Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [27,3,Mod(2,27)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(27, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("27.2");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 27.f (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 | 2.4 | ||
Character | 27.2 | ||
Dual form | 27.3.f.a.14.4 |
-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of on generators for .
Coefficient data
For each we display the coefficients of the -expansion , the Satake parameters , and the Satake angles .
1.14332 | + | 0.201599i | 0.571662 | + | 0.100799i | 0.452004 | − | 0.892016i | ||
0.119658 | + | 0.992815i | ||||||||
1.10490 | + | 2.78912i | 0.368300 | + | 0.929707i | |||||
−2.49222 | − | 0.907094i | −0.623055 | − | 0.226774i | |||||
−3.46013 | − | 4.12362i | −0.692026 | − | 0.824724i | 0.299574 | − | 0.954073i | ||
−0.991599 | + | 0.129349i | ||||||||
0.700975 | + | 3.41162i | 0.116829 | + | 0.568603i | |||||
9.89907 | − | 3.60297i | 1.41415 | − | 0.514709i | 0.481807 | − | 0.876278i | ||
0.932346 | + | 0.361568i | ||||||||
−6.68824 | − | 3.86146i | −0.836030 | − | 0.482682i | |||||
−6.55839 | + | 6.16340i | −0.728710 | + | 0.684822i | |||||
−3.12473 | − | 5.41219i | −0.312473 | − | 0.541219i | |||||
−7.54888 | + | 8.99640i | −0.686262 | + | 0.817855i | −0.990898 | − | 0.134614i | ||
0.304636 | + | 0.952469i | ||||||||
−0.223658 | − | 7.95335i | −0.0186382 | − | 0.662780i | |||||
1.95057 | + | 11.0622i | 0.150044 | + | 0.850940i | 0.963178 | + | 0.268864i | ||
−0.813134 | + | 0.582076i | ||||||||
12.0442 | − | 2.12372i | 0.860300 | − | 0.151694i | |||||
7.67818 | − | 14.2069i | 0.511879 | − | 0.947127i | |||||
1.25834 | + | 1.05588i | 0.0786465 | + | 0.0659923i | |||||
2.73630 | − | 1.57980i | 0.160959 | − | 0.0929296i | −0.417357 | − | 0.908743i | ||
0.578316 | + | 0.815813i | ||||||||
−8.74091 | + | 5.72460i | −0.485606 | + | 0.318033i | |||||
2.26051 | − | 3.91532i | 0.118974 | − | 0.206069i | −0.800387 | − | 0.599483i | ||
0.919361 | + | 0.393414i | ||||||||
4.88289 | + | 13.4156i | 0.244145 | + | 0.670782i | |||||
20.9866 | + | 23.6288i | 0.999361 | + | 1.12518i | |||||
−10.4445 | + | 8.76396i | −0.474749 | + | 0.398362i | |||||
6.80880 | − | 18.7070i | 0.296035 | − | 0.813349i | −0.699118 | − | 0.715007i | ||
0.995153 | − | 0.0983427i | ||||||||
3.38024 | − | 22.9208i | 0.140843 | − | 0.955035i | |||||
−0.690550 | + | 3.91630i | −0.0276220 | + | 0.156652i | |||||
13.0409i | 0.501575i | |||||||||
−24.4368 | − | 11.4822i | −0.905068 | − | 0.425267i | |||||
−27.9389 | −0.997818 | |||||||||
24.9744 | + | 4.40366i | 0.861187 | + | 0.151851i | 0.586763 | − | 0.809758i | ||
0.274424 | + | 0.961609i | ||||||||
11.6428 | − | 14.6952i | 0.388092 | − | 0.489840i | |||||
−20.7874 | − | 7.56598i | −0.670560 | − | 0.244064i | −0.0157712 | − | 0.999876i | ||
−0.654789 | + | 0.755812i | ||||||||
21.0826 | + | 25.1253i | 0.658832 | + | 0.785165i | |||||
−33.4328 | − | 11.1146i | −1.01312 | − | 0.336807i | |||||
3.44696 | − | 1.25459i | 0.101381 | − | 0.0368998i | |||||
−49.1093 | − | 28.3533i | −1.40312 | − | 0.810093i | |||||
21.9358 | − | 9.41147i | 0.609326 | − | 0.261430i | |||||
−8.82807 | − | 15.2907i | −0.238596 | − | 0.413261i | 0.721715 | − | 0.692190i | ||
−0.960312 | + | 0.278929i | ||||||||
3.37382 | − | 4.02076i | 0.0887847 | − | 0.105810i | |||||
−28.6987 | + | 17.6630i | −0.735864 | + | 0.452898i | |||||
7.21898 | + | 40.9409i | 0.180475 | + | 1.02352i | |||||
−12.2557 | + | 2.16101i | −0.298920 | + | 0.0527076i | −0.321096 | − | 0.947046i | ||
0.0221770 | + | 0.999754i | ||||||||
19.2309 | + | 31.2462i | 0.457880 | + | 0.743958i | |||||
27.9211 | + | 23.4286i | 0.649329 | + | 0.544851i | 0.906867 | − | 0.421417i | ||
−0.257539 | + | 0.966268i | ||||||||
26.9741 | − | 15.5735i | 0.613047 | − | 0.353943i | |||||
48.1084 | + | 5.71818i | 1.06908 | + | 0.127071i | |||||
11.5560 | − | 20.0156i | 0.251217 | − | 0.435121i | |||||
−4.24091 | − | 11.6518i | −0.0902320 | − | 0.247910i | 0.886365 | − | 0.462987i | ||
−0.976597 | + | 0.215076i | ||||||||
−1.55462 | + | 4.67631i | −0.0323880 | + | 0.0974232i | |||||
47.4740 | − | 39.8354i | 0.968857 | − | 0.812967i | |||||
−1.57905 | + | 4.33839i | −0.0315809 | + | 0.0867679i | |||||
7.42960 | + | 5.88634i | 0.145678 | + | 0.115419i | |||||
5.17323 | − | 29.3388i | 0.0994852 | − | 0.564209i | |||||
84.6210i | 1.59662i | 0.602245 | + | 0.798311i | ||||||
−0.602245 | + | 0.798311i | ||||||||
−25.6244 | − | 18.0543i | −0.474526 | − | 0.334340i | |||||
63.2178 | 1.14942 | |||||||||
−80.1200 | − | 14.1273i | −1.43071 | − | 0.252274i | |||||
13.4179 | + | 1.97880i | 0.235402 | + | 0.0347158i | |||||
27.6661 | + | 10.0696i | 0.477002 | + | 0.173614i | |||||
−43.8854 | − | 52.3006i | −0.743820 | − | 0.886451i | 0.252890 | − | 0.967495i | ||
−0.996711 | + | 0.0810443i | ||||||||
−32.0227 | + | 28.4419i | −0.533712 | + | 0.474032i | |||||
−73.3637 | + | 26.7022i | −1.20268 | + | 0.437741i | −0.864160 | − | 0.503217i | ||
−0.338523 | + | 0.940958i | ||||||||
−22.2414 | − | 12.8411i | −0.358733 | − | 0.207114i | |||||
−42.7155 | + | 84.6415i | −0.678023 | + | 1.34352i | |||||
15.7537 | + | 27.2863i | 0.246152 | + | 0.426348i | |||||
38.8672 | − | 46.3201i | 0.597956 | − | 0.712617i | |||||
−35.9839 | − | 19.4476i | −0.545210 | − | 0.294661i | |||||
