Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [220,3,Mod(31,220)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(220, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([5, 0, 6]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("220.31");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 220.s (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 | 31.2 | ||
Character | 220.31 | ||
Dual form | 220.3.s.b.71.2 |
-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 .
−1.96516 | − | 0.371672i | −0.982581 | − | 0.185836i | |||||
0.447988 | + | 0.616603i | 0.149329 | + | 0.205534i | 0.877128 | − | 0.480257i | ||
−0.727799 | + | 0.685791i | ||||||||
3.72372 | + | 1.46079i | 0.930930 | + | 0.365197i | |||||
−0.690983 | − | 2.12663i | −0.138197 | − | 0.425325i | |||||
−0.651195 | − | 1.37823i | −0.108533 | − | 0.229705i | |||||
−5.62557 | + | 7.74293i | −0.803652 | + | 1.10613i | 0.188619 | + | 0.982050i | ||
−0.992272 | + | 0.124082i | ||||||||
−6.77478 | − | 4.25469i | −0.846847 | − | 0.531836i | |||||
2.60165 | − | 8.00705i | 0.289072 | − | 0.889672i | |||||
0.567486 | + | 4.43598i | 0.0567486 | + | 0.443598i | |||||
−8.56295 | − | 6.90477i | −0.778450 | − | 0.627706i | |||||
0.767455 | + | 2.95047i | 0.0639546 | + | 0.245873i | |||||
−0.964498 | + | 2.96842i | −0.0741921 | + | 0.228340i | −0.981275 | − | 0.192612i | ||
0.907083 | + | 0.420952i | ||||||||
13.9330 | − | 13.1252i | 0.995212 | − | 0.937517i | |||||
1.00173 | − | 1.37877i | 0.0667821 | − | 0.0919177i | |||||
11.7322 | + | 10.8791i | 0.733262 | + | 0.679946i | |||||
−0.505552 | − | 1.55593i | −0.0297384 | − | 0.0915253i | 0.935086 | − | 0.354422i | ||
−0.964824 | + | 0.262896i | ||||||||
−8.08865 | + | 14.7682i | −0.449369 | + | 0.820455i | |||||
−8.88888 | − | 12.2345i | −0.467836 | − | 0.643921i | 0.508275 | − | 0.861195i | ||
−0.976111 | + | 0.217274i | ||||||||
0.533527 | − | 8.92835i | 0.0266763 | − | 0.446417i | |||||
−7.29450 | −0.347357 | |||||||||
14.2613 | + | 16.7516i | 0.648240 | + | 0.761436i | |||||
− | 9.12329i | − | 0.396665i | −0.980135 | − | 0.198332i | ||||
0.980135 | − | 0.198332i | ||||||||
−0.411568 | − | 6.08339i | −0.0171486 | − | 0.253475i | |||||
−4.04508 | + | 2.93893i | −0.161803 | + | 0.117557i | |||||
2.99867 | − | 5.47495i | 0.115334 | − | 0.210575i | |||||
12.6264 | − | 4.10257i | 0.467645 | − | 0.151947i | |||||
−32.2588 | + | 20.6147i | −1.15210 | + | 0.736240i | |||||
−40.1611 | − | 29.1787i | −1.38486 | − | 1.00616i | −0.996407 | − | 0.0846969i | ||
−0.388458 | − | 0.921466i | ||||||||
−2.48101 | + | 2.33718i | −0.0827004 | + | 0.0779060i | |||||
−33.6488 | − | 10.9332i | −1.08545 | − | 0.352683i | −0.288961 | − | 0.957341i | ||
−0.796485 | + | 0.604658i | ||||||||
−19.0122 | − | 25.7398i | −0.594131 | − | 0.804369i | |||||
0.421397 | − | 8.37319i | 0.0127696 | − | 0.253733i | |||||
0.415197 | + | 3.24555i | 0.0122117 | + | 0.0954574i | |||||
20.3535 | + | 6.61325i | 0.581528 | + | 0.188950i | |||||
21.3844 | − | 26.0155i | 0.594012 | − | 0.722654i | |||||
−42.9061 | − | 31.1731i | −1.15962 | − | 0.842516i | −0.169893 | − | 0.985462i | ||
−0.989730 | + | 0.142946i | ||||||||
12.9209 | + | 27.3465i | 0.340023 | + | 0.719645i | |||||
−2.26242 | + | 0.735104i | −0.0580107 | + | 0.0188488i | |||||
−4.36688 | + | 17.3473i | −0.109172 | + | 0.433684i | |||||
−3.78700 | + | 2.75142i | −0.0923659 | + | 0.0671077i | −0.633010 | − | 0.774144i | ||
0.540644 | + | 0.841252i | ||||||||
14.3349 | + | 2.71116i | 0.341306 | + | 0.0645513i | |||||
24.1885i | 0.562523i | 0.959631 | + | 0.281261i | ||||||
−0.959631 | + | 0.281261i | ||||||||
−21.7996 | − | 38.2201i | −0.495446 | − | 0.868639i | |||||
−18.8257 | −0.418349 | |||||||||
−3.39087 | + | 17.9287i | −0.0737145 | + | 0.389755i | |||||
6.89694 | + | 9.49282i | 0.146743 | + | 0.201975i | 0.876061 | − | 0.482200i | ||
−0.729318 | + | 0.684175i | ||||||||
−1.45223 | + | 12.1078i | −0.0302548 | + | 0.252246i | |||||
−13.1641 | − | 40.5150i | −0.268655 | − | 0.826836i | |||||
9.04156 | − | 4.27202i | 0.180831 | − | 0.0854404i | |||||
0.732909 | − | 1.00876i | 0.0143708 | − | 0.0197797i | |||||
−7.92776 | + | 9.64464i | −0.152457 | + | 0.185474i | |||||
−11.5593 | + | 35.5760i | −0.218101 | + | 0.671244i | 0.780818 | + | 0.624758i | ||
−0.998919 | + | 0.0464864i | ||||||||
−26.3377 | + | 3.36933i | −0.487736 | + | 0.0623951i | |||||
−8.76701 | + | 22.9813i | −0.159400 | + | 0.417842i | |||||
71.0557 | − | 28.5216i | 1.26885 | − | 0.509314i | |||||
3.56171 | − | 10.9618i | 0.0624861 | − | 0.192313i | |||||
68.0781 | + | 72.2677i | 1.17376 | + | 1.24599i | |||||
33.0063 | − | 45.4293i | 0.559430 | − | 0.769989i | −0.431824 | − | 0.901958i | ||
0.991254 | + | 0.131969i | ||||||||
5.74425 | − | 3.67082i | 0.0957376 | − | 0.0611803i | |||||
27.3220 | + | 84.0884i | 0.447902 | + | 1.37850i | 0.879270 | + | 0.476323i | ||
−0.431369 | + | 0.902176i | ||||||||
62.0618 | + | 33.9917i | 1.00100 | + | 0.548254i | |||||
47.3623 | + | 65.1886i | 0.751782 | + | 1.03474i | |||||
27.7953 | + | 57.6491i | 0.434301 | + | 0.900768i | |||||
6.97917 | 0.107372 | |||||||||
−3.94019 | + | 16.2981i | −0.0596999 | + | 0.246940i | |||||
− | 58.1153i | − | 0.867392i | −0.901059 | − | 0.433696i | ||||
0.901059 | − | 0.433696i | ||||||||
0.390351 | − | 6.53235i | 0.00574045 | − | 0.0960640i | |||||
5.62544 | − | 4.08712i | 0.0815281 | − | 0.0592337i | |||||
−37.5399 | − | 20.5609i | −0.536285 | − | 0.293727i | |||||
95.0277 | − | 30.8764i | 1.33842 | − | 0.434878i | 0.449637 | − | 0.893211i | ||
0.888781 | + | 0.458333i | ||||||||
−51.6931 | + | 43.1768i | −0.717959 | + | 0.599677i | |||||
−29.7244 | − | 21.5961i | −0.407184 | − | 0.295836i | 0.365277 | − | 0.930899i | ||
−0.772461 | + | 0.635063i | ||||||||
72.7312 | + | 77.2071i | 0.982855 | + | 1.04334i | |||||
−3.62430 | − | 1.17761i | −0.0483240 | − | 0.0157014i | |||||
−15.2277 | − | 58.5426i | −0.200364 | − | 0.770298i | |||||
101.635 | − | 27.4591i | 1.31993 | − | 0.356612i | |||||
4.71924 | − | 0.603722i | 0.0605030 | − | 0.00774003i | |||||
70.8877 | + | 23.0328i | 0.897313 | + | 0.291555i | 0.721127 | − | 0.692802i | ||
0.176185 | + | 0.984357i | ||||||||
15.0291 | − | 32.4673i | 0.187864 | − | 0.405841i | |||||
−53.1147 | − | 38.5901i | −0.655737 | − | 0.476421i | |||||
8.46469 | − | 3.99946i | 0.103228 | − | 0.0487739i | |||||
