Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [63,3,Mod(40,63)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(63, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 5]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("63.40");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 63.t (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 | 40.11 | ||
Character | 63.40 | ||
Dual form | 63.3.t.a.52.11 |
-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 .
2.24050 | 1.12025 | 0.560124 | − | 0.828409i | ||||||
0.560124 | + | 0.828409i | ||||||||
2.95463 | − | 0.519775i | 0.984876 | − | 0.173258i | |||||
1.01982 | 0.254955 | |||||||||
−1.67528 | + | 0.967222i | −0.335055 | + | 0.193444i | −0.658083 | − | 0.752945i | ||
0.323028 | + | 0.946389i | ||||||||
6.61983 | − | 1.16455i | 1.10331 | − | 0.194092i | |||||
−6.98642 | + | 0.435817i | −0.998060 | + | 0.0622596i | |||||
−6.67708 | −0.834635 | |||||||||
8.45967 | − | 3.07148i | 0.939963 | − | 0.341276i | |||||
−3.75345 | + | 2.16706i | −0.375345 | + | 0.216706i | |||||
0.186168 | − | 0.322453i | 0.0169244 | − | 0.0293139i | −0.857439 | − | 0.514585i | ||
0.874364 | + | 0.485271i | ||||||||
3.01319 | − | 0.530076i | 0.251099 | − | 0.0441730i | |||||
5.01827 | + | 2.89730i | 0.386021 | + | 0.222869i | 0.680435 | − | 0.732809i | ||
−0.294414 | + | 0.955678i | ||||||||
−15.6530 | + | 0.976446i | −1.11807 | + | 0.0697462i | |||||
−4.44709 | + | 3.72855i | −0.296472 | + | 0.248570i | |||||
−19.0392 | −1.18995 | |||||||||
9.96576 | − | 5.75374i | 0.586221 | − | 0.338455i | −0.177381 | − | 0.984142i | ||
0.763602 | + | 0.645687i | ||||||||
18.9538 | − | 6.88165i | 1.05299 | − | 0.382314i | |||||
18.2323 | + | 10.5264i | 0.959593 | + | 0.554021i | 0.896048 | − | 0.443958i | ||
0.0635451 | + | 0.997979i | ||||||||
−1.70848 | + | 0.986391i | −0.0854239 | + | 0.0493195i | |||||
−20.4158 | + | 4.91904i | −0.972179 | + | 0.234240i | |||||
0.417109 | − | 0.722455i | 0.0189595 | − | 0.0328389i | |||||
−13.6417 | − | 23.6282i | −0.593119 | − | 1.02731i | −0.993809 | − | 0.111099i | ||
0.400690 | − | 0.916214i | ||||||||
−19.7283 | + | 3.47058i | −0.822013 | + | 0.144608i | |||||
−10.6290 | + | 18.4099i | −0.425159 | + | 0.736396i | |||||
11.2434 | + | 6.49139i | 0.432439 | + | 0.249669i | |||||
23.3987 | − | 13.4722i | 0.866619 | − | 0.498971i | |||||
−7.12488 | + | 0.444454i | −0.254460 | + | 0.0158734i | |||||
−20.1404 | − | 34.8842i | −0.694497 | − | 1.20290i | −0.970350 | − | 0.241704i | ||
0.275853 | − | 0.961200i | ||||||||
−9.96367 | + | 8.35380i | −0.332122 | + | 0.278460i | |||||
48.8145i | 1.57466i | 0.616530 | + | 0.787331i | ||||||
−0.616530 | + | 0.787331i | ||||||||
−15.9490 | −0.498406 | |||||||||
0.382456 | − | 1.04950i | 0.0115896 | − | 0.0318029i | |||||
22.3282 | − | 12.8912i | 0.656713 | − | 0.379154i | |||||
11.2827 | − | 7.48753i | 0.322362 | − | 0.213929i | |||||
8.62732 | − | 3.13236i | 0.239648 | − | 0.0870099i | |||||
14.7691 | − | 25.5809i | 0.399166 | − | 0.691376i | −0.594457 | − | 0.804127i | ||
0.993623 | + | 0.112751i | ||||||||
40.8493 | + | 23.5844i | 1.07498 | + | 0.620641i | |||||
16.3331 | + | 5.95208i | 0.418797 | + | 0.152617i | |||||
11.1860 | − | 6.45822i | 0.279649 | − | 0.161455i | |||||
19.6397 | + | 11.3390i | 0.479016 | + | 0.276560i | 0.720006 | − | 0.693968i | ||
−0.240990 | + | 0.970528i | ||||||||
−45.7414 | + | 11.0211i | −1.08908 | + | 0.262407i | |||||
10.7407 | + | 18.6035i | 0.249785 | + | 0.432639i | 0.963466 | − | 0.267831i | ||
−0.713681 | + | 0.700470i | ||||||||
0.189858 | − | 0.328844i | 0.00431495 | − | 0.00747372i | |||||
−11.2015 | + | 13.3280i | −0.248922 | + | 0.296177i | |||||
−30.5642 | − | 52.9388i | −0.664440 | − | 1.15084i | |||||
− | 53.3035i | − | 1.13412i | −0.823677 | − | 0.567059i | ||||
0.823677 | − | 0.567059i | ||||||||
−56.2539 | + | 9.89612i | −1.17196 | + | 0.206169i | |||||
48.6201 | − | 6.08960i | 0.992247 | − | 0.124278i | |||||
−23.8141 | + | 41.2473i | −0.476283 | + | 0.824946i | |||||
26.4545 | − | 22.1801i | 0.518716 | − | 0.434904i | |||||
5.11773 | + | 2.95472i | 0.0984178 | + | 0.0568216i | |||||
43.7300 | + | 75.7426i | 0.825094 | + | 1.42911i | 0.901847 | + | 0.432055i | ||
−0.0767530 | + | 0.997050i | ||||||||
52.4247 | − | 30.1844i | 0.970827 | − | 0.558971i | |||||
0.720265i | 0.0130957i | |||||||||
46.6489 | − | 2.90999i | 0.833016 | − | 0.0519641i | |||||
59.3409 | + | 21.6249i | 1.04107 | + | 0.379385i | |||||
−45.1245 | − | 78.1579i | −0.778008 | − | 1.34755i | |||||
9.23111i | 0.156460i | 0.996935 | + | 0.0782298i | ||||||
−0.996935 | + | 0.0782298i | ||||||||
−4.53522 | + | 3.80244i | −0.0755870 | + | 0.0633740i | |||||
− | 70.5346i | − | 1.15631i | −0.815929 | − | 0.578153i | ||||
0.815929 | − | 0.578153i | ||||||||
109.369i | 1.76401i | |||||||||
−57.7642 | + | 25.1456i | −0.916892 | + | 0.399136i | |||||
40.4233 | 0.631614 | |||||||||
−11.2093 | −0.172451 | |||||||||
0.856890 | − | 2.35139i | 0.0129832 | − | 0.0356271i | |||||
−75.5440 | −1.12752 | −0.563761 | − | 0.825938i | ||||||
−0.563761 | + | 0.825938i | ||||||||
10.1633 | − | 5.86777i | 0.149460 | − | 0.0862907i | |||||
−52.5876 | − | 62.7219i | −0.762139 | − | 0.909013i | |||||
25.2787 | − | 16.7758i | 0.361125 | − | 0.239654i | |||||
−97.4729 | −1.37286 | −0.686429 | − | 0.727197i | ||||||
−0.686429 | + | 0.727197i | ||||||||
−56.4859 | + | 20.5086i | −0.784526 | + | 0.284841i | |||||
−75.3269 | + | 43.4900i | −1.03188 | + | 0.595754i | −0.917521 | − | 0.397687i | ||
−0.114354 | + | 0.993440i | ||||||||
33.0902 | − | 57.3139i | 0.447165 | − | 0.774512i | |||||
−21.8356 | + | 59.9191i | −0.291142 | + | 0.798922i | |||||
18.5936 | + | 10.7350i | 0.244653 | + | 0.141250i | |||||
−1.16012 | + | 2.33393i | −0.0150665 | + | 0.0303108i | |||||
36.5942 | + | 13.3356i | 0.469156 | + | 0.170969i | |||||
−47.1994 | −0.597461 | −0.298730 | − | 0.954338i | ||||||
−0.298730 | + | 0.954338i | ||||||||
31.8960 | − | 18.4152i | 0.398700 | − | 0.230190i | |||||
62.1320 | − | 51.9675i | 0.767061 | − | 0.641574i | |||||
44.0025 | + | 25.4049i | 0.536616 | + | 0.309816i | |||||
−81.1770 | + | 46.8676i | −0.978036 | + | 0.564669i | −0.901677 | − | 0.432411i | ||
−0.0763594 | + | 0.997080i | ||||||||
−20.8204 | + | 5.01653i | −0.247861 | + | 0.0597206i | |||||
−11.1303 | + | 19.2782i | −0.130944 | + | 0.226802i | |||||
24.0646 | + | 41.6810i | 0.279821 | + | 0.484663i | |||||
−77.6394 | − | 92.6014i | −0.892407 | − | 1.06438i | |||||
−1.24306 | + | 2.15305i | −0.0141257 | + | 0.0244664i | |||||
−25.6803 | − | 14.8266i | −0.288543 | − | 0.166590i | 0.348742 | − | 0.937219i | ||
−0.637285 | + | 0.770628i | ||||||||
−25.0969 | + | 29.8612i | −0.278854 | + | 0.331792i | |||||