−16.8654 | − | 95.6483i | −0.251722 | − | 1.42759i | −0.804349 | − | 0.594157i | ||
0.552627 | − | 0.833429i | ||||||||
−8.25249 | + | 1.45514i | −0.121360 | + | 0.0213991i | |||||
59.6992 | − | 1.67882i | 0.865206 | − | 0.0243307i | |||||
−50.4319 | − | 42.3174i | −0.720455 | − | 0.604534i | |||||
105.364 | − | 60.8322i | 1.48401 | − | 0.856791i | 0.484171 | − | 0.874973i | ||
0.999835 | + | 0.0181820i | ||||||||
67.6638 | − | 15.8973i | 0.939775 | − | 0.220796i | |||||
−45.5705 | + | 78.9304i | −0.624254 | + | 1.08124i | 0.364431 | + | 0.931230i | ||
−0.988685 | + | 0.150009i | ||||||||
−7.01076 | − | 19.2619i | −0.0947401 | − | 0.260296i | |||||
−11.6860 | + | 2.40109i | −0.155814 | + | 0.0320146i | |||||
−9.18525 | + | 7.70734i | −0.120859 | + | 0.101412i | |||||
−42.3131 | + | 116.254i | −0.549521 | + | 1.50980i | |||||
−36.3728 | + | 14.4089i | −0.466317 | + | 0.184730i | |||||
−3.54032 | + | 20.0781i | −0.0448142 | + | 0.254154i | −0.998982 | − | 0.0451196i | ||
0.954167 | + | 0.299273i | ||||||||
− | 8.84240i | − | 0.110530i | |||||||
5.02506 | − | 80.8440i | 0.0620378 | − | 0.998074i | |||||
−14.4479 | −0.176194 | |||||||||
31.1219 | + | 5.48763i | 0.374963 | + | 0.0661161i | 0.357954 | − | 0.933739i | ||
0.0170090 | + | 0.999855i | ||||||||
−30.8697 | − | 77.9250i | −0.367496 | − | 0.927678i | |||||
−15.9824 | − | 5.81713i | −0.188029 | − | 0.0684369i | |||||
27.1997 | + | 32.4154i | 0.316276 | + | 0.376923i | |||||
15.3119 | + | 74.5223i | 0.175999 | + | 0.856578i | |||||
85.2279 | − | 31.0204i | 0.968499 | − | 0.352505i | |||||
59.7756 | + | 34.5114i | 0.671636 | + | 0.387769i | 0.796696 | − | 0.604380i | ||
−0.125060 | + | 0.992149i | ||||||||
53.8507 | + | 16.2363i | 0.598341 | + | 0.180404i | |||||
59.1656 | + | 102.478i | 0.650171 | + | 1.12613i | |||||
−33.9381 | + | 40.4458i | −0.368892 | + | 0.439629i | |||||
−1.86551 | − | 66.3381i | −0.0200592 | − | 0.713313i | |||||
−2.49974 | − | 14.1767i | −0.0265930 | − | 0.150816i | |||||
−23.9669 | + | 4.22602i | −0.252283 | + | 0.0444844i | |||||
−46.7833 | + | 86.5629i | −0.487326 | + | 0.901696i | |||||
−61.1335 | − | 51.2971i | −0.630243 | − | 0.528836i | 0.270762 | − | 0.962646i | ||
−0.901004 | + | 0.433810i | ||||||||
62.3089 | − | 35.9741i | 0.635806 | − | 0.367083i | |||||
−5.93989 | − | 105.529i | −0.0599989 | − | 1.06595i | |||||
5.27346 | − | 9.13390i | 0.0527346 | − | 0.0913390i | |||||
−1.63372 | − | 4.48862i | −0.0161755 | − | 0.0444417i | 0.931342 | − | 0.364145i | ||
−0.947518 | + | 0.319704i | ||||||||
7.30776 | + | 8.22780i | 0.0716447 | + | 0.0806647i | |||||
−55.3795 | + | 46.4689i | −0.537665 | + | 0.451154i | −0.870738 | − | 0.491746i | ||
0.333074 | + | 0.942901i | ||||||||
29.6704 | − | 81.5188i | 0.285293 | − | 0.783835i | |||||
24.8199 | − | 168.299i | 0.236380 | − | 1.60285i | |||||
−17.0595 | + | 96.7493i | −0.160939 | + | 0.912729i | |||||
158.133i | 1.47788i | 0.673773 | + | 0.738938i | ||||||
−0.673773 | + | 0.738938i | ||||||||
50.4865 | + | 50.7827i | 0.467468 | + | 0.470211i | |||||
−18.5788 | −0.170448 | −0.0852240 | − | 0.996362i | ||||||
−0.0852240 | + | 0.996362i | ||||||||
72.2785 | + | 12.7447i | 0.657077 | + | 0.115860i | |||||
32.8934 | − | 41.5172i | 0.296337 | − | 0.374029i | |||||
16.2607 | + | 5.91842i | 0.145185 | + | 0.0528430i | |||||
−11.5806 | − | 13.8012i | −0.102483 | − | 0.122134i | 0.712365 | − | 0.701809i | ||
−0.814848 | + | 0.579675i | ||||||||
14.9421 | + | 4.96746i | 0.131071 | + | 0.0435742i | |||||
−100.700 | + | 36.6518i | −0.875652 | + | 0.318711i | |||||
−58.2473 | − | 33.6291i | −0.502131 | − | 0.289906i | |||||
−80.9734 | − | 60.5283i | −0.692081 | − | 0.517336i | |||||
−39.6315 | − | 68.6438i | −0.335860 | − | 0.581727i | |||||
21.3948 | − | 25.4974i | 0.179788 | − | 0.214264i | |||||
−106.213 | + | 65.3702i | −0.885107 | + | 0.544752i | |||||
−2.93828 | − | 16.6638i | −0.0242833 | − | 0.137717i | |||||
−89.2617 | + | 15.7392i | −0.731653 | + | 0.129010i | |||||
−19.5686 | − | 31.7949i | −0.159095 | − | 0.258495i | |||||
44.9437 | + | 37.7122i | 0.362449 | + | 0.304131i | |||||
−98.0067 | + | 56.5842i | −0.784054 | + | 0.452674i | |||||
−65.9013 | + | 88.1614i | −0.523026 | + | 0.699693i | |||||
78.1067 | − | 135.285i | 0.615013 | − | 1.06523i | −0.375369 | − | 0.926876i | ||
0.990382 | − | 0.138359i | ||||||||
−32.3605 | − | 88.9098i | −0.252817 | − | 0.694608i | |||||
−34.4952 | + | 103.762i | −0.267405 | + | 0.804354i | |||||
53.7759 | − | 45.1233i | 0.413661 | − | 0.347102i | |||||
33.6955 | − | 92.5776i | 0.257217 | − | 0.706699i | −0.742119 | − | 0.670268i | ||
0.999336 | − | 0.0364307i | ||||||||
73.2400 | + | 58.0268i | 0.554848 | + | 0.439597i | |||||
8.27018 | − | 46.9025i | 0.0621818 | − | 0.352651i | |||||
− | 112.757i | − | 0.841471i | |||||||
37.2062 | + | 140.498i | 0.275602 | + | 1.04073i | |||||
−24.4014 | −0.179422 | |||||||||
−64.6590 | − | 11.4011i | −0.471963 | − | 0.0832199i | −0.0673925 | − | 0.997727i | ||
−0.404571 | + | 0.914507i | ||||||||
68.5941 | + | 10.1159i | 0.497058 | + | 0.0733034i | |||||
117.744 | + | 42.8553i | 0.847080 | + | 0.308312i | 0.728849 | − | 0.684674i | ||
0.118231 | + | 0.992986i | ||||||||
96.6721 | + | 115.209i | 0.690515 | + | 0.822924i | |||||
27.8125 | − | 24.7025i | 0.197252 | − | 0.175195i | |||||
132.729 | − | 48.3096i | 0.934714 | − | 0.340208i | |||||
