Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [115,5,Mod(114,115)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(115, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("115.114");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 115.c (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: | |
Twist minimal: | yes |
Sato-Tate group: |
Embedding invariants
Embedding label | 114.12 | ||
Character | 115.114 | ||
Dual form | 115.5.c.c.114.34 |
-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 .
− | 4.94563i | − | 1.23641i | −0.786018 | − | 0.618204i | ||||
0.786018 | − | 0.618204i | ||||||||
− | 6.82837i | − | 0.758708i | −0.925252 | − | 0.379354i | ||||
0.925252 | − | 0.379354i | ||||||||
−8.45927 | −0.528705 | |||||||||
22.1235 | + | 11.6426i | 0.884941 | + | 0.465703i | |||||
−33.7706 | −0.938072 | |||||||||
47.4193 | 0.967741 | 0.483870 | − | 0.875140i | ||||||
0.483870 | + | 0.875140i | ||||||||
− | 37.2937i | − | 0.582713i | |||||||
34.3734 | 0.424362 | |||||||||
57.5800 | − | 109.415i | 0.575800 | − | 1.09415i | |||||
− | 121.460i | − | 1.00380i | −0.864926 | − | 0.501900i | ||||
0.864926 | − | 0.501900i | ||||||||
57.7631i | 0.401132i | |||||||||
− | 25.2927i | − | 0.149661i | −0.997196 | − | 0.0748304i | ||||
0.997196 | − | 0.0748304i | ||||||||
− | 234.518i | − | 1.19652i | |||||||
79.4999 | − | 151.068i | 0.353333 | − | 0.671412i | |||||
−319.789 | −1.24918 | |||||||||
130.920 | 0.453010 | 0.226505 | − | 0.974010i | ||||||
0.226505 | + | 0.974010i | ||||||||
− | 169.998i | − | 0.524685i | |||||||
292.655i | 0.810679i | 0.914166 | + | 0.405339i | ||||||
−0.914166 | + | 0.405339i | ||||||||
−187.149 | − | 98.4878i | −0.467872 | − | 0.246220i | |||||
− | 323.797i | − | 0.734233i | |||||||
−600.696 | −1.24111 | |||||||||
−215.187 | + | 483.255i | −0.406781 | + | 0.913526i | |||||
−254.655 | −0.442109 | |||||||||
353.900 | + | 515.150i | 0.566241 | + | 0.824240i | |||||
−125.088 | −0.185042 | |||||||||
− | 787.812i | − | 1.08067i | |||||||
−401.133 | −0.511649 | |||||||||
−790.956 | −0.940495 | −0.470247 | − | 0.882535i | ||||||
−0.470247 | + | 0.882535i | ||||||||
−747.125 | − | 393.177i | −0.830139 | − | 0.436864i | |||||
365.318 | 0.380144 | 0.190072 | − | 0.981770i | ||||||
0.190072 | + | 0.981770i | ||||||||
984.861i | 0.961778i | |||||||||
−829.373 | −0.761591 | |||||||||
− | 647.481i | − | 0.560105i | |||||||
1049.08 | + | 552.083i | 0.856393 | + | 0.450680i | |||||
−290.774 | −0.224362 | |||||||||
−471.550 | −0.344449 | −0.172224 | − | 0.985058i | ||||||
−0.172224 | + | 0.985058i | ||||||||
1447.36 | 1.00233 | |||||||||
−172.708 | −0.113549 | |||||||||
434.195 | − | 825.067i | 0.271372 | − | 0.515667i | |||||
−1821.57 | −1.08362 | −0.541812 | − | 0.840500i | ||||||
−0.541812 | + | 0.840500i | ||||||||
−1601.38 | −0.907811 | |||||||||
−7.12217 | −0.00385190 | −0.00192595 | − | 0.999998i | ||||||
−0.00192595 | + | 0.999998i | ||||||||
1027.46i | 0.530714i | |||||||||
760.460 | + | 400.195i | 0.375536 | + | 0.197627i | |||||
2390.00 | + | 1064.24i | 1.12949 | + | 0.502948i | |||||
− | 2540.24i | − | 1.14995i | −0.818171 | − | 0.574975i | ||||
0.818171 | − | 0.574975i | ||||||||
2183.64i | 0.947760i | |||||||||
−152.410 | −0.0634778 | |||||||||
2547.74 | − | 1750.26i | 1.01910 | − | 0.700104i | |||||
− | 893.969i | − | 0.343702i | |||||||
213.958i | 0.0791264i | |||||||||
2852.07 | 1.01533 | 0.507666 | − | 0.861554i | ||||||
0.507666 | + | 0.861554i | ||||||||
−3896.23 | −1.33616 | |||||||||
1414.11 | − | 2687.12i | 0.467473 | − | 0.888304i | |||||
− | 1768.44i | − | 0.563915i | |||||||
1998.36 | 0.615068 | |||||||||
3911.78i | 1.16284i | |||||||||
−4053.87 | −1.16457 | −0.582285 | − | 0.812985i | ||||||
−0.582285 | + | 0.812985i | ||||||||
−672.512 | + | 1277.92i | −0.186809 | + | 0.354978i | |||||
3186.31i | 0.856304i | 0.903707 | + | 0.428152i | ||||||
−0.903707 | + | 0.428152i | ||||||||
− | 1806.73i | − | 0.470013i | |||||||
1629.96 | 0.410673 | |||||||||
−245.867 | −0.0600262 | |||||||||
294.472 | − | 559.563i | 0.0696976 | − | 0.132441i | |||||
4101.77i | 0.941638i | |||||||||
6094.08 | 1.35756 | 0.678779 | − | 0.734342i | ||||||
0.678779 | + | 0.734342i | ||||||||
−1107.49 | −0.239508 | |||||||||