−36.3225 | − | 18.0547i | −0.399148 | − | 0.198403i | |||||
−13.9121 | − | 24.0965i | −0.151218 | − | 0.261918i | |||||
25.3726 | + | 144.229i | 0.272823 | + | 1.55085i | |||||
− | 119.426i | − | 1.27049i | |||||||
−40.7255 | −0.428689 | |||||||||
−47.1234 | + | 8.28989i | −0.490869 | + | 0.0863531i | |||||
122.538 | − | 70.7471i | 1.26327 | − | 0.729351i | 0.289567 | − | 0.957158i | ||
0.973706 | + | 0.227806i | ||||||||
108.933 | − | 13.6437i | 1.11156 | − | 0.139222i | |||||
0.584513 | − | 3.29966i | 0.00590417 | − | 0.0333299i | |||||
−10.8396 | + | 18.7748i | −0.108396 | + | 0.187748i | |||||
40.6345 | + | 23.4603i | 0.402321 | + | 0.232280i | 0.687485 | − | 0.726198i | ||
−0.285164 | + | 0.958479i | ||||||||
59.2712 | − | 49.6944i | 0.581090 | − | 0.487200i | |||||
−113.923 | + | 65.7733i | −1.10605 | + | 0.638576i | −0.937802 | − | 0.347169i | ||
−0.168244 | + | 0.985745i | ||||||||
−33.5074 | − | 19.3455i | −0.322187 | − | 0.186015i | |||||
29.4442 | − | 27.9873i | 0.280421 | − | 0.266546i | |||||
97.9768 | + | 169.701i | 0.924310 | + | 1.60095i | |||||
69.9586 | − | 121.172i | 0.653819 | − | 1.13245i | −0.328369 | − | 0.944549i | ||
0.982188 | − | 0.187899i | ||||||||
23.8624 | − | 13.7392i | 0.220948 | − | 0.127215i | |||||
55.5420 | + | 96.2016i | 0.509560 | + | 0.882583i | 0.999939 | + | 0.0110739i | ||
−0.490379 | + | 0.871509i | ||||||||
1.61375i | 0.0146704i | |||||||||
30.3410 | − | 83.2587i | 0.273343 | − | 0.750079i | |||||
133.016 | − | 8.29763i | 1.18764 | − | 0.0740860i | |||||
50.7636 | − | 87.9252i | 0.449236 | − | 0.778099i | −0.549101 | − | 0.835756i | ||
0.998336 | + | 0.0576571i | ||||||||
132.953 | + | 48.4506i | 1.16626 | + | 0.425005i | |||||
45.7074 | + | 26.3892i | 0.397456 | + | 0.229471i | |||||
−20.5396 | − | 35.5756i | −0.177065 | − | 0.306686i | |||||
51.3519 | + | 9.09666i | 0.438906 | + | 0.0777492i | |||||
20.6823i | 0.175273i | |||||||||
−67.1174 | + | 44.5413i | −0.564012 | + | 0.374296i | |||||
29.6936 | − | 24.8958i | 0.247446 | − | 0.207465i | |||||
60.4307 | + | 104.669i | 0.499427 | + | 0.865033i | |||||
− | 158.032i | − | 1.29535i | |||||||
63.9216 | + | 23.2942i | 0.519688 | + | 0.189384i | |||||
49.7820i | 0.401468i | |||||||||
− | 89.4834i | − | 0.715867i | |||||||
−129.420 | + | 56.3385i | −1.02715 | + | 0.447131i | |||||
−49.1014 | −0.386625 | −0.193312 | − | 0.981137i | ||||||
−0.193312 | + | 0.981137i | ||||||||
154.364 | 1.20597 | |||||||||
41.4045 | + | 49.3837i | 0.320965 | + | 0.382819i | |||||
−25.1145 | −0.193188 | |||||||||
−107.596 | + | 62.1204i | −0.821341 | + | 0.474202i | −0.850879 | − | 0.525362i | ||
0.0295376 | + | 0.999564i | ||||||||
0.390035 | − | 1.07029i | 0.00295481 | − | 0.00810829i | |||||
−131.966 | − | 65.5959i | −0.992224 | − | 0.493203i | |||||
−169.256 | −1.26310 | |||||||||
−26.1687 | + | 45.2014i | −0.193842 | + | 0.334826i | |||||
−66.5422 | + | 38.4182i | −0.489281 | + | 0.282487i | |||||
−2.31536 | + | 4.01032i | −0.0169004 | + | 0.0292724i | −0.874352 | − | 0.485292i | ||
0.857452 | + | 0.514565i | ||||||||
−117.822 | − | 140.528i | −0.853785 | − | 1.01832i | |||||
37.7043 | + | 21.7686i | 0.271254 | + | 0.156608i | 0.629457 | − | 0.777035i | ||
−0.358204 | + | 0.933644i | ||||||||
11.5063 | − | 7.63592i | 0.0821876 | − | 0.0545423i | |||||
−27.7058 | − | 157.492i | −0.196495 | − | 1.11697i | |||||
−218.387 | −1.53794 | |||||||||
1.86849 | − | 1.07877i | 0.0130664 | − | 0.00754386i | |||||
−161.066 | + | 58.4787i | −1.11851 | + | 0.406102i | |||||
67.4815 | + | 38.9605i | 0.465390 | + | 0.268693i | |||||
−168.770 | + | 97.4391i | −1.15596 | + | 0.667391i | |||||
140.489 | − | 43.2640i | 0.955709 | − | 0.294313i | |||||
15.0618 | − | 26.0879i | 0.101769 | − | 0.176269i | |||||
13.1304 | + | 22.7425i | 0.0881232 | + | 0.152634i | 0.906718 | − | 0.421738i | ||
−0.818595 | + | 0.574372i | ||||||||
−48.9226 | + | 134.248i | −0.326151 | + | 0.894990i | |||||
−59.9365 | + | 103.813i | −0.396931 | + | 0.687504i | −0.993346 | − | 0.115172i | ||
0.596415 | + | 0.802676i | ||||||||
−121.738 | − | 70.2857i | −0.800910 | − | 0.462406i | |||||
66.6345 | − | 79.2844i | 0.435520 | − | 0.518199i | |||||
−2.59924 | + | 5.22916i | −0.0168782 | + | 0.0339556i | |||||
−47.2145 | − | 81.7779i | −0.304610 | − | 0.527599i | |||||
16.6568 | + | 6.07004i | 0.106774 | + | 0.0389105i | |||||
− | 195.955i | − | 1.24812i | −0.781377 | − | 0.624059i | ||||
0.781377 | − | 0.624059i | ||||||||
−105.750 | −0.669304 | |||||||||
168.575 | + | 201.061i | 1.06022 | + | 1.26454i | |||||
26.7190 | − | 15.4262i | 0.166994 | − | 0.0964139i | |||||
105.604 | + | 159.131i | 0.655928 | + | 0.988392i | |||||
139.206 | − | 116.433i | 0.859299 | − | 0.718722i | |||||
41.8418 | − | 72.4721i | 0.256698 | − | 0.444614i | −0.708657 | − | 0.705553i | ||
0.965355 | + | 0.260939i | ||||||||
20.0289 | + | 11.5637i | 0.122127 | + | 0.0705102i | |||||
0.374376 | + | 2.12811i | 0.00226894 | + | 0.0128977i | |||||
−181.877 | + | 105.007i | −1.09564 | + | 0.632569i | |||||
215.835 | + | 124.612i | 1.29242 | + | 0.746181i | 0.979083 | − | 0.203460i | ||
0.313340 | + | 0.949641i | ||||||||
136.318 | − | 32.8449i | 0.811415 | − | 0.195505i | |||||
−67.7113 | − | 117.279i | −0.400659 | − | 0.693961i | |||||
−24.9373 | + | 43.1927i | −0.146690 | + | 0.254075i | |||||
186.571 | + | 33.0497i | 1.09106 | + | 0.193273i | |||||
10.9536 | + | 18.9722i | 0.0636837 | + | 0.110303i | |||||
278.453i | 1.60956i | 0.593575 | + | 0.804779i | ||||||
−0.593575 | + | 0.804779i | ||||||||
−173.951 | − | 207.473i | −0.999716 | − | 1.19237i | |||||
66.2351 | − | 133.252i | 0.378486 | − | 0.761438i | |||||
−3.54451 | + | 6.13926i | −0.0201392 | + | 0.0348822i | |||||
4.79810 | + | 27.2745i | 0.0271079 | + | 0.154093i | |||||
−57.5367 | − | 33.2188i | −0.323240 | − | 0.186623i | |||||
−128.758 | − | 223.015i | −0.719317 | − | 1.24589i | −0.961271 | − | 0.275605i | ||
0.241954 | − | 0.970288i | ||||||||
−11.4235 | + | 13.5921i | −0.0634638 | + | 0.0755117i | |||||
− | 29.2542i | − | 0.161625i | −0.996729 | − | 0.0808126i | ||||
0.996729 | − | 0.0808126i | ||||||||
−81.3803 | − | 40.4515i | −0.447144 | − | 0.222261i | |||||
−36.6621 | − | 208.404i | −0.200340 | − | 1.13882i | |||||
91.0870 | + | 157.767i | 0.495038 | + | 0.857431i | |||||
57.1402i | 0.308866i | |||||||||
56.8471 | + | 323.144i | 0.305630 | + | 1.73733i | |||||
− | 4.28466i | − | 0.0229126i | |||||||
− | 54.3599i | − | 0.289149i | |||||||
−157.602 | + | 104.320i | −0.833872 | + | 0.551959i | |||||
−91.2452 | −0.480238 | |||||||||
−60.7704 | −0.318170 | −0.159085 | − | 0.987265i | ||||||
−0.159085 | + | 0.987265i | ||||||||
119.436 | − | 21.0110i | 0.622062 | − | 0.109432i | |||||
24.8767 | 0.128895 | 0.0644474 | − | 0.997921i | ||||||