−38.8899 | + | 12.6361i | −0.468553 | + | 0.152242i | −0.533771 | − | 0.845629i | ||
0.0652183 | + | 0.997871i | ||||||||
−27.1627 | − | 10.6557i | −0.323365 | − | 0.126854i | |||||
−2.95955 | + | 2.15024i | −0.0348183 | + | 0.0252970i | |||||
8.99017 | − | 47.5343i | 0.104537 | − | 0.552724i | |||||
− | 37.8351i | − | 0.434887i | |||||||
28.6345 | + | 83.2110i | 0.325392 | + | 0.945579i | |||||
116.343 | 1.30722 | 0.653612 | − | 0.756830i | ||||||
0.653612 | + | 0.756830i | ||||||||
36.9955 | + | 6.99698i | 0.411062 | + | 0.0777442i | |||||
−17.5584 | − | 24.1671i | −0.192950 | − | 0.265572i | |||||
13.3272 | − | 33.9726i | 0.144861 | − | 0.369267i | |||||
−8.33285 | − | 25.6459i | −0.0896005 | − | 0.275762i | |||||
−10.0254 | − | 21.2183i | −0.106653 | − | 0.225727i | |||||
−19.8761 | + | 27.3572i | −0.209223 | + | 0.287970i | |||||
7.35400 | − | 23.2541i | 0.0766041 | − | 0.242230i | |||||
13.7668 | − | 42.3699i | 0.141926 | − | 0.436803i | −0.854677 | − | 0.519160i | ||
0.996603 | + | 0.0823573i | ||||||||
10.8113 | + | 84.5112i | 0.110320 | + | 0.862359i | |||||
−77.5646 | + | 50.6002i | −0.783481 | + | 0.511113i | |||||
−19.3559 | + | 5.03472i | −0.193559 | + | 0.0503472i | |||||
−38.1746 | + | 117.489i | −0.377967 | + | 1.16326i | 0.563489 | + | 0.826124i | ||
−0.941455 | + | 0.337138i | ||||||||
−1.81521 | + | 1.70998i | −0.0177962 | + | 0.0167645i | |||||
−115.343 | + | 158.756i | −1.11983 | + | 1.54132i | −0.313761 | + | 0.949502i | ||
−0.806073 | + | 0.591816i | ||||||||
19.1640 | − | 16.0067i | 0.184269 | − | 0.153911i | |||||
5.04037 | + | 15.5127i | 0.0480035 | + | 0.147740i | |||||
35.9385 | − | 65.6162i | 0.339043 | − | 0.619021i | |||||
28.1635 | + | 38.7638i | 0.263211 | + | 0.362278i | 0.920083 | − | 0.391723i | ||
−0.656872 | + | 0.754002i | ||||||||
53.0102 | + | 3.16771i | 0.490835 | + | 0.0293306i | |||||
11.5938 | 0.106365 | 0.0531824 | − | 0.998585i | ||||||
0.0531824 | + | 0.998585i | ||||||||
25.7701 | − | 41.9035i | 0.234273 | − | 0.380941i | |||||
− | 40.4212i | − | 0.364155i | |||||||
−150.237 | + | 29.6401i | −1.34140 | + | 0.264644i | |||||
−108.027 | + | 78.4859i | −0.955988 | + | 0.694566i | −0.952215 | − | 0.305427i | ||
−0.00377227 | + | 0.999993i | ||||||||
−11.0735 | + | 20.2179i | −0.0971362 | + | 0.177350i | |||||
−19.4018 | + | 6.30404i | −0.168712 | + | 0.0548177i | |||||
−106.925 | − | 167.320i | −0.921764 | − | 1.44242i | |||||
21.2590 | + | 15.4456i | 0.181701 | + | 0.132013i | |||||
−81.7476 | + | 77.0085i | −0.692776 | + | 0.652614i | |||||
14.8915 | + | 4.83853i | 0.125138 | + | 0.0406599i | |||||
−12.6527 | + | 5.07877i | −0.105439 | + | 0.0423231i | |||||
25.6484 | + | 118.250i | 0.211970 | + | 0.977276i | |||||
−22.4388 | − | 175.402i | −0.183925 | − | 1.43772i | |||||
−3.39306 | − | 1.10247i | −0.0275859 | − | 0.00896319i | |||||
−109.328 | − | 89.8659i | −0.881675 | − | 0.724725i | |||||
9.04508 | + | 6.57164i | 0.0723607 | + | 0.0525731i | |||||
−68.8458 | − | 145.709i | −0.546395 | − | 1.15642i | |||||
−4.42432 | + | 1.43755i | −0.0348372 | + | 0.0113193i | −0.326384 | − | 0.945237i | ||
0.291547 | + | 0.956557i | ||||||||
−33.1956 | − | 123.621i | −0.259341 | − | 0.965786i | |||||
−14.9147 | + | 10.8361i | −0.115618 | + | 0.0840012i | |||||
−13.7152 | − | 2.59396i | −0.105502 | − | 0.0199535i | |||||
− | 234.292i | − | 1.78849i | −0.447576 | − | 0.894246i | ||||
0.447576 | − | 0.894246i | ||||||||
13.8006 | − | 30.5639i | 0.104550 | − | 0.231544i | |||||
144.736 | 1.08824 | |||||||||
−21.5998 | + | 114.206i | −0.161193 | + | 0.852283i | |||||
−17.4493 | − | 24.0169i | −0.129254 | − | 0.177903i | |||||
−3.19499 | + | 12.6920i | −0.0234926 | + | 0.0933239i | |||||
−18.7864 | − | 57.8185i | −0.137127 | − | 0.422033i | 0.858788 | − | 0.512331i | ||
−0.995915 | + | 0.0902985i | ||||||||
−12.5740 | + | 5.94104i | −0.0911157 | + | 0.0430510i | |||||
4.30579 | − | 5.92642i | 0.0309769 | − | 0.0426361i | −0.793248 | − | 0.608899i | ||
0.824225 | + | 0.566263i | ||||||||
66.1301 | + | 54.3581i | 0.472358 | + | 0.388272i | |||||
−2.76355 | + | 8.50534i | −0.0195997 | + | 0.0603215i | |||||
−198.221 | + | 25.3580i | −1.39592 | + | 0.178577i | |||||
28.7552 | − | 18.7588i | 0.201085 | − | 0.131180i | |||||
117.633 | − | 65.6365i | 0.816895 | − | 0.455809i | |||||
−34.3017 | + | 105.570i | −0.236563 | + | 0.728067i | |||||
50.3867 | + | 53.4875i | 0.345114 | + | 0.366353i | |||||
19.0843 | − | 26.2672i | 0.129825 | − | 0.178689i | |||||
−114.233 | − | 178.757i | −0.771844 | − | 1.20782i | |||||
−22.0579 | − | 67.8872i | −0.148039 | − | 0.455619i | 0.849350 | − | 0.527830i | ||
−0.997389 | + | 0.0722117i | ||||||||
6.68465 | + | 3.66123i | 0.0445643 | + | 0.0244082i | |||||
−26.4721 | − | 36.4357i | −0.175312 | − | 0.241296i | 0.712315 | − | 0.701860i | ||
−0.887626 | + | 0.460565i | ||||||||
8.16624 | + | 120.705i | 0.0537252 | + | 0.794115i | |||||
−13.7737 | −0.0900240 | |||||||||
−209.934 | + | 16.1869i | −1.36321 | + | 0.105110i | |||||
79.1131i | 0.510407i | |||||||||
−9.49845 | − | 0.567594i | −0.0608875 | − | 0.00363842i | |||||
215.708 | − | 156.721i | 1.37393 | − | 0.998222i | 0.376517 | − | 0.926410i | ||
0.997418 | − | 0.0718124i | ||||||||
−130.745 | − | 71.6101i | −0.827501 | − | 0.453229i | |||||
−27.1147 | + | 8.81009i | −0.170532 | + | 0.0554094i | |||||
−41.6019 | + | 58.2176i | −0.260012 | + | 0.363860i | |||||
70.6410 | + | 51.3237i | 0.438764 | + | 0.318781i | |||||
90.0361 | + | 95.5769i | 0.555778 | + | 0.589981i | |||||
−73.9072 | − | 24.0139i | −0.453418 | − | 0.147324i | 0.0733999 | − | 0.997303i | ||
−0.526818 | + | 0.849978i | ||||||||
−18.1210 | + | 4.71350i | −0.110494 | + | 0.0287408i | |||||
−18.0978 | + | 4.88958i | −0.109684 | + | 0.0296338i | |||||
81.1214 | − | 10.3777i | 0.488683 | − | 0.0625162i | |||||
35.7406 | + | 11.6128i | 0.214016 | + | 0.0695379i | 0.414063 | − | 0.910248i | ||
−0.200047 | + | 0.979786i | ||||||||
49.4186 | + | 31.0358i | 0.294158 | + | 0.184737i | |||||
128.843 | + | 93.6096i | 0.762382 | + | 0.553903i | |||||
6.61519 | − | 3.12559i | 0.0389129 | − | 0.0183858i | |||||
−121.088 | + | 39.3439i | −0.708117 | + | 0.230081i | |||||
−35.3343 | + | 90.0712i | −0.205432 | + | 0.523670i | |||||
243.517 | − | 176.926i | 1.40761 | − | 1.02269i | 0.413949 | − | 0.910300i | ||
0.993664 | − | 0.112391i | ||||||||