3299.84 | + | 1469.38i | 0.693099 | + | 0.308628i | |||||
2730.40 | − | 5188.37i | 0.557225 | − | 1.05885i | |||||
4387.94 | 0.870449 | 0.435225 | − | 0.900322i | ||||||
0.435225 | + | 0.900322i | ||||||||
− | 1281.91i | − | 0.247282i | |||||||
3217.13i | 0.603702i | 0.953355 | + | 0.301851i | ||||||
−0.953355 | + | 0.301851i | ||||||||
2332.11i | 0.425879i | |||||||||
3517.64 | − | 2416.56i | 0.625357 | − | 0.429611i | |||||
− | 2475.65i | − | 0.428610i | |||||||
− | 5759.54i | − | 0.971419i | |||||||
854.149i | 0.140393i | |||||||||
8824.58i | 1.41397i | 0.707229 | + | 0.706984i | ||||||
−0.707229 | + | 0.706984i | ||||||||
−7074.86 | − | 3723.17i | −1.10545 | − | 0.581746i | |||||
−2595.23 | −0.395554 | |||||||||
9008.82i | 1.33980i | |||||||||
12862.0 | 1.86704 | 0.933519 | − | 0.358527i | ||||||
0.933519 | + | 0.358527i | ||||||||
2739.08i | 0.388192i | |||||||||
2896.41 | + | 1524.24i | 0.400887 | + | 0.210968i | |||||
35.2236i | 0.00476252i | |||||||||
5400.94i | 0.713561i | |||||||||
−4529.68 | −0.584928 | |||||||||
5490.66i | 0.693178i | 0.938017 | + | 0.346589i | ||||||
−0.938017 | + | 0.346589i | ||||||||
1979.22 | − | 3760.95i | 0.244348 | − | 0.464315i | |||||
− | 1199.36i | − | 0.144833i | |||||||
1820.33 | − | 4087.99i | 0.215067 | − | 0.482985i | |||||
− | 2494.53i | − | 0.288418i | |||||||
−12563.1 | −1.42181 | |||||||||
−3407.26 | + | 6474.56i | −0.377536 | + | 0.717403i | |||||
6724.99 | 0.729708 | |||||||||
−15520.6 | −1.64955 | −0.824775 | − | 0.565461i | ||||||
−0.824775 | + | 0.565461i | ||||||||
753.765i | 0.0784845i | |||||||||
− | 4174.98i | − | 0.425975i | |||||||
−2993.74 | − | 4357.80i | −0.299374 | − | 0.435780i | |||||
3046.74 | 0.298671 | 0.149336 | − | 0.988787i | ||||||
0.149336 | + | 0.988787i | ||||||||
−4421.24 | −0.424956 | |||||||||
−6210.09 | −0.585361 | −0.292680 | − | 0.956210i | ||||||
−0.292680 | + | 0.956210i | ||||||||
−943.257 | −0.0872094 | |||||||||
3769.83 | − | 7163.52i | 0.341935 | − | 0.649752i | |||||
− | 14105.3i | − | 1.25536i | |||||||
1863.57 | 0.162771 | 0.0813857 | − | 0.996683i | ||||||
0.0813857 | + | 0.996683i | ||||||||
6664.32i | 0.571358i | |||||||||
− | 3764.74i | − | 0.316870i | −0.987369 | − | 0.158435i | ||||
0.987369 | − | 0.158435i | ||||||||
−13289.5 | − | 6993.65i | −1.09831 | − | 0.577988i | |||||
3219.92i | 0.261336i | |||||||||
−15164.2 | −1.20888 | |||||||||
−10.8182 | −0.000847225 | −0.000423612 | − | 1.00000i | ||||||
−0.000423612 | 1.00000i | |||||||||
− | 9883.14i | − | 0.760475i | |||||||
−10387.0 | + | 8185.97i | −0.785409 | + | 0.618977i | |||||
6690.91 | 0.497244 | |||||||||
− | 869.394i | − | 0.0635104i | |||||||
20048.9i | 1.43988i | |||||||||
6208.12 | 0.438396 | |||||||||
−5633.86 | − | 2964.84i | −0.391240 | − | 0.205892i | |||||
−111.498 | −0.00761547 | |||||||||
15758.3 | 1.05874 | |||||||||
12438.4i | 0.822154i | |||||||||
−3090.33 | −0.200984 | |||||||||
1831.84 | + | 15517.2i | 0.117238 | + | 0.993104i | |||||
− | 8061.18i | − | 0.507759i | |||||||
− | 16809.7i | − | 1.04221i | −0.853494 | − | 0.521103i | ||||
0.853494 | − | 0.521103i | ||||||||
16973.7i | 1.03599i | |||||||||
48.6328i | 0.00292247i | |||||||||
−2767.39 | − | 1456.35i | −0.163751 | − | 0.0861747i | |||||
4191.57 | 0.244250 | 0.122125 | − | 0.992515i | ||||||
0.122125 | + | 0.992515i | ||||||||
7015.89 | 0.402657 | |||||||||
13877.5i | 0.784527i | |||||||||
− | 30139.1i | − | 1.67850i | |||||||
9172.17 | − | 17429.2i | 0.503274 | − | 0.956333i | |||||
− | 4882.48i | − | 0.263975i | |||||||
8299.84 | 0.442210 | 0.221105 | − | 0.975250i | ||||||
0.221105 | + | 0.975250i | ||||||||
7267.00 | − | 16319.8i | 0.381590 | − | 0.856953i | |||||
24420.7 | 1.26395 | 0.631973 | − | 0.774990i | ||||||
0.631973 | + | 0.774990i | ||||||||
−8874.47 | − | 4670.22i | −0.452779 | − | 0.238277i | |||||
−17345.7 | −0.872476 | |||||||||
− | 21701.1i | − | 1.07623i | |||||||
−3072.05 | −0.150230 | |||||||||
−10992.2 | −0.530103 | |||||||||
−17498.7 | − | 9208.77i | −0.832282 | − | 0.437992i | |||||
15910.7 | 0.746421 | |||||||||
1040.71i | 0.0481611i | |||||||||
3988.97 | 0.182112 | |||||||||
− | 104.420i | − | 0.00470339i | −0.999997 | − | 0.00235170i | ||||
0.999997 | − | 0.00235170i | ||||||||
