Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [45,3,Mod(7,45)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(45, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([8, 3]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("45.7");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 45.k (of order , degree , minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | |
Analytic rank: | |
Dimension: | |
Relative dimension: | over |
Twist minimal: | yes |
Sato-Tate group: |
Embedding invariants
Embedding label | 22.1 | ||
Character | 45.22 | ||
Dual form | 45.3.k.a.43.1 |
-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 .
−0.930497 | + | 3.47266i | −0.465249 | + | 1.73633i | 0.190815 | + | 0.981626i | ||
−0.656063 | + | 0.754706i | ||||||||
0.635068 | + | 2.93201i | 0.211689 | + | 0.977337i | |||||
−7.72947 | − | 4.46261i | −1.93237 | − | 1.11565i | |||||
4.99913 | − | 0.0933744i | 0.999826 | − | 0.0186749i | |||||
−10.7728 | − | 0.522853i | −1.79547 | − | 0.0871422i | |||||
1.28323 | − | 4.78910i | 0.183319 | − | 0.684157i | −0.811665 | − | 0.584123i | ||
0.994984 | − | 0.100033i | ||||||||
12.5207 | − | 12.5207i | 1.56509 | − | 1.56509i | |||||
−8.19338 | + | 3.72405i | −0.910375 | + | 0.413783i | |||||
−4.32742 | + | 17.4472i | −0.432742 | + | 1.74472i | |||||
1.37764 | + | 2.38615i | 0.125240 | + | 0.216923i | 0.921827 | − | 0.387602i | ||
−0.796587 | + | 0.604525i | ||||||||
8.17569 | − | 25.4969i | 0.681307 | − | 2.12474i | |||||
2.45318 | + | 9.15539i | 0.188706 | + | 0.704261i | 0.993807 | + | 0.111123i | ||
−0.805101 | + | 0.593138i | ||||||||
15.4369 | + | 8.91249i | 1.10263 | + | 0.636606i | |||||
3.44856 | + | 14.5982i | 0.229904 | + | 0.973213i | |||||
13.9793 | + | 24.2129i | 0.873708 | + | 1.51331i | |||||
9.17504 | + | 9.17504i | 0.539708 | + | 0.539708i | 0.923443 | − | 0.383735i | ||
−0.383735 | + | 0.923443i | ||||||||
−5.30846 | − | 31.9181i | −0.294914 | − | 1.77323i | |||||
− | 32.1912i | − | 1.69427i | −0.531375 | − | 0.847137i | ||||
0.531375 | − | 0.847137i | ||||||||
−39.0573 | − | 21.5874i | −1.95286 | − | 1.07937i | |||||
14.8566 | + | 0.721059i | 0.707459 | + | 0.0343361i | |||||
−9.56819 | + | 2.56379i | −0.434918 | + | 0.116536i | |||||
0.179412 | + | 0.669573i | 0.00780050 | + | 0.0291119i | 0.969716 | − | 0.244234i | ||
−0.961916 | + | 0.273346i | ||||||||
44.6624 | + | 28.7594i | 1.86093 | + | 1.19831i | |||||
24.9826 | − | 0.933581i | 0.999302 | − | 0.0373432i | |||||
−34.0763 | −1.31063 | |||||||||
−16.1223 | − | 21.6581i | −0.597122 | − | 0.802150i | |||||
−31.2906 | + | 31.2906i | −1.11752 | + | 1.11752i | |||||
−30.1349 | + | 17.3984i | −1.03913 | + | 0.599944i | −0.919588 | − | 0.392884i | ||
−0.119546 | + | 0.992829i | ||||||||
−53.9035 | − | 1.60790i | −1.79678 | − | 0.0535968i | |||||
12.8482 | − | 22.2537i | 0.414457 | − | 0.717860i | −0.580914 | − | 0.813965i | ||
0.995371 | + | 0.0961042i | ||||||||
−28.6765 | + | 7.68384i | −0.896140 | + | 0.240120i | |||||
−6.12132 | + | 5.55463i | −0.185494 | + | 0.168322i | |||||
−40.3992 | + | 23.3245i | −1.18821 | + | 0.686014i | |||||
5.96788 | − | 24.0611i | 0.170511 | − | 0.687461i | |||||
79.9494 | + | 7.77893i | 2.22082 | + | 0.216081i | |||||
−13.0331 | − | 13.0331i | −0.352245 | − | 0.352245i | 0.508699 | − | 0.860944i | ||
−0.860944 | + | 0.508699i | ||||||||
111.789 | + | 29.9538i | 2.94182 | + | 0.788259i | |||||
−25.2858 | + | 13.0070i | −0.648353 | + | 0.333514i | |||||
61.4236 | − | 63.7618i | 1.53559 | − | 1.59405i | |||||
20.2139 | − | 35.0116i | 0.493023 | − | 0.853941i | −0.506945 | − | 0.861979i | ||
0.999968 | + | 0.00803768i | ||||||||
−16.3280 | + | 50.9211i | −0.388763 | + | 1.21241i | |||||
3.68527 | + | 0.987466i | 0.0857040 | + | 0.0229643i | 0.301416 | − | 0.953493i | ||
−0.215712 | + | 0.976457i | ||||||||
− | 24.5915i | − | 0.558899i | |||||||
−40.6120 | + | 19.3821i | −0.902489 | + | 0.430712i | |||||
−2.49214 | −0.0541770 | |||||||||
0.993231 | − | 3.70679i | 0.0211326 | − | 0.0788679i | −0.954554 | − | 0.298037i | ||
0.975687 | + | 0.219169i | ||||||||
−62.1147 | + | 56.3644i | −1.29406 | + | 1.17426i | |||||
21.1465 | + | 12.2089i | 0.431561 | + | 0.249162i | |||||
−20.0042 | + | 87.6247i | −0.400084 | + | 1.75249i | |||||
−21.0745 | + | 32.7281i | −0.413226 | + | 0.641727i | |||||
21.8952 | − | 81.7139i | 0.421061 | − | 1.57142i | |||||
−31.2240 | + | 31.2240i | −0.589132 | + | 0.589132i | −0.937396 | − | 0.348265i | ||
0.348265 | + | 0.937396i | ||||||||
90.2129 | − | 35.8346i | 1.67061 | − | 0.663603i | |||||
7.10982 | + | 11.8000i | 0.129269 | + | 0.214546i | |||||
−43.8959 | − | 76.0300i | −0.783856 | − | 1.35768i | |||||
94.3850 | − | 20.4436i | 1.65588 | − | 0.358659i | |||||
−32.3783 | − | 120.837i | −0.558247 | − | 2.08340i | |||||
−36.8611 | − | 21.2818i | −0.624765 | − | 0.360708i | 0.153957 | − | 0.988078i | ||
−0.778722 | + | 0.627369i | ||||||||
38.4905 | − | 128.226i | 0.641509 | − | 2.13710i | |||||
−6.56994 | − | 11.3795i | −0.107704 | − | 0.186549i | 0.807136 | − | 0.590366i | ||
−0.914840 | + | 0.403817i | ||||||||
65.3243 | + | 65.3243i | 1.05362 | + | 1.05362i | |||||
7.32081 | + | 44.0177i | 0.116203 | + | 0.698694i | |||||
5.10100i | 0.0797032i | |||||||||
13.1186 | + | 45.5399i | 0.201825 | + | 0.700614i | |||||
−13.5935 | − | 26.4259i | −0.205962 | − | 0.400392i | |||||
−44.9977 | + | 12.0571i | −0.671607 | + | 0.179957i | −0.578479 | − | 0.815697i | ||
−0.0931285 | + | 0.995654i | ||||||||
−29.9735 | − | 111.863i | −0.440787 | − | 1.64504i | |||||
−1.84926 | + | 0.951261i | −0.0268008 | + | 0.0137864i | |||||
78.0031 | + | 43.1133i | 1.11433 | + | 0.615904i | |||||
−114.062 | −1.60651 | −0.803254 | − | 0.595637i | ||||||
−0.803254 | + | 0.595637i | ||||||||
−55.9592 | + | 149.215i | −0.777212 | + | 2.07243i | |||||
−18.7982 | + | 18.7982i | −0.257510 | + | 0.257510i | −0.824041 | − | 0.566531i | ||
0.566531 | + | 0.824041i | ||||||||
57.3867 | − | 33.1322i | 0.775496 | − | 0.447733i | |||||
18.6029 | + | 72.6563i | 0.248038 | + | 0.968750i | |||||
−143.657 | + | 248.821i | −1.89022 | + | 3.27396i | |||||
13.1953 | − | 3.53568i | 0.171368 | − | 0.0459179i | |||||
−21.6407 | − | 99.9120i | −0.277445 | − | 1.28092i | |||||
−18.3057 | + | 10.5688i | −0.231717 | + | 0.133782i | −0.611364 | − | 0.791350i | ||
0.379647 | + | 0.925132i | ||||||||
72.1453 | + | 119.738i | 0.901816 | + | 1.49673i | |||||
53.2629 | − | 61.0251i | 0.657567 | − | 0.753396i | |||||
102.774 | + | 102.774i | 1.25335 | + | 1.25335i | |||||
−14.7688 | − | 3.95730i | −0.177938 | − | 0.0476783i | 0.168750 | − | 0.985659i | ||
−0.346688 | + | 0.937981i | ||||||||
−111.616 | − | 71.8727i | −1.32876 | − | 0.855628i | |||||
46.7239 | + | 45.0105i | 0.549693 | + | 0.529535i | |||||
−6.85828 | + | 11.8789i | −0.0797474 | + | 0.138127i | |||||
−70.1499 | − | 77.3067i | −0.806321 | − | 0.888582i | |||||
47.1254 | + | 12.6272i | 0.535516 | + | 0.143491i | |||||
− | 92.4405i | − | 1.03866i | −0.854575 | − | 0.519329i | ||||
0.854575 | − | 0.519329i | ||||||||
−29.5180 | − | 159.067i | −0.327978 | − | 1.76741i | |||||
46.9941 | 0.516418 | |||||||||
1.60129 | − | 5.97609i | 0.0174053 | − | 0.0649574i | |||||
73.4075 | + | 23.5384i | 0.789328 | + | 0.253101i | |||||
11.9482 | + | 6.89832i | 0.127109 | + | 0.0733864i | |||||
−3.00583 | − | 160.928i | −0.0316404 | − | 1.69398i | |||||
−40.7406 | − | 79.2000i | −0.424382 | − | 0.825000i | |||||