−14.0622 | + | 74.3522i | −0.0808175 | + | 0.427311i | |||||
− | 47.8539i | − | 0.273451i | |||||||
−25.3442 | − | 174.166i | −0.144001 | − | 0.989577i | |||||
42.7983 | 0.241798 | |||||||||
−228.633 | − | 43.2413i | −1.28445 | − | 0.242929i | |||||
−183.916 | − | 253.139i | −1.02746 | − | 1.41418i | −0.906835 | − | 0.421486i | ||
−0.120629 | − | 0.992698i | ||||||||
−70.1016 | − | 27.5004i | −0.389454 | − | 0.152780i | |||||
73.7817 | + | 227.077i | 0.407634 | + | 1.25457i | 0.918676 | + | 0.395012i | ||
−0.511042 | + | 0.859556i | ||||||||
25.5229 | + | 54.0182i | 0.140236 | + | 0.296803i | |||||
−39.6092 | + | 54.5174i | −0.216444 | + | 0.297909i | |||||
−38.8167 | + | 61.8083i | −0.210961 | + | 0.335914i | |||||
−36.6462 | + | 112.785i | −0.198087 | + | 0.609650i | |||||
6.84355 | + | 53.4953i | 0.0367933 | + | 0.287609i | |||||
−6.41431 | + | 16.8141i | −0.0343011 | + | 0.0899149i | |||||
11.8153 | + | 45.4236i | 0.0628471 | + | 0.241615i | |||||
−39.2648 | + | 120.845i | −0.207750 | + | 0.639390i | |||||
49.2277 | − | 46.3739i | 0.259093 | − | 0.244073i | |||||
−181.210 | + | 249.414i | −0.948742 | + | 1.30583i | 0.00334140 | + | 0.999994i | ||
−0.952084 | + | 0.305837i | ||||||||
−23.0947 | + | 42.9647i | −0.120285 | + | 0.223775i | |||||
−105.817 | − | 325.671i | −0.548274 | − | 1.68741i | −0.713075 | − | 0.701088i | ||
0.164801 | − | 0.986327i | ||||||||
−42.8017 | + | 78.1469i | −0.220627 | + | 0.402819i | |||||
3.12659 | + | 4.30338i | 0.0160338 | + | 0.0220686i | |||||
10.1644 | − | 170.096i | 0.0518590 | − | 0.867839i | |||||
−310.061 | −1.57391 | −0.786956 | − | 0.617009i | ||||||
−0.786956 | + | 0.617009i | ||||||||
171.234 | − | 70.6090i | 0.864816 | − | 0.356611i | |||||
275.222i | 1.38302i | 0.722365 | + | 0.691512i | ||||||
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39.9088 | − | 2.70000i | 0.199544 | − | 0.0135000i | |||||
35.8340 | − | 26.0349i | 0.178279 | − | 0.129527i | |||||
118.687 | − | 216.697i | 0.587559 | − | 1.07276i | |||||
451.858 | − | 146.817i | 2.22590 | − | 0.723239i | |||||
4.20274 | − | 2.68572i | 0.0206017 | − | 0.0131653i | |||||
8.46799 | + | 6.15236i | 0.0413073 | + | 0.0300115i | |||||
285.672 | − | 269.111i | 1.38676 | − | 1.30636i | |||||
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158.344 | + | 51.4490i | 0.750445 | + | 0.243834i | 0.659173 | − | 0.751992i | ||
0.0912723 | + | 0.995826i | ||||||||
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273.948 | − | 199.035i | 1.26243 | − | 0.917212i | |||||
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5.10626 | 0.0231052 | |||||||||
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157.104 | + | 216.236i | 0.704504 | + | 0.969666i | 0.999898 | + | 0.0142908i | ||
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306.256 | − | 2.40899i | 1.36721 | − | 0.0107544i | |||||
13.0082 | + | 40.0352i | 0.0578144 | + | 0.177934i | |||||
241.461 | − | 114.087i | 1.06841 | − | 0.504810i | |||||
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0.606342 | + | 0.795204i | ||||||||
29.2757 | − | 35.6158i | 0.128402 | − | 0.156210i | |||||
85.0594 | − | 261.786i | 0.371438 | − | 1.14317i | −0.574412 | − | 0.818566i | ||
0.945850 | − | 0.324603i | ||||||||
40.4708 | − | 5.17734i | 0.175960 | − | 0.0225102i | |||||
62.4624 | + | 50.3668i | 0.270400 | + | 0.218038i | |||||
147.936 | + | 368.552i | 0.637655 | + | 1.58859i | |||||
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15.4220 | − | 21.2266i | 0.0656256 | − | 0.0903259i | |||||
189.269 | − | 120.951i | 0.801988 | − | 0.512504i | |||||
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26.7523 | − | 5.27795i | 0.111468 | − | 0.0219915i | |||||
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44.8904 | − | 14.5858i | 0.181743 | − | 0.0590518i | |||||
181.446 | + | 217.235i | 0.731637 | + | 0.875947i | |||||
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81.1371 | + | 311.930i | 0.321972 | + | 1.23782i | |||||
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33.3372 | − | 15.7514i | 0.129214 | − | 0.0610520i | |||||
482.742 | − | 156.852i | 1.86387 | − | 0.605608i | |||||
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0.932733 | − | 0.360569i | ||||||||
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83.6441 | 0.315638 | |||||||||
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0.558755 | − | 0.829333i | ||||||||
25.3643 | + | 53.6824i | 0.0939417 | + | 0.198824i | |||||
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0.836868 | + | 0.547405i | ||||||||
10.9960 | − | 23.7544i | 0.0404263 | − | 0.0873325i | |||||
7.03553 | − | 21.6531i | 0.0257712 | − | 0.0793155i | |||||
15.4287 | + | 120.605i | 0.0563093 | + | 0.440164i | |||||
54.9305 | + | 2.76448i | 0.199747 | + | 0.0100527i | |||||
26.9180 | − | 7.00172i | 0.0975290 | − | 0.0253685i | |||||
94.9161 | − | 292.122i | 0.342657 | − | 1.05459i | −0.620169 | − | 0.784469i | ||
0.962826 | − | 0.270123i | ||||||||
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52.6783 | + | 162.127i | 0.187467 | + | 0.576965i | 0.999982 | − | 0.00597528i | ||
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0.220743 | − | 0.975332i | ||||||||
398.960 | + | 23.8405i | 1.40479 | + | 0.0839454i | |||||
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231.641 | − | 168.297i | 0.801524 | − | 0.582342i | |||||
106.646 | − | 194.712i | 0.367743 | − | 0.671422i | |||||
32.2927 | − | 10.4925i | 0.110972 | − | 0.0360568i | |||||
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158.047 | + | 393.743i | 0.533944 | + | 1.33021i | |||||
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18.1156 | + | 141.608i | 0.0607905 | + | 0.475193i | |||||
27.0817 | + | 8.79939i | 0.0905744 | + | 0.0294294i | |||||
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38.4798 | + | 81.4409i | 0.127417 | + | 0.269672i | |||||
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28.8148 | − | 240.241i | 0.0947855 | − | 0.790266i | |||||
159.946 | − | 116.207i | 0.524412 | − | 0.381008i | |||||
27.0675 | + | 5.11928i | 0.0884559 | + | 0.0167297i | |||||
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0.901425 | − | 0.432935i | ||||||||
418.571 | + | 46.2167i | 1.35900 | + | 0.150054i | |||||
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29.4041 | − | 155.470i | 0.0948519 | − | 0.501516i | |||||