−11951.4 | − | 17396.9i | −0.531175 | − | 0.773197i | |||||
−27841.9 | −1.22108 | −0.610542 | − | 0.791984i | ||||||
−0.610542 | + | 0.791984i | ||||||||
10914.2 | 0.472393 | |||||||||
4500.15 | 0.192240 | |||||||||
−28484.6 | −1.20107 | |||||||||
8082.13 | + | 4253.25i | 0.336405 | + | 0.177034i | |||||
1460.98 | 0.0600338 | |||||||||
−46395.1 | −1.88223 | −0.941116 | − | 0.338084i | ||||||
−0.941116 | + | 0.338084i | ||||||||
43643.1 | 1.74824 | |||||||||
− | 19475.0i | − | 0.770340i | |||||||
−11466.3 | + | 21788.6i | −0.447903 | + | 0.851117i | |||||
−10204.0 | + | 22915.6i | −0.393659 | + | 0.884056i | |||||
12835.1i | 0.489066i | |||||||||
29520.0i | 1.11107i | 0.831493 | + | 0.555535i | ||||||
−0.831493 | + | 0.555535i | ||||||||
15409.2 | 0.572917 | |||||||||
−18348.7 | − | 9656.05i | −0.673963 | − | 0.354676i | |||||
− | 63610.9i | − | 2.30842i | |||||||
− | 37239.6i | − | 1.33528i | −0.744485 | − | 0.667639i | ||||
0.744485 | − | 0.667639i | ||||||||
−12075.6 | −0.427847 | |||||||||
27921.3 | 0.977602 | |||||||||
7538.35 | − | 14324.6i | 0.260843 | − | 0.495659i | |||||
10059.5i | 0.344022i | |||||||||
60.2484 | 0.00203652 | |||||||||
19212.6i | 0.641940i | 0.947089 | + | 0.320970i | ||||||
−0.947089 | + | 0.320970i | ||||||||
26711.1 | 0.882252 | |||||||||
16781.7 | + | 24428.1i | 0.547974 | + | 0.797651i | |||||
38841.5i | 1.25392i | |||||||||
27681.3i | 0.883569i | |||||||||
27154.8 | 0.857051 | |||||||||
54673.8 | 1.70637 | 0.853185 | − | 0.521609i | ||||||
0.853185 | + | 0.521609i | ||||||||
−6432.94 | − | 3385.36i | −0.198547 | − | 0.104486i | |||||
60172.9i | 1.83672i | 0.395742 | + | 0.918362i | ||||||
−0.395742 | + | 0.918362i | ||||||||
−5931.60 | −0.179073 | |||||||||
21757.3 | 0.649685 | |||||||||
18022.3 | + | 8025.12i | 0.532324 | + | 0.237037i | |||||
−10432.3 | − | 5490.06i | −0.304817 | − | 0.160411i | |||||
−12337.0 | −0.356603 | |||||||||
− | 15901.5i | − | 0.454731i | |||||||
21488.6i | 0.607984i | |||||||||
− | 37357.5i | − | 1.04581i | |||||||
32020.8 | + | 16851.1i | 0.887002 | + | 0.466788i | |||||
48565.0i | 1.33124i | 0.746290 | + | 0.665621i | ||||||
−0.746290 | + | 0.665621i | ||||||||
1678.87i | 0.0455424i | |||||||||
22851.5i | 0.613479i | 0.951793 | + | 0.306740i | ||||||
−0.951793 | + | 0.306740i | ||||||||
76759.3i | 2.03952i | |||||||||
−3820.91 | − | 2010.77i | −0.100484 | − | 0.0528801i | |||||
1289.28 | 0.0335610 | |||||||||
− | 14182.4i | − | 0.365441i | −0.983165 | − | 0.182720i | ||||
0.983165 | − | 0.182720i | ||||||||
−20647.9 | −0.526679 | |||||||||
44550.7i | 1.12499i | 0.826801 | + | 0.562495i | ||||||
−0.826801 | + | 0.562495i | ||||||||
19211.8 | − | 13198.2i | 0.480296 | − | 0.329956i | |||||
− | 41612.7i | − | 1.02999i | |||||||
− | 15068.1i | − | 0.369279i | |||||||
−37506.6 | −0.910155 | |||||||||
7562.33i | 0.181717i | |||||||||
−40299.6 | − | 21207.8i | −0.958943 | − | 0.504647i | |||||
30712.8i | 0.723745i | |||||||||
−7396.71 | + | 16611.1i | −0.172623 | + | 0.387666i | |||||
8088.33i | 0.186953i | |||||||||
35545.8 | 0.813760 | |||||||||
−35428.1 | − | 18644.2i | −0.803359 | − | 0.422771i | |||||
−41236.0 | −0.926215 | −0.463108 | − | 0.886302i | ||||||
−0.463108 | + | 0.886302i | ||||||||
−24126.4 | −0.536810 | |||||||||
− | 29962.5i | − | 0.660417i | |||||||
− | 9216.53i | − | 0.201252i | |||||||
−157.567 | − | 82.9205i | −0.00340871 | − | 0.00179384i | |||||
−29380.4 | −0.629724 | |||||||||
17323.1 | 0.367881 | |||||||||
−18619.0 | −0.391781 | |||||||||
21967.7 | 0.458033 | |||||||||
−11962.3 | + | 22731.1i | −0.247155 | + | 0.469650i | |||||
− | 3311.31i | − | 0.0677978i | |||||||
15924.5 | 0.323118 | |||||||||
− | 15976.4i | − | 0.321269i | −0.987014 | − | 0.160634i | ||||
0.987014 | − | 0.160634i | ||||||||
46701.4i | 0.930752i | |||||||||
12164.7 | + | 17707.4i | 0.240291 | + | 0.349776i | |||||
53.5029i | 0.00104752i | |||||||||
48395.1 | 0.939181 | 0.469590 | − | 0.882884i | ||||||
0.469590 | + | 0.882884i | ||||||||
−16904.7 | −0.325190 | |||||||||
− | 69898.5i | − | 1.33290i | −0.745551 | − | 0.666449i | ||||
0.745551 | − | 0.666449i | ||||||||
40484.8 | + | 51370.5i | 0.765308 | + | 0.971086i | |||||
−39328.3 | −0.737023 | |||||||||
29497.6i | 0.548039i | |||||||||
