i | |||||
1396.47 | + | 114.905i | 1.74341 | + | 0.143451i | |||||
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580.528 | + | 630.256i | 0.722049 | + | 0.783901i | |||||
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161.652 | + | 121.664i | 0.200560 | + | 0.150948i | |||||
351.936 | − | 324.168i | 0.436104 | − | 0.401695i | |||||
244.958 | 0.303166 | |||||||||
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12.3037 | + | 32.7467i | 0.0151898 | + | 0.0404280i | |||||
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927.814 | + | 535.673i | 1.14263 | + | 0.659696i | |||||
173.134 | − | 554.100i | 0.212957 | − | 0.681550i | |||||
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891.592 | − | 821.244i | 1.09264 | − | 1.00643i | |||||
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515.147i | 0.627463i | 0.949512 | + | 0.313732i | ||||||
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37.3605 | − | 119.569i | 0.0454507 | − | 0.145461i | |||||
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0.821233 | − | 0.570594i | ||||||||
287.495 | − | 415.137i | 0.347217 | − | 0.501373i | |||||
133.486 | − | 231.205i | 0.161021 | − | 0.278896i | −0.774214 | − | 0.632924i | ||
0.935235 | + | 0.354027i | ||||||||
35.7613i | 0.0430859i | |||||||||
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655.820 | + | 80.1331i | 0.788245 | + | 0.0963138i | |||||
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50.1041 | + | 223.272i | 0.0600768 | + | 0.267712i | |||||
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154.447 | + | 1106.75i | 0.184524 | + | 1.32228i | |||||
84.0886 | + | 145.646i | 0.100344 | + | 0.173802i | |||||
702.552 | + | 405.618i | 0.837368 | + | 0.483455i | 0.856369 | − | 0.516365i | ||
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35.4854 | + | 38.5251i | 0.0422445 | + | 0.0458632i | |||||
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103.850 | − | 59.9578i | 0.123337 | − | 0.0712088i | |||||
911.024 | − | 839.142i | 1.08069 | − | 0.995423i | |||||
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139.781 | + | 134.668i | 0.165422 | + | 0.159370i | |||||
11.1909 | + | 7.75003i | 0.0132280 | + | 0.00916079i | |||||
273.131 | − | 473.076i | 0.322468 | − | 0.558531i | |||||
181.246i | 0.213734i | |||||||||
991.359 | + | 1076.28i | 1.16768 | + | 1.26770i | |||||
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294.569 | + | 510.209i | 0.345333 | + | 0.598135i | 0.985414 | − | 0.170173i | ||
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17.3361 | − | 10.0090i | 0.0202998 | − | 0.0117201i | |||||
94.4325 | + | 199.808i | 0.110447 | + | 0.233693i | |||||
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1354.80 | − | 782.195i | 1.58086 | − | 0.912713i | 0.586131 | − | 0.810216i | ||
0.994733 | − | 0.102496i | ||||||||
219.959 | − | 21.8842i | 0.256362 | − | 0.0255060i | |||||
219.269 | − | 379.785i | 0.255261 | − | 0.442124i | −0.709706 | − | 0.704498i | ||