197.511 | + | 271.850i | 0.635082 | + | 0.874116i | 0.998341 | − | 0.0575722i | ||
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18.4550 | + | 4.64572i | 0.0591507 | + | 0.0148901i | |||||
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0.631626 | − | 0.775273i | ||||||||
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105.905 | − | 145.766i | 0.336207 | − | 0.462749i | |||||
230.320 | + | 189.320i | 0.728860 | + | 0.599113i | |||||
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0.930492 | + | 0.366313i | ||||||||
56.5592 | − | 7.23550i | 0.177859 | − | 0.0227531i | |||||
142.425 | + | 527.159i | 0.446474 | + | 1.65254i | |||||
103.392 | − | 98.9447i | 0.323101 | − | 0.309202i | |||||
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136.314 | + | 74.6604i | 0.418142 | + | 0.229020i | |||||
5.19386 | + | 7.14874i | 0.0158834 | + | 0.0218616i | |||||
37.3625 | − | 2.52773i | 0.113910 | − | 0.00770650i | |||||
−112.301 | −0.341342 | |||||||||
37.3825 | − | 2.88236i | 0.113280 | − | 0.00873443i | |||||
276.676i | 0.835878i | 0.908475 | + | 0.417939i | ||||||
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28.3271 | + | 20.5808i | 0.0840567 | + | 0.0610707i | 0.629020 | − | 0.777389i | ||
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212.642 | + | 325.957i | 0.623584 | + | 0.955887i | |||||
252.580 | − | 32.3121i | 0.738539 | − | 0.0944798i | |||||
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102.914 | − | 163.872i | 0.299170 | − | 0.476371i | |||||
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254.573 | − | 82.7158i | 0.733640 | − | 0.238374i | 0.0817130 | − | 0.996656i | ||
0.651927 | + | 0.758282i | ||||||||
55.2692 | − | 140.888i | 0.158819 | − | 0.404849i | |||||
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0.464474 | + | 0.885587i | ||||||||
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41.4374i | 0.118055i | |||||||||
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265.736 | 0.752792 | 0.376396 | − | 0.926459i | ||||||
0.376396 | + | 0.926459i | ||||||||
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433.228 | + | 169.952i | 1.21693 | + | 0.477394i | |||||
3.68775 | + | 11.3497i | 0.0103298 | + | 0.0317919i | |||||
267.340 | + | 565.815i | 0.746761 | + | 1.58049i | |||||
338.315 | − | 465.651i | 0.942383 | − | 1.29708i | −0.0124461 | − | 0.999923i | ||
0.954829 | − | 0.297156i | ||||||||
127.540 | + | 80.0975i | 0.354278 | + | 0.222493i | |||||
40.8845 | − | 125.829i | 0.113253 | − | 0.348558i | |||||
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98.1011 | − | 92.4139i | 0.268036 | − | 0.252497i | |||||
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0.394206 | + | 0.919022i | ||||||||
99.2536 | − | 107.036i | 0.269711 | − | 0.290859i | |||||
12.1783 | + | 37.4809i | 0.0330035 | + | 0.101574i | |||||
113.935 | − | 208.021i | 0.307932 | − | 0.562219i | |||||
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6.43402 | − | 107.671i | 0.0172957 | − | 0.289437i | |||||
569.644 | 1.52719 | 0.763597 | − | 0.645693i | ||||||
0.763597 | + | 0.645693i | ||||||||
18.8545 | − | 30.6584i | 0.0504130 | − | 0.0819742i | |||||
8.52124i | 0.0227233i | |||||||||
−6.33623 | − | 93.6561i | −0.0168517 | − | 0.249085i | |||||
125.350 | − | 91.0721i | 0.332493 | − | 0.241571i | |||||
122.076 | − | 222.886i | 0.322953 | − | 0.589645i | |||||
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448.807 | − | 422.788i | 1.17489 | − | 1.10678i | |||||
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61.3535 | − | 75.8490i | 0.159775 | − | 0.197524i | |||||
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86.9047 | + | 679.325i | 0.225142 | + | 1.75991i | |||||
193.678 | + | 62.9299i | 0.500461 | + | 0.162610i | |||||
113.157 | − | 137.663i | 0.291642 | − | 0.354802i | |||||
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−0.410495 | − | 0.911863i | ||||||||
−4.54480 | − | 9.61889i | −0.0116533 | − | 0.0246638i | |||||
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144.465 | − | 104.960i | 0.367596 | − | 0.267074i | |||||
609.319 | + | 115.241i | 1.54650 | + | 0.292489i | |||||
− | 166.667i | − | 0.421942i | |||||||
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−25.3917 | −0.0639590 | −0.0319795 | − | 0.999489i | ||||||
−0.0319795 | + | 0.999489i | ||||||||
102.292 | − | 540.856i | 0.257015 | − | 1.35893i | |||||
64.8399 | + | 89.2445i | 0.162506 | + | 0.223670i | |||||
−79.4307 | − | 9.52702i | −0.198577 | − | 0.0238176i | |||||
−3.42431 | − | 10.5389i | −0.00853942 | − | 0.0262816i | 0.946696 | − | 0.322128i | ||
−0.955235 | + | 0.295847i | ||||||||
−80.0961 | + | 37.8444i | −0.199244 | + | 0.0941403i | |||||
64.9084 | − | 89.3388i | 0.161063 | − | 0.221684i | |||||
−313.779 | + | 381.733i | −0.776681 | + | 0.944883i | |||||
−45.3654 | + | 139.620i | −0.112013 | + | 0.344741i | |||||
−942.541 | + | 120.577i | −2.32153 | + | 0.296989i | |||||
152.160 | + | 563.190i | 0.373857 | + | 1.38376i | |||||
−9.25727 | + | 3.71584i | −0.0226894 | + | 0.00910746i | |||||
81.7829 | − | 251.702i | 0.199958 | − | 0.615408i | −0.799925 | − | 0.600101i | ||
0.999883 | − | 0.0153078i | ||||||||
−14.3543 | − | 15.2377i | −0.0350105 | − | 0.0371651i | |||||
27.2349 | − | 37.4857i | 0.0662651 | − | 0.0912060i | |||||
−661.413 | + | 422.671i | −1.60537 | + | 1.02590i | |||||
166.077 | + | 511.132i | 0.402123 | + | 1.23761i | |||||
134.734 | + | 73.7951i | 0.325445 | + | 0.178249i | |||||
53.7445 | + | 73.9729i | 0.129505 | + | 0.178248i | |||||
94.7437 | − | 31.6101i | 0.227749 | − | 0.0759859i | |||||
5.58319 | 0.0133889 | |||||||||
78.1804 | − | 323.383i | 0.187035 | − | 0.773642i | |||||
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0.976836 | − | 0.213992i | ||||||||
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360.024 | − | 261.573i | 0.855163 | − | 0.621312i | −0.0714016 | − | 0.997448i | ||
0.926565 | + | 0.376135i | ||||||||
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93.9528 | − | 30.5271i | 0.222111 | − | 0.0721682i | |||||
229.677 | − | 191.838i | 0.541690 | − | 0.452448i | |||||
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200.900 | + | 65.2764i | 0.466125 | + | 0.151453i | 0.532657 | − | 0.846331i | ||
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192.768 | + | 89.2324i | 0.446222 | + | 0.206557i | |||||