− | 64869.9i | − | 1.19490i | −0.801906 | − | 0.597450i | ||||
0.801906 | − | 0.597450i | ||||||||
−4299.70 | −0.0785248 | |||||||||
29575.0 | − | 56199.0i | 0.535536 | − | 1.01764i | |||||
34292.8 | 0.615714 | |||||||||
60257.5 | 1.07279 | |||||||||
− | 30703.1i | − | 0.542036i | |||||||
−29088.5 | −0.509243 | −0.254621 | − | 0.967041i | ||||||
−0.254621 | + | 0.967041i | ||||||||
−25423.2 | + | 48309.8i | −0.441375 | + | 0.838711i | |||||
− | 60948.1i | − | 1.04936i | −0.851298 | − | 0.524682i | ||||
0.851298 | − | 0.524682i | ||||||||
551.429i | 0.00941583i | |||||||||
− | 46091.6i | − | 0.780565i | |||||||
− | 26953.8i | − | 0.452732i | |||||||
−3371.85 | − | 1774.45i | −0.0561741 | − | 0.0295618i | |||||
61515.6 | 1.01652 | |||||||||
7402.03 | 0.121327 | |||||||||
− | 13624.1i | − | 0.221515i | |||||||
− | 87826.7i | − | 1.41654i | |||||||
76742.6 | − | 9059.61i | 1.22788 | − | 0.144954i | |||||
− | 21475.3i | − | 0.340873i | −0.985369 | − | 0.170437i | ||||
0.985369 | − | 0.170437i | ||||||||
−13788.3 | −0.217125 | |||||||||
58696.1 | + | 26136.6i | 0.916997 | + | 0.408327i | |||||
−83134.8 | −1.28859 | |||||||||
10408.1 | − | 19777.7i | 0.160063 | − | 0.304156i | |||||
80012.0 | 1.22089 | |||||||||
89616.4i | 1.35682i | 0.734685 | + | 0.678409i | ||||||
−0.734685 | + | 0.678409i | ||||||||
240.520 | 0.00361336 | |||||||||
−22360.6 | −0.333337 | |||||||||
−2491.02 | + | 4733.50i | −0.0368494 | + | 0.0700222i | |||||
−27187.8 | −0.399111 | |||||||||
− | 20730.0i | − | 0.301992i | |||||||
21291.6 | 0.307820 | 0.153910 | − | 0.988085i | ||||||
0.153910 | + | 0.988085i | ||||||||
30930.3i | 0.443789i | |||||||||
63097.7 | + | 33205.4i | 0.898508 | + | 0.472843i | |||||
68633.0 | 0.969995 | |||||||||
37492.3 | 0.525919 | |||||||||
−51551.5 | −0.717748 | |||||||||
−117290. | −1.62090 | −0.810450 | − | 0.585808i | ||||||
−0.810450 | + | 0.585808i | ||||||||
−86198.3 | − | 45362.2i | −1.18242 | − | 0.622252i | |||||
−110364. | −1.50276 | −0.751379 | − | 0.659871i | ||||||
−0.751379 | + | 0.659871i | ||||||||
−41866.7 | −0.565889 | |||||||||
−8189.69 | −0.109886 | |||||||||
− | 41048.0i | − | 0.546752i | |||||||
62570.1 | − | 42984.7i | 0.827373 | − | 0.568393i | |||||
−27914.3 | − | 12429.9i | −0.366445 | − | 0.163173i | |||||
− | 12201.9i | − | 0.159025i | −0.996834 | − | 0.0795127i | ||||
0.996834 | − | 0.0795127i | ||||||||
− | 120776.i | − | 1.56275i | |||||||
12557.2 | 0.161319 | |||||||||
20589.2 | − | 39124.1i | 0.262617 | − | 0.499032i | |||||
− | 138763.i | − | 1.75737i | −0.477405 | − | 0.878683i | ||||
0.477405 | − | 0.878683i | ||||||||
85785.4i | 1.07874i | |||||||||
−2905.51 | −0.0362785 | −0.0181392 | − | 0.999835i | ||||||
−0.0181392 | + | 0.999835i | ||||||||
−37118.8 | −0.460211 | |||||||||
44210.7 | + | 23266.0i | 0.544299 | + | 0.286439i | |||||
15193.2i | 0.185745i | |||||||||
−86377.6 | −1.04867 | |||||||||
33853.0i | 0.408142i | |||||||||
−66381.0 | −0.794782 | |||||||||
−45543.2 | + | 86542.3i | −0.541536 | + | 1.02904i | |||||
105981.i | 1.25153i | |||||||||
− | 27214.5i | − | 0.319180i | |||||||
−96882.7 | −1.12852 | −0.564262 | − | 0.825596i | ||||||
−0.564262 | + | 0.825596i | ||||||||
5146.99 | 0.0595468 | |||||||||
−89685.9 | − | 47197.5i | −1.03058 | − | 0.542345i | |||||
17585.8i | 0.200715i | |||||||||
−95687.5 | −1.08478 | |||||||||
−516.423 | −0.00581531 | |||||||||
12222.8 | + | 5442.66i | 0.136719 | + | 0.0608792i | |||||
−29756.6 | + | 20442.4i | −0.330629 | + | 0.227137i | |||||
−337.728 | −0.00372764 | |||||||||
137696.i | 1.50976i | |||||||||
− | 20804.3i | − | 0.226604i | |||||||
− | 93587.9i | − | 1.01268i | |||||||
−37096.9 | + | 70492.3i | −0.398784 | + | 0.757778i | |||||
− | 22256.1i | − | 0.237687i | |||||||
− | 80278.2i | − | 0.851767i | −0.904778 | − | 0.425884i | ||||
0.904778 | − | 0.425884i | ||||||||
48721.5i | 0.513594i | |||||||||
42404.8i | 0.444118i | |||||||||
21035.0 | − | 39971.2i | 0.218887 | − | 0.415934i | |||||
99847.5 | 1.03233 | 0.516163 | − | 0.856491i | ||||||
0.516163 | + | 0.856491i | ||||||||
6440.91i | 0.0661664i | |||||||||
9836.64 | 0.100406 | 0.0502028 | − | 0.998739i | ||||||
0.0502028 | + | 0.998739i | ||||||||
229453.i | 2.32721i | |||||||||