0.0644474 | + | 0.997921i | ||||||||
274.545 | − | 158.508i | 1.41518 | − | 0.817054i | |||||
−33.1194 | + | 5.82633i | −0.169843 | + | 0.0298786i | |||||
49.5837 | − | 6.21029i | 0.252978 | − | 0.0316851i | |||||
174.320 | 0.884873 | 0.442437 | − | 0.896800i | ||||||
0.442437 | + | 0.896800i | ||||||||
1.30960 | − | 7.39287i | 0.00661413 | − | 0.0373377i | |||||
250.227 | − | 144.468i | 1.25742 | − | 0.725972i | 0.284848 | − | 0.958573i | ||
0.972572 | + | 0.232600i | ||||||||
70.9705 | − | 122.924i | 0.354852 | − | 0.614622i | |||||
−223.204 | + | 39.2659i | −1.11047 | + | 0.195353i | |||||
91.0413 | + | 52.5627i | 0.450699 | + | 0.260211i | |||||
155.912 | + | 234.938i | 0.768042 | + | 1.15733i | |||||
26.9788 | − | 22.6197i | 0.132249 | − | 0.110881i | |||||
−43.8692 | −0.213996 | |||||||||
−255.243 | + | 147.365i | −1.23905 | + | 0.715363i | |||||
−187.978 | − | 157.986i | −0.908107 | − | 0.763218i | |||||
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6.78854 | − | 3.91937i | 0.0324811 | − | 0.0187530i | |||||
65.9697 | − | 62.7055i | 0.314141 | − | 0.298597i | |||||
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44.5967 | + | 77.2437i | 0.210362 | + | 0.364357i | |||||
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156.742 | − | 271.485i | 0.732439 | − | 1.26862i | |||||
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124.442 | + | 215.539i | 0.570833 | + | 0.988712i | |||||
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0.734539i | 0.00333881i | |||||||||
66.6812 | 0.301725 | |||||||||
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14.0772 | − | 8.12745i | 0.0631263 | − | 0.0364460i | −0.468105 | − | 0.883673i | ||
0.531231 | + | 0.847227i | ||||||||
111.426 | − | 6.95085i | 0.497439 | − | 0.0310306i | |||||
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60.5170 | + | 22.0535i | 0.265425 | + | 0.0967259i | |||||
158.134 | − | 91.2986i | 0.690541 | − | 0.398684i | −0.113274 | − | 0.993564i | ||
0.803815 | + | 0.594880i | ||||||||
102.407 | + | 59.1248i | 0.445249 | + | 0.257064i | |||||
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134.479 | + | 232.925i | 0.579652 | + | 1.00399i | |||||
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0.947515 | − | 0.319710i | ||||||||
115.054 | + | 20.3810i | 0.491683 | + | 0.0870984i | |||||
51.5563 | + | 89.2982i | 0.219389 | + | 0.379992i | |||||
9.41406i | 0.0398901i | |||||||||
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0.950957 | + | 0.309324i | ||||||||
84.6692 | − | 70.9888i | 0.352788 | − | 0.295786i | |||||
243.343 | + | 140.494i | 1.00972 | + | 0.582964i | 0.911110 | − | 0.412162i | ||
0.0986123 | + | 0.995126i | ||||||||
135.395 | + | 234.510i | 0.559482 | + | 0.969051i | |||||
156.566 | − | 185.839i | 0.644303 | − | 0.764771i | |||||
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143.216 | + | 52.1906i | 0.582179 | + | 0.212157i | |||||
60.9963 | + | 105.649i | 0.246949 | + | 0.427728i | |||||
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16.5983i | 0.0661286i | 0.999453 | + | 0.0330643i | ||||||
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184.159 | 0.719371 | |||||||||
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0.636636 | + | 0.771164i | ||||||||
92.7666 | + | 110.644i | 0.359561 | + | 0.428852i | |||||
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178.327 | − | 308.872i | 0.678050 | − | 1.17442i | −0.297517 | − | 0.954717i | ||
0.975567 | − | 0.219701i | ||||||||
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0.779043 | + | 0.626970i | ||||||||
84.4762 | + | 48.7724i | 0.303871 | + | 0.175440i | |||||
149.933 | + | 412.955i | 0.537395 | + | 1.48012i | |||||
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0.784748 | − | 0.619815i | ||||||||
−99.4046 | −0.350016 | |||||||||
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151.192 | + | 87.2908i | 0.521352 | + | 0.301003i | |||||
325.280 | − | 272.723i | 1.11780 | − | 0.937194i | |||||
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314.765 | − | 96.9329i | 1.07063 | − | 0.329704i | |||||
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0.0119384 | − | 10.0531i | 4.01967e−5 | − | 0.0338488i | |||||
29.4185 | + | 50.9544i | 0.0987198 | + | 0.170988i | |||||
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68.2226 | + | 118.165i | 0.223681 | + | 0.387426i | |||||
149.294 | − | 177.636i | 0.487890 | − | 0.580511i | |||||
432.680i | 1.40938i | 0.709515 | + | 0.704691i | ||||||
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167.189i | 0.537586i | 0.963198 | + | 0.268793i | ||||||
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0.910697 | − | 0.413075i | ||||||||
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72.4497 | − | 97.9966i | 0.229999 | − | 0.311100i | |||||
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377.691 | + | 450.477i | 1.18771 | + | 1.41660i | |||||
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143.720 | − | 394.381i | 0.447725 | − | 1.22860i | |||||
236.606 | + | 356.532i | 0.734802 | + | 1.10724i | |||||
242.265 | 0.750045 | |||||||||
63.3633 | − | 52.9974i | 0.195566 | − | 0.163572i | |||||
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93.7463 | − | 162.373i | 0.287565 | − | 0.498078i | |||||
214.109 | + | 255.371i | 0.654768 | + | 0.780950i | |||||
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0.838787 | + | 4.76803i | 0.00254178 | + | 0.0144486i | |||||
34.1563 | 0.103191 | 0.0515956 | − | 0.998668i | ||||||
0.0515956 | + | 0.998668i | ||||||||
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46.3707 | − | 261.769i | 0.139251 | − | 0.786094i | |||||
483.576 | + | 279.193i | 1.44783 | + | 0.835907i | |||||
126.557 | − | 73.0678i | 0.377783 | − | 0.218113i | |||||
388.701 | − | 93.6549i | 1.15685 | − | 0.278735i | |||||
205.854 | − | 356.550i | 0.610844 | − | 1.05801i | −0.380255 | − | 0.924882i | ||
0.991099 | − | 0.133130i | ||||||||
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104.286 | − | 286.172i | 0.307629 | − | 0.844165i | |||||
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15.7404 | + | 9.08773i | 0.0461595 | + | 0.0266502i | |||||
418.010 | + | 74.0478i | 1.22225 | + | 0.216514i | |||||
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148.765 | + | 54.2127i | 0.431202 | + | 0.157138i | |||||
623.874i | 1.80310i | |||||||||
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0.392022 | + | 0.919956i | ||||||||
148.399 | − | 298.550i | 0.423998 | − | 0.852999i | |||||
156.454 | + | 0.185795i | 0.445738 | + | 0.000529331i | |||||
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397.017 | + | 229.218i | 1.12469 | + | 0.649343i | 0.942595 | − | 0.333937i | ||