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0.762064 | − | 0.647502i | ||||||||
157.173 | − | 118.392i | 0.357211 | − | 0.269073i | |||||
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0.276503 | − | 0.961013i | ||||||||
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10.6072 | − | 32.6455i | 0.0234154 | − | 0.0720651i | |||||
189.642 | − | 178.648i | 0.417713 | − | 0.393497i | |||||
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196.860i | 0.425183i | 0.977141 | + | 0.212592i | ||||||
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365.669 | − | 667.635i | 0.784697 | − | 1.43269i | |||||
276.586 | − | 89.8681i | 0.592261 | − | 0.192437i | 0.00247492 | − | 0.999997i | ||
0.589786 | + | 0.807560i | ||||||||
56.5998 | + | 88.5699i | 0.120940 | + | 0.189252i | |||||
449.983 | + | 326.931i | 0.959451 | + | 0.697082i | |||||
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193.269 | + | 62.7969i | 0.410338 | + | 0.133327i | |||||
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48.3836 | + | 39.7706i | 0.101646 | + | 0.0835518i | |||||
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133.918 | − | 97.2969i | 0.278415 | − | 0.202280i | |||||
727.306 | + | 137.556i | 1.50893 | + | 0.285385i | |||||
66.5498i | 0.137784i | |||||||||
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256.315 | + | 352.787i | 0.526314 | + | 0.724409i | 0.986563 | − | 0.163381i | ||
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172.670 | − | 685.927i | 0.353831 | − | 1.40559i | |||||
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172.253 | − | 81.3875i | 0.351537 | − | 0.166097i | |||||
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161.204 | + | 129.987i | 0.325664 | + | 0.262600i | |||||
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0.712217 | + | 0.701960i | ||||||||
24.0816 | + | 37.6839i | 0.0481632 | + | 0.0753678i | |||||
8.85087 | + | 27.2402i | 0.0176664 | + | 0.0543716i | |||||
232.224 | + | 127.191i | 0.462597 | + | 0.253368i | |||||
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276.234 | 0.546999 | |||||||||
152.830 | − | 130.110i | 0.302035 | − | 0.257134i | |||||
121.381i | 0.239410i | |||||||||
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0.506647 | + | 0.862154i | ||||||||
4.89077 | + | 2.67871i | 0.00958975 | + | 0.00525238i | |||||
334.433 | − | 108.664i | 0.654469 | − | 0.212650i | |||||
56.9725 | − | 508.820i | 0.111274 | − | 0.993790i | |||||
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424.720 | + | 450.857i | 0.826304 | + | 0.877155i | |||||
417.314 | + | 135.594i | 0.810319 | + | 0.263289i | |||||
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218.185 | + | 70.8928i | 0.420396 | + | 0.136595i | |||||
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267.153 | + | 194.098i | 0.512770 | + | 0.372549i | 0.813874 | − | 0.581042i | ||
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755.766 | − | 357.090i | 1.44783 | − | 0.684080i | |||||
836.001 | − | 271.633i | 1.59847 | − | 0.519375i | 0.631744 | − | 0.775177i | ||
0.966729 | + | 0.255802i | ||||||||
342.252 | − | 872.440i | 0.653153 | − | 1.66496i | |||||
29.5069 | − | 21.4380i | 0.0562035 | − | 0.0408343i | |||||
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57.8825i | 0.109834i | |||||||||
96.0371 | − | 93.6514i | 0.181888 | − | 0.177370i | |||||
445.766 | 0.842657 | |||||||||
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538.956 | + | 211.429i | 1.01307 | + | 0.397422i | |||||
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62.9756 | − | 86.6784i | 0.117711 | − | 0.162016i | |||||
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73.6938 | − | 226.806i | 0.137232 | − | 0.422358i | |||||
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236.223 | − | 727.020i | 0.436641 | − | 1.34384i | −0.454754 | − | 0.890617i | ||
0.891395 | − | 0.453227i | ||||||||
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14.5055 | − | 242.743i | 0.0264698 | − | 0.442961i | |||||
744.382 | 1.35589 | |||||||||
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750.717i | 1.36246i | |||||||||
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24.6908 | − | 15.7785i | 0.0444080 | − | 0.0283785i | |||||
90.6342 | + | 65.8496i | 0.162719 | + | 0.118222i | 0.666165 | − | 0.745805i | ||
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433.636 | − | 408.497i | 0.777126 | − | 0.732074i | |||||
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166.845 | + | 299.016i | 0.297937 | + | 0.533958i | |||||
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846.470 | + | 275.035i | 1.50350 | + | 0.488517i | 0.941036 | − | 0.338306i | ||
0.562463 | + | 0.826822i | ||||||||
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241.555 | + | 175.500i | 0.427531 | + | 0.310619i | |||||
318.838 | + | 674.808i | 0.563318 | + | 1.19224i | |||||
597.600 | − | 194.172i | 1.05397 | − | 0.342455i | |||||
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0.125491 | + | 0.992095i | ||||||||
50.6477 | + | 9.57901i | 0.0888555 | + | 0.0168053i | |||||
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0.878043 | − | 0.478581i | ||||||||
134.479 | − | 27.8473i | 0.235103 | − | 0.0486840i | |||||
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26.8127 | + | 36.9045i | 0.0466307 | + | 0.0641817i | |||||
533.913 | − | 72.5751i | 0.926932 | − | 0.125999i | |||||
262.876 | + | 809.048i | 0.455590 | + | 1.40216i | 0.870441 | + | 0.492273i | ||
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153.405 | − | 211.144i | 0.264948 | − | 0.364670i | |||||
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120.937 | − | 372.207i | 0.208154 | − | 0.640631i | |||||
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344.626 | − | 224.821i | 0.591125 | − | 0.385627i | |||||
109.492 | + | 272.777i | 0.187486 | + | 0.467083i | |||||
18.1573 | − | 55.8826i | 0.0310382 | − | 0.0955258i | |||||
430.003 | + | 456.466i | 0.733794 | + | 0.778952i | |||||
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0.670811 | + | 0.741628i | ||||||||
109.435 | − | 69.9337i | 0.186115 | − | 0.118935i | |||||
165.339 | + | 508.860i | 0.280711 | + | 0.863938i | |||||
220.255 | + | 120.635i | 0.373313 | + | 0.204466i | |||||
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542.114 | 0.914189 | 0.457094 | − | 0.889418i | ||||||