36060.5 | + | 18977.0i | 0.363421 | + | 0.191252i | |||||
− | 74649.5i | − | 0.747572i | |||||||
− | 104833.i | − | 1.04323i | −0.853182 | − | 0.521613i | ||||
0.853182 | − | 0.521613i | ||||||||
−96316.0 | −0.952454 | |||||||||
96069.4i | 0.944069i | |||||||||
−5439.45 | − | 2862.53i | −0.0531196 | − | 0.0279544i | |||||
− | 12725.1i | − | 0.123496i | |||||||
113332. | + | 50465.4i | 1.09305 | + | 0.486723i | |||||
38314.3i | 0.367245i | |||||||||
21953.8 | 0.209131 | |||||||||
13029.5 | − | 8951.09i | 0.123356 | − | 0.0847441i | |||||
145995. | 1.37374 | |||||||||
−25707.0 | −0.240412 | |||||||||
67933.0i | 0.631442i | |||||||||
− | 120456.i | − | 1.11285i | |||||||
−47755.3 | + | 90745.7i | −0.438524 | + | 0.833294i | |||||
−38032.9 | −0.347139 | −0.173569 | − | 0.984822i | ||||||
−0.173569 | + | 0.984822i | ||||||||
−108803. | −0.987112 | |||||||||
−16208.8 | −0.146171 | |||||||||
−184173. | −1.65095 | |||||||||
134823. | + | 70950.9i | 1.20136 | + | 0.632220i | |||||
103547.i | 0.917186i | |||||||||
−33040.3 | −0.290927 | −0.145463 | − | 0.989364i | ||||||
−0.145463 | + | 0.989364i | ||||||||
− | 138088.i | − | 1.20871i | |||||||
73.8708i | 0.000642796i | |||||||||
−24501.5 | − | 12894.0i | −0.211951 | − | 0.111540i | |||||
− | 44371.5i | − | 0.381589i | |||||||
49750.8 | 0.425351 | |||||||||
−121081. | −1.02917 | |||||||||
265.612i | 0.00224456i | |||||||||
55896.8 | + | 70926.6i | 0.469622 | + | 0.595896i | |||||
95018.6 | 0.793700 | |||||||||
− | 43160.3i | − | 0.358448i | −0.983808 | − | 0.179224i | ||||
0.983808 | − | 0.179224i | ||||||||
− | 45688.0i | − | 0.377263i | |||||||
−91666.3 | −0.752591 | −0.376296 | − | 0.926500i | ||||||
−0.376296 | + | 0.926500i | ||||||||
120812. | − | 82996.1i | 0.986222 | − | 0.677519i | |||||
−19925.9 | −0.161735 | |||||||||
119621. | 0.965433 | |||||||||
51870.6i | 0.416267i | 0.978100 | + | 0.208133i | ||||||
−0.978100 | + | 0.208133i | ||||||||
136902. | 1.09245 | |||||||||
97076.6 | + | 51086.9i | 0.770296 | + | 0.405371i | |||||
− | 46447.0i | − | 0.366486i | |||||||
− | 42391.4i | − | 0.332614i | |||||||
− | 270396.i | − | 2.10977i | |||||||
240529.i | 1.86629i | 0.359499 | + | 0.933146i | ||||||
−0.359499 | + | 0.933146i | ||||||||
14924.7 | − | 28360.3i | 0.115160 | − | 0.218830i | |||||
44674.0 | 0.342800 | |||||||||
297593. | 2.27094 | |||||||||
761.351i | 0.00577792i | |||||||||
10145.7i | 0.0765738i | |||||||||
−37455.7 | + | 71174.1i | −0.281146 | + | 0.534240i | |||||
− | 107604.i | − | 0.803275i | |||||||
−188291. | −1.39797 | −0.698983 | − | 0.715139i | ||||||
−0.698983 | + | 0.715139i | ||||||||
68814.5 | − | 154540.i | 0.508141 | − | 1.14115i | |||||
−62613.5 | −0.459849 | |||||||||
−27151.8 | + | 51594.5i | −0.198333 | + | 0.376878i | |||||
135243. | 0.982577 | |||||||||
21101.9i | 0.152488i | |||||||||
156696. | 1.12626 | 0.563132 | − | 0.826367i | ||||||
0.563132 | + | 0.826367i | ||||||||
−78643.0 | −0.562233 | |||||||||
105958. | − | 12508.5i | 0.753476 | − | 0.0889493i | |||||
−94734.8 | −0.670091 | |||||||||
20005.4i | 0.140755i | |||||||||
−184756. | −1.29305 | |||||||||
148654.i | 1.03490i | 0.855714 | + | 0.517449i | ||||||
−0.855714 | + | 0.517449i | ||||||||
28823.0 | − | 54770.1i | 0.199605 | − | 0.379294i | |||||
−114783. | −0.790730 | |||||||||
240185. | 1.64596 | |||||||||
122905. | 0.837859 | 0.418929 | − | 0.908019i | ||||||
0.418929 | + | 0.908019i | ||||||||
115903. | 0.786017 | |||||||||
67056.0 | − | 127421.i | 0.452393 | − | 0.859648i | |||||
113015. | 0.758511 | |||||||||
−244.813 | −0.00163460 | |||||||||
131293. | 0.872125 | |||||||||
− | 122657.i | − | 0.810578i | −0.914189 | − | 0.405289i | ||||
0.914189 | − | 0.405289i | ||||||||
−9944.51 | + | 18896.8i | −0.0653814 | + | 0.124239i | |||||
−28172.3 | + | 63267.6i | −0.184276 | + | 0.413836i | |||||
5683.94i | 0.0369894i | |||||||||
− | 28621.6i | − | 0.185314i | |||||||
−70140.9 | −0.451834 | |||||||||
−102741. | + | 195231.i | −0.658490 | + | 1.25128i | |||||
35317.3i | 0.225215i | |||||||||
− | 99402.5i | − | 0.630691i | −0.948977 | − | 0.315345i | ||||
0.948977 | − | 0.315345i | ||||||||
220332. | 1.39095 | |||||||||
94760.7 | 0.595227 | |||||||||
−113173. | − | 164739.i | −0.707334 | − | 1.02962i | |||||