−40.7091 | + | 151.928i | −0.419681 | + | 1.56627i | 0.355590 | + | 0.934642i | ||
−0.775271 | + | 0.631629i | ||||||||
−62.0742 | + | 62.0742i | −0.633411 | + | 0.633411i | |||||
−20.1737 | − | 14.4202i | −0.203775 | − | 0.145659i | |||||
−197.268 | − | 104.271i | −1.97268 | − | 1.04271i | |||||
41.2983 | + | 71.5307i | 0.408894 | + | 0.708225i | 0.994766 | − | 0.102178i | ||
−0.585872 | + | 0.810404i | ||||||||
−94.0438 | − | 103.638i | −0.921998 | − | 1.01606i | |||||
−12.9609 | − | 48.3706i | −0.125834 | − | 0.469617i | 0.874034 | − | 0.485864i | ||
−0.999868 | + | 0.0162466i | ||||||||
145.348 | + | 83.9166i | 1.39757 | + | 0.806890i | |||||
74.3375 | + | 2.21744i | 0.707976 | + | 0.0211184i | |||||
−79.3765 | − | 137.484i | −0.748835 | − | 1.29702i | |||||
−57.4669 | − | 57.4669i | −0.537074 | − | 0.537074i | 0.385595 | − | 0.922668i | ||
−0.922668 | + | 0.385595i | ||||||||
27.9654 | + | 239.353i | 0.258939 | + | 2.21623i | |||||
− | 145.852i | − | 1.33809i | −0.743220 | − | 0.669047i | ||||
0.743220 | − | 0.669047i | ||||||||
−47.5932 | + | 13.7101i | −0.432665 | + | 0.124638i | |||||
29.9362 | − | 46.4900i | 0.269696 | − | 0.418829i | |||||
133.897 | − | 35.8775i | 1.19551 | − | 0.320335i | |||||
14.0319 | + | 52.3679i | 0.124176 | + | 0.463432i | 0.999809 | − | 0.0195453i | ||
−0.875633 | + | 0.482978i | ||||||||
−16.8313 | + | 346.790i | −0.147643 | + | 3.04202i | |||||
0.959422 | + | 3.33053i | 0.00834280 | + | 0.0289611i | |||||
310.569 | 2.67732 | |||||||||
−54.1950 | − | 65.8778i | −0.463205 | − | 0.563058i | |||||
108.204 | − | 108.204i | 0.916980 | − | 0.916980i | |||||
55.7139 | − | 32.1664i | 0.468184 | − | 0.270306i | |||||
225.959 | + | 139.602i | 1.88299 | + | 1.16335i | |||||
56.7042 | − | 98.2145i | 0.468630 | − | 0.811690i | |||||
45.6304 | − | 12.2266i | 0.374019 | − | 0.100218i | |||||
115.492 | + | 37.0328i | 0.938956 | + | 0.301080i | |||||
−198.619 | + | 114.673i | −1.60177 | + | 0.924780i | |||||
124.804 | − | 6.99982i | 0.998431 | − | 0.0559986i | |||||
−159.671 | − | 15.5357i | −1.26723 | − | 0.123299i | |||||
50.4054 | + | 50.4054i | 0.396893 | + | 0.396893i | 0.877136 | − | 0.480243i | ||
−0.480243 | + | 0.877136i | ||||||||
−132.420 | − | 35.4818i | −1.03453 | − | 0.277202i | |||||
−0.554864 | + | 11.4324i | −0.00430127 | + | 0.0886230i | |||||
−170.352 | + | 3.18185i | −1.31040 | + | 0.0244758i | |||||
−89.6936 | + | 155.354i | −0.684684 | + | 1.18591i | 0.288852 | + | 0.957374i | ||
−0.973536 | + | 0.228534i | ||||||||
72.1027 | − | 15.6173i | 0.546232 | − | 0.118313i | |||||
−154.167 | − | 41.3089i | −1.15915 | − | 0.310593i | |||||
− | 167.481i | − | 1.24986i | |||||||
−82.6198 | − | 106.766i | −0.611998 | − | 0.790859i | |||||
229.756 | 1.68938 | |||||||||
−36.5154 | + | 136.277i | −0.266536 | + | 0.994725i | 0.694768 | + | 0.719234i | ||
−0.961304 | + | 0.275491i | ||||||||
−1.58268 | − | 7.30699i | −0.0114687 | − | 0.0529492i | |||||
236.063 | + | 136.291i | 1.69829 | + | 0.980510i | 0.947381 | + | 0.320108i | ||
0.750912 | + | 0.660402i | ||||||||
−153.504 | + | 159.347i | −1.09646 | + | 1.13820i | |||||
11.4991 | + | 0.558104i | 0.0815540 | + | 0.00395818i | |||||
106.134 | − | 396.099i | 0.747426 | − | 2.78943i | |||||
−18.4665 | + | 18.4665i | −0.129137 | + | 0.129137i | |||||
−204.708 | − | 146.326i | −1.42158 | − | 1.01615i | |||||
−149.024 | + | 89.7906i | −1.02775 | + | 0.619245i | |||||
−47.7882 | − | 82.7716i | −0.327317 | − | 0.566929i | |||||
−22.3673 | + | 69.7552i | −0.152158 | + | 0.474525i | |||||
42.5772 | + | 158.900i | 0.287684 | + | 1.07365i | |||||
174.004 | + | 100.461i | 1.16781 | + | 0.674235i | 0.953163 | − | 0.302457i | ||
0.214646 | + | 0.976692i | ||||||||
−269.621 | − | 3.00491i | −1.79747 | − | 0.0200327i | |||||
58.6560 | + | 101.595i | 0.388450 | + | 0.672816i | 0.992241 | − | 0.124327i | ||
−0.603791 | + | 0.797143i | ||||||||
−403.057 | − | 403.057i | −2.65169 | − | 2.65169i | |||||
−109.343 | − | 41.0063i | −0.714659 | − | 0.268015i | |||||
49.1129i | 0.318915i | |||||||||
62.1517 | − | 112.449i | 0.400979 | − | 0.725475i | |||||
253.491 | + | 12.3030i | 1.62494 | + | 0.0788657i | |||||
−205.058 | + | 54.9450i | −1.30610 | + | 0.349968i | −0.843753 | − | 0.536731i | ||
−0.462346 | + | 0.886700i | ||||||||
−19.6684 | − | 73.4036i | −0.124484 | − | 0.464580i | |||||
−111.378 | − | 71.7197i | −0.700493 | − | 0.451067i | |||||
−142.640 | + | 41.0902i | −0.891500 | + | 0.256814i | |||||
3.43688 | 0.0213471 | |||||||||
162.359 | + | 241.748i | 1.00221 | + | 1.49227i | |||||
61.1545 | − | 61.1545i | 0.375181 | − | 0.375181i | −0.494179 | − | 0.869360i | ||
0.869360 | + | 0.494179i | ||||||||
−312.486 | + | 180.414i | −1.90540 | + | 1.10008i | |||||
−30.0826 | + | 28.3399i | −0.182319 | + | 0.171757i | |||||
27.4847 | − | 47.6049i | 0.165571 | − | 0.286777i | |||||
234.945 | − | 62.9533i | 1.40686 | − | 0.376966i | 0.526054 | − | 0.850451i | ||
0.880802 | + | 0.473486i | ||||||||
195.044 | − | 176.988i | 1.16098 | − | 1.05350i | |||||
68.5552 | − | 39.5803i | 0.405652 | − | 0.234203i | |||||
−199.783 | + | 120.374i | −1.17519 | + | 0.708084i | |||||
119.882 | + | 263.755i | 0.701062 | + | 1.54243i | |||||
−24.0785 | − | 24.0785i | −0.139991 | − | 0.139991i | |||||
−16.3284 | − | 4.37517i | −0.0943835 | − | 0.0252900i | 0.211318 | − | 0.977417i | ||
−0.305702 | + | 0.952127i | ||||||||
333.734 | − | 171.673i | 1.91801 | − | 0.986629i | |||||
27.5875 | − | 120.842i | 0.157643 | − | 0.690525i | |||||
−38.5171 | + | 66.7135i | −0.218847 | + | 0.379054i | |||||
38.9891 | − | 121.593i | 0.220277 | − | 0.686964i | |||||
321.015 | + | 86.0157i | 1.80345 | + | 0.483234i | |||||
274.512i | 1.53359i | 0.641895 | + | 0.766793i | ||||||
−0.641895 | + | 0.766793i | ||||||||
400.404 | + | 31.4226i | 2.22447 | + | 0.174570i | |||||
−261.649 | −1.44557 | −0.722787 | − | 0.691070i | ||||||
−0.722787 | + | 0.691070i | ||||||||
−43.7279 | + | 163.195i | −0.240263 | + | 0.896674i | |||||
29.1924 | − | 26.4899i | 0.159521 | − | 0.144753i | |||||
10.6299 | + | 6.13718i | 0.0577712 | + | 0.0333542i | |||||
−66.3709 | − | 63.9370i | −0.358762 | − | 0.345606i | |||||
−150.046 | + | 233.017i | −0.806701 | + | 1.25278i | |||||
−9.25307 | + | 34.5329i | −0.0494817 | + | 0.184668i | |||||
−24.2191 | + | 24.2191i | −0.128825 | + | 0.128825i | |||||
−124.411 | + | 49.4189i | −0.658261 | + | 0.261476i | |||||
561.646 | + | 139.305i | 2.95603 | + | 0.733183i | |||||
−89.7939 | − | 155.528i | −0.470125 | − | 0.814280i | 0.529291 | − | 0.848440i | ||
−0.999416 | + | 0.0341597i | ||||||||
−14.9562 | + | 3.23948i | −0.0778968 | + | 0.0168723i | |||||
6.95596 | + | 25.9600i | 0.0360412 | + | 0.134508i | 0.981602 | − | 0.190937i | ||
−0.945561 | + | 0.325445i | ||||||||
−489.716 | − | 282.738i | −2.52431 | − | 1.45741i | |||||
−125.192 | + | 67.3849i | −0.642012 | + | 0.345564i | |||||
−108.967 | − | 188.737i | −0.555956 | − | 0.962944i | |||||
118.588 | + | 118.588i | 0.601967 | + | 0.601967i | 0.940834 | − | 0.338867i | ||
−0.338867 | + | 0.940834i | ||||||||
68.8481 | − | 56.6385i | 0.347718 | − | 0.286053i | |||||
− | 23.9129i | − | 0.120166i | −0.998193 | − | 0.0600828i | ||||
0.998193 | − | 0.0600828i | ||||||||
301.111 | − | 324.489i | 1.50555 | − | 1.62244i | |||||
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44.6524 | + | 166.645i | 0.219963 | + | 0.820912i | |||||
308.948 | − | 158.923i | 1.51445 | − | 0.779035i | |||||