0.457094 | + | 0.889418i | ||||||||
248.793 | + | 153.005i | 0.418844 | + | 0.257583i | |||||
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17.0315 | − | 285.015i | 0.0285763 | − | 0.478213i | |||||
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0.115814 | + | 0.993271i | ||||||||
19.5435 | + | 23.3983i | 0.0325725 | + | 0.0389971i | |||||
123.566 | + | 89.7761i | 0.205601 | + | 0.149378i | 0.685821 | − | 0.727770i | ||
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317.480 | + | 337.018i | 0.527375 | + | 0.559830i | |||||
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233.752 | − | 136.254i | 0.386367 | − | 0.225212i | |||||
186.786 | − | 23.8952i | 0.308228 | − | 0.0394310i | |||||
2.97708 | + | 0.967311i | 0.00490457 | + | 0.00159359i | 0.311468 | − | 0.950257i | ||
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292.955 | + | 212.844i | 0.481042 | + | 0.349498i | |||||
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0.446993 | + | 0.894538i | ||||||||
−98.7986 | + | 522.384i | −0.160910 | + | 0.850788i | |||||
7.97757i | 0.0129717i | |||||||||
−805.382 | − | 246.394i | −1.30744 | − | 0.399991i | |||||
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293.912 | + | 55.5877i | 0.475586 | + | 0.0899478i | |||||
169.667 | + | 233.527i | 0.274099 | + | 0.377265i | 0.923768 | − | 0.382952i | ||
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7.72542 | − | 23.7764i | 0.0123607 | − | 0.0380423i | |||||
86.1312 | + | 673.279i | 0.137590 | + | 1.07553i | |||||
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1032.17 | − | 268.481i | 1.64359 | − | 0.427518i | |||||
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0.783380 | + | 0.621543i | ||||||||
−382.251 | − | 457.647i | −0.604828 | − | 0.724125i | |||||
39.2125 | + | 120.684i | 0.0619471 | + | 0.190654i | |||||
37.0626 | − | 67.6686i | 0.0584584 | − | 0.106733i | |||||
6.11426 | + | 8.41556i | 0.00962875 | + | 0.0132528i | |||||
−113.837 | − | 6.80251i | −0.178989 | − | 0.0106958i | |||||
132.962 | 0.208732 | |||||||||
−83.9583 | − | 1088.89i | −0.131596 | − | 1.70672i | |||||
− | 841.221i | − | 1.31646i | |||||||
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0.981820 | + | 0.189813i | ||||||||
35.0854 | − | 64.0585i | 0.0546501 | − | 0.0997797i | |||||
1023.68 | − | 332.614i | 1.59204 | − | 0.517284i | 0.626916 | − | 0.779087i | ||
0.965121 | + | 0.261803i | ||||||||
188.074 | + | 294.307i | 0.292041 | + | 0.456998i | |||||
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195.651 | + | 487.426i | 0.301931 | + | 0.752200i | |||||
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102.832 | − | 543.712i | 0.155336 | − | 0.821318i | |||||
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346.654 | − | 908.698i | 0.516623 | − | 1.35424i | |||||
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0.744141 | − | 0.668023i | ||||||||
178.518 | + | 97.7756i | 0.263301 | + | 0.144212i | |||||
250.621 | + | 344.950i | 0.369103 | + | 0.508026i | |||||
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914.777i | 1.33935i | 0.742654 | + | 0.669675i | ||||||
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431.259 | − | 313.328i | 0.615205 | − | 0.446972i | −0.236038 | − | 0.971744i | ||
0.851243 | + | 0.524771i | ||||||||
15.4011 | − | 81.4312i | 0.0219389 | − | 0.115999i | |||||
802.028i | 1.14087i | |||||||||
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19.9972 | 0.0283649 | |||||||||
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340.137 | + | 1046.83i | 0.479742 | + | 1.47649i | 0.839454 | + | 0.543431i | ||
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190.894 | + | 404.019i | 0.268865 | + | 0.569041i | |||||
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248.209 | 0.342357 | |||||||||
146.274 | − | 112.353i | 0.201479 | − | 0.154757i | |||||
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0.591438 | − | 0.806350i | ||||||||
16.1310 | + | 238.432i | 0.0221579 | + | 0.327517i | |||||
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546.876 | − | 515.172i | 0.745063 | − | 0.701870i | |||||
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344.268i | 0.460867i | |||||||||
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3.16710 | − | 16.7456i | 0.00422280 | − | 0.0223275i | |||||
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0.897263 | + | 0.441496i | ||||||||
705.686 | − | 90.2770i | 0.930985 | − | 0.119099i | |||||
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251.053 | − | 100.772i | 0.330332 | − | 0.132595i | |||||
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0.999301 | − | 0.0373757i | ||||||||
4.86236 | + | 5.16160i | 0.00638106 | + | 0.00677375i | |||||
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9.51737 | + | 29.2915i | 0.0124410 | + | 0.0382895i | |||||
878.637 | + | 481.236i | 1.14705 | + | 0.628246i | |||||
103.019 | + | 141.793i | 0.134314 | + | 0.184867i | |||||
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179.484 | + | 435.267i | 0.233097 | + | 0.565282i | |||||
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81.7041 | − | 1367.28i | 0.105834 | − | 1.77109i | |||||
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0.340707 | + | 0.940169i | ||||||||
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168.244 | − | 54.6658i | 0.217089 | − | 0.0705365i | |||||
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312.978 | + | 227.392i | 0.402803 | + | 0.292654i | |||||
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67.3244 | + | 21.8750i | 0.0864241 | + | 0.0280809i | |||||
5.35620 | + | 20.5918i | 0.00686693 | + | 0.0263998i | |||||
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29.6101 | − | 3.78796i | 0.0378646 | − | 0.00484394i | |||||
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286.324 | − | 618.543i | 0.365209 | − | 0.788958i | |||||
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0.305477 | + | 0.952199i | ||||||||
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116.944 | − | 84.9651i | 0.148218 | − | 0.107687i | |||||
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740.771 | − | 12.7920i | 0.935317 | − | 0.0161515i | |||||
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49.8989 | + | 9.43739i | 0.0628449 | + | 0.0118859i | |||||