−114.245 | − | 65.9593i | −0.798915 | − | 0.461254i | |||||
−14.7605 | + | 0.830824i | −0.102503 | + | 0.00576961i | |||||
−68.2557 | − | 118.222i | −0.470729 | − | 0.815326i | |||||
−68.0142 | + | 81.0562i | −0.465851 | + | 0.555179i | |||||
163.560 | + | 88.3966i | 1.11265 | + | 0.601337i | |||||
8.13142 | + | 46.1156i | 0.0549420 | + | 0.311592i | |||||
198.691 | − | 35.0346i | 1.33350 | − | 0.235132i | 0.538953 | − | 0.842336i | ||
0.794546 | + | 0.607204i | ||||||||
−13.8450 | + | 0.389338i | −0.0922999 | + | 0.00259559i | |||||
98.1613 | + | 82.3671i | 0.650075 | + | 0.545478i | 0.907094 | − | 0.420929i | ||
−0.257019 | + | 0.966406i | ||||||||
−30.2377 | + | 17.4577i | −0.198932 | + | 0.114853i | |||||
−8.20877 | + | 27.2259i | −0.0536521 | + | 0.177947i | |||||
−71.8144 | + | 124.386i | −0.466327 | + | 0.807703i | |||||
40.7277 | + | 111.898i | 0.262759 | + | 0.721926i | |||||
87.5455 | − | 17.9877i | 0.561189 | − | 0.115306i | |||||
−106.439 | + | 89.3129i | −0.677955 | + | 0.568872i | −0.915408 | − | 0.402527i | ||
0.237453 | + | 0.971399i | ||||||||
−8.09547 | + | 22.2421i | −0.0512371 | + | 0.140773i | |||||
−236.018 | + | 93.4977i | −1.48439 | + | 0.588036i | |||||
30.6586 | − | 173.873i | 0.191616 | − | 1.08671i | |||||
− | 209.714i | − | 1.30257i | |||||||
22.0433 | − | 91.4179i | 0.136070 | − | 0.564308i | |||||
39.8569 | 0.244521 | 0.122261 | − | 0.992498i | ||||||
0.122261 | + | 0.992498i | ||||||||
32.5042 | + | 5.73136i | 0.198196 | + | 0.0349473i | |||||
69.8494 | + | 176.322i | 0.423329 | + | 1.06862i | |||||
34.4762 | + | 12.5483i | 0.207688 | + | 0.0755921i | |||||
−106.672 | − | 127.127i | −0.638757 | − | 0.761241i | 0.345416 | − | 0.938450i | ||
−0.984173 | + | 0.177208i | ||||||||
−49.1218 | − | 239.074i | −0.292391 | − | 1.42306i | |||||
40.2401 | − | 14.6462i | 0.238107 | − | 0.0866639i | |||||
−17.1004 | − | 9.87292i | −0.100591 | − | 0.0580760i | |||||
9.30634 | + | 39.6106i | 0.0544231 | + | 0.231641i | |||||
−48.3337 | − | 83.7164i | −0.281010 | − | 0.486723i | |||||
−7.00006 | + | 8.34234i | −0.0404628 | + | 0.0482216i | −0.785896 | − | 0.618358i | ||
0.745434 | + | 0.666580i | ||||||||
2.48282 | + | 88.2901i | 0.0142691 | + | 0.507414i | |||||
7.27451 | + | 41.2558i | 0.0415686 | + | 0.235747i | |||||
−18.9982 | + | 3.34989i | −0.107944 | + | 0.0190335i | |||||
97.3837 | − | 180.189i | 0.550191 | − | 1.01801i | |||||
61.3854 | + | 51.5085i | 0.344862 | + | 0.289374i | |||||
−244.720 | + | 141.289i | −1.36715 | + | 0.789326i | −0.990564 | − | 0.137054i | ||
−0.376590 | + | 0.926380i | ||||||||
−114.710 | − | 57.8898i | −0.637277 | − | 0.321610i | |||||
54.3996 | − | 94.2228i | 0.300550 | − | 0.520568i | −0.675711 | − | 0.737167i | ||
0.976261 | + | 0.216599i | ||||||||
46.9861 | + | 129.093i | 0.258165 | + | 0.709303i | |||||
−155.535 | − | 175.117i | −0.849919 | − | 0.956923i | |||||
−117.775 | + | 98.8252i | −0.640083 | + | 0.537094i | |||||
−32.5066 | + | 89.3112i | −0.175711 | + | 0.482763i | |||||
11.2408 | − | 76.2221i | 0.0604345 | − | 0.409796i | |||||
−6.44344 | + | 36.5426i | −0.0344569 | + | 0.195415i | |||||
32.8857i | 0.174924i | |||||||||
−283.272 | − | 25.6182i | −1.49879 | − | 0.135546i | |||||
−28.2539 | −0.148705 | |||||||||
106.979 | + | 18.8633i | 0.560100 | + | 0.0987607i | 0.446529 | − | 0.894769i | ||
0.113571 | + | 0.993530i | ||||||||
−58.6984 | + | 74.0877i | −0.305721 | + | 0.385873i | |||||
−188.040 | − | 68.4410i | −0.974301 | − | 0.354617i | −0.194679 | − | 0.980867i | ||
−0.779622 | + | 0.626250i | ||||||||
−59.5540 | − | 70.9737i | −0.306980 | − | 0.365844i | |||||
172.137 | + | 57.2262i | 0.882752 | + | 0.293468i | |||||
−154.450 | + | 56.2152i | −0.788011 | + | 0.286812i | |||||
253.494 | + | 146.355i | 1.28677 | + | 0.742918i | 0.978077 | − | 0.208243i | ||
0.308694 | + | 0.951161i | ||||||||
14.4833 | − | 121.851i | 0.0731478 | − | 0.615409i | |||||
41.1548 | + | 71.2822i | 0.206808 | + | 0.358202i | 0.950707 | − | 0.310090i | ||
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19.7412 | − | 23.5267i | 0.0987060 | − | 0.117633i | |||||
248.140 | − | 152.721i | 1.23453 | − | 0.759807i | |||||
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263.090 | − | 46.3898i | 1.29601 | − | 0.228521i | |||||
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62.3061 | − | 187.417i | 0.296696 | − | 0.892462i | |||||
88.7425 | − | 74.4638i | 0.420581 | − | 0.352909i | −0.407803 | − | 0.913070i | ||
0.828384 | + | 0.560161i | ||||||||
76.7592 | − | 210.894i | 0.362072 | − | 0.994784i | |||||
286.085 | + | 226.661i | 1.34312 | + | 1.06413i | |||||
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119.101 | + | 171.158i | 0.551395 | + | 0.792396i | |||||
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186.281 | − | 67.8007i | 0.835341 | − | 0.304039i | 0.111292 | − | 0.993788i | ||
0.724049 | + | 0.689749i | ||||||||
299.224 | + | 172.757i | 1.33582 | + | 0.771236i | |||||
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121.729 | − | 70.2803i | 0.522442 | − | 0.301632i | −0.215491 | − | 0.976506i | ||
0.737933 | + | 0.674874i | ||||||||
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0.788060 | + | 0.615598i | ||||||||
24.6625 | − | 9.76996i | 0.102761 | − | 0.0407082i | |||||
52.8609 | − | 299.789i | 0.219340 | − | 1.24394i | −0.653875 | − | 0.756602i | ||
0.873215 | − | 0.487335i | ||||||||