0.964966 | + | 0.262374i | ||||||||
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97.5254 | + | 434.589i | 0.113270 | + | 0.504750i | |||||
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0.790331 | − | 0.612680i | ||||||||
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2.48212 | + | 4.29916i | 0.00286951 | + | 0.00497013i | |||||
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410.767 | + | 711.468i | 0.473233 | + | 0.819664i | |||||
255.331 | − | 147.416i | 0.293822 | − | 0.169638i | |||||
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17.2641i | 0.0197983i | |||||||||
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249.084 | + | 143.809i | 0.284667 | + | 0.164353i | |||||
737.459 | − | 165.492i | 0.841848 | − | 0.188918i | |||||
152.759 | 0.174184 | 0.0870920 | − | 0.996200i | ||||||
0.0870920 | + | 0.996200i | ||||||||
− | 101.008i | − | 0.115043i | |||||||
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1343.46 | + | 775.645i | 1.52492 | + | 0.880414i | 0.999564 | + | 0.0295323i | ||
0.525358 | + | 0.850882i | ||||||||
−43.4235 | + | 62.7026i | −0.0492330 | + | 0.0710914i | |||||
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−22.6112 | + | 72.3651i | −0.0255493 | + | 0.0817685i | |||||
7.22579 | + | 12.5154i | 0.00815552 | + | 0.0141258i | |||||
809.756 | − | 467.513i | 0.912916 | − | 0.527072i | 0.0315475 | − | 0.999502i | ||
0.881368 | + | 0.472430i | ||||||||
−449.267 | − | 140.378i | −0.505932 | − | 0.158083i | |||||
26.8889 | + | 46.5729i | 0.0302462 | + | 0.0523880i | |||||
−58.2295 | + | 33.6188i | −0.0654265 | + | 0.0377740i | |||||
943.325 | + | 775.065i | 1.05873 | + | 0.869883i | |||||
−1246.02 | −1.39688 | |||||||||
74.4759 | + | 42.9987i | 0.0833996 | + | 0.0481508i | |||||
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−113.323 | − | 196.281i | −0.126195 | − | 0.218575i | |||||
−1934.57 | − | 1116.93i | −2.15192 | − | 1.24241i | |||||
−676.081 | − | 468.207i | −0.751202 | − | 0.520230i | |||||
−178.486 | − | 309.146i | −0.198097 | − | 0.343115i | |||||
141.662 | − | 81.7884i | 0.157053 | − | 0.0906745i | |||||
439.743 | + | 477.412i | 0.486980 | + | 0.528695i | |||||
394.263 | 0.436131 | |||||||||
−10.6764 | − | 6.16400i | −0.0117971 | − | 0.00681105i | |||||
221.154 | − | 203.704i | 0.244099 | − | 0.224839i | |||||
1149.05 | 1.26687 | 0.633433 | − | 0.773797i | ||||||
0.633433 | + | 0.773797i | ||||||||
847.173 | + | 489.116i | 0.933010 | + | 0.538674i | |||||
−318.786 | − | 674.512i | −0.350699 | − | 0.742037i | |||||
−11.3006 | − | 26.5790i | −0.0124182 | − | 0.0292077i | |||||
443.854 | − | 256.259i | 0.487216 | − | 0.281294i | −0.236203 | − | 0.971704i | ||
0.723419 | + | 0.690410i | ||||||||
−622.415 | − | 675.732i | −0.682472 | − | 0.740934i | |||||
624.051 | + | 1080.89i | 0.683517 | + | 1.18389i | |||||
97.6180i | 0.106803i | |||||||||
26.2261 | − | 24.1568i | 0.0286625 | − | 0.0264009i | |||||
460.896 | − | 798.295i | 0.503161 | − | 0.871501i | |||||
381.971 | − | 220.531i | 0.416544 | − | 0.240492i | |||||