37.4715 | + | 51.5752i | 0.0471340 | + | 0.0648744i | |||||
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88.5703 | + | 272.591i | 0.111130 | + | 0.342022i | 0.991120 | − | 0.132969i | ||
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11.2834 | − | 15.5303i | 0.0141219 | − | 0.0194371i | |||||
152.553 | + | 48.2443i | 0.190692 | + | 0.0603053i | |||||
302.683 | − | 931.563i | 0.377882 | − | 1.16300i | |||||
2.81230 | + | 21.9834i | 0.00350660 | + | 0.0274108i | |||||
105.413 | + | 390.166i | 0.131274 | + | 0.485886i | |||||
171.467 | − | 44.6009i | 0.213268 | − | 0.0554737i | |||||
60.3346 | − | 185.691i | 0.0749498 | − | 0.230672i | |||||
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148.485 | − | 204.373i | 0.183997 | − | 0.253250i | |||||
758.506 | − | 633.544i | 0.938745 | − | 0.784089i | |||||
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0.335958 | − | 0.941877i | ||||||||
141.043 | − | 257.515i | 0.174127 | − | 0.317920i | |||||
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1897.06 | + | 113.362i | 2.33628 | + | 0.139608i | |||||
20.2577 | 0.0249172 | |||||||||
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173.766i | 0.213210i | |||||||||
19.5731 | − | 3.86157i | 0.0239866 | − | 0.00473232i | |||||
295.934 | − | 215.009i | 0.362220 | − | 0.263168i | |||||
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22.5451 | + | 35.2796i | 0.0274941 | + | 0.0430239i | |||||
360.162 | + | 261.673i | 0.438688 | + | 0.318725i | 0.785113 | − | 0.619352i | ||
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1456.88 | − | 584.788i | 1.76806 | − | 0.709694i | |||||
22.9036 | + | 35.1087i | 0.0277619 | + | 0.0425560i | |||||
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323.516 | + | 105.117i | 0.391192 | + | 0.127106i | 0.498007 | − | 0.867173i | ||
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157.617 | + | 114.515i | 0.190128 | + | 0.138136i | 0.678777 | − | 0.734344i | ||
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222.644 | − | 72.3415i | 0.267923 | − | 0.0870536i | |||||
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0.144852 | − | 0.989453i | ||||||||
31.8542 | − | 126.540i | 0.0379216 | − | 0.150643i | |||||
501.631 | + | 1543.86i | 0.596469 | + | 1.83574i | |||||
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514.472 | + | 422.889i | 0.609564 | + | 0.501053i | |||||
110.045 | − | 338.683i | 0.130230 | − | 0.400808i | |||||
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87.8894 | − | 270.496i | 0.103521 | − | 0.318605i | |||||
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164.029 | + | 256.680i | 0.192523 | + | 0.301268i | |||||
321.857 | + | 990.574i | 0.377323 | + | 1.16128i | 0.941898 | + | 0.335900i | ||
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1484.36 | + | 812.994i | 1.73812 | + | 0.951984i | |||||
167.339 | + | 230.323i | 0.195719 | + | 0.269384i | |||||
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0.866963 | − | 0.498372i | ||||||||
215.963 | + | 12.9052i | 0.251120 | + | 0.0150061i | |||||
27.6243 | − | 20.0702i | 0.0320839 | − | 0.0233103i | |||||
−370.540 | − | 202.947i | −0.429860 | − | 0.235438i | |||||
−630.616 | + | 204.900i | −0.730725 | + | 0.237427i | −0.650667 | − | 0.759363i | ||
−0.0800582 | + | 0.996790i | ||||||||
−345.655 | − | 247.002i | −0.400063 | − | 0.285882i | |||||
−544.521 | − | 395.618i | −0.629504 | − | 0.457361i | |||||
−496.042 | − | 526.568i | −0.572797 | − | 0.608047i | |||||
207.544 | + | 67.4353i | 0.239382 | + | 0.0777800i | |||||
1310.86 | − | 340.970i | 1.51020 | − | 0.392823i | |||||
−447.972 | − | 686.692i | −0.515503 | − | 0.790209i | |||||
167.836 | − | 21.4709i | 0.192915 | − | 0.0246792i | |||||
172.511 | + | 56.0521i | 0.198060 | + | 0.0643537i | |||||
−78.5451 | − | 49.3278i | −0.0900747 | − | 0.0565686i | |||||
−303.441 | − | 220.463i | −0.347584 | − | 0.252535i | |||||
249.490 | − | 117.881i | 0.285458 | − | 0.134875i | |||||
−101.767 | + | 33.0663i | −0.116306 | + | 0.0377900i | |||||
40.9064 | − | 104.275i | 0.0466968 | − | 0.119035i | |||||
−1166.19 | + | 847.283i | −1.32974 | + | 0.966116i | −0.329989 | + | 0.943985i | ||
−0.999755 | + | 0.0221308i | ||||||||
−211.298 | + | 1117.21i | −0.240658 | + | 1.27245i | |||||
− | 238.979i | − | 0.271876i | |||||||
−352.873 | + | 174.243i | −0.400992 | + | 0.198004i | |||||
338.683 | 0.384431 | 0.192215 | − | 0.981353i | ||||||
0.192215 | + | 0.981353i | ||||||||
704.812 | + | 133.301i | 0.799107 | + | 0.151135i | |||||
783.323 | + | 1078.15i | 0.887116 | + | 1.22101i | 0.974399 | + | 0.224827i | ||
−0.0872829 | + | 0.996184i | ||||||||
19.0143 | + | 7.45917i | 0.0215094 | + | 0.00843797i | |||||
−29.5729 | − | 91.0160i | −0.0334157 | − | 0.102843i | |||||
465.520 | + | 985.253i | 0.525417 | + | 1.11202i | |||||
952.972 | − | 1311.65i | 1.07438 | − | 1.47875i | 0.208811 | − | 0.977956i | ||
0.865565 | − | 0.500796i | ||||||||
−171.979 | + | 273.844i | −0.193671 | + | 0.308383i | |||||
13.7585 | − | 42.3442i | 0.0154763 | − | 0.0476313i | |||||
66.0230 | + | 516.095i | 0.0741831 | + | 0.579882i | |||||
188.363 | + | 697.190i | 0.211406 | + | 0.782480i | |||||
269.138 | + | 1034.70i | 0.301724 | + | 1.15997i | |||||
54.8338 | − | 168.761i | 0.0614040 | − | 0.188982i | |||||
−79.2000 | + | 74.6086i | −0.0885906 | + | 0.0834548i | |||||
−411.249 | + | 566.036i | −0.459496 | + | 0.632442i | |||||
1143.93 | + | 438.405i | 1.27671 | + | 0.489291i | |||||
6.70657 | + | 20.6407i | 0.00747666 | + | 0.0230108i | |||||
354.951 | − | 648.066i | 0.395268 | − | 0.721677i | |||||
1032.36 | + | 1420.92i | 1.14834 | + | 1.58055i | |||||
−10.0440 | + | 168.082i | −0.0111600 | + | 0.186758i | |||||
61.1975 | 0.0679218 | |||||||||
−100.098 | − | 24.1996i | −0.110974 | − | 0.0268288i | |||||
− | 176.443i | − | 0.195396i | |||||||
1065.79 | − | 72.1052i | 1.17897 | − | 0.0797624i | |||||
431.926 | − | 313.812i | 0.477266 | − | 0.346754i | |||||
−32.9782 | + | 60.2113i | −0.0363998 | + | 0.0664584i | |||||
−702.346 | + | 228.206i | −0.774362 | + | 0.251605i | −0.669431 | − | 0.742874i | ||
−0.104931 | + | 0.994480i | ||||||||
−439.075 | + | 280.587i | −0.483563 | + | 0.309017i | |||||
841.427 | + | 611.332i | 0.925662 | + | 0.672533i | |||||
97.2406 | − | 91.6033i | 0.106858 | − | 0.100663i | |||||