97.7829 | − | 176.915i | 0.476990 | − | 0.862999i | |||||
180.035 | 0.873956 | |||||||||
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76.8130 | − | 44.3480i | 0.367526 | − | 0.212191i | |||||
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0.981062 | + | 0.193694i | ||||||||
380.685 | − | 102.004i | 1.79568 | − | 0.481152i | |||||
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253.036 | − | 146.090i | 1.18241 | − | 0.682665i | |||||
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506.496 | + | 135.715i | 2.32338 | + | 0.622547i | |||||
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133.588 | + | 147.217i | 0.601750 | + | 0.663141i | |||||
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147.195i | 0.657119i | |||||||||
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48.9929 | − | 182.844i | 0.215828 | − | 0.805480i | −0.770046 | − | 0.637988i | ||
0.985874 | − | 0.167491i | ||||||||
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−12.4585 | + | 0.232702i | −0.0541676 | + | 0.00101175i | |||||
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191.869 | − | 191.869i | 0.823473 | − | 0.823473i | −0.163131 | − | 0.986604i | ||
0.986604 | + | 0.163131i | ||||||||
279.200 | − | 126.902i | 1.19316 | − | 0.542315i | |||||
4.61917 | − | 18.6235i | 0.0196561 | − | 0.0792488i | |||||
189.945 | + | 328.994i | 0.804850 | + | 1.39404i | |||||
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106.787 | + | 184.961i | 0.443101 | + | 0.767473i | 0.997918 | − | 0.0644993i | ||
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288.303 | + | 288.303i | 1.19133 | + | 1.19133i | |||||
212.752 | + | 117.412i | 0.875522 | + | 0.483178i | |||||
117.276i | 0.480640i | |||||||||
106.854 | + | 59.0594i | 0.436139 | + | 0.241059i | |||||
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294.723 | − | 78.9708i | 1.19321 | − | 0.319720i | |||||
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2.22363 | − | 45.8155i | 0.00893025 | − | 0.183998i | |||||
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48.4611 | 0.193072 | 0.0965360 | − | 0.995329i | ||||||
0.0965360 | + | 0.995329i | ||||||||
139.848 | − | 372.903i | 0.554952 | − | 1.47978i | |||||
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236.231 | − | 409.164i | 0.922777 | − | 1.59830i | |||||
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101.827 | − | 410.543i | 0.391641 | − | 1.57901i | |||||
182.114 | − | 254.775i | 0.697755 | − | 0.976151i | |||||
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286.904 | − | 496.932i | 1.07859 | − | 1.86816i | |||||
271.037 | − | 58.7060i | 1.01512 | − | 0.219873i | |||||
401.614 | + | 107.612i | 1.49856 | + | 0.401538i | |||||
271.965i | 1.01102i | 0.862821 | + | 0.505510i | ||||||
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447.640 | − | 187.565i | 1.65793 | − | 0.694686i | |||||
283.330 | 1.04550 | 0.522749 | − | 0.852487i | ||||||
0.522749 | + | 0.852487i | ||||||||
−93.8935 | + | 350.415i | −0.345197 | + | 1.28829i | |||||
29.8444 | + | 137.787i | 0.109320 | + | 0.504715i | |||||
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36.6447 | + | 58.3260i | 0.133254 | + | 0.212094i | |||||
18.5389 | + | 0.899774i | 0.0671698 | + | 0.00326005i | |||||
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124.137 | + | 463.286i | 0.438647 | + | 1.63705i | 0.732184 | + | 0.681107i | ||
−0.293537 | + | 0.955948i | ||||||||
881.639 | + | 509.015i | 3.10436 | + | 1.79230i | |||||
469.934 | − | 111.013i | 1.64889 | − | 0.389520i | |||||
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206.342 | − | 169.749i | 0.716467 | − | 0.589407i | |||||
− | 120.637i | − | 0.417430i | |||||||
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229.189 | − | 61.4111i | 0.784895 | − | 0.210312i | |||||
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0.816499 | − | 0.577346i | ||||||||
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29.4685 | − | 68.3073i | 0.0992207 | − | 0.229991i | |||||
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180.446 | − | 644.612i | 0.601487 | − | 2.14871i | |||||
9.45814 | − | 16.3820i | 0.0314224 | − | 0.0544252i | |||||
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779.443 | − | 450.011i | 2.56396 | − | 1.48030i | |||||
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244.144 | − | 341.555i | 0.797857 | − | 1.11619i | |||||
364.680 | + | 364.680i | 1.18788 | + | 1.18788i | 0.977652 | + | 0.210232i | ||
0.210232 | + | 0.977652i | ||||||||
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133.592 | − | 68.7200i | 0.432337 | − | 0.222395i | |||||
332.664 | + | 320.465i | 1.07311 | + | 1.03376i | |||||
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0.652898 | + | 0.757446i | ||||||||
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343.429 | + | 92.0214i | 1.09722 | + | 0.293998i | 0.761631 | − | 0.648011i | ||
0.335586 | + | 0.942010i | ||||||||
− | 763.222i | − | 2.43064i | |||||||
40.7078 | + | 219.367i | 0.129231 | + | 0.696402i | |||||
188.657 | 0.597017 | |||||||||
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0.954575 | + | 0.297971i | ||||||||
352.696 | − | 320.045i | 1.10911 | − | 1.00643i | |||||
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0.476303 | + | 25.5006i | 0.00148845 | + | 0.0796893i | |||||
131.998 | − | 204.989i | 0.411209 | − | 0.638595i | |||||
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295.356 | − | 295.356i | 0.914414 | − | 0.914414i | |||||
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69.8340 | + | 226.435i | 0.214874 | + | 0.696723i | |||||
155.465 | + | 269.273i | 0.476886 | + | 0.825992i | |||||
427.640 | − | 92.6260i | 1.30777 | − | 0.283260i | |||||
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96.8582 | + | 167.763i | 0.292623 | + | 0.506838i | 0.974429 | − | 0.224695i | ||
−0.681806 | + | 0.731533i | ||||||||
96.4953 | + | 96.4953i | 0.290649 | + | 0.290649i | |||||
155.321 | + | 58.2491i | 0.466428 | + | 0.174922i | |||||
874.462i | 2.61815i | |||||||||
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190.227 | + | 369.802i | 0.566151 | + | 1.10060i | |||||
88.6729 | − | 23.7598i | 0.263124 | − | 0.0705039i | −0.124845 | − | 0.992176i | ||
0.387969 | + | 0.921672i | ||||||||
73.6588 | + | 274.898i | 0.217925 | + | 0.813309i | |||||
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70.8008 | 0.207627 | |||||||||
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257.393 | − | 257.393i | 0.750417 | − | 0.750417i | |||||
58.5061 | − | 33.7785i | 0.170076 | − | 0.0981933i | |||||
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30.3870 | − | 52.6318i | 0.0878236 | − | 0.152115i | |||||
5.84253 | − | 1.56550i | 0.0168372 | − | 0.00451153i | −0.250391 | − | 0.968145i | ||
0.267228 | + | 0.963633i | ||||||||
197.232 | + | 910.591i | 0.566759 | + | 2.61664i | |||||
67.8704 | − | 39.1850i | 0.194471 | − | 0.112278i | −0.399603 | − | 0.916688i | ||
0.594074 | + | 0.804410i | ||||||||
393.973 | + | 208.245i | 1.12564 | + | 0.594986i | |||||
158.737 | − | 200.737i | 0.452242 | − | 0.571901i | |||||
−57.8408 | − | 57.8408i | −0.164320 | − | 0.164320i | |||||
38.2322 | + | 10.2443i | 0.108307 | + | 0.0290207i | 0.312565 | − | 0.949896i | ||
−0.204259 | + | 0.978917i | ||||||||
385.971 | + | 248.538i | 1.09031 | + | 0.702084i | |||||