0.182099 | + | 0.983280i | ||||||||
10.7501 | + | 61.1084i | 0.0303676 | + | 0.172623i | |||||
163.294 | − | 94.2779i | 0.459983 | − | 0.265572i | |||||
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6.42758 | − | 11.1329i | 0.0179041 | − | 0.0310109i | −0.856935 | − | 0.515425i | ||
0.874839 | + | 0.484414i | ||||||||
74.7932 | − | 88.9919i | 0.207759 | − | 0.247200i | |||||
41.1103 | + | 71.2051i | 0.113879 | + | 0.197244i | |||||
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232.955 | + | 277.848i | 0.641748 | + | 0.765421i | |||||
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84.1290 | − | 145.716i | 0.230490 | − | 0.399221i | |||||
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535.505 | + | 309.174i | 1.45914 | + | 0.842436i | 0.998969 | − | 0.0453934i | ||
0.460173 | + | 0.887829i | ||||||||
259.728 | + | 449.863i | 0.705784 | + | 1.22245i | |||||
200.972 | + | 35.6009i | 0.544641 | + | 0.0964795i | |||||
128.022i | 0.346006i | |||||||||
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25.8754 | + | 147.087i | 0.0695576 | + | 0.395396i | |||||
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− | 9.59975i | − | 0.0256678i | |||||||
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355.912i | 0.946575i | |||||||||
− | 233.411i | − | 0.619128i | |||||||
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18.5015 | 0.0488165 | 0.0244083 | − | 0.999702i | ||||||
0.0244083 | + | 0.999702i | ||||||||
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49.0332 | − | 28.3093i | 0.128024 | − | 0.0739147i | −0.434620 | − | 0.900614i | ||
0.562644 | + | 0.826699i | ||||||||
456.089 | − | 80.2347i | 1.18773 | − | 0.208944i | |||||
−0.313904 | − | 5.03207i | −0.000815334 | − | 0.0130703i | |||||
55.7361 | 0.144394 | |||||||||
148.003 | + | 124.389i | 0.382438 | + | 0.321420i | |||||
124.966 | − | 72.1492i | 0.322077 | − | 0.185951i | |||||
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−0.999321 | + | 0.0368521i | ||||||||
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390.563 | 0.991277 | |||||||||
79.0721 | − | 45.6523i | 0.200182 | − | 0.115575i | |||||
0.596097 | − | 3.36505i | 0.00150530 | − | 0.00849761i | |||||
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560.632 | − | 323.681i | 1.40862 | − | 0.813269i | |||||
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202.367 | − | 350.511i | 0.505919 | − | 0.876277i | |||||
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−0.934219 | + | 0.356701i | ||||||||
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41.4398 | + | 23.9253i | 0.102574 | + | 0.0592209i | |||||
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349.321 | + | 526.378i | 0.860397 | + | 1.29650i | |||||
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432.530i | 1.05753i | 0.848768 | + | 0.528765i | ||||||
−0.848768 | + | 0.528765i | ||||||||
−98.2886 | −0.239728 | |||||||||
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−4.02308 | − | 64.4924i | −0.00974110 | − | 0.156156i | |||||
−421.164 | − | 353.967i | −1.01730 | − | 0.854993i | |||||
90.6626 | − | 157.032i | 0.218464 | − | 0.378391i | |||||
−80.0365 | − | 46.2091i | −0.192395 | − | 0.111080i | |||||
122.717 | + | 44.7203i | 0.294285 | + | 0.107243i | |||||
15.2097 | − | 8.78132i | 0.0363868 | − | 0.0210080i | |||||
−150.801 | − | 87.0648i | −0.359906 | − | 0.207792i | 0.309134 | − | 0.951019i | ||
−0.669040 | + | 0.743227i | ||||||||
30.0278 | − | 28.5420i | 0.0714947 | − | 0.0679571i | |||||
−175.470 | − | 303.923i | −0.416793 | − | 0.721907i | 0.578822 | − | 0.815454i | ||
−0.995615 | + | 0.0935470i | ||||||||
−335.180 | + | 580.549i | −0.794265 | + | 1.37571i | |||||
−163.721 | − | 450.930i | −0.387047 | − | 1.06603i | |||||
−291.989 | − | 505.739i | −0.688653 | − | 1.19278i | |||||
244.625i | 0.575588i | |||||||||
−645.254 | + | 113.512i | −1.51468 | + | 0.266461i | |||||
30.7402 | + | 492.785i | 0.0719911 | + | 1.15406i | |||||
71.3451 | − | 123.573i | 0.166694 | − | 0.288723i | |||||
4.95997 | − | 4.15856i | 0.0115617 | − | 0.00969362i | |||||
−80.6296 | − | 46.5515i | −0.187511 | − | 0.108259i | |||||
367.837 | + | 637.113i | 0.853451 | + | 1.47822i | 0.878075 | + | 0.478524i | ||
−0.0246236 | + | 0.999697i | ||||||||
−445.494 | + | 256.501i | −1.03124 | + | 0.593752i | |||||
− | 134.778i | − | 0.311266i | −0.987815 | − | 0.155633i | ||||
0.987815 | − | 0.155633i | ||||||||
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219.634 | + | 80.0386i | 0.504905 | + | 0.183997i | |||||
56.6427 | + | 98.1081i | 0.129915 | + | 0.225019i | |||||
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5.84694i | 0.0133188i | 0.999978 | + | 0.00665939i | ||||||
−0.999978 | + | 0.00665939i | ||||||||
− | 4.80927i | − | 0.0109302i | |||||||
392.606 | − | 200.852i | 0.890263 | − | 0.455447i | |||||
149.399 | 0.338007 | |||||||||
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30.9423 | − | 84.9088i | 0.0696900 | − | 0.191236i | |||||
57.3623 | 0.128904 | |||||||||
31.5398 | − | 18.2095i | 0.0707170 | − | 0.0408285i | |||||
50.6163 | + | 60.3707i | 0.113236 | + | 0.135057i | |||||
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46.7901 | 0.104209 | 0.0521047 | − | 0.998642i | ||||||
0.0521047 | + | 0.998642i | ||||||||
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78.3131 | − | 4.88522i | 0.172117 | − | 0.0107367i | |||||
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554.340 | 1.21300 | 0.606499 | − | 0.795084i | ||||||
0.606499 | + | 0.795084i | ||||||||
354.298 | − | 204.554i | 0.773577 | − | 0.446625i | |||||
155.670 | − | 268.891i | 0.339151 | − | 0.585819i | |||||
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0.366935 | + | 0.930246i | ||||||||
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0.867052 | + | 0.498218i | ||||||||
383.458 | + | 664.169i | 0.826418 | + | 1.43140i | |||||
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391.858 | − | 678.718i | 0.840897 | − | 1.45648i | |||||
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52.3697 | + | 9.27694i | 0.111901 | + | 0.0198225i | |||||
527.782 | − | 32.9234i | 1.12533 | − | 0.0701991i | |||||
115.512 | + | 200.072i | 0.245770 | + | 0.425686i | |||||
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7.99834 | 0.0169098 | |||||||||
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602.583 | + | 506.441i | 1.26328 | + | 1.06172i | |||||
111.163 | − | 192.540i | 0.232559 | − | 0.402804i | |||||
165.785 | + | 95.7160i | 0.346106 | + | 0.199825i | 0.662969 | − | 0.748647i | ||
−0.316863 | + | 0.948471i | ||||||||
70.9266 | − | 59.4666i | 0.147764 | − | 0.123889i | |||||
148.231 | − | 85.5813i | 0.308173 | − | 0.177924i | |||||