233065.i | 1.44940i | 0.689065 | + | 0.724700i | ||||||
−0.689065 | + | 0.724700i | ||||||||
−205801. | −1.27349 | |||||||||
− | 9239.88i | − | 0.0568927i | |||||||
−25773.2 | −0.157909 | |||||||||
−57415.7 | − | 30215.2i | −0.350042 | − | 0.184211i | |||||
185494.i | 1.12532i | |||||||||
57274.4i | 0.345758i | |||||||||
−33339.4 | −0.200280 | |||||||||
92352.0 | 0.552077 | 0.276038 | − | 0.961147i | ||||||
0.276038 | + | 0.961147i | ||||||||
−104886. | + | 199307.i | −0.623950 | + | 1.18564i | |||||
− | 56674.4i | − | 0.335508i | |||||||
52532.9 | 0.309483 | |||||||||
−192232. | −1.12700 | |||||||||
82152.4 | + | 36581.4i | 0.479313 | + | 0.213432i | |||||
284553. | + | 149747.i | 1.65222 | + | 0.869486i | |||||
24909.8 | 0.143941 | |||||||||
− | 166754.i | − | 0.958966i | |||||||
− | 175797.i | − | 1.00614i | |||||||
− | 64162.6i | − | 0.365472i | −0.983162 | − | 0.182736i | ||||
0.983162 | − | 0.182736i | ||||||||
−31890.0 | + | 60598.2i | −0.180782 | + | 0.343527i | |||||
− | 125400.i | − | 0.707514i | −0.935337 | − | 0.353757i | ||||
0.935337 | − | 0.353757i | ||||||||
203938.i | 1.14518i | |||||||||
− | 87316.5i | − | 0.487995i | |||||||
− | 106364.i | − | 0.591647i | |||||||
46332.5 | + | 67443.3i | 0.256512 | + | 0.373389i | |||||
−148183. | −0.816545 | |||||||||
151092.i | 0.828680i | |||||||||
−15764.4 | −0.0860580 | |||||||||
20977.1i | 0.113980i | |||||||||
−410.094 | + | 779.271i | −0.00221792 | + | 0.00421455i | |||||
− | 202228.i | − | 1.08864i | −0.838876 | − | 0.544322i | ||||
0.838876 | − | 0.544322i | ||||||||
251934.i | 1.34995i | |||||||||
−231136. | −1.23280 | −0.616400 | − | 0.787433i | ||||||
−0.616400 | + | 0.787433i | ||||||||
− | 85673.9i | − | 0.454851i | |||||||
−62880.9 | + | 119488.i | −0.332308 | + | 0.631459i | |||||
31847.0i | 0.167531i | |||||||||
−141427. | − | 62975.6i | −0.740576 | − | 0.329769i | |||||
− | 108644.i | − | 0.566316i | |||||||
282237. | 1.46449 | 0.732243 | − | 0.681044i | ||||||
0.732243 | + | 0.681044i | ||||||||
−100213. | − | 52737.2i | −0.517627 | − | 0.272403i | |||||
−5238.85 | −0.0269376 | |||||||||
−16376.5 | −0.0838258 | |||||||||
− | 123666.i | − | 0.630147i | −0.949067 | − | 0.315073i | ||||
0.949067 | − | 0.315073i | ||||||||
− | 27238.2i | − | 0.138169i | |||||||
−63925.5 | + | 121473.i | −0.322815 | + | 0.613421i | |||||
−79013.2 | −0.397219 | |||||||||
−713.019 | −0.00356850 | |||||||||
−11658.9 | −0.0580898 | |||||||||
−258480. | −1.28214 | −0.641069 | − | 0.767483i | ||||||
−0.641069 | + | 0.767483i | ||||||||
87574.4 | − | 60162.3i | 0.432466 | − | 0.297098i | |||||
221248.i | 1.08774i | |||||||||
91.5142 | 0.000447932 | |||||||||
190115.i | 0.926445i | |||||||||
− | 239344.i | − | 1.16121i | |||||||
13963.7 | − | 26534.1i | 0.0674492 | − | 0.128169i | |||||
− | 74526.0i | − | 0.358409i | |||||||
−184081. | −0.881407 | −0.440703 | − | 0.897653i | ||||||
−0.440703 | + | 0.897653i | ||||||||
−345692. | −1.64800 | |||||||||
− | 103140.i | − | 0.489556i | |||||||
87866.8 | − | 69247.3i | 0.415250 | − | 0.327256i | |||||
−39428.1 | −0.185526 | −0.0927628 | − | 0.995688i | ||||||
−0.0927628 | + | 0.995688i | ||||||||
194503.i | 0.911261i | |||||||||
157266.i | 0.733623i | 0.930295 | + | 0.366812i | ||||||
−0.930295 | + | 0.366812i | ||||||||
252939. | 1.17484 | |||||||||
29042.8 | − | 55187.8i | 0.134317 | − | 0.255233i | |||||
−320823. | −1.47738 | |||||||||
397293. | 1.82170 | 0.910851 | − | 0.412735i | ||||||
0.910851 | + | 0.412735i | ||||||||
7354.45i | 0.0335783i | |||||||||
288977. | 1.31377 | |||||||||
−277940. | − | 146267.i | −1.25822 | − | 0.662140i | |||||
316803.i | 1.42806i | |||||||||
151184.i | 0.678611i | |||||||||
865.058i | 0.00386654i | |||||||||
− | 298011.i | − | 1.32640i | |||||||
−150761. | + | 103571.i | −0.668194 | + | 0.459039i | |||||
−52516.2 | −0.231782 | |||||||||
98035.0 | 0.430868 | |||||||||
143861.i | 0.629632i | |||||||||
137130.i | 0.597668i | 0.954305 | + | 0.298834i | ||||||
−0.954305 | + | 0.298834i | ||||||||
148781. | + | 78296.3i | 0.645749 | + | 0.339828i | |||||
11926.8i | 0.0515505i | |||||||||
−301427. | −1.29744 | |||||||||
156476. | + | 69676.9i | 0.670740 | + | 0.298672i | |||||
943.193 | 0.00402634 | |||||||||