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129.694 | + | 142.926i | 0.363290 | + | 0.400353i | |||||
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0.986725 | − | 0.162398i | ||||||||
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243.464 | − | 908.619i | 0.672552 | − | 2.51000i | |||||
323.977 | + | 103.884i | 0.892499 | + | 0.286183i | |||||
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64.8269 | + | 126.024i | 0.177123 | + | 0.344328i | |||||
112.479 | − | 419.779i | 0.306483 | − | 1.14381i | −0.625177 | − | 0.780483i | ||
0.931661 | − | 0.363329i | ||||||||
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283.790 | − | 170.991i | 0.766999 | − | 0.462137i | |||||
109.467 | + | 189.602i | 0.295059 | + | 0.511058i | |||||
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0.256647 | − | 0.966505i | ||||||||
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99.7824 | + | 361.481i | 0.266086 | + | 0.963949i | |||||
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0.919571 | − | 0.392923i | ||||||||
−694.925 | + | 1257.30i | −1.82875 | + | 3.30869i | |||||
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623.648 | − | 167.106i | 1.63259 | − | 0.437450i | |||||
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0.655212 | − | 0.755445i | ||||||||
19.9375 | − | 410.790i | 0.0519206 | − | 1.06977i | |||||
65.6351 | − | 18.9074i | 0.170481 | − | 0.0491102i | |||||
−96.6228 | −0.250318 | |||||||||
−33.8722 | + | 5.63346i | −0.0875251 | + | 0.0145567i | |||||
992.656 | − | 992.656i | 2.55839 | − | 2.55839i | |||||
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0.223905 | + | 0.974611i | ||||||||
−117.514 | − | 497.452i | −0.301318 | − | 1.27552i | |||||
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417.634 | − | 111.905i | 1.06539 | − | 0.285471i | |||||
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−90.5255 | + | 54.5440i | −0.229178 | + | 0.138086i | |||||
91.5801 | + | 201.488i | 0.231263 | + | 0.508808i | |||||
120.533 | + | 120.533i | 0.303609 | + | 0.303609i | 0.842424 | − | 0.538815i | ||
−0.538815 | + | 0.842424i | ||||||||
83.0416 | + | 22.2509i | 0.208647 | + | 0.0559069i | |||||
23.2117 | − | 478.253i | 0.0581748 | − | 1.19863i | |||||
371.844 | + | 591.850i | 0.929610 | + | 1.47962i | |||||
226.669 | − | 392.602i | 0.565259 | − | 0.979057i | −0.431766 | − | 0.901985i | ||
0.997026 | − | 0.0770720i | ||||||||
491.056 | − | 106.362i | 1.22153 | − | 0.264581i | |||||
235.260 | + | 63.0377i | 0.583772 | + | 0.156421i | |||||
− | 737.193i | − | 1.82473i | |||||||
260.570 | − | 310.046i | 0.643382 | − | 0.765545i | |||||
−620.251 | −1.52771 | |||||||||
13.1439 | − | 49.0538i | 0.0322946 | − | 0.120525i | |||||
145.911 | + | 673.648i | 0.357624 | + | 1.65110i | |||||
427.158 | + | 246.620i | 1.04440 | + | 0.602982i | 0.921075 | − | 0.389385i | ||
0.123320 | + | 0.992367i | ||||||||
523.379 | + | 504.186i | 1.27653 | + | 1.22972i | |||||
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20.4191 | − | 9.28087i | 0.0493214 | − | 0.0224176i | |||||
−74.2008 | − | 18.4040i | −0.178797 | − | 0.0443470i | |||||
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−249.691 | + | 778.693i | −0.598778 | + | 1.86737i | |||||
82.5314 | + | 308.011i | 0.197444 | + | 0.736870i | |||||
−22.7963 | − | 13.1615i | −0.0544066 | − | 0.0314116i | 0.472550 | − | 0.881304i | ||
−0.526957 | + | 0.849892i | ||||||||
−564.694 | − | 348.879i | −1.34451 | − | 0.830664i | |||||
243.419 | + | 421.613i | 0.578192 | + | 1.00146i | 0.995687 | + | 0.0927780i | ||
−0.417495 | + | 0.908679i | ||||||||
346.284 | + | 346.284i | 0.820579 | + | 0.820579i | |||||
5.66635 | + | 34.0700i | 0.0133956 | + | 0.0805437i | |||||
781.894i | 1.84409i | |||||||||
237.782 | + | 220.650i | 0.559486 | + | 0.519177i | |||||
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0.0850137 | + | 0.996380i | ||||||||
299.025 | − | 693.133i | 0.692189 | − | 1.60447i | |||||
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396.671 | − | 229.018i | 0.913989 | − | 0.527692i | |||||
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0.384903 | + | 0.922957i | ||||||||
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291.806i | 0.649901i | 0.945731 | + | 0.324951i | ||||||
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−162.417 | − | 792.439i | −0.360926 | − | 1.76098i | |||||
111.390 | 0.246985 | |||||||||
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589.367 | + | 340.271i | 1.29817 | + | 0.749497i | |||||
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925.800 | − | 1437.74i | 2.03026 | − | 3.15293i | |||||
121.316 | − | 452.757i | 0.265462 | − | 0.990716i | −0.696506 | − | 0.717551i | ||
0.961967 | − | 0.273165i | ||||||||
376.313 | − | 376.313i | 0.821645 | − | 0.821645i | |||||
50.7907 | − | 346.636i | 0.110655 | − | 0.755199i | |||||
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0.459293 | − | 0.888285i | ||||||||
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0.0830044 | + | 0.996549i | ||||||||
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369.171 | + | 110.817i | 0.793917 | + | 0.238316i | |||||
487.764 | + | 844.831i | 1.04670 | + | 1.81294i | |||||
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124.911 | + | 751.052i | 0.266904 | + | 1.60481i | |||||
230.970i | 0.492474i | |||||||||
60.3749 | + | 33.3699i | 0.128457 | + | 0.0709998i | |||||
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139.550 | − | 372.109i | 0.292558 | − | 0.780104i | |||||
333.786 | − | 333.786i | 0.698297 | − | 0.698297i | |||||
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0.303632 | + | 0.952789i | ||||||||
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87.3504 | − | 151.295i | 0.181602 | − | 0.314543i | |||||
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2.18265 | + | 10.0770i | 0.00451894 | + | 0.0208633i | |||||
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218.143 | + | 140.469i | 0.446100 | + | 0.287257i | |||||
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0.739582 | + | 0.673066i | ||||||||
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1096.96i | 2.22056i | |||||||||
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718.435 | 1.44846 | |||||||||
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157.033 | + | 50.3532i | 0.315327 | + | 0.101111i | |||||
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333.786 | + | 648.881i | 0.666239 | + | 1.29517i | |||||
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0.374234 | + | 0.927334i | ||||||||
642.796 | + | 459.472i | 1.27539 | + | 0.911651i | |||||
213.135 | + | 353.735i | 0.422049 | + | 0.700466i | |||||
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159.587 | + | 175.868i | 0.314768 | + | 0.346880i | |||||
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679.279 | + | 392.182i | 1.33454 | + | 0.770495i | 0.985991 | − | 0.166797i | ||
0.348546 | + | 0.937292i | ||||||||
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65.9040 | + | 114.149i | 0.128971 | + | 0.223384i | |||||
813.324 | + | 813.324i | 1.58852 | + | 1.58852i | |||||
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− | 1675.66i | − | 3.26003i | |||||||
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55.3070 | − | 85.8900i | 0.107184 | − | 0.166453i | |||||
10.2133 | − | 2.73664i | 0.0197549 | − | 0.00529330i | |||||