545.209 | + | 314.777i | 1.13114 | + | 0.653064i | |||||
394.734 | + | 415.283i | 0.817255 | + | 0.859799i | |||||
61.6283 | + | 106.743i | 0.127331 | + | 0.220544i | |||||
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350.784 | − | 416.372i | 0.721778 | − | 0.856733i | |||||
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470.966i | 0.965093i | |||||||||
85.9578 | − | 235.876i | 0.175783 | − | 0.482365i | |||||
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0.821386 | + | 0.570373i | ||||||||
65.1884 | + | 23.7559i | 0.132497 | + | 0.0482843i | |||||
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136.662 | + | 236.705i | 0.276644 | + | 0.479161i | |||||
2.21228 | + | 6.09320i | 0.00446926 | + | 0.0123095i | |||||
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680.986 | − | 42.4803i | 1.37019 | − | 0.0854735i | |||||
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13.7715 | + | 23.8529i | 0.0275982 | + | 0.0478014i | 0.879495 | − | 0.475909i | ||
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− | 91.2568i | − | 0.182514i | |||||||
702.482 | + | 255.997i | 1.40216 | + | 0.510973i | |||||
37.1884i | 0.0740805i | |||||||||
49.4903i | 0.0983902i | 0.998789 | + | 0.0491951i | ||||||
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385.696 | − | 167.899i | 0.765270 | − | 0.333133i | |||||
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0.389249 | + | 0.921133i | ||||||||
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507.312 | − | 336.668i | 0.992782 | − | 0.658842i | |||||
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568.425 | + | 0.675026i | 1.10804 | + | 0.00131584i | |||||
165.318 | − | 95.4464i | 0.321630 | − | 0.185693i | |||||
127.235 | − | 220.377i | 0.247058 | − | 0.427917i | |||||
42.2251 | + | 50.3624i | 0.0818316 | + | 0.0976015i | |||||
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144.733 | + | 822.727i | 0.278869 | + | 1.58522i | |||||
74.8456 | 0.143934 | |||||||||
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−0.212306 | + | 0.977203i | ||||||||
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126.439 | − | 428.136i | 0.240837 | − | 0.815498i | |||||
399.541 | − | 692.026i | 0.759584 | − | 1.31564i | |||||
280.866 | + | 486.474i | 0.532953 | + | 0.923101i | |||||
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65.7048 | + | 113.804i | 0.123273 | + | 0.213516i | |||||
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270.662i | 0.505911i | |||||||||
504.413 | 0.941070 | |||||||||
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7.08792 | − | 16.8114i | 0.0131501 | − | 0.0311900i | |||||
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120.883 | + | 69.7918i | 0.223031 | + | 0.128767i | |||||
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−0.989633 | + | 0.143620i | ||||||||
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8.86688 | + | 15.3579i | 0.0161216 | + | 0.0279234i | |||||
− | 848.024i | − | 1.53906i | |||||||
351.132 | + | 418.799i | 0.636108 | + | 0.758694i | |||||
329.755 | − | 20.5703i | 0.596302 | − | 0.0371977i | |||||
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29.7000 | + | 168.828i | 0.0535136 | + | 0.304195i | |||||
38.4515 | + | 22.2000i | 0.0691574 | + | 0.0399280i | |||||
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−0.908767 | + | 0.417304i | ||||||||
335.924 | + | 925.223i | 0.602015 | + | 1.65811i | |||||
124.477i | 0.222677i | |||||||||
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165.535 | + | 286.715i | 0.294546 | + | 0.510168i | |||||
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0.993229 | − | 0.116174i | ||||||||
−28.2549 | − | 160.613i | −0.0500974 | − | 0.284776i | |||||
196.399i | 0.347608i | |||||||||
− | 786.000i | − | 1.38869i | |||||||
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650.834 | 1.14584 | |||||||||
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172.059 | 0.301330 | 0.150665 | − | 0.988585i | ||||||
0.150665 | + | 0.988585i | ||||||||
1.90552 | − | 1.10015i | 0.00333133 | − | 0.00192334i | |||||
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579.990 | 1.00868 | |||||||||
341.968 | − | 124.160i | 0.593694 | − | 0.215555i | |||||
27.4829 | − | 15.8672i | 0.0476306 | − | 0.0274996i | −0.475996 | − | 0.879448i | ||
0.523626 | + | 0.851948i | ||||||||
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73.5014 | − | 12.9303i | 0.126946 | − | 0.0223321i | |||||
68.8189 | + | 39.7326i | 0.118653 | + | 0.0685045i | |||||
546.711 | − | 362.815i | 0.940983 | − | 0.624466i | |||||
728.789 | − | 611.035i | 1.25222 | − | 1.04989i | |||||
32.5646 | 0.0558569 | |||||||||
502.964 | − | 290.386i | 0.861240 | − | 0.497237i | |||||
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−0.344779 | + | 0.938684i | ||||||||
143.273 | − | 44.1215i | 0.243662 | − | 0.0750365i | |||||
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515.051 | − | 90.6072i | 0.871491 | − | 0.153312i | |||||
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0.0267479 | − | 22.5239i | 4.50302e−5 | − | 0.0379190i | |||||
69.3590 | − | 139.536i | 0.116570 | − | 0.234515i | |||||
13.3906 | + | 23.1932i | 0.0224674 | + | 0.0389147i | |||||
664.236 | − | 556.912i | 1.11262 | − | 0.932852i | |||||
− | 354.215i | − | 0.592333i | |||||||
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145.798 | − | 400.085i | 0.242997 | − | 0.666808i | |||||
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0.303778 | + | 0.952743i | ||||||||
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296.314 | + | 107.982i | 0.488967 | + | 0.178189i | |||||
280.441 | − | 161.913i | 0.462012 | − | 0.266742i | −0.250878 | − | 0.968019i | ||
0.712890 | + | 0.701276i | ||||||||
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582.779 | + | 613.116i | 0.956944 | + | 1.00676i | |||||
152.852 | + | 264.748i | 0.250578 | + | 0.434014i | |||||
154.436 | − | 267.492i | 0.252760 | − | 0.437793i | |||||
67.9551 | − | 80.8557i | 0.111038 | − | 0.132117i | |||||
310.620 | + | 538.010i | 0.506721 | + | 0.877667i | 0.999970 | + | 0.00777855i | ||
−0.493248 | + | 0.869888i | ||||||||
969.418i | 1.57886i | |||||||||
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7.74622 | − | 15.5838i | 0.0125750 | − | 0.0252984i | |||||
372.353 | − | 644.935i | 0.603490 | − | 1.04527i | −0.388799 | − | 0.921323i | ||
0.992288 | − | 0.123952i | ||||||||
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−0.622930 | + | 0.782278i | ||||||||
−48.1502 | − | 83.3986i | −0.0776616 | − | 0.134514i | |||||
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374.587i | 0.602230i | |||||||||
185.875 | + | 92.3926i | 0.298355 | + | 0.148303i | |||||