− | 19.6445i | − | 0.0811755i | |||||||
231.036 | − | 75.3090i | 0.950765 | − | 0.309913i | |||||
207.060 | 0.848606 | |||||||||
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47.7214 | + | 17.3692i | 0.193204 | + | 0.0703205i | |||||
109.815 | + | 130.873i | 0.442803 | + | 0.527712i | |||||
19.0809 | + | 92.8661i | 0.0766302 | + | 0.372956i | |||||
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183.234 | − | 172.198i | 0.727120 | − | 0.683327i | |||||
116.897 | + | 202.472i | 0.462044 | + | 0.800284i | |||||
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0.124863 | − | 0.992174i | ||||||||
180.688 | + | 203.437i | 0.684425 | + | 0.770593i | |||||
348.945 | − | 292.799i | 1.31677 | − | 1.10490i | |||||
18.9110 | − | 51.9576i | 0.0710940 | − | 0.195329i | |||||
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0.807907 | − | 0.589310i | ||||||||
14.2145 | + | 168.136i | 0.0526464 | + | 0.622725i | |||||
115.698 | 0.426931 | 0.213465 | − | 0.976951i | ||||||
0.213465 | + | 0.976951i | ||||||||
5.11128 | + | 0.901257i | 0.0187915 | + | 0.00331344i | |||||
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108.352 | − | 39.4370i | 0.391163 | − | 0.142372i | −0.138949 | − | 0.990300i | ||
0.530112 | + | 0.847928i | ||||||||
125.980 | + | 72.7347i | 0.453166 | + | 0.261635i | |||||
182.964 | − | 78.5001i | 0.655785 | − | 0.281362i | |||||
218.970 | + | 379.267i | 0.782035 | + | 1.35452i | |||||
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0.664607 | + | 0.747193i | ||||||||
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0.537652 | − | 0.843167i | ||||||||
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75.5275 | − | 227.187i | 0.259545 | − | 0.780712i | |||||
185.169 | − | 155.375i | 0.634141 | − | 0.532107i | |||||
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169.181 | + | 134.039i | 0.575446 | + | 0.455917i | |||||
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136.357i | 0.460665i | |||||||||
287.769 | − | 133.166i | 0.968920 | − | 0.448369i | |||||
234.232 | 0.786012 | |||||||||
220.222 | + | 38.8311i | 0.736529 | + | 0.129870i | |||||
31.3022 | + | 4.61628i | 0.104341 | + | 0.0153876i | |||||
360.806 | + | 131.323i | 1.19869 | + | 0.436287i | |||||
95.6252 | + | 113.962i | 0.316640 | + | 0.377356i | |||||
10.7142 | − | 9.51612i | 0.0353604 | − | 0.0314063i | |||||
6.97859 | − | 2.54000i | 0.0229559 | − | 0.00835526i | |||||
363.957 | + | 210.131i | 1.19330 | + | 0.688954i | |||||
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210.907 | − | 251.350i | 0.684764 | − | 0.816070i | |||||
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24.0064 | + | 136.147i | 0.0774399 | + | 0.439184i | |||||
442.280 | − | 77.9859i | 1.42212 | − | 0.250759i | 0.590921 | − | 0.806730i | ||
0.831202 | + | 0.555971i | ||||||||
260.149 | − | 7.31570i | 0.833810 | − | 0.0234478i | |||||
8.30206 | + | 6.96625i | 0.0265241 | + | 0.0222564i | 0.655953 | − | 0.754801i | ||
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496.830 | − | 116.728i | 1.57724 | − | 0.370566i | |||||
27.0360 | − | 46.8278i | 0.0855570 | − | 0.148189i | |||||
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0.764539 | − | 0.644577i | ||||||||
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58.0083 | − | 159.376i | 0.181276 | − | 0.498051i | |||||
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42.2781 | − | 239.771i | 0.131299 | − | 0.744631i | |||||
− | 14.2846i | − | 0.0442249i | |||||||
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45.5694 | + | 8.03512i | 0.139784 | + | 0.0246476i | |||||
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90.3137 | + | 32.8715i | 0.275347 | + | 0.100218i | |||||
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44.3141 | + | 215.675i | 0.134285 | + | 0.653561i | |||||
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152.140 | + | 45.8713i | 0.456878 | + | 0.137752i | |||||
−96.3325 | − | 166.853i | −0.288421 | − | 0.499559i | |||||
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1.45928 | + | 51.8924i | 0.00434309 | + | 0.154442i | |||||
78.0147 | + | 442.443i | 0.231498 | + | 1.31289i | 0.849865 | + | 0.527000i | ||
−0.618368 | + | 0.785889i | ||||||||
48.9602 | − | 8.63300i | 0.144853 | − | 0.0255414i | |||||
25.6978 | − | 47.5485i | 0.0758047 | − | 0.140261i | |||||
34.5551 | + | 28.9952i | 0.101633 | + | 0.0852799i | |||||
224.988 | − | 129.897i | 0.659789 | − | 0.380929i | |||||
2.65471 | + | 47.1639i | 0.00776232 | + | 0.137906i | |||||
68.3305 | − | 118.352i | 0.199214 | − | 0.345049i | |||||
−96.2747 | − | 264.512i | −0.279868 | − | 0.768932i | |||||
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0.767227 | + | 0.641376i | ||||||||
29.4382 | − | 199.615i | 0.0845925 | − | 0.573607i | |||||
41.6381 | − | 236.141i | 0.119307 | − | 0.676622i | −0.865221 | − | 0.501391i | ||
0.984527 | − | 0.175231i | ||||||||
48.6353i | 0.138958i | |||||||||
79.3531 | − | 292.722i | 0.226077 | − | 0.833967i | |||||
−385.187 | −1.09428 | |||||||||
25.2020 | + | 4.44379i | 0.0713937 | + | 0.0125886i | 0.209231 | − | 0.977866i | ||
−0.137837 | + | 0.990455i | ||||||||
147.667 | − | 186.382i | 0.417139 | − | 0.526502i | |||||
−615.423 | − | 223.996i | −1.73359 | − | 0.630974i | |||||
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94.7544 | + | 31.5007i | 0.265418 | + | 0.0882374i | |||||