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2.45844 | − | 50.6534i | 0.00473687 | − | 0.0975981i | |||||
734.448 | + | 405.938i | 1.41240 | + | 0.780650i | |||||
763.749 | 1.46593 | 0.732964 | − | 0.680267i | ||||||
0.732964 | + | 0.680267i | ||||||||
715.292 | + | 869.489i | 1.37029 | + | 1.66569i | |||||
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0.380445 | + | 0.924803i | ||||||||
1386.57 | − | 800.535i | 2.64612 | − | 1.52774i | |||||
371.830 | + | 4.14403i | 0.708247 | + | 0.00789338i | |||||
194.842 | − | 337.476i | 0.370421 | − | 0.641589i | |||||
322.061 | − | 86.2959i | 0.611121 | − | 0.163749i | |||||
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457.711 | − | 264.260i | 0.865239 | − | 0.499546i | |||||
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381.272 | + | 37.0970i | 0.718026 | + | 0.0698625i | |||||
1007.28 | + | 1007.28i | 1.89339 | + | 1.89339i | |||||
370.133 | + | 99.1769i | 0.694434 | + | 0.186073i | |||||
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67.2782i | 0.124820i | |||||||||
162.152 | + | 1193.94i | 0.300281 | + | 2.21101i | |||||
120.576 | 0.222876 | 0.111438 | − | 0.993771i | ||||||
0.111438 | + | 0.993771i | ||||||||
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59.6213 | − | 222.510i | 0.108997 | − | 0.406782i | −0.889771 | − | 0.456407i | ||
0.998768 | + | 0.0496252i | ||||||||
890.397 | − | 890.397i | 1.62481 | − | 1.62481i | |||||
96.2077 | + | 68.7695i | 0.175242 | + | 0.125263i | |||||
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560.075 | + | 970.078i | 1.01647 | + | 1.76058i | |||||
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27.1244 | + | 101.230i | 0.0490496 | + | 0.183056i | |||||
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145.314 | − | 235.205i | 0.261827 | − | 0.423792i | |||||
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−0.216586 | − | 0.976264i | ||||||||
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36.1626i | 0.0646915i | |||||||||
666.017 | − | 191.859i | 1.18932 | − | 0.342605i | |||||
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876.788 | − | 234.935i | 1.56012 | − | 0.418033i | |||||
71.6752 | + | 267.496i | 0.127309 | + | 0.475125i | 0.999911 | − | 0.0133066i | ||
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−86.3915 | − | 55.6299i | −0.153176 | − | 0.0986346i | |||||
75.0372 | + | 260.483i | 0.132809 | + | 0.461033i | |||||
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830.591 | − | 479.542i | 1.45974 | − | 0.842780i | 0.460740 | − | 0.887535i | ||
0.998998 | + | 0.0447548i | ||||||||
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0.602933 | + | 0.797792i | ||||||||
225.145 | − | 60.3275i | 0.393611 | − | 0.105468i | |||||
398.983 | − | 362.047i | 0.696306 | − | 0.631845i | |||||
624.080 | − | 360.313i | 1.08725 | − | 0.627723i | |||||
5.10726 | + | 16.5602i | 0.00888219 | + | 0.0288003i | |||||
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670.378 | + | 670.378i | 1.16183 | + | 1.16183i | 0.984074 | + | 0.177761i | ||
0.177761 | + | 0.984074i | ||||||||
418.933 | + | 112.253i | 0.724797 | + | 0.194209i | |||||
−71.6975 | + | 36.8813i | −0.123830 | + | 0.0636983i | |||||
1552.57 | − | 28.9992i | 2.67685 | − | 0.0499986i | |||||
−37.9038 | + | 65.6513i | −0.0652388 | + | 0.112997i | |||||
517.987 | − | 1615.41i | 0.890013 | − | 2.77562i | |||||
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470.735i | 0.806053i | |||||||||
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729.675 | 1.24518 | |||||||||
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−0.991289 | + | 0.131705i | ||||||||
484.177 | − | 439.354i | 0.823431 | − | 0.747201i | |||||
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530.820 | − | 551.027i | 0.899696 | − | 0.933945i | |||||
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133.375 | − | 497.762i | 0.225295 | − | 0.840814i | |||||
292.884 | − | 292.884i | 0.493902 | − | 0.493902i | −0.415631 | − | 0.909533i | ||
0.909533 | + | 0.415631i | ||||||||
209.788 | + | 165.894i | 0.353178 | + | 0.279283i | |||||
275.517 | − | 166.006i | 0.463054 | − | 0.279002i | |||||
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70.1130 | − | 15.1863i | 0.117442 | − | 0.0254377i | |||||
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−0.816972 | + | 0.576677i | ||||||||
1142.63 | + | 676.788i | 1.90438 | + | 1.12798i | |||||
−99.8075 | − | 172.872i | −0.166069 | − | 0.287640i | 0.770965 | − | 0.636877i | ||
−0.937034 | + | 0.349237i | ||||||||
48.0883 | + | 48.0883i | 0.0798810 | + | 0.0798810i | |||||
323.782 | − | 266.362i | 0.536952 | − | 0.441728i | |||||
− | 1047.04i | − | 1.73350i | |||||||
274.301 | − | 496.282i | 0.453390 | − | 0.820301i | |||||
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−0.509159 | + | 0.860672i | ||||||||
247.352 | + | 923.131i | 0.406829 | + | 1.51831i | |||||
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226.970 | − | 65.3831i | 0.372083 | − | 0.107185i | |||||
36.3737 | 0.0595314 | |||||||||
662.167 | + | 804.911i | 1.08197 | + | 1.31521i | |||||
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0.680796 | + | 0.732473i | ||||||||
−1605.75 | + | 927.078i | −2.61522 | + | 1.50990i | |||||
580.815 | + | 174.348i | 0.944415 | + | 0.283492i | |||||
120.946 | − | 209.485i | 0.196341 | − | 0.340072i | |||||
253.302 | − | 67.8722i | 0.410539 | − | 0.110004i | −0.0476380 | − | 0.998865i | ||
0.458177 | + | 0.888861i | ||||||||
114.334 | + | 527.864i | 0.185007 | + | 0.854149i | |||||
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0.118235 | + | 0.992986i | ||||||||
−982.214 | + | 591.809i | −1.58422 | + | 0.954531i | |||||
11.6091 | − | 14.6808i | 0.0186942 | − | 0.0236405i | |||||
−521.044 | − | 521.044i | −0.837691 | − | 0.837691i | |||||
−442.707 | − | 118.623i | −0.710605 | − | 0.190406i | |||||
−668.417 | − | 430.412i | −1.07118 | − | 0.689764i | |||||
623.257 | − | 46.6465i | 0.997211 | − | 0.0746344i | |||||
−639.119 | + | 1106.99i | −1.02096 | + | 1.76835i | |||||
178.810 | + | 197.053i | 0.285184 | + | 0.314278i | |||||
1830.18 | + | 490.396i | 2.91431 | + | 0.780886i | |||||
− | 239.158i | − | 0.380219i | |||||||
−799.665 | − | 62.7556i | −1.26931 | − | 0.0996121i | |||||
263.490 | 0.417576 | 0.208788 | − | 0.977961i | ||||||
0.208788 | + | 0.977961i | ||||||||
−96.8714 | + | 361.529i | −0.153277 | + | 0.572039i | |||||
389.133 | + | 124.777i | 0.614744 | + | 0.197120i | |||||
−80.4505 | − | 46.4481i | −0.126894 | − | 0.0732620i | |||||
256.690 | + | 247.276i | 0.404236 | + | 0.389412i | |||||
540.838 | + | 1051.39i | 0.850375 | + | 1.65313i | |||||
−59.9014 | + | 223.555i | −0.0940367 | + | 0.350950i | |||||
243.730 | − | 243.730i | 0.382023 | − | 0.382023i | |||||
934.554 | − | 424.773i | 1.46253 | − | 0.664746i | |||||
−665.298 | − | 165.014i | −1.03953 | − | 0.257834i | |||||
−459.262 | − | 795.464i | −0.716477 | − | 1.24097i | −0.962387 | − | 0.271682i | ||
0.245911 | − | 0.969293i | ||||||||
589.034 | + | 649.127i | 0.917498 | + | 1.01110i | |||||
10.9456 | + | 40.8497i | 0.0170228 | + | 0.0635298i | 0.973915 | − | 0.226914i | ||
−0.956892 | + | 0.290444i | ||||||||
−26.5652 | − | 15.3374i | −0.0412504 | − | 0.0238159i | |||||
−1.70635 | + | 57.2037i | −0.00264550 | + | 0.0886879i | |||||
750.843 | + | 1300.50i | 1.16230 | + | 2.01316i | |||||