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− | 579.359i | − | 0.925493i | |||||||
18.0204 | − | 15.1088i | 0.0287407 | − | 0.0240970i | |||||
− | 199.838i | − | 0.318214i | |||||||
− | 339.911i | − | 0.540399i | |||||||
162.323 | − | 219.561i | 0.257656 | − | 0.348509i | |||||
325.873 | 0.516439 | 0.258220 | − | 0.966086i | ||||||
0.258220 | + | 0.966086i | ||||||||
315.154 | 0.498662 | |||||||||
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−453.730 | −0.715663 | |||||||||
82.2584 | − | 47.4919i | 0.129541 | − | 0.0747904i | |||||
171.916 | + | 205.046i | 0.270308 | + | 0.322400i | |||||
261.633 | + | 110.308i | 0.410726 | + | 0.173168i | |||||
−33.6030 | −0.0526693 | |||||||||
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89.3312 | − | 154.726i | 0.139362 | − | 0.241383i | −0.787893 | − | 0.615812i | ||
0.927255 | + | 0.374429i | ||||||||
322.003 | − | 883.608i | 0.501563 | − | 1.37634i | |||||
−60.1837 | − | 34.7471i | −0.0935983 | − | 0.0540390i | 0.452470 | − | 0.891780i | ||
−0.546069 | + | 0.837740i | ||||||||
107.697 | + | 162.285i | 0.167232 | + | 0.251995i | |||||
−117.129 | − | 42.6840i | −0.181595 | − | 0.0661767i | |||||
542.793 | 0.840236 | |||||||||
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−0.165119 | + | 0.986274i | ||||||||
−414.860 | + | 346.991i | −0.640216 | + | 0.535480i | |||||
2.97660 | + | 1.71854i | 0.00458644 | + | 0.00264798i | |||||
−239.012 | + | 137.993i | −0.367710 | + | 0.212298i | |||||
−240.121 | − | 996.586i | −0.368849 | − | 1.53085i | |||||
42.6710 | − | 73.9084i | 0.0654463 | − | 0.113356i | |||||
−391.218 | − | 677.609i | −0.599108 | − | 1.03769i | −0.992953 | − | 0.118509i | ||
0.393845 | − | 0.919177i | ||||||||
479.711 | + | 572.157i | 0.733502 | + | 0.874857i | |||||
120.168 | − | 208.138i | 0.183463 | − | 0.317768i | |||||
−373.924 | − | 215.885i | −0.570006 | − | 0.329093i | |||||
−503.662 | + | 599.276i | −0.766608 | + | 0.912141i | |||||
52.0480 | + | 834.362i | 0.0791004 | + | 1.26803i | |||||
90.6800 | + | 157.062i | 0.137602 | + | 0.238334i | 0.926589 | − | 0.376077i | ||
−0.788986 | + | 0.614411i | ||||||||
0.381795 | + | 2.17029i | 0.000578477 | + | 0.00328832i | |||||
192.972i | 0.291940i | 0.989289 | + | 0.145970i | ||||||
−0.989289 | + | 0.145970i | ||||||||
76.5270 | 0.115600 | |||||||||
197.018 | − | 34.6592i | 0.297162 | − | 0.0522764i | |||||
542.025 | − | 312.939i | 0.816303 | − | 0.471293i | |||||
284.525 | − | 17.7489i | 0.427857 | − | 0.0266900i | |||||
103.893 | − | 586.493i | 0.155996 | − | 0.880620i | |||||
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220.112 | + | 127.082i | 0.329509 | + | 0.190242i | |||||
37.3683 | − | 31.3306i | 0.0558570 | − | 0.0468319i | |||||
283.551 | − | 163.708i | 0.423210 | − | 0.244340i | |||||
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325.611 | − | 78.4539i | 0.484540 | − | 0.116747i | |||||
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461.215 | − | 798.849i | 0.684296 | − | 1.18524i | |||||
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233.653 | − | 641.167i | 0.344621 | − | 0.945674i | |||||
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190.268 | + | 33.7047i | 0.278170 | + | 0.0492759i | |||||
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506.796i | 0.735553i | |||||||||
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1215.74i | 1.75939i | 0.475538 | + | 0.879695i | ||||||
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283.972i | 0.410364i | |||||||||
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−84.2201 | −0.121180 | |||||||||
518.405 | + | 618.307i | 0.744834 | + | 0.888373i | |||||
260.966 | 0.374413 | |||||||||
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350.535 | + | 0.416273i | 0.499337 | + | 0.000592981i | |||||
538.550 | − | 310.932i | 0.766074 | − | 0.442293i | |||||
7.52554 | − | 13.0346i | 0.0106897 | − | 0.0185151i | |||||
198.745 | + | 237.045i | 0.281908 | + | 0.336235i | |||||
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365.860 | − | 211.229i | 0.515295 | − | 0.297506i | |||||
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171.470 | + | 98.9981i | 0.240828 | + | 0.139042i | |||||
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101.928 | − | 279.699i | 0.142158 | − | 0.390097i | |||||
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0.710283 | + | 0.703917i | ||||||||
213.268 | − | 253.754i | 0.296205 | − | 0.352437i | |||||
767.247 | − | 509.170i | 1.06414 | − | 0.706199i | |||||
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792.014 | + | 288.625i | 1.09546 | + | 0.399204i | |||||
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856.287 | 1.18109 | |||||||||
521.934 | + | 622.517i | 0.718917 | + | 0.857461i | |||||
570.198 | − | 329.204i | 0.784317 | − | 0.452826i | −0.0536411 | − | 0.998560i | ||
0.837958 | + | 0.545735i | ||||||||
242.528 | + | 120.553i | 0.333143 | + | 0.165595i | |||||
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188.491 | − | 326.475i | 0.258206 | − | 0.447226i | |||||
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322.167 | − | 186.003i | 0.439518 | − | 0.253756i | −0.263875 | − | 0.964557i | ||
0.703393 | + | 0.710801i | ||||||||
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217.572 | + | 376.846i | 0.295614 | + | 0.512019i | |||||
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450.278 | + | 79.7637i | 0.610132 | + | 0.108081i | |||||
470.172 | + | 814.362i | 0.636227 | + | 1.10198i | 0.986254 | + | 0.165238i | ||
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58.2726i | 0.0787467i | |||||||||
235.135 | + | 280.448i | 0.317321 | + | 0.378473i | |||||
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0.787983 | + | 0.615697i | ||||||||
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1014.86i | 1.34955i | |||||||||
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41.4524 | 0.0546866 | |||||||||
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271.927 | 0.357799 | |||||||||
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0.657911 | + | 0.753096i | ||||||||
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544.122 | − | 95.7213i | 0.708492 | − | 0.124637i | |||||
91.6783 | + | 52.9305i | 0.119218 | + | 0.0688303i | 0.558423 | − | 0.829556i | ||
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195.869 | − | 164.221i | 0.254045 | − | 0.212998i | |||||
25.3697 | 0.0328623 | |||||||||
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331.601 | + | 278.694i | 0.428425 | + | 0.360070i | |||||
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238.717 | + | 413.470i | 0.306440 | + | 0.530770i | |||||