265.451 | + | 107.550i | 0.289163 | + | 0.117156i | |||||
314.275 | + | 544.341i | 0.341975 | + | 0.592318i | 0.984799 | − | 0.173695i | ||
−0.642824 | + | 0.766014i | ||||||||
49.3507i | 0.0536421i | |||||||||
−229.330 | + | 51.4636i | −0.249001 | + | 0.0558779i | |||||
100.485 | − | 174.046i | 0.108986 | − | 0.188770i | |||||
472.324 | − | 200.818i | 0.511727 | − | 0.217570i | |||||
856.717 | + | 267.689i | 0.927183 | + | 0.289707i | |||||
−1257.31 | −1.35926 | |||||||||
−200.265 | − | 115.623i | −0.216269 | − | 0.124863i | |||||
−56.4924 | + | 686.572i | −0.0609411 | + | 0.740638i | |||||
928.677 | 1.00073 | |||||||||
203.102 | + | 117.261i | 0.218625 | + | 0.126223i | 0.605313 | − | 0.795987i | ||
−0.386689 | + | 0.922210i | ||||||||
−36.3294 | − | 39.4414i | −0.0390639 | − | 0.0424101i | |||||
−240.922 | + | 417.289i | −0.258778 | + | 0.448216i | |||||
− | 165.590i | − | 0.177672i | |||||||
1292.26 | + | 403.778i | 1.38506 | + | 0.432773i | |||||
92.9128 | 0.0994784 | |||||||||
− | 488.353i | − | 0.522303i | |||||||
108.732 | + | 328.200i | 0.116166 | + | 0.350641i | |||||
−598.868 | −0.639133 | −0.319567 | − | 0.947564i | ||||||
−0.319567 | + | 0.947564i | ||||||||
143.189i | 0.152653i | |||||||||
−478.950 | − | 519.978i | −0.510064 | − | 0.553757i | |||||
17.8253 | 0.0189631 | |||||||||
−219.420 | − | 126.682i | −0.233178 | − | 0.134625i | 0.378859 | − | 0.925454i | ||
−0.612037 | + | 0.790829i | ||||||||
−62.5432 | − | 19.5422i | −0.0663941 | − | 0.0207454i | |||||
−209.830 | + | 363.436i | −0.222513 | + | 0.385404i | |||||
− | 315.167i | − | 0.333864i | |||||||
59.9017 | − | 147.848i | 0.0633880 | − | 0.156453i | |||||
119.189 | − | 206.442i | 0.125993 | − | 0.218226i | |||||
1553.39i | 1.64033i | 0.572130 | + | 0.820163i | ||||||
−0.572130 | + | 0.820163i | ||||||||
153.404 | + | 166.545i | 0.161818 | + | 0.175680i | |||||
−842.521 | − | 102.946i | −0.887799 | − | 0.108478i | |||||
164.878 | + | 95.1925i | 0.173556 | + | 0.100203i | |||||
−274.944 | + | 253.250i | −0.289110 | + | 0.266299i | |||||
428.837 | 0.450459 | |||||||||
373.494 | − | 215.637i | 0.391914 | − | 0.226272i | −0.291075 | − | 0.956700i | ||
0.682989 | + | 0.730429i | ||||||||
−38.7181 | + | 18.2988i | −0.0405850 | + | 0.0191811i | |||||
37.8575 | + | 65.5711i | 0.0396414 | + | 0.0686609i | |||||
258.729 | + | 149.377i | 0.270637 | + | 0.156252i | |||||
−2381.36 | + | 534.397i | −2.48836 | + | 0.558409i | |||||
−308.454 | −0.321978 | |||||||||
−494.716 | + | 285.624i | −0.515867 | + | 0.297836i | |||||
−167.143 | − | 52.2253i | −0.174107 | − | 0.0544014i | |||||
−375.984 | − | 651.223i | −0.391242 | − | 0.677651i | |||||
207.372 | + | 156.075i | 0.215564 | + | 0.162240i | |||||
214.175 | + | 17.6227i | 0.222404 | + | 0.0182998i | |||||
184.768 | − | 320.028i | 0.191668 | − | 0.331980i | |||||
128.471i | 0.133130i | |||||||||
82.3352 | − | 18.4767i | 0.0852331 | − | 0.0191270i | |||||
548.133 | − | 949.394i | 0.566839 | − | 0.981794i | −0.430037 | − | 0.902811i | ||