1556.35 | + | 505.690i | 1.70840 | + | 0.555093i | 0.990066 | − | 0.140603i | ||
0.718336 | + | 0.695697i | ||||||||
161.042 | − | 89.8577i | 0.176581 | − | 0.0985282i | |||||
420.262 | + | 160.323i | 0.460308 | + | 0.175601i | |||||
−61.1954 | − | 478.358i | −0.0669534 | − | 0.523368i | |||||
143.308 | + | 46.5634i | 0.156620 | + | 0.0508890i | |||||
699.151 | − | 850.563i | 0.763266 | − | 0.928563i | |||||
1814.11 | + | 1318.03i | 1.97831 | + | 1.43733i | |||||
18.5576 | + | 39.2763i | 0.0202152 | + | 0.0427847i | |||||
855.560 | − | 277.988i | 0.930968 | − | 0.302490i | 0.196010 | − | 0.980602i | ||
0.734959 | + | 0.678112i | ||||||||
158.265 | + | 39.8403i | 0.172027 | + | 0.0433047i | |||||
163.907 | − | 119.085i | 0.177966 | − | 0.129300i | |||||
160.513 | + | 30.3579i | 0.174092 | + | 0.0329262i | |||||
311.862i | 0.337879i | |||||||||
159.017 | + | 278.796i | 0.172097 | + | 0.301728i | |||||
265.174 | 0.286675 | |||||||||
73.1672 | − | 386.861i | 0.0790142 | − | 0.417777i | |||||
971.084 | + | 1336.58i | 1.04756 | + | 1.44184i | |||||
12.4950 | + | 1588.49i | 0.0134644 | + | 1.71173i | |||||
−140.272 | − | 431.712i | −0.150992 | − | 0.464707i | 0.846741 | − | 0.532006i | ||
−0.997733 | + | 0.0672996i | ||||||||
109.036 | − | 51.5181i | 0.117243 | − | 0.0553958i | |||||
−378.666 | + | 521.189i | −0.406730 | + | 0.559816i | |||||
−966.739 | + | 1176.10i | −1.03727 | + | 1.26191i | |||||
−79.1411 | + | 243.571i | −0.0848243 | + | 0.261062i | |||||
−576.937 | + | 73.8064i | −0.617706 | + | 0.0790218i | |||||
40.1895 | + | 2.02261i | 0.0429834 | + | 0.00216322i | |||||
−78.3089 | − | 195.091i | −0.0836634 | − | 0.208430i | |||||
336.677 | − | 1036.19i | 0.359314 | − | 1.10585i | −0.594152 | − | 0.804353i | ||
0.953466 | − | 0.301501i | ||||||||
−762.777 | − | 809.719i | −0.813195 | − | 0.863240i | |||||
152.039 | − | 209.264i | 0.161916 | − | 0.222859i | |||||
88.4349 | − | 56.5136i | 0.0940796 | − | 0.0601208i | |||||
−524.773 | − | 1615.08i | −0.557676 | − | 1.71635i | −0.688771 | − | 0.724979i | ||
0.131095 | − | 0.991370i | ||||||||
−356.465 | − | 195.239i | −0.378413 | − | 0.207260i | |||||
25.1020 | + | 34.5499i | 0.0266193 | + | 0.0366383i | |||||
881.469 | − | 173.905i | 0.933760 | − | 0.184221i | |||||
284.123 | 0.300659 | |||||||||
−405.196 | + | 344.959i | −0.428325 | + | 0.364650i | |||||
− | 343.409i | − | 0.362628i | −0.983425 | − | 0.181314i | ||||
0.983425 | − | 0.181314i | ||||||||
−13.5545 | + | 226.829i | −0.0142980 | + | 0.239271i | |||||
92.7753 | − | 67.4052i | 0.0977611 | − | 0.0710276i | |||||
−132.635 | − | 72.6454i | −0.139616 | − | 0.0764689i | |||||
−27.9628 | + | 9.08566i | −0.0294035 | + | 0.00955379i | |||||
−80.3000 | − | 96.1386i | −0.0843487 | − | 0.100986i | |||||
793.582 | + | 576.571i | 0.832720 | + | 0.605006i | 0.920327 | − | 0.391149i | ||
−0.0876078 | + | 0.996155i | ||||||||
−431.893 | − | 458.472i | −0.452718 | − | 0.480578i | |||||
655.623 | + | 213.025i | 0.686516 | + | 0.223063i | |||||
−59.3499 | − | 228.170i | −0.0620815 | − | 0.238672i | |||||
−261.243 | + | 323.981i | −0.272981 | + | 0.338538i | |||||
776.734 | − | 99.3660i | 0.810787 | − | 0.103722i | |||||
553.368 | + | 179.800i | 0.577026 | + | 0.187487i | |||||
107.328 | + | 19.4258i | 0.111800 | + | 0.0202353i | |||||
235.243 | + | 170.914i | 0.244790 | + | 0.177850i | |||||
−299.332 | + | 141.431i | −0.311156 | + | 0.147017i | |||||
383.655 | − | 124.657i | 0.398396 | − | 0.129447i | |||||
−1378.15 | − | 540.638i | −1.42962 | − | 0.560828i | |||||
−619.463 | + | 450.066i | −0.641931 | + | 0.466390i | |||||
24.7347 | − | 130.781i | 0.0256052 | − | 0.135384i | |||||
1153.83i | 1.19321i | 0.802536 | + | 0.596604i | ||||||
−0.802536 | + | 0.596604i | ||||||||
329.357 | − | 910.246i | 0.340245 | − | 0.940337i | |||||
−18.8564 | −0.0194597 | |||||||||
195.765 | + | 37.0250i | 0.201819 | + | 0.0381701i | |||||
−92.5275 | − | 127.353i | −0.0952910 | − | 0.131157i | 0.758709 | − | 0.651429i | ||
−0.854000 | + | 0.520273i | ||||||||
247.639 | − | 631.261i | 0.254773 | − | 0.649445i | |||||
21.6653 | + | 66.6789i | 0.0222665 | + | 0.0685292i | |||||
−372.579 | − | 788.548i | −0.382525 | − | 0.809598i | |||||
6.99126 | − | 9.62264i | 0.00717052 | − | 0.00986937i | |||||
−594.264 | + | 1283.78i | −0.608877 | + | 1.31535i | |||||
95.6163 | − | 294.277i | 0.0978672 | − | 0.301204i | −0.890123 | − | 0.455720i | ||
0.987990 | + | 0.154516i | ||||||||
15.0314 | + | 117.499i | 0.0153695 | + | 0.120142i | |||||
−996.239 | − | 803.321i | −1.01761 | − | 0.820552i | |||||
−368.755 | + | 95.9179i | −0.376281 | + | 0.0978754i | |||||
30.1629 | − | 92.8318i | 0.0307471 | − | 0.0946297i | |||||
1391.74 | − | 1311.06i | 1.41725 | − | 1.33509i | |||||
719.649 | − | 990.512i | 0.732094 | − | 1.00764i | −0.266940 | − | 0.963713i | ||
0.999035 | − | 0.0439284i | ||||||||
18.2966 | + | 21.9054i | 0.0185941 | + | 0.0222616i | |||||
214.247 | + | 659.383i | 0.217509 | + | 0.669425i | |||||
78.0264 | − | 142.460i | 0.0791343 | − | 0.144483i | |||||
−50.3097 | − | 69.2453i | −0.0509723 | − | 0.0701574i | |||||
188.466 | + | 11.2621i | 0.190755 | + | 0.0113989i | |||||
220.679 | 0.223133 | |||||||||
−268.479 | − | 315.360i | −0.271191 | − | 0.318546i | |||||
2.98244i | 0.00300952i | 0.999999 | + | 0.00150476i | ||||||
−0.999999 | + | 0.00150476i | ||||||||
358.320 | + | 1073.98i | 0.361209 | + | 1.08264i | |||||
−170.599 | + | 123.947i | −0.171802 | + | 0.124821i | |||||
918.759 | − | 1677.46i | 0.924304 | − | 1.68759i | |||||
585.294 | − | 190.174i | 0.588236 | − | 0.191129i | |||||
−67.1287 | − | 105.046i | −0.0673983 | − | 0.105468i | |||||
−1322.62 | − | 960.939i | −1.32660 | − | 0.963830i | −0.999825 | − | 0.0187281i | ||
−0.326774 | − | 0.945102i | ||||||||
216.865 | − | 204.293i | 0.217300 | − | 0.204702i | |||||
−669.640 | − | 217.579i | −0.670310 | − | 0.217797i |
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 220.3.s.b.31.2 | ✓ | 96 | |
4.3 | odd | 2 | inner | 220.3.s.b.31.21 | yes | 96 | |
11.5 | even | 5 | inner | 220.3.s.b.71.21 | yes | 96 | |
44.27 | odd | 10 | inner | 220.3.s.b.71.2 | yes | 96 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
220.3.s.b.31.2 | ✓ | 96 | 1.1 | even | 1 | trivial | |
220.3.s.b.31.21 | yes | 96 | 4.3 | odd | 2 | inner | |
220.3.s.b.71.2 | yes | 96 | 44.27 | odd | 10 | inner | |
220.3.s.b.71.21 | yes | 96 | 11.5 | even | 5 | inner |