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189.532 | + | 328.278i | 0.241442 | + | 0.418189i | |||||
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0.845029 | − | 0.534720i | ||||||||
177.775 | 0.225602 | |||||||||
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204.360 | − | 353.962i | 0.257705 | − | 0.446358i | |||||
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255.186 | − | 147.332i | 0.320585 | − | 0.185090i | |||||
138.377 | + | 79.8921i | 0.173622 | + | 0.100241i | 0.584293 | − | 0.811543i | ||
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169.521 | − | 293.620i | 0.211902 | − | 0.367025i | |||||
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32.3859i | 0.0403311i | |||||||||
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264.939i | 0.326682i | 0.986570 | + | 0.163341i | ||||||
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159.002 | + | 239.594i | 0.195816 | + | 0.295067i | |||||
175.604 | + | 63.9934i | 0.215995 | + | 0.0787127i | |||||
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161.881i | 0.198627i | |||||||||
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452.245i | 0.553544i | |||||||||
969.081i | 1.18470i | |||||||||
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1507.56 | 1.83625 | 0.918126 | − | 0.396289i | ||||||
0.918126 | + | 0.396289i | ||||||||
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1234.84 | 1.50041 | 0.750207 | − | 0.661203i | ||||||
0.750207 | + | 0.661203i | ||||||||
760.672 | − | 439.174i | 0.923145 | − | 0.532978i | |||||
15.2560 | + | 18.1960i | 0.0184921 | + | 0.0220558i | |||||
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642.770 | 0.777231 | 0.388616 | − | 0.921400i | ||||||
0.388616 | + | 0.921400i | ||||||||
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831.340 | − | 479.974i | 1.00282 | − | 0.578980i | 0.0937403 | − | 0.995597i | ||
0.909082 | + | 0.416617i | ||||||||
203.129 | − | 351.830i | 0.244734 | − | 0.423892i | |||||
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202.855 | + | 117.119i | 0.243816 | + | 0.140767i | |||||
449.499 | − | 340.435i | 0.539614 | − | 0.408685i | |||||
274.947 | + | 100.196i | 0.329672 | + | 0.120139i | |||||
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6.92308 | − | 3.99704i | 0.00828120 | − | 0.00478115i | |||||
657.640 | + | 1142.20i | 0.785711 | + | 1.36463i | |||||
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0.235518 | + | 0.971870i | ||||||||
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284.812 | + | 339.699i | 0.337856 | + | 0.402965i | |||||
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226.870 | + | 130.984i | 0.268486 | + | 0.155010i | |||||
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548.081i | 0.644801i | |||||||||
−805.907 | −0.947012 | |||||||||
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1068.57 | − | 616.937i | 1.25271 | − | 0.723255i | 0.281067 | − | 0.959688i | ||
0.971648 | + | 0.236433i | ||||||||
68.8733 | + | 1104.08i | 0.0806479 | + | 1.29284i | |||||
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344.080 | + | 198.655i | 0.401493 | + | 0.231802i | 0.687128 | − | 0.726536i | ||
−0.285635 | + | 0.958339i | ||||||||
11.1128 | − | 9.31724i | 0.0129520 | − | 0.0108593i | |||||
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0.198603 | + | 0.980080i | ||||||||
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824.138 | + | 1427.45i | 0.956076 | + | 1.65597i | |||||
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0.861430 | + | 0.507876i | ||||||||
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− | 301.969i | − | 0.348695i | |||||||
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492.088 | + | 179.326i | 0.565618 | + | 0.206122i | |||||
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−370.858 | − | 642.346i | −0.425296 | − | 0.736635i | |||||
819.328 | − | 974.869i | 0.938520 | − | 1.11669i | |||||
− | 1286.93i | − | 1.47246i | |||||||
38.9984 | + | 625.168i | 0.0445696 | + | 0.714478i | |||||
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86.7339 | + | 150.227i | 0.0988984 | + | 0.171297i | 0.911229 | − | 0.411900i | ||
−0.812331 | + | 0.583197i | ||||||||
13.1000i | 0.0149203i | |||||||||
−139.201 | − | 50.7274i | −0.158363 | − | 0.0577104i | |||||
− | 13.7133i | − | 0.0155833i | |||||||
1381.76i | 1.56840i | 0.620507 | + | 0.784201i | ||||||
−0.620507 | + | 0.784201i | ||||||||
879.632 | − | 450.008i | 0.997315 | − | 0.510213i | |||||
1346.90 | 1.52537 | 0.762685 | − | 0.646771i | ||||||
0.762685 | + | 0.646771i | ||||||||
68.0028 | 0.0769262 | |||||||||
−34.4187 | − | 41.0515i | −0.0388911 | − | 0.0463859i | |||||
−359.192 | −0.405408 | |||||||||
532.683 | − | 307.545i | 0.600544 | − | 0.346724i | −0.168711 | − | 0.985665i | ||
0.769256 | + | 0.638941i | ||||||||
−202.590 | + | 555.926i | −0.228141 | + | 0.626042i | |||||
343.043 | − | 21.3992i | 0.385875 | − | 0.0240711i | |||||
128.520 | 0.144404 | |||||||||
−5.19007 | − | 29.7094i | −0.00582499 | − | 0.0333438i | |||||
14.3561 | − | 8.28852i | 0.0160943 | − | 0.00929206i | |||||
561.095 | − | 971.844i | 0.628325 | − | 1.08829i | |||||
113.406 | + | 135.260i | 0.126852 | + | 0.151298i | |||||
431.410 | + | 249.074i | 0.482022 | + | 0.278295i | |||||
−1078.45 | + | 67.2746i | −1.20363 | + | 0.0750832i | |||||
−82.1748 | − | 467.118i | −0.0916107 | − | 0.520756i | |||||
104.833 | 0.116740 | |||||||||
1702.86 | − | 983.145i | 1.89417 | − | 1.09360i | |||||
−34.0331 | + | 192.122i | −0.0378146 | + | 0.213469i | |||||
871.606 | + | 503.222i | 0.967376 | + | 0.558515i | |||||
16.3838 | − | 9.45917i | 0.0181638 | − | 0.0104869i | |||||
−310.792 | − | 326.970i | −0.344177 | − | 0.362093i | |||||
−338.953 | + | 587.084i | −0.374948 | + | 0.649429i | |||||
28.2953 | + | 49.0089i | 0.0312655 | + | 0.0541534i | |||||
−275.874 | + | 757.025i | −0.304497 | + | 0.835568i | |||||
249.391 | − | 431.958i | 0.274962 | − | 0.476249i | −0.695163 | − | 0.718852i | ||
0.970126 | + | 0.242603i | ||||||||
−26.9768 | − | 15.5751i | −0.0297102 | − | 0.0171532i | |||||
415.812 | + | 73.6583i | 0.457439 | + | 0.0810323i | |||||
175.460 | − | 10.9453i | 0.192813 | − | 0.0120278i | |||||
462.758 | + | 801.521i | 0.507967 | + | 0.879825i | 0.999957 | + | 0.00922428i | ||
−0.491990 | + | 0.870601i | ||||||||
−1129.81 | − | 411.723i | −1.23882 | − | 0.451450i | |||||
34.9010i | 0.0382268i | |||||||||
1242.00 | 1.35886 | |||||||||
262.992 | + | 313.674i | 0.287423 | + | 0.342813i | |||||
161.268 | − | 93.1080i | 0.176057 | − | 0.101646i | |||||
724.636 | − | 480.891i | 0.790224 | − | 0.524418i | |||||
348.779 | − | 602.449i | 0.379933 | − | 0.656262i | |||||
544.947 | − | 943.877i | 0.592979 | − | 1.02707i | −0.400850 | − | 0.916144i | ||