0.996876 | − | 0.0789825i | ||||||||
− | 313.795i | − | 0.324169i | |||||||
1727.07 | + | 539.640i | 1.78233 | + | 0.556904i | |||||
−4.19775 | − | 7.27071i | −0.00432757 | − | 0.00749558i | |||||
88.2684 | − | 50.9618i | 0.0909046 | − | 0.0524838i | −0.453859 | − | 0.891074i | ||
0.544763 | + | 0.838590i | ||||||||
−422.169 | + | 837.223i | −0.434331 | + | 0.861341i | |||||
521.736 | − | 903.674i | 0.536214 | − | 0.928750i | |||||
239.346 | − | 138.187i | 0.245735 | − | 0.141875i | |||||
538.695 | + | 750.176i | 0.552507 | + | 0.769411i | |||||
−74.1120 | + | 128.366i | −0.0759345 | + | 0.131522i | |||||
874.681 | − | 504.997i | 0.895272 | − | 0.516886i | 0.0196090 | − | 0.999808i | ||
0.875663 | + | 0.482922i | ||||||||
−13.4432 | + | 12.3825i | −0.0137456 | + | 0.0126611i | |||||
−1173.33 | + | 2032.26i | −1.19850 | + | 2.07586i | |||||
99.8756i | 0.101914i | |||||||||
47.5381 | − | 22.4673i | 0.0484588 | − | 0.0229024i | |||||
24.5534 | + | 42.5278i | 0.0250035 | + | 0.0433073i | |||||
−1248.07 | + | 720.573i | −1.26965 | + | 0.733035i | −0.974922 | − | 0.222546i | ||
−0.294731 | + | 0.955580i | ||||||||
173.340 | + | 188.189i | 0.176159 | + | 0.191249i | |||||
6.74436 | + | 11.6816i | 0.00684706 | + | 0.0118595i | |||||
−495.834 | + | 286.270i | −0.502874 | + | 0.290335i | |||||
−13.5920 | − | 60.5682i | −0.0137710 | − | 0.0613660i | |||||
419.629 | + | 986.969i | 0.424726 | + | 0.998957i | |||||
611.566i | 0.618368i | |||||||||
−58.3886 | − | 4.80432i | −0.0589784 | − | 0.00485285i | |||||
−698.522 | + | 1209.87i | −0.704865 | + | 1.22086i | 0.261875 | + | 0.965102i | ||
−0.966740 | + | 0.255761i | ||||||||
616.723 | + | 356.065i | 0.621696 | + | 0.358937i | |||||
299.358 | − | 958.071i | 0.301468 | − | 0.964824i | |||||
−76.3697 | −0.0768307 | |||||||||
21.2205i | 0.0213272i | |||||||||
−705.030 | + | 649.401i | −0.707861 | + | 0.652009i | |||||
682.194 | − | 1181.60i | 0.684247 | − | 1.18515i | −0.289426 | − | 0.957200i | ||
0.973673 | − | 0.227950i | ||||||||
−9.42691 | − | 5.44263i | −0.00944580 | − | 0.00545354i | |||||
198.129 | + | 1419.78i | 0.198328 | + | 1.42120i |
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 117.3.k.a.113.13 | yes | 52 | |
3.2 | odd | 2 | 351.3.k.a.152.14 | 52 | |||
9.2 | odd | 6 | 117.3.u.a.74.14 | yes | 52 | ||
9.7 | even | 3 | 351.3.u.a.35.13 | 52 | |||
13.3 | even | 3 | 117.3.u.a.68.14 | yes | 52 | ||
39.29 | odd | 6 | 351.3.u.a.341.13 | 52 | |||
117.16 | even | 3 | 351.3.k.a.224.13 | 52 | |||
117.29 | odd | 6 | inner | 117.3.k.a.29.14 | ✓ | 52 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
117.3.k.a.29.14 | ✓ | 52 | 117.29 | odd | 6 | inner | |
117.3.k.a.113.13 | yes | 52 | 1.1 | even | 1 | trivial | |
117.3.u.a.68.14 | yes | 52 | 13.3 | even | 3 | ||
117.3.u.a.74.14 | yes | 52 | 9.2 | odd | 6 | ||
351.3.k.a.152.14 | 52 | 3.2 | odd | 2 | |||
351.3.k.a.224.13 | 52 | 117.16 | even | 3 | |||
351.3.u.a.35.13 | 52 | 9.7 | even | 3 | |||
351.3.u.a.341.13 | 52 | 39.29 | odd | 6 |