−343371. | − | 180700.i | −1.45975 | − | 0.768201i | |||||
−227952. | −0.965097 | |||||||||
− | 333190.i | − | 1.40487i | −0.711750 | − | 0.702433i | ||||
0.711750 | − | 0.702433i | ||||||||
118829. | 0.498980 | |||||||||
201574. | 0.842977 | |||||||||
−8775.78 | + | 16675.9i | −0.0365505 | + | 0.0694541i | |||||
72764.5 | 0.301826 | 0.150913 | − | 0.988547i | ||||||
0.150913 | + | 0.988547i | ||||||||
− | 105220.i | − | 0.434676i | |||||||
−103552. | −0.426053 | |||||||||
− | 36607.7i | − | 0.150010i | |||||||
48607.6 | − | 92365.3i | 0.198378 | − | 0.376963i | |||||
−116825. | −0.474867 | |||||||||
208073. | 0.842369 | |||||||||
−434359. | −1.75142 | |||||||||
−64799.7 | −0.260239 | −0.130119 | − | 0.991498i | ||||||
−0.130119 | + | 0.991498i | ||||||||
−15496.0 | − | 131265.i | −0.0619842 | − | 0.525059i | |||||
−254286. | −1.01309 | |||||||||
−106209. | −0.421458 | |||||||||
66136.2 | 0.261399 | 0.130699 | − | 0.991422i | ||||||
0.130699 | + | 0.991422i | ||||||||
− | 60787.2i | − | 0.239304i | |||||||
67404.7 | + | 35472.0i | 0.264306 | + | 0.139092i | |||||
129262. | − | 290289.i | 0.504859 | − | 1.13378i | |||||
− | 190657.i | − | 0.741714i | |||||||
142198.i | 0.551019i | |||||||||
−278831. | −1.07623 | −0.538115 | − | 0.842871i | ||||||
−0.538115 | + | 0.842871i | ||||||||
−97813.4 | − | 51474.7i | −0.376061 | − | 0.197903i | |||||
152554.i | 0.584227i | |||||||||
− | 124130.i | − | 0.473518i | |||||||
230557. | 0.876080 | |||||||||
443210. | 1.67758 | |||||||||
−137389. | − | 72301.6i | −0.518010 | − | 0.272605i | |||||
− | 411.398i | − | 0.00154512i | |||||||
−308537. | −1.15432 | |||||||||
110587.i | 0.412140i | |||||||||
131191. | 0.487045 | |||||||||
−20868.2 | − | 10981.9i | −0.0771751 | − | 0.0406137i | |||||
− | 335750.i | − | 1.23692i | −0.785817 | − | 0.618459i | ||||
0.785817 | − | 0.618459i | ||||||||
134461.i | 0.493463i | |||||||||
343493. | 1.25578 | 0.627891 | − | 0.778301i | ||||||
0.627891 | + | 0.778301i | ||||||||
−35457.6 | −0.129136 | |||||||||
166804. | − | 114592.i | 0.605184 | − | 0.415752i | |||||
− | 105301.i | − | 0.380592i | |||||||
47827.4 | 0.172209 | |||||||||
265224. | 0.951362 | |||||||||
−187230. | − | 207981.i | −0.669058 | − | 0.743210i | |||||
164222. | − | 312058.i | 0.584627 | − | 1.11092i | |||||
−139345. | −0.494200 | |||||||||
− | 117394.i | − | 0.414783i | |||||||
46072.4i | 0.162176i | |||||||||
− | 185423.i | − | 0.650251i | |||||||
41228.7 | + | 21696.8i | 0.144043 | + | 0.0758032i | |||||
− | 227271.i | − | 0.791068i | |||||||
− | 373333.i | − | 1.29464i | |||||||
580073.i | 2.00409i | |||||||||
18511.7i | 0.0637191i | |||||||||
−77589.9 | + | 147438.i | −0.266083 | + | 0.505618i | |||||
317068. | 1.08332 | 0.541661 | − | 0.840597i | ||||||
0.541661 | + | 0.840597i | ||||||||
545820.i | 1.85802i | |||||||||
410883. | 1.39354 | |||||||||
128938.i | 0.435695i | |||||||||
43831.3 | − | 83289.3i | 0.147568 | − | 0.280412i | |||||
40503.2i | 0.135864i | |||||||||
5272.95i | 0.0176230i | 0.999961 | + | 0.00881148i | ||||||
−0.999961 | + | 0.00881148i | ||||||||
−70210.6 | −0.233799 | |||||||||
109524.i | 0.363383i | |||||||||
−212586. | − | 309448.i | −0.702765 | − | 1.02297i | |||||
− | 231477.i | − | 0.762439i | |||||||
54798.5 | − | 123063.i | 0.179842 | − | 0.403878i | |||||
418455.i | 1.36835i | |||||||||
−60345.9 | −0.196620 | |||||||||
−37488.2 | + | 71235.9i | −0.121705 | + | 0.231267i | |||||
−206582. | −0.668254 | |||||||||
279435. | 0.900679 | 0.450340 | − | 0.892857i | ||||||
0.450340 | + | 0.892857i | ||||||||
− | 62103.4i | − | 0.199456i | |||||||
180.139i | 0.000576479i | |||||||||
−335485. | − | 176550.i | −1.06979 | − | 0.562979i | |||||
−108581. | −0.345008 | |||||||||
−686273. | −2.17282 | |||||||||
−259566. | −0.818902 | −0.409451 | − | 0.912332i | ||||||
−0.409451 | + | 0.912332i | ||||||||
146732. | 0.461282 | |||||||||
−239.337 | − | 125.952i | −0.000749744 | − | 0.000394556i | |||||
14369.6i | 0.0448550i | |||||||||
−123064. | −0.382794 | |||||||||
− | 163642.i | − | 0.507223i | |||||||
− | 298678.i | − | 0.922527i | −0.887263 | − | 0.461264i | ||||
0.887263 | − | 0.461264i | ||||||||
115065. | − | 218650.i | 0.354156 | − | 0.672976i | |||||
335764.i | 1.02982i | 0.857244 | + | 0.514910i | ||||||