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16.7796 | + | 9.68773i | 0.0467399 | + | 0.0269853i | 0.523188 | − | 0.852217i | ||
−0.476448 | + | 0.879203i | ||||||||
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170.280 | + | 294.934i | 0.471690 | + | 0.816992i | |||||
81.1916 | − | 96.7604i | 0.224286 | − | 0.267294i | |||||
43.2308 | − | 26.6070i | 0.119093 | − | 0.0732976i | |||||
−54.4967 | − | 309.066i | −0.149716 | − | 0.849083i | |||||
483.159 | − | 85.1939i | 1.32372 | − | 0.233408i | |||||
−142.524 | − | 231.571i | −0.389409 | − | 0.632709i | |||||
299.305 | + | 251.147i | 0.815545 | + | 0.684324i | 0.951924 | − | 0.306333i | ||
−0.136379 | + | 0.990657i | ||||||||
28.3201 | − | 16.3506i | 0.0769569 | − | 0.0444311i | |||||
67.0585 | − | 89.7095i | 0.181730 | − | 0.243115i | |||||
−55.1707 | + | 95.5584i | −0.149110 | + | 0.258266i | |||||
304.886 | + | 837.669i | 0.821796 | + | 2.25787i | |||||
−55.5257 | + | 167.022i | −0.149263 | + | 0.448983i | |||||
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0.440419 | + | 0.897792i | ||||||||
−14.7339 | + | 40.4810i | −0.0393954 | + | 0.108238i | |||||
−266.108 | − | 210.833i | −0.709621 | − | 0.562221i | |||||
−16.6287 | + | 94.3061i | −0.0442253 | + | 0.250814i | |||||
284.862i | 0.755603i | |||||||||
−318.707 | − | 86.3973i | −0.843140 | − | 0.228564i | |||||
3.48118 | 0.00918518 | 0.00459259 | − | 0.999989i | ||||||
0.00459259 | + | 0.999989i | ||||||||
63.5643 | + | 11.2081i | 0.167274 | + | 0.0294950i | |||||
463.626 | + | 68.3730i | 1.21687 | + | 0.179457i | |||||
118.509 | + | 43.1337i | 0.310233 | + | 0.112916i | |||||
11.0730 | + | 13.1963i | 0.0289112 | + | 0.0344550i | 0.780306 | − | 0.625398i | ||
−0.751395 | + | 0.659853i | ||||||||
212.225 | − | 188.494i | 0.552670 | − | 0.490870i | |||||
625.797 | − | 227.772i | 1.62545 | − | 0.591615i | |||||
−201.193 | − | 116.159i | −0.521226 | − | 0.300930i | |||||
−327.518 | + | 18.4350i | −0.846299 | + | 0.0476356i | |||||
105.827 | + | 183.298i | 0.272750 | + | 0.472417i | |||||
203.618 | − | 242.662i | 0.523439 | − | 0.623810i | −0.437952 | − | 0.898999i | ||
0.961390 | + | 0.275189i | ||||||||
185.271 | + | 100.131i | 0.475055 | + | 0.256745i | |||||
−10.9225 | − | 61.9446i | −0.0279348 | − | 0.158426i | |||||
−471.340 | + | 83.1100i | −1.20240 | + | 0.212015i | |||||
295.440 | − | 8.30814i | 0.751756 | − | 0.0211403i | |||||
260.321 | + | 218.435i | 0.660713 | + | 0.554404i | |||||
95.0446 | − | 54.8740i | 0.240619 | − | 0.138922i | |||||
−80.9210 | + | 268.389i | −0.204346 | + | 0.677750i | |||||
−134.041 | + | 232.165i | −0.337634 | + | 0.584800i | −0.983987 | − | 0.178239i | ||
0.646353 | + | 0.763039i | ||||||||
32.6829 | + | 89.7955i | 0.0821178 | + | 0.225617i | |||||
139.955 | − | 28.7560i | 0.350763 | − | 0.0720703i | |||||
−5.00408 | + | 4.19892i | −0.0125102 | + | 0.0104973i | |||||
33.3356 | − | 91.5887i | 0.0831311 | − | 0.228401i | −0.891162 | − | 0.453685i | ||
0.974293 | + | 0.225285i | ||||||||
314.493 | − | 124.585i | 0.782321 | − | 0.309914i | |||||
43.1494 | − | 244.712i | 0.107070 | − | 0.607227i | |||||
12.6686i | 0.0313578i | |||||||||
−350.757 | + | 259.009i | −0.866067 | + | 0.639528i | |||||
310.149 | 0.763914 | |||||||||
204.203 | + | 36.0065i | 0.501727 | + | 0.0884680i | |||||
−26.9611 | − | 68.0584i | −0.0660810 | − | 0.166810i | |||||
380.898 | + | 138.636i | 0.931292 | + | 0.338962i | 0.762721 | − | 0.646727i | ||
0.168570 | + | 0.985690i | ||||||||
49.9916 | + | 59.5777i | 0.121931 | + | 0.145311i | |||||
−39.6426 | − | 192.939i | −0.0964539 | − | 0.469437i | |||||
180.170 | − | 65.5764i | 0.437305 | − | 0.159166i | |||||
−622.862 | − | 359.609i | −1.50814 | − | 0.870725i | |||||
47.5751 | + | 202.494i | 0.114916 | + | 0.489116i | |||||
−85.0569 | − | 147.323i | −0.204956 | − | 0.354995i | |||||
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0.309828 | + | 0.950793i | ||||||||
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326.760 | − | 565.966i | 0.770661 | − | 1.33482i | |||||
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410.223i | 0.895683i | |||||||||
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284.213 | 0.617855 | |||||||||
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429.586i | 0.885745i | |||||||||
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454.010 | 0.932258 | 0.466129 | − | 0.884717i | ||||||
0.466129 | + | 0.884717i | ||||||||
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104.621i | 0.204338i | |||||||||
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727.808i | 1.35029i | |||||||||
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803.120 | 1.48451 | 0.742255 | − | 0.670117i | ||||||
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132.281 | + | 23.3247i | 0.244060 | + | 0.0430344i | |||||
322.905 | + | 47.6203i | 0.594668 | + | 0.0876984i | |||||
97.3813 | + | 35.4439i | 0.179010 | + | 0.0651542i | |||||
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0.400345 | + | 0.916364i | ||||||||
150.803 | + | 87.0659i | 0.275187 | + | 0.158879i | |||||
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575.120 | − | 332.045i | 1.03253 | − | 0.596132i | 0.114822 | − | 0.993386i | ||
0.917709 | + | 0.397254i | ||||||||
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224.892 | + | 268.016i | 0.393168 | + | 0.468559i | |||||