0.993829 | − | 0.110925i | ||||||||
−305.192 | − | 176.203i | −0.331730 | − | 0.191525i | |||||
224.896 | + | 1278.41i | 0.244187 | + | 1.38807i | |||||
−263.602 | + | 152.191i | −0.285903 | + | 0.165066i | |||||
−489.146 | − | 282.408i | −0.529952 | − | 0.305968i | |||||
−2.25850 | + | 7.64751i | −0.00244426 | + | 0.00827653i | |||||
313.961 | + | 543.797i | 0.339418 | + | 0.587889i | |||||
2.13331 | − | 3.69500i | 0.00230379 | − | 0.00399028i | |||||
−761.727 | + | 906.333i | −0.821712 | + | 0.977705i | |||||
321.219 | + | 556.368i | 0.346142 | + | 0.599535i | |||||
− | 537.759i | − | 0.578858i | −0.957199 | − | 0.289429i | ||||
0.957199 | − | 0.289429i | ||||||||
−407.787 | − | 486.372i | −0.438480 | − | 0.522981i | |||||
950.557 | + | 400.768i | 1.02101 | + | 0.430470i | |||||
178.364 | − | 308.936i | 0.191378 | − | 0.331476i | |||||
86.9008 | + | 493.982i | 0.0931413 | + | 0.529456i | |||||
−200.137 | − | 115.549i | −0.214279 | − | 0.123714i | |||||
4.14421 | + | 7.17799i | 0.00443231 | + | 0.00767699i | |||||
−342.881 | − | 60.7391i | −0.366326 | − | 0.0648922i | |||||
647.389i | 0.690917i | 0.938434 | + | 0.345459i | ||||||
−0.938434 | + | 0.345459i | ||||||||
1182.49 | − | 73.7646i | 1.26065 | − | 0.0786403i | |||||
−134.406 | − | 764.023i | −0.143137 | − | 0.813656i | |||||
52.5781 | + | 91.0680i | 0.0559342 | + | 0.0968808i | |||||
131.133i | 0.139355i | 0.997570 | + | 0.0696777i | ||||||
−0.997570 | + | 0.0696777i | ||||||||
−228.200 | − | 1297.19i | −0.242250 | − | 1.37706i | |||||
− | 618.732i | − | 0.656132i | |||||||
− | 175.753i | − | 0.186179i | |||||||
163.126 | − | 327.201i | 0.172620 | − | 0.346244i | |||||
17.9202 | 0.0189432 | |||||||||
418.984 | 0.442433 | 0.221217 | − | 0.975225i | ||||||
0.221217 | + | 0.975225i | ||||||||
−142.221 | + | 25.0193i | −0.150022 | + | 0.0263916i | |||||
−504.015 | −0.531101 | |||||||||
−868.371 | + | 501.354i | −0.914075 | + | 0.527742i | |||||
−598.352 | + | 105.261i | −0.629182 | + | 0.110685i | |||||
448.149 | − | 297.406i | 0.470744 | − | 0.312401i | |||||
−1131.25 | −1.18704 | −0.593520 | − | 0.804819i | ||||||
−0.593520 | + | 0.804819i | ||||||||
1350.09 | + | 1134.68i | 1.41518 | + | 1.18939i | |||||
101.807 | − | 58.7785i | 0.106604 | − | 0.0615481i | |||||
50.5987 | − | 87.6396i | 0.0529275 | − | 0.0916732i | |||||
−44.3136 | + | 7.79560i | −0.0463047 | + | 0.00814587i | |||||
371.440 | + | 214.451i | 0.387725 | + | 0.223853i | |||||
14.4283 | − | 29.0268i | 0.0150451 | − | 0.0302678i | |||||
−179.766 | + | 150.720i | −0.187256 | + | 0.157000i | |||||
−1421.86 | −1.47956 | |||||||||
332.111 | − | 191.745i | 0.345230 | − | 0.199319i | |||||
219.649 | − | 1239.95i | 0.228088 | − | 1.28759i | |||||
248.166 | + | 143.279i | 0.257433 | + | 0.148629i | |||||
−41.6754 | + | 24.0613i | −0.0431869 | + | 0.0249340i | |||||
884.401 | + | 930.439i | 0.915528 | + | 0.963187i | |||||
−115.840 | + | 200.640i | −0.119793 | + | 0.207488i | −0.919686 | − | 0.392656i | ||
0.799893 | + | 0.600143i | ||||||||
−403.501 | − | 698.884i | −0.416840 | − | 0.721987i | |||||
715.802 | − | 125.923i | 0.738702 | − | 0.129952i | |||||
−306.626 | + | 531.091i | −0.316109 | + | 0.547517i | |||||
402.557 | + | 232.416i | 0.414579 | + | 0.239358i | 0.692755 | − | 0.721173i | ||
−0.278176 | + | 0.960530i | ||||||||
159.668 | − | 189.522i | 0.164268 | − | 0.194982i | |||||
−272.905 | − | 135.652i | −0.280478 | − | 0.139416i | |||||
−502.782 | − | 870.843i | −0.516203 | − | 0.894089i | |||||
−283.181 | + | 237.426i | −0.290442 | + | 0.243514i | |||||
1342.93i | 1.37595i | |||||||||
−1778.98 | −1.82086 | −0.910429 | − | 0.413666i | ||||||
−0.910429 | + | 0.413666i | ||||||||
192.588 | − | 528.480i | 0.196920 | − | 0.540368i | |||||
−9.56174 | + | 5.52047i | −0.00976684 | + | 0.00563889i | |||||
−77.0597 | + | 58.3624i | −0.0786324 | + | 0.0595535i | |||||
765.348 | + | 643.237i | 0.780172 | + | 0.655695i | |||||
−91.5977 | + | 158.652i | −0.0932767 | + | 0.161560i | |||||
199.156 | + | 114.983i | 0.202601 | + | 0.116972i | 0.597868 | − | 0.801595i | ||
−0.395267 | + | 0.918566i | ||||||||
−426.810 | − | 155.537i | −0.433750 | − | 0.158066i | |||||
−292.034 | + | 168.606i | −0.296482 | + | 0.171174i | |||||
−899.400 | − | 519.269i | −0.912170 | − | 0.526642i | |||||
262.202 | + | 1088.23i | 0.265656 | + | 1.10257i | |||||
62.2052 | + | 107.743i | 0.0629607 | + | 0.109051i | |||||
293.045 | − | 507.568i | 0.296304 | − | 0.513213i | |||||
4.95661 | + | 13.6518i | 0.00500667 | + | 0.0137897i | |||||
−561.974 | − | 973.368i | −0.567078 | − | 0.982208i | −0.996853 | − | 0.0792720i | ||
0.429775 | − | 0.902936i | ||||||||
− | 778.543i | − | 0.784822i | |||||||
100.919 | − | 17.7536i | 0.101631 | − | 0.0178787i | |||||
1525.75 | − | 95.1770i | 1.53496 | − | 0.0957515i | |||||
−279.466 | + | 484.050i | −0.280870 | + | 0.486482i | |||||
−219.758 | + | 184.251i | −0.220640 | + | 0.184991i | |||||
−554.198 | − | 319.966i | −0.555866 | − | 0.320929i | 0.195619 | − | 0.980680i | ||
−0.751484 | + | 0.659751i | ||||||||
30.8550 | + | 53.4424i | 0.0309168 | + | 0.0535495i | |||||
0.947100 | − | 797.533i | 0.000948048 | − | 0.798332i |
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 63.3.t.a.40.11 | yes | 28 | |
3.2 | odd | 2 | 189.3.t.a.145.4 | 28 | |||
7.2 | even | 3 | 441.3.l.b.391.4 | 28 | |||
7.3 | odd | 6 | 63.3.k.a.31.4 | ✓ | 28 | ||
7.4 | even | 3 | 441.3.k.b.31.4 | 28 | |||
7.5 | odd | 6 | 441.3.l.a.391.4 | 28 | |||
7.6 | odd | 2 | 441.3.t.a.166.11 | 28 | |||
9.2 | odd | 6 | 189.3.k.a.19.11 | 28 | |||
9.7 | even | 3 | 63.3.k.a.61.4 | yes | 28 | ||
21.17 | even | 6 | 189.3.k.a.10.11 | 28 | |||
63.16 | even | 3 | 441.3.l.a.97.4 | 28 | |||
63.25 | even | 3 | 441.3.t.a.178.11 | 28 | |||
63.34 | odd | 6 | 441.3.k.b.313.4 | 28 | |||
63.38 | even | 6 | 189.3.t.a.73.4 | 28 | |||
63.52 | odd | 6 | inner | 63.3.t.a.52.11 | yes | 28 | |
63.61 | odd | 6 | 441.3.l.b.97.4 | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
63.3.k.a.31.4 | ✓ | 28 | 7.3 | odd | 6 | ||
63.3.k.a.61.4 | yes | 28 | 9.7 | even | 3 | ||
63.3.t.a.40.11 | yes | 28 | 1.1 | even | 1 | trivial | |
63.3.t.a.52.11 | yes | 28 | 63.52 | odd | 6 | inner | |
189.3.k.a.10.11 | 28 | 21.17 | even | 6 | |||
189.3.k.a.19.11 | 28 | 9.2 | odd | 6 | |||
189.3.t.a.73.4 | 28 | 63.38 | even | 6 | |||
189.3.t.a.145.4 | 28 | 3.2 | odd | 2 | |||
441.3.k.b.31.4 | 28 | 7.4 | even | 3 | |||
441.3.k.b.313.4 | 28 | 63.34 | odd | 6 | |||
441.3.l.a.97.4 | 28 | 63.16 | even | 3 | |||
441.3.l.a.391.4 | 28 | 7.5 | odd | 6 | |||
441.3.l.b.97.4 | 28 | 63.61 | odd | 6 | |||
441.3.l.b.391.4 | 28 | 7.2 | even | 3 | |||
441.3.t.a.166.11 | 28 | 7.6 | odd | 2 | |||
441.3.t.a.178.11 | 28 | 63.25 | even | 3 |