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−0.716757 | + | 0.697323i | ||||||||
−97.1884 | − | 1430.97i | −0.149982 | − | 2.20829i | |||||
− | 117.275i | − | 0.180701i | |||||||
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206.927 | − | 321.350i | 0.317860 | − | 0.493626i | |||||
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137.591 | + | 513.495i | 0.210705 | + | 0.786363i | 0.987634 | + | 0.156775i | ||
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1130.31 | 1.72303 | |||||||||
84.0155 | − | 224.027i | 0.127877 | − | 0.340984i | |||||
48.3691 | − | 48.3691i | 0.0735093 | − | 0.0735093i | |||||
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0.449997 | + | 0.893030i | ||||||||
358.992 | − | 84.8054i | 0.543928 | − | 0.128493i | |||||
11.3687 | − | 19.6912i | 0.0171993 | − | 0.0297900i | −0.857298 | − | 0.514821i | ||
0.874497 | + | 0.485031i | ||||||||
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58.3528 | − | 1202.30i | 0.0872240 | − | 1.79716i | |||||
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18.1021 | − | 31.3537i | 0.0269777 | − | 0.0467268i | |||||
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619.582 | + | 166.017i | 0.920628 | + | 0.246681i | 0.687854 | − | 0.725849i | ||
0.232774 | + | 0.972531i | ||||||||
330.040i | 0.489673i | |||||||||
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−0.983402 | + | 0.181440i | ||||||||
−123.783 | − | 571.486i | −0.182570 | − | 0.842900i | |||||
675.360 | + | 389.919i | 0.994639 | + | 0.574255i | |||||
1148.58 | − | 21.4534i | 1.68909 | − | 0.0315490i | |||||
567.214 | + | 27.5294i | 0.832913 | + | 0.0404250i | |||||
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599.384 | − | 599.384i | 0.877576 | − | 0.877576i | −0.115708 | − | 0.993283i | ||
0.993283 | + | 0.115708i | ||||||||
250.413 | − | 2573.67i | 0.366101 | − | 3.76267i | |||||
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654.336 | + | 1133.34i | 0.953842 | + | 1.65210i | |||||
135.597 | − | 422.878i | 0.197376 | − | 0.615543i | |||||
27.6082 | + | 103.035i | 0.0401282 | + | 0.149761i | |||||
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0.495583 | − | 0.868561i | ||||||||
106.685 | + | 106.685i | 0.154169 | + | 0.154169i | |||||
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21.7458i | 0.0313340i | |||||||||
1192.83 | + | 659.293i | 1.71631 | + | 0.948624i | |||||
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506.696 | − | 135.769i | 0.726967 | − | 0.194790i | |||||
72.9231 | + | 272.153i | 0.104474 | + | 0.389904i | |||||
684.413 | + | 440.713i | 0.979131 | + | 0.630491i | |||||
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549.388 | + | 738.026i | 0.782604 | + | 1.05132i | |||||
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57.5377 | + | 1.71631i | 0.0816137 | + | 0.00243448i | |||||
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395.563 | − | 105.991i | 0.559495 | − | 0.149916i | |||||
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−0.999948 | + | 0.0101629i | ||||||||
493.594 | − | 1990.06i | 0.695203 | − | 2.80290i | |||||
110.627 | − | 154.765i | 0.155593 | − | 0.217673i | |||||
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17.2056 | + | 4.61022i | 0.0241312 | + | 0.00646594i | |||||
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1225.04 | − | 2121.83i | 1.71095 | − | 2.96345i | |||||
120.273 | − | 375.088i | 0.167745 | − | 0.523135i | |||||
404.918 | + | 108.497i | 0.563952 | + | 0.151110i | |||||
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0.988269 | − | 0.152724i | ||||||||
−1037.02 | − | 712.387i | −1.44031 | − | 0.989426i | |||||
−248.283 | −0.344360 | |||||||||
628.340 | − | 2345.00i | 0.870278 | − | 3.24792i | |||||
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2022.41 | + | 1167.64i | 2.79338 | + | 1.61276i | |||||
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73.8261 | − | 275.523i | 0.101549 | − | 0.378986i | −0.896382 | − | 0.443283i | ||
0.997931 | + | 0.0642969i | ||||||||
588.400 | − | 588.400i | 0.808242 | − | 0.808242i | |||||
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24.7525 | + | 42.8726i | 0.0338611 | + | 0.0586492i | |||||
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0.724006 | − | 0.689793i | ||||||||
1353.09 | + | 781.206i | 1.84345 | + | 1.06431i | |||||
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1147.21i | 1.55238i | 0.630497 | + | 0.776192i | ||||||
−0.630497 | + | 0.776192i | ||||||||
227.686 | + | 790.387i | 0.307684 | + | 1.06809i | |||||
418.712 | + | 813.980i | 0.565064 | + | 1.09849i | |||||
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226.953 | + | 847.001i | 0.305455 | + | 1.13997i | 0.932553 | + | 0.361034i | ||
−0.627098 | + | 0.778941i | ||||||||
1213.83 | − | 624.397i | 1.63150 | − | 0.839244i | |||||
879.246 | + | 485.970i | 1.18020 | + | 0.652308i | |||||
2325.68 | 3.11754 | |||||||||
135.744 | − | 22.5762i | 0.181719 | − | 0.0302225i | |||||
225.628 | − | 225.628i | 0.301642 | − | 0.301642i | |||||
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147.537 | − | 255.542i | 0.196455 | − | 0.340269i | −0.750922 | − | 0.660391i | ||
0.947376 | + | 0.320122i | ||||||||
103.637 | − | 27.7694i | 0.137815 | − | 0.0369274i | |||||
30.7761 | + | 142.088i | 0.0408713 | + | 0.188696i | |||||
1026.88 | − | 592.872i | 1.36192 | − | 0.786303i | |||||
302.715 | + | 502.410i | 0.400947 | + | 0.665444i | |||||
1182.17 | + | 173.217i | 1.56372 | + | 0.229123i | |||||
89.6510 | + | 89.6510i | 0.118429 | + | 0.118429i | 0.763838 | − | 0.645408i | ||
−0.645408 | + | 0.763838i | ||||||||
1034.28 | + | 277.135i | 1.36449 | + | 0.365614i | |||||
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80.6635 | − | 139.713i | 0.105997 | − | 0.183592i | −0.808148 | − | 0.588979i | ||
0.914145 | + | 0.405387i | ||||||||
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1602.86i | 2.09798i | |||||||||
−550.448 | − | 194.786i | −0.719540 | − | 0.254622i | |||||
1542.52 | 2.01373 | |||||||||
104.416 | − | 389.686i | 0.136136 | − | 0.508065i | |||||
1349.70 | + | 432.785i | 1.75742 | + | 0.563522i | |||||
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−0.581823 | + | 0.813316i | ||||||||
4.58589 | + | 245.522i | 0.00595570 | + | 0.318859i | |||||
−639.604 | − | 1243.40i | −0.829578 | − | 1.61270i | |||||
62.0835 | − | 231.699i | 0.0804190 | − | 0.300128i | |||||
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−0.936907 | + | 0.349578i | ||||||||
11.9549 | − | 122.869i | 0.0154456 | − | 0.158745i | |||||
300.204 | − | 567.949i | 0.387361 | − | 0.732837i | |||||
1392.55 | + | 2411.96i | 1.79452 | + | 3.10819i | |||||
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1268.38 | + | 37.8350i | 1.62613 | + | 0.0485064i | |||||
−157.137 | − | 272.169i | −0.201200 | − | 0.348488i | |||||
−22.8655 | − | 22.8655i | −0.0292398 | − | 0.0292398i | |||||
862.659 | + | 372.161i | 1.10174 | + | 0.475301i | |||||
682.690i | 0.870778i | |||||||||
−1019.98 | + | 293.824i | −1.29934 | + | 0.374298i | |||||
1047.48 | − | 1626.70i | 1.33267 | − | 2.06960i | |||||
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−0.353899 | + | 0.935284i | ||||||||
−387.409 | − | 1445.83i | −0.491635 | − | 1.83481i | |||||
15.7635 | − | 324.790i | 0.0199791 | − | 0.411648i | |||||
−105.179 | − | 365.118i | −0.133138 | − | 0.462174i | |||||
268.801 | 0.339824 | |||||||||