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625.722i | 1.05518i | 0.849499 | + | 0.527591i | ||||||
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355.860 | − | 94.2376i | 0.599091 | − | 0.158649i | |||||
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87.4307 | + | 29.0660i | 0.145718 | + | 0.0484434i | |||||
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386.043 | + | 222.882i | 0.641268 | + | 0.370236i | |||||
700.128 | + | 523.351i | 1.16107 | + | 0.867912i | |||||
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0.933330 | − | 0.359019i | ||||||||
146.031 | − | 25.7492i | 0.240182 | − | 0.0423506i | |||||
420.075 | + | 682.533i | 0.689778 | + | 1.12074i | |||||
373.759 | + | 313.621i | 0.612720 | + | 0.514133i | |||||
120.623 | − | 69.6414i | 0.197418 | − | 0.113979i | |||||
45.1545 | − | 60.4067i | 0.0737819 | − | 0.0987038i | |||||
533.889 | − | 924.724i | 0.870945 | − | 1.50852i | 0.00992514 | − | 0.999951i | ||
0.861020 | − | 0.508571i | ||||||||
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731.912 | − | 614.147i | 1.18817 | − | 0.996991i | |||||
144.247 | − | 396.317i | 0.233788 | − | 0.642328i | −0.766212 | − | 0.642588i | ||
1.00000 | 0.000260046i | |||||||||
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104.335 | − | 591.711i | 0.168554 | − | 0.955915i | −0.776771 | − | 0.629783i | ||
0.945324 | − | 0.326131i | ||||||||
− | 315.820i | − | 0.509386i | |||||||
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521.392 | 0.838250 | |||||||||
716.066 | + | 126.262i | 1.14938 | + | 0.202667i | |||||
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665.870 | + | 242.357i | 1.06539 | + | 0.387771i | |||||
8.08756 | + | 9.63837i | 0.0129194 | + | 0.0153968i | |||||
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346.285 | − | 126.037i | 0.551409 | − | 0.200696i | |||||
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591.571 | − | 33.2977i | 0.939001 | − | 0.0528535i | |||||
554.621 | + | 960.632i | 0.878956 | + | 1.52240i | 0.852488 | + | 0.522747i | ||
0.0264679 | + | 0.999650i | ||||||||
101.209 | − | 120.617i | 0.160141 | − | 0.190849i | |||||
305.740 | + | 165.239i | 0.483002 | + | 0.261040i | |||||
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673.021 | − | 18.9262i | 1.05821 | − | 0.0297581i | |||||
533.269 | + | 447.466i | 0.837157 | + | 0.702458i | |||||
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222.504i | 0.343900i | 0.985106 | + | 0.171950i | ||||||
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801.803 | 1.23544 | |||||||||
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521.584i | 0.773864i | |||||||||
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149.739 | − | 318.679i | 0.213303 | − | 0.453959i | |||||
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465.317 | + | 561.178i | 0.638295 | + | 0.769792i | |||||
569.582 | 0.780250 | |||||||||
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162.027 | − | 193.097i | 0.218956 | − | 0.260942i | |||||
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3.98012 | + | 0.701803i | 0.00525082 | + | 0.000925861i | |||||
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176.615 | + | 64.2827i | 0.232388 | + | 0.0845825i | |||||
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516.291 | + | 171.639i | 0.677547 | + | 0.225248i | |||||
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602.634 | − | 370.900i | 0.784680 | − | 0.482942i | |||||
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210.794 | + | 579.152i | 0.271642 | + | 0.746330i | |||||
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101.800 | 0.129847 | |||||||||
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339.459 | + | 50.0616i | 0.431882 | + | 0.0636915i | |||||
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1021.88i | 1.26313i | 0.775321 | + | 0.631567i | ||||||
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226.211 | + | 82.3342i | 0.277901 | + | 0.101148i | |||||
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407.542 | + | 235.294i | 0.498217 | + | 0.287646i | |||||
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549.829 | − | 96.9497i | 0.667268 | − | 0.117657i | |||||
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229.713 | + | 258.633i | 0.276429 | + | 0.311231i | |||||
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421.103 | + | 423.574i | 0.503110 | + | 0.506062i | |||||
136.221 | 0.162555 | |||||||||
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0.214282 | + | 0.976772i | ||||||||
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1065.74 | − | 655.926i | 1.25529 | − | 0.772587i | |||||
2.53306 | + | 14.3657i | 0.00298008 | + | 0.0169008i | |||||
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595.279 | + | 499.498i | 0.697865 | + | 0.585578i | 0.921165 | − | 0.389171i | ||
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131.138 | − | 175.434i | 0.153378 | − | 0.205185i | |||||
610.623 | − | 1057.63i | 0.713345 | − | 1.23555i | |||||
368.296 | + | 1011.88i | 0.429750 | + | 1.18073i | 0.945965 | + | 0.324269i | ||
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144.945 | − | 435.995i | 0.168934 | − | 0.508153i | |||||
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0.605963 | + | 0.795493i | ||||||||
−177.974 | + | 488.979i | −0.206946 | + | 0.568580i | |||||
−308.267 | − | 244.235i | −0.358034 | − | 0.283664i | |||||
53.1375 | − | 301.358i | 0.0616444 | − | 0.349603i | |||||
− | 1599.17i | − | 1.85304i | −0.376244 | − | 0.926520i | ||||
0.376244 | − | 0.926520i | ||||||||
−226.698 | − | 856.057i | −0.262382 | − | 0.990807i | |||||
58.6217 | 0.0677708 | |||||||||
−802.629 | − | 141.525i | −0.926823 | − | 0.163424i | |||||
−828.094 | − | 122.123i | −0.955126 | − | 0.140857i | |||||
580.776 | + | 211.385i | 0.669097 | + | 0.243531i | |||||
−153.906 | − | 183.418i | −0.177107 | − | 0.211067i | |||||
355.484 | − | 315.733i | 0.408602 | − | 0.362912i | |||||
1025.19 | − | 373.137i | 1.17702 | − | 0.428400i | |||||
124.260 | + | 71.7413i | 0.142500 | + | 0.0822722i | |||||
717.103 | − | 40.3635i | 0.821423 | − | 0.0462354i | |||||
−52.2449 | − | 90.4908i | −0.0597767 | − | 0.103536i | |||||
−766.304 | + | 913.245i | −0.875776 | + | 1.04371i | |||||
637.954 | + | 344.785i | 0.728258 | + | 0.393590i | |||||
−65.7402 | − | 372.831i | −0.0749603 | − | 0.425121i | −0.999075 | − | 0.0430055i | ||
0.924115 | − | 0.382116i | ||||||||
506.396 | − | 89.2913i | 0.576761 | − | 0.101698i | |||||
−1037.09 | + | 29.1642i | −1.17985 | + | 0.0331789i | |||||
79.5498 | + | 66.7502i | 0.0903975 | + | 0.0758525i | |||||
−1046.81 | + | 604.374i | −1.18820 | + | 0.686009i | −0.957898 | − | 0.287109i | ||
−0.230305 | + | 0.973119i | ||||||||
−186.924 | + | 619.967i | −0.211932 | + | 0.702910i | |||||
298.144 | − | 516.401i | 0.337649 | − | 0.584826i | −0.646341 | − | 0.763049i | ||
0.983990 | + | 0.178223i | ||||||||
−32.1941 | − | 88.4525i | −0.0364186 | − | 0.100059i | |||||
−1079.99 | + | 221.902i | −1.22033 | + | 0.250737i | |||||
−539.694 | + | 452.857i | −0.609136 | + | 0.511126i | |||||
34.7360 | − | 95.4364i | 0.0391612 | − | 0.107595i | −0.918571 | − | 0.395256i | ||
0.957732 | + | 0.287662i | ||||||||
−380.316 | + | 150.661i | −0.428283 | + | 0.169663i | |||||
285.757 | − | 1620.61i | 0.321436 | − | 1.82296i | |||||
− | 431.356i | − | 0.484670i | |||||||
689.371 | + | 655.489i | 0.773705 | + | 0.735678i | |||||
−525.755 | −0.589412 | |||||||||
−55.2071 | − | 9.73450i | −0.0618220 | − | 0.0109009i | |||||
258.802 | + | 653.301i | 0.289488 | + | 0.730761i | |||||
1429.39 | + | 520.255i | 1.59708 | + | 0.581290i | |||||
−640.678 | − | 763.531i | −0.715043 | − | 0.852155i | |||||
135.019 | + | 657.131i | 0.150523 | + | 0.732588i | |||||
438.061 | − | 159.441i | 0.487818 | − | 0.177551i | |||||
−485.835 | − | 280.497i | −0.540417 | − | 0.312010i | |||||
21.7104 | + | 92.4062i | 0.0241227 | + | 0.102674i | |||||
133.684 | + | 231.548i | 0.148373 | + | 0.256990i | |||||
109.065 | − | 129.979i | 0.120915 | − | 0.144101i | |||||
32.3796 | + | 1151.43i | 0.0358578 | + | 1.27511i | |||||
24.1609 | + | 137.023i | 0.0267267 | + | 0.151575i | |||||
−576.769 | + | 101.700i | −0.637313 | + | 0.112376i | |||||
−212.197 | + | 392.626i | −0.234213 | + | 0.433362i | |||||
1321.91 | + | 1109.21i | 1.45745 | + | 1.22295i | 0.926906 | + | 0.375293i | ||
0.530547 | + | 0.847656i | ||||||||
11.8330 | − | 6.83179i | 0.0130319 | − | 0.00752400i | |||||
38.3797 | + | 19.3688i | 0.0422219 | + | 0.0213078i | |||||
369.753 | − | 640.431i | 0.406322 | − | 0.703771i | |||||
106.953 | + | 293.850i | 0.117401 | + | 0.322558i | 0.984450 | − | 0.175666i | ||
−0.867048 | + | 0.498224i | ||||||||
14.7950 | + | 16.6577i | 0.0162226 | + | 0.0182650i | |||||
−284.305 | + | 238.560i | −0.311396 | + | 0.261292i | |||||
−58.4144 | + | 160.492i | −0.0639107 | + | 0.175593i | |||||
−183.944 | + | 1247.30i | −0.201032 | + | 1.36316i | |||||
162.732 | − | 922.898i | 0.177655 | − | 1.00753i | |||||
− | 1037.84i | − | 1.13177i | |||||||
−98.6384 | − | 8.92054i | −0.107449 | − | 0.00971737i | |||||
198.504 | 0.216000 | 0.108000 | − | 0.994151i | ||||||
0.108000 | + | 0.994151i | ||||||||
815.035 | + | 143.713i | 0.885908 | + | 0.156209i | |||||
1075.58 | − | 1357.57i | 1.16784 | − | 1.47401i | |||||
−856.844 | − | 311.866i | −0.929332 | − | 0.338249i | |||||
878.459 | + | 1046.91i | 0.951743 | + | 1.13424i | |||||
934.076 | + | 310.530i | 1.01090 | + | 0.336072i | |||||
65.9791 | − | 24.0144i | 0.0713287 | − | 0.0259615i | |||||
360.397 | + | 208.075i | 0.389197 | + | 0.224703i | |||||
76.7941 | − | 646.087i | 0.0828416 | − | 0.696966i | |||||
415.883 | + | 720.330i | 0.448149 | + | 0.776218i | |||||
854.746 | − | 1018.65i | 0.920071 | − | 1.09650i | −0.0749849 | − | 0.997185i | ||
0.995056 | − | 0.0993136i | ||||||||
−353.206 | + | 217.385i | −0.379791 | + | 0.233748i | |||||
−48.6528 | − | 275.924i | −0.0522587 | − | 0.296374i | |||||
−367.127 | + | 64.7343i | −0.393913 | + | 0.0694574i | |||||
706.187 | + | 1147.41i | 0.756899 | + | 1.22980i | |||||
−90.6501 | − | 76.0644i | −0.0970557 | − | 0.0814394i | |||||
172.983 | − | 99.8717i | 0.185008 | − | 0.106815i | |||||
307.843 | + | 717.503i | 0.328892 | + | 0.766563i | |||||
−675.671 | + | 1170.30i | −0.721100 | + | 1.24898i | 0.239459 | + | 0.970906i | ||
−0.960559 | + | 0.278076i | ||||||||
−406.260 | − | 1116.19i | −0.433113 | − | 1.18997i | |||||
−10.2568 | + | 30.8524i | −0.0109231 | + | 0.0328567i | |||||
135.608 | − | 113.789i | 0.144264 | − | 0.121052i | |||||
265.840 | − | 730.391i | 0.282508 | − | 0.776186i | −0.714553 | − | 0.699581i | ||