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88.0662 | − | 88.0662i | 0.111055 | − | 0.111055i | |||||
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860.450 | − | 230.557i | 1.07961 | − | 0.289281i | 0.325175 | − | 0.945654i | ||
0.754437 | + | 0.656373i | ||||||||
1639.21 | + | 525.620i | 2.05415 | + | 0.658671i | |||||
43.1229 | − | 24.8970i | 0.0539711 | − | 0.0311602i | |||||
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344.253 | + | 757.400i | 0.429779 | + | 0.945568i | |||||
1152.46 | + | 1152.46i | 1.43698 | + | 1.43698i | |||||
−70.7526 | − | 18.9581i | −0.0881104 | − | 0.0236091i | |||||
−60.4680 | + | 1245.88i | −0.0752090 | + | 1.54960i | |||||
17.1814 | − | 0.320916i | 0.0213433 | − | 0.000398654i | |||||
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1412.70 | + | 378.532i | 1.74839 | + | 0.468480i | |||||
− | 1398.60i | − | 1.72880i | −0.502802 | − | 0.864402i | ||||
0.502802 | − | 0.864402i | ||||||||
834.225 | + | 1193.37i | 1.02991 | + | 1.47329i | |||||
−347.451 | −0.428423 | −0.214211 | − | 0.976787i | ||||||
−0.214211 | + | 0.976787i | ||||||||
398.533 | − | 1487.34i | 0.490804 | − | 1.83170i | |||||
179.934 | + | 830.726i | 0.221321 | + | 1.02180i | |||||
158.117 | + | 91.2888i | 0.194247 | + | 0.112148i | |||||
300.009 | − | 311.430i | 0.368109 | − | 0.382122i | |||||
−1087.05 | − | 52.7594i | −1.33217 | − | 0.0646561i | |||||
31.7877 | − | 118.633i | 0.0389079 | − | 0.145206i | |||||
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0.391848 | − | 0.920030i | ||||||||
464.627 | − | 1449.00i | 0.565239 | − | 1.76277i | |||||
65.3381 | + | 243.845i | 0.0793902 | + | 0.296288i | 0.994193 | − | 0.107613i | ||
−0.914803 | + | 0.403901i | ||||||||
−767.914 | − | 443.356i | −0.931935 | − | 0.538053i | |||||
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−379.347 | − | 657.049i | −0.459258 | − | 0.795458i | |||||
1054.44 | + | 1054.44i | 1.27502 | + | 1.27502i | 0.943419 | + | 0.331604i | ||
0.331604 | + | 0.943419i | ||||||||
9.13529 | + | 54.9276i | 0.0110330 | + | 0.0663377i | |||||
− | 819.644i | − | 0.988714i | −0.869259 | − | 0.494357i | ||||
0.869259 | − | 0.494357i | ||||||||
132.955 | − | 240.550i | 0.160186 | − | 0.289819i | |||||
−445.911 | − | 21.6420i | −0.536596 | − | 0.0260434i | |||||
−46.7017 | + | 12.5137i | −0.0561318 | + | 0.0150405i | |||||
82.0024 | + | 306.037i | 0.0984423 | + | 0.367392i | |||||
−2471.80 | − | 1591.66i | −2.96379 | − | 1.90847i | |||||
1168.64 | − | 336.649i | 1.39957 | − | 0.403173i | |||||
−791.631 | −0.946928 | |||||||||
−689.113 | + | 80.5143i | −0.823313 | + | 0.0961939i | |||||
66.9173 | − | 66.9173i | 0.0798536 | − | 0.0798536i | |||||
425.345 | − | 245.573i | 0.506966 | − | 0.292697i | −0.224619 | − | 0.974447i | ||
0.731586 | + | 0.681749i | ||||||||
958.524 | − | 902.996i | 1.14110 | − | 1.07499i | |||||
184.907 | − | 320.269i | 0.219866 | − | 0.380819i | |||||
−1690.62 | + | 453.001i | −2.00786 | + | 0.538006i | |||||
560.932 | − | 509.003i | 0.665399 | − | 0.603799i | |||||
−1052.88 | + | 607.880i | −1.24749 | + | 0.720237i | |||||
339.020 | − | 204.268i | 0.401207 | − | 0.241738i | |||||
−123.586 | − | 12.0247i | −0.146083 | − | 0.0142136i | |||||
−397.594 | − | 397.594i | −0.469415 | − | 0.469415i | |||||
−1192.51 | − | 319.533i | −1.40627 | − | 0.376808i | |||||
−1279.53 | + | 658.190i | −1.50710 | + | 0.775253i | |||||
−987.500 | + | 620.421i | −1.16176 | + | 0.729907i | |||||
6.38831 | − | 11.0649i | 0.00750682 | − | 0.0130022i | |||||
−932.536 | + | 2908.23i | −1.09453 | + | 3.41342i | |||||
336.484 | + | 90.1607i | 0.394472 | + | 0.105698i | 0.450602 | − | 0.892725i | ||
−0.0561301 | + | 0.998423i | ||||||||
− | 234.218i | − | 0.274260i | |||||||
623.932 | + | 1307.35i | 0.729745 | + | 1.52906i | |||||
−1439.05 | −1.68114 | |||||||||
210.885 | − | 787.034i | 0.246074 | − | 0.918359i | −0.726767 | − | 0.686884i | ||
0.972841 | − | 0.231475i | ||||||||
208.592 | − | 189.281i | 0.243114 | − | 0.220607i | |||||
101.706 | + | 58.7201i | 0.118401 | + | 0.0683587i | 0.558031 | − | 0.829820i | ||
−0.439630 | + | 0.898179i | ||||||||
−122.620 | − | 118.123i | −0.142581 | − | 0.137353i | |||||
325.556 | − | 505.579i | 0.378114 | − | 0.587199i | |||||
−68.1886 | + | 254.483i | −0.0791051 | + | 0.295224i | |||||
−148.570 | + | 148.570i | −0.172155 | + | 0.172155i | −0.787926 | − | 0.615770i | ||
0.615770 | + | 0.787926i | ||||||||
628.748 | + | 497.196i | 0.727718 | + | 0.575458i | |||||
−82.0360 | − | 20.3474i | −0.0948394 | − | 0.0235230i | |||||
202.797 | + | 351.254i | 0.234176 | + | 0.405605i | |||||
353.710 | − | 76.6128i | 0.407970 | − | 0.0883654i | |||||
294.304 | + | 1098.36i | 0.339060 | + | 1.26539i | |||||
−50.4374 | − | 29.1200i | −0.0580407 | − | 0.0335098i | |||||
1652.35 | − | 889.380i | 1.89925 | − | 1.02228i | |||||
−220.775 | − | 382.393i | −0.253473 | − | 0.439028i | |||||
−1826.18 | − | 1826.18i | −2.09424 | − | 2.09424i | |||||
−232.244 | − | 1396.41i | −0.266030 | − | 1.59955i | |||||
80.2251i | 0.0917907i | |||||||||
126.630 | − | 606.680i | 0.144720 | − | 0.693349i | |||||
325.609 | + | 632.986i | 0.371700 | + | 0.722587i | |||||
480.790 | − | 128.827i | 0.548221 | − | 0.146895i | 0.0259318 | − | 0.999664i | ||
0.522289 | + | 0.852768i | ||||||||
−104.690 | − | 390.709i | −0.119237 | − | 0.444998i | |||||
541.444 | − | 278.520i | 0.615977 | − | 0.316860i | |||||
−186.322 | + | 337.106i | −0.211730 | + | 0.383075i | |||||
306.447 | 0.347840 | 0.173920 | − | 0.984760i | ||||||
0.173920 | + | 0.984760i | ||||||||
277.430 | − | 739.765i | 0.314547 | − | 0.838736i | |||||
930.058 | − | 930.058i | 1.05329 | − | 1.05329i | 0.0547963 | − | 0.998498i | ||
0.998498 | − | 0.0547963i | ||||||||
950.617 | − | 548.839i | 1.07536 | − | 0.620859i | |||||
183.558 | − | 611.498i | 0.207410 | − | 0.690958i | |||||
286.676 | − | 496.538i | 0.323563 | − | 0.560427i | |||||
−130.986 | + | 35.0975i | −0.147673 | + | 0.0395688i | −0.331898 | − | 0.943315i | ||
0.184225 | + | 0.982884i | ||||||||
−207.265 | − | 956.911i | −0.233407 | − | 1.07760i | |||||
306.078 | − | 176.714i | 0.344295 | − | 0.198779i | |||||
1612.83 | + | 400.029i | 1.81216 | + | 0.449471i | |||||
218.992 | + | 43.0224i | 0.245783 | + | 0.0482855i | |||||
2532.24 | + | 2532.24i | 2.83884 | + | 2.83884i | |||||
−119.326 | − | 31.9733i | −0.133624 | − | 0.0358044i | |||||
−1821.98 | − | 1173.23i | −2.03801 | − | 1.31233i | |||||
25.6324 | + | 1372.32i | 0.0286395 | + | 1.53332i | |||||
−339.852 | + | 588.641i | −0.379299 | + | 0.656965i | |||||
−13.2457 | − | 14.5971i | −0.0147667 | − | 0.0162732i | |||||
−1013.34 | − | 271.524i | −1.12844 | − | 0.302366i | |||||
894.149i | 0.994604i | |||||||||
2004.60 | + | 119.698i | 2.22734 | + | 0.132998i | |||||
−572.962 | −0.635918 | |||||||||
−103.649 | + | 386.822i | −0.114910 | + | 0.428849i | |||||
54.0387 | + | 17.3277i | 0.0598435 | + | 0.0191891i | |||||
831.374 | + | 479.994i | 0.919661 | + | 0.530967i | |||||
−1308.02 | + | 24.4313i | −1.44532 | + | 0.0269959i | |||||
−578.771 | − | 1125.14i | −0.638820 | − | 1.24187i | |||||
35.1572 | − | 131.208i | 0.0387621 | − | 0.144662i | −0.943833 | − | 0.330423i | ||
0.982595 | + | 0.185761i | ||||||||
−1194.65 | + | 1194.65i | −1.31569 | + | 1.31569i | |||||
−604.757 | − | 432.282i | −0.665299 | − | 0.475557i | |||||
−203.363 | + | 819.914i | −0.223476 | + | 0.901004i | |||||