0.997062 | − | 0.0766044i | ||||||||
−379.313 | − | 300.523i | −0.402667 | − | 0.319027i | |||||
−43.0206 | + | 243.982i | −0.0456210 | + | 0.258729i | |||||
− | 112.150i | − | 0.118803i | |||||||
874.517 | + | 1256.75i | 0.925415 | + | 1.32989i | |||||
−496.949 | −0.525316 | |||||||||
−270.124 | − | 47.6301i | −0.285242 | − | 0.0502958i | 0.0291967 | − | 0.999574i | ||
−0.314438 | + | 0.949278i | ||||||||
160.480 | + | 23.6668i | 0.169283 | + | 0.0249649i | |||||
−962.034 | − | 350.152i | −1.01373 | − | 0.368969i | |||||
13.4167 | + | 15.9894i | 0.0141229 | + | 0.0168310i | |||||
489.501 | − | 434.765i | 0.514723 | − | 0.457166i | |||||
−241.551 | + | 87.9173i | −0.253730 | + | 0.0923501i | |||||
858.313 | + | 495.548i | 0.900644 | + | 0.519987i | 0.877409 | − | 0.479743i | ||
0.0232347 | + | 0.999730i | ||||||||
−484.421 | − | 739.664i | −0.507779 | − | 0.775329i | |||||
−292.376 | − | 506.410i | −0.306153 | − | 0.530272i | |||||
251.751 | − | 300.025i | 0.263338 | − | 0.313834i | |||||
−786.020 | − | 424.808i | −0.821338 | − | 0.443896i | |||||
25.4760 | + | 144.482i | 0.0265929 | + | 0.150816i | |||||
−681.141 | + | 120.104i | −0.710262 | + | 0.125238i | |||||
508.613 | − | 14.3028i | 0.529806 | − | 0.0148988i | |||||
−361.298 | − | 303.165i | −0.375961 | − | 0.315468i | |||||
199.405 | − | 115.126i | 0.207281 | − | 0.119674i | |||||
−974.635 | − | 1037.10i | −1.01208 | − | 1.07694i | |||||
−403.678 | + | 699.190i | −0.418753 | + | 0.725301i | |||||
368.418 | + | 1012.22i | 0.381780 | + | 1.04893i | |||||
715.464 | − | 147.004i | 0.740646 | − | 0.152178i | |||||
239.352 | − | 200.840i | 0.247520 | − | 0.207694i | −0.510583 | − | 0.859828i | ||
0.758104 | + | 0.652134i | ||||||||
−44.6946 | + | 122.797i | −0.0461721 | + | 0.126857i | |||||
39.8416 | − | 15.7831i | 0.0411162 | − | 0.0162880i | |||||
−86.6041 | + | 491.156i | −0.0892826 | + | 0.506347i | |||||
487.838i | 0.502407i | 0.967934 | + | 0.251204i | ||||||
−0.967934 | + | 0.251204i | ||||||||
−644.105 | − | 21.8847i | −0.662659 | − | 0.0225151i | |||||
1319.96 | 1.35659 | |||||||||
519.080 | + | 91.5279i | 0.532937 | + | 0.0939711i | |||||
−49.3558 | − | 124.590i | −0.0506214 | − | 0.127785i | |||||
−120.511 | − | 43.8624i | −0.123474 | − | 0.0449410i | |||||
−413.839 | − | 493.194i | −0.423582 | − | 0.504805i | 0.511478 | − | 0.859297i | ||
−0.935059 | + | 0.354492i | ||||||||
27.9387 | + | 135.977i | 0.0285672 | + | 0.139035i | |||||
−761.718 | + | 277.243i | −0.778057 | + | 0.283190i | |||||
766.227 | + | 442.382i | 0.781865 | + | 0.451410i | |||||
121.847 | − | 114.509i | 0.124207 | − | 0.116726i | |||||
183.483 | + | 317.802i | 0.186846 | + | 0.323627i | |||||
−989.779 | + | 1179.57i | −1.00690 | + | 1.19997i | −0.0271699 | + | 0.999631i | ||
−0.979726 | + | 0.200341i | ||||||||
8.10498 | + | 288.216i | 0.00823676 | + | 0.292902i | |||||
−273.610 | − | 1551.72i | −0.277777 | − | 1.57535i | |||||
91.6108 | − | 16.1534i | 0.0929115 | − | 0.0163828i | |||||
186.316 | − | 344.739i | 0.188770 | − | 0.349279i | |||||
−103.177 | − | 86.5756i | −0.104430 | − | 0.0876271i | |||||
628.389 | − | 362.801i | 0.635378 | − | 0.366836i | |||||
−552.581 | + | 361.897i | −0.558163 | + | 0.365552i | |||||
−155.571 | + | 269.456i | −0.156984 | + | 0.271903i | −0.933780 | − | 0.357849i | ||
0.776796 | + | 0.629752i | ||||||||
−248.155 | − | 681.799i | −0.250156 | − | 0.687297i | |||||
−1196.67 | − | 1347.33i | −1.20511 | − | 1.35683i | |||||
1139.84 | − | 956.439i | 1.14672 | − | 0.962213i | |||||
151.540 | − | 416.352i | 0.152301 | − | 0.418445i | |||||
36.6844 | − | 248.751i | 0.0368318 | − | 0.249750i | |||||
−8.37502 | + | 47.4971i | −0.00840022 | + | 0.0476400i | −0.988720 | − | 0.149777i | ||
0.980320 | + | 0.197417i | ||||||||
141.953i | 0.142238i | |||||||||
40.1592 | + | 475.021i | 0.0401994 | + | 0.475496i |
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 27.3.f.a.2.4 | ✓ | 30 | |
3.2 | odd | 2 | 81.3.f.a.8.2 | 30 | |||
4.3 | odd | 2 | 432.3.bc.a.353.3 | 30 | |||
9.2 | odd | 6 | 243.3.f.b.188.4 | 30 | |||
9.4 | even | 3 | 243.3.f.d.107.2 | 30 | |||
9.5 | odd | 6 | 243.3.f.a.107.4 | 30 | |||
9.7 | even | 3 | 243.3.f.c.188.2 | 30 | |||
27.4 | even | 9 | 243.3.f.a.134.4 | 30 | |||
27.5 | odd | 18 | 243.3.f.c.53.2 | 30 | |||
27.11 | odd | 18 | 729.3.b.a.728.12 | 30 | |||
27.13 | even | 9 | 81.3.f.a.71.2 | 30 | |||
27.14 | odd | 18 | inner | 27.3.f.a.14.4 | yes | 30 | |
27.16 | even | 9 | 729.3.b.a.728.19 | 30 | |||
27.22 | even | 9 | 243.3.f.b.53.4 | 30 | |||
27.23 | odd | 18 | 243.3.f.d.134.2 | 30 | |||
108.95 | even | 18 | 432.3.bc.a.257.3 | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
27.3.f.a.2.4 | ✓ | 30 | 1.1 | even | 1 | trivial | |
27.3.f.a.14.4 | yes | 30 | 27.14 | odd | 18 | inner | |
81.3.f.a.8.2 | 30 | 3.2 | odd | 2 | |||
81.3.f.a.71.2 | 30 | 27.13 | even | 9 | |||
243.3.f.a.107.4 | 30 | 9.5 | odd | 6 | |||
243.3.f.a.134.4 | 30 | 27.4 | even | 9 | |||
243.3.f.b.53.4 | 30 | 27.22 | even | 9 | |||
243.3.f.b.188.4 | 30 | 9.2 | odd | 6 | |||
243.3.f.c.53.2 | 30 | 27.5 | odd | 18 | |||
243.3.f.c.188.2 | 30 | 9.7 | even | 3 | |||
243.3.f.d.107.2 | 30 | 9.4 | even | 3 | |||
243.3.f.d.134.2 | 30 | 27.23 | odd | 18 | |||
432.3.bc.a.257.3 | 30 | 108.95 | even | 18 | |||
432.3.bc.a.353.3 | 30 | 4.3 | odd | 2 | |||
729.3.b.a.728.12 | 30 | 27.11 | odd | 18 | |||
729.3.b.a.728.19 | 30 | 27.16 | even | 9 |