545.263 | + | 944.423i | 0.598532 | + | 1.03669i | 0.993038 | + | 0.117795i | ||
−0.394506 | + | 0.918894i | ||||||||
1814.44 | + | 1999.55i | 1.98951 | + | 2.19249i | |||||
−10.9035 | − | 40.6924i | −0.0119425 | − | 0.0445700i | |||||
1459.39 | + | 842.579i | 1.59671 | + | 0.921859i | |||||
143.463 | − | 135.152i | 0.156790 | − | 0.147707i | |||||
660.594 | + | 1144.18i | 0.721173 | + | 1.24911i | |||||
628.907 | + | 628.907i | 0.685831 | + | 0.685831i | |||||
1156.49 | + | 498.923i | 1.25979 | + | 0.543489i | |||||
− | 367.996i | − | 0.400431i | −0.979752 | − | 0.200215i | ||||
0.979752 | − | 0.200215i | ||||||||
53.7133 | + | 29.6880i | 0.0583840 | + | 0.0322695i | |||||
−837.650 | + | 1300.84i | −0.909501 | + | 1.41242i | |||||
1727.79 | − | 462.959i | 1.87396 | − | 0.502125i | |||||
−279.815 | − | 1044.28i | −0.303158 | − | 1.13140i | |||||
17.7319 | − | 365.347i | 0.0191904 | − | 0.395398i | |||||
−337.767 | − | 313.432i | −0.365153 | − | 0.338845i | |||||
−3276.11 | −3.53792 | |||||||||
286.328 | + | 348.052i | 0.308876 | + | 0.375460i | |||||
730.476 | − | 730.476i | 0.787151 | − | 0.787151i | |||||
62.7337 | − | 36.2193i | 0.0675282 | − | 0.0389874i | −0.465856 | − | 0.884861i | ||
0.533384 | + | 0.845873i | ||||||||
−728.343 | + | 1178.89i | −0.783165 | + | 1.26763i | |||||
393.020 | − | 680.731i | 0.422148 | − | 0.731182i | |||||
−2339.28 | + | 626.810i | −2.50996 | + | 0.672542i | |||||
−585.517 | − | 187.748i | −0.627563 | − | 0.201231i | |||||
902.137 | − | 520.849i | 0.965886 | − | 0.557655i | |||||
−43.0328 | + | 173.499i | −0.0460244 | + | 0.185560i | |||||
−1503.40 | − | 146.278i | −1.60620 | − | 0.156280i | |||||
−887.903 | − | 887.903i | −0.947602 | − | 0.947602i | 0.0510921 | − | 0.998694i | ||
−0.998694 | + | 0.0510921i | ||||||||
−802.082 | − | 214.917i | −0.855099 | − | 0.229123i | |||||
−51.7075 | + | 1065.38i | −0.0550666 | + | 1.13459i | |||||
−118.813 | + | 123.336i | −0.126397 | + | 0.131208i | |||||
190.349 | − | 329.694i | 0.202284 | − | 0.350366i | −0.746980 | − | 0.664846i | ||
0.949264 | + | 0.314480i | ||||||||
2237.78 | − | 484.698i | 2.37556 | − | 0.514541i | |||||
27.0694 | + | 7.25323i | 0.0287056 | + | 0.00769165i | |||||
− | 1190.02i | − | 1.26061i | |||||||
−617.333 | + | 258.668i | −0.653263 | + | 0.273723i | |||||
−37.7930 | −0.0399504 | |||||||||
−139.605 | + | 521.012i | −0.147418 | + | 0.550172i | 0.852218 | + | 0.523187i | ||
−0.999636 | + | 0.0269844i | ||||||||
119.810 | + | 553.145i | 0.126382 | + | 0.583487i | |||||
−218.221 | − | 125.990i | −0.229948 | − | 0.132761i | |||||
2820.75 | + | 643.959i | 2.96921 | + | 0.677852i | |||||
−77.4265 | − | 3.75785i | −0.0814159 | − | 0.00395148i | |||||
294.831 | − | 1100.33i | 0.309697 | − | 1.15580i | |||||
−52.0743 | + | 52.0743i | −0.0546425 | + | 0.0546425i | −0.733900 | − | 0.679258i | ||
0.679258 | + | 0.733900i | ||||||||
1162.36 | + | 830.858i | 1.21841 | + | 0.870920i | |||||
−463.413 | − | 769.118i | −0.485250 | − | 0.805359i | |||||
585.940 | + | 1014.88i | 0.612908 | + | 1.06159i | |||||
87.8236 | − | 273.889i | 0.0917697 | − | 0.286196i | |||||
−190.265 | − | 710.080i | −0.198607 | − | 0.741210i | |||||
605.788 | + | 349.752i | 0.631687 | + | 0.364705i | |||||
−74.4654 | + | 17.5911i | −0.0775682 | + | 0.0183241i | |||||
150.349 | + | 260.413i | 0.156451 | + | 0.270981i | |||||
444.118 | + | 444.118i | 0.461662 | + | 0.461662i | |||||
684.858 | + | 256.838i | 0.711171 | + | 0.266707i | |||||
− | 1906.20i | − | 1.97739i | |||||||
37.1977 | + | 129.128i | 0.0385469 | + | 0.133811i | |||||
−37.0249 | − | 1.79698i | −0.0383280 | − | 0.00186023i | |||||
278.265 | − | 74.5608i | 0.287761 | − | 0.0771053i | −0.112051 | − | 0.993702i | ||
0.399812 | + | 0.916597i | ||||||||
−519.740 | − | 1939.70i | −0.536921 | − | 2.00382i | |||||
1053.56 | + | 678.415i | 1.08726 | + | 0.700119i | |||||
−2474.55 | − | 1367.72i | −2.55109 | − | 1.41002i | |||||
−227.938 | −0.234745 | −0.117373 | − | 0.993088i | ||||||
−0.117373 | + | 0.993088i | ||||||||
−1120.49 | − | 1856.96i | −1.15277 | − | 1.91046i | |||||
955.634 | − | 955.634i | 0.982152 | − | 0.982152i | |||||
2230.86 | − | 1287.99i | 2.29041 | − | 1.32237i | |||||
−619.560 | + | 348.556i | −0.635447 | + | 0.357493i | |||||
183.687 | − | 318.155i | 0.188203 | − | 0.325978i | |||||
613.083 | − | 164.275i | 0.627516 | − | 0.168142i | 0.0689735 | − | 0.997618i | ||
0.558542 | + | 0.829476i | ||||||||
−690.781 | + | 626.832i | −0.706320 | + | 0.640932i | |||||
220.577 | − | 127.350i | 0.225308 | − | 0.130082i | |||||
−562.365 | − | 933.345i | −0.573842 | − | 0.952393i | |||||
543.161 | + | 1195.02i | 0.553681 | + | 1.21817i | |||||
−531.988 | − | 531.988i | −0.541739 | − | 0.541739i | |||||
−1316.59 | − | 352.779i | −1.33936 | − | 0.358880i | −0.483163 | − | 0.875531i | ||
−0.856196 | + | 0.516651i | ||||||||
1909.72 | − | 982.361i | 1.94077 | − | 0.998334i | |||||
603.908 | + | 581.761i | 0.613104 | + | 0.590621i | |||||
811.616 | − | 1405.76i | 0.823140 | − | 1.42572i | |||||
17.4289 | − | 54.3542i | 0.0176584 | − | 0.0550701i | |||||
−2630.47 | − | 704.832i | −2.66242 | − | 0.713393i | |||||
2.64472i | 0.00267414i | |||||||||
338.892 | − | 289.572i | 0.342315 | − | 0.292497i | |||||
1111.32 | 1.12141 | 0.560705 | − | 0.828016i | ||||||
0.560705 | + | 0.828016i | ||||||||
−197.447 | + | 736.881i | −0.199039 | + | 0.742823i | |||||
−430.373 | + | 390.530i | −0.433406 | + | 0.393283i | |||||
−1760.76 | − | 1016.58i | −1.77139 | − | 1.02271i | |||||
−2.23286 | − | 119.544i | −0.00224408 | − | 0.120145i | |||||
−221.644 | + | 344.206i | −0.222534 | + | 0.345589i | |||||
−164.802 | + | 615.048i | −0.165297 | + | 0.616898i | 0.832705 | + | 0.553717i | ||
−0.998002 | + | 0.0631810i | ||||||||
842.493 | − | 842.493i | 0.844182 | − | 0.844182i | |||||
−72.1478 | + | 492.394i | −0.0722200 | + | 0.492887i |
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 45.3.k.a.22.1 | yes | 40 | |
3.2 | odd | 2 | 135.3.l.a.37.10 | 40 | |||
5.2 | odd | 4 | 225.3.o.b.193.1 | 40 | |||
5.3 | odd | 4 | inner | 45.3.k.a.13.10 | yes | 40 | |
5.4 | even | 2 | 225.3.o.b.157.10 | 40 | |||
9.2 | odd | 6 | 135.3.l.a.127.1 | 40 | |||
9.4 | even | 3 | 405.3.g.h.82.1 | 20 | |||
9.5 | odd | 6 | 405.3.g.g.82.10 | 20 | |||
9.7 | even | 3 | inner | 45.3.k.a.7.10 | ✓ | 40 | |
15.8 | even | 4 | 135.3.l.a.118.1 | 40 | |||
45.7 | odd | 12 | 225.3.o.b.43.10 | 40 | |||
45.13 | odd | 12 | 405.3.g.h.163.1 | 20 | |||
45.23 | even | 12 | 405.3.g.g.163.10 | 20 | |||
45.34 | even | 6 | 225.3.o.b.7.1 | 40 | |||
45.38 | even | 12 | 135.3.l.a.73.10 | 40 | |||
45.43 | odd | 12 | inner | 45.3.k.a.43.1 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
45.3.k.a.7.10 | ✓ | 40 | 9.7 | even | 3 | inner | |
45.3.k.a.13.10 | yes | 40 | 5.3 | odd | 4 | inner | |
45.3.k.a.22.1 | yes | 40 | 1.1 | even | 1 | trivial | |
45.3.k.a.43.1 | yes | 40 | 45.43 | odd | 12 | inner | |
135.3.l.a.37.10 | 40 | 3.2 | odd | 2 | |||
135.3.l.a.73.10 | 40 | 45.38 | even | 12 | |||
135.3.l.a.118.1 | 40 | 15.8 | even | 4 | |||
135.3.l.a.127.1 | 40 | 9.2 | odd | 6 | |||
225.3.o.b.7.1 | 40 | 45.34 | even | 6 | |||
225.3.o.b.43.10 | 40 | 45.7 | odd | 12 | |||
225.3.o.b.157.10 | 40 | 5.4 | even | 2 | |||
225.3.o.b.193.1 | 40 | 5.2 | odd | 4 | |||
405.3.g.g.82.10 | 20 | 9.5 | odd | 6 | |||
405.3.g.g.163.10 | 20 | 45.23 | even | 12 | |||
405.3.g.h.82.1 | 20 | 9.4 | even | 3 | |||
405.3.g.h.163.1 | 20 | 45.13 | odd | 12 |