−0.857244 | + | 0.514910i | ||||||||
25987.3 | 0.0794271 | |||||||||
331620. | 1.01002 | |||||||||
427192.i | 1.29658i | |||||||||
−325104. | + | 60170.4i | −0.983300 | + | 0.181990i | |||||
−8451.29 | −0.0254729 | |||||||||
159733.i | 0.479782i | 0.970800 | + | 0.239891i | ||||||
−0.970800 | + | 0.239891i | ||||||||
328296.i | 0.982675i | |||||||||
156038. | 0.465452 | |||||||||
148027. | + | 77899.5i | 0.440031 | + | 0.231568i | |||||
609908. | 1.80681 | |||||||||
524141. | 1.54740 | |||||||||
− | 346411.i | − | 1.01919i | |||||||
119978. | 0.351785 | |||||||||
10122.0 | − | 19234.1i | 0.0295770 | − | 0.0562030i | |||||
479146.i | 1.39532i | |||||||||
− | 524199.i | − | 1.52132i | −0.649151 | − | 0.760659i | ||||
0.649151 | − | 0.760659i | ||||||||
− | 8803.68i | − | 0.0254630i | |||||||
106912.i | 0.308175i | |||||||||
−233422. | + | 443553.i | −0.670559 | + | 1.27421i | |||||
−96842.7 | −0.277263 | |||||||||
150797. | 0.430277 | |||||||||
− | 272680.i | − | 0.775432i | −0.921779 | − | 0.387716i | ||||
0.921779 | − | 0.387716i | ||||||||
473235.i | 1.34123i | |||||||||
137346. | + | 72278.6i | 0.387954 | + | 0.204162i | |||||
883.318i | 0.00248671i | |||||||||
304209. | 0.853539 | |||||||||
26917.4 | − | 60449.6i | 0.0752716 | − | 0.169041i | |||||
−372361. | −1.03779 | −0.518896 | − | 0.854838i | ||||||
−0.518896 | + | 0.854838i | ||||||||
−90122.4 | − | 131185.i | −0.250340 | − | 0.364404i | |||||
686200. | 1.89977 | 0.949887 | − | 0.312594i | ||||||
0.949887 | + | 0.312594i | ||||||||
1670.28i | 0.00460889i | |||||||||
209474. | 0.576097 | |||||||||
235522. | 0.645592 | |||||||||
−2466.73 | − | 1298.13i | −0.00673924 | − | 0.00354655i | |||||
−102890. | −0.280175 | |||||||||
− | 39449.6i | − | 0.107069i | −0.998566 | − | 0.0535346i | ||||
0.998566 | − | 0.0535346i | ||||||||
−288224. | −0.779693 | |||||||||
256109.i | 0.690542i | |||||||||
348629. | + | 183467.i | 0.936923 | + | 0.493059i | |||||
−64249.5 | −0.172102 | |||||||||
−38068.0 | −0.101638 | |||||||||
−328168. | −0.873323 | −0.436662 | − | 0.899626i | ||||||
−0.436662 | + | 0.899626i | ||||||||
−397026. | −1.05313 | |||||||||
−144815. | + | 275180.i | −0.382880 | + | 0.727557i | |||||
−214794. | −0.566059 | |||||||||
−676661. | −1.77746 | −0.888731 | − | 0.458428i | ||||||
−0.888731 | + | 0.458428i | ||||||||
209719. | 0.549111 | |||||||||
334267.i | 0.872394i | 0.899851 | + | 0.436197i | ||||||
−0.899851 | + | 0.436197i | ||||||||
−68368.9 | − | 35979.4i | −0.177859 | − | 0.0935989i | |||||
380714. | + | 169527.i | 0.987224 | + | 0.439598i | |||||
− | 493809.i | − | 1.27638i | |||||||
260363.i | 0.670816i | |||||||||
55230.1 | 0.141843 | |||||||||
−140134. | + | 364624.i | −0.358743 | + | 0.933436i | |||||
− | 48648.4i | − | 0.124142i | |||||||
− | 242720.i | − | 0.617406i | |||||||
392469. | 0.995145 | |||||||||
−61735.2 | −0.156038 | |||||||||
93853.0 | − | 178342.i | 0.236465 | − | 0.449337i | |||||
331904.i | 0.833592i | 0.909000 | + | 0.416796i | ||||||
−0.909000 | + | 0.416796i | ||||||||
329101. | 0.823938 | |||||||||
281575.i | 0.702727i | |||||||||
−518464. | −1.28985 | |||||||||
195709. | − | 371891.i | 0.485359 | − | 0.922290i | |||||
164744.i | 0.407282i | |||||||||
3854.87i | 0.00950015i | |||||||||
475124. | 1.16725 | |||||||||
150828. | 0.369386 | |||||||||
−197618. | + | 375519.i | −0.482466 | + | 0.916794i | |||||
− | 802258.i | − | 1.95253i | −0.216579 | − | 0.976265i | ||||
0.216579 | − | 0.976265i | ||||||||
−62933.9 | −0.152691 | |||||||||
−143766. | −0.347724 | −0.173862 | − | 0.984770i | ||||||
−0.173862 | + | 0.984770i | ||||||||
86318.7 | − | 193849.i | 0.208129 | − | 0.467405i | |||||
−566.212 | + | 1075.93i | −0.00136100 | + | 0.00258621i | |||||
189489. | 0.454065 | |||||||||
756331.i | 1.80677i | 0.428828 | + | 0.903386i | ||||||
−0.428828 | + | 0.903386i | ||||||||
96785.7i | 0.230495i | |||||||||
492382.i | 1.16900i | |||||||||
−44268.8 | − | 64439.3i | −0.104778 | − | 0.152519i | |||||
− | 118289.i | − | 0.279114i | |||||||
− | 249718.i | − | 0.587428i | |||||||
442957.i | 1.03881i | 0.854529 | + | 0.519404i | ||||||
−0.854529 | + | 0.519404i | ||||||||
127137.i | 0.297247i | |||||||||
92732.3 | + | 48800.7i | 0.216147 | + | 0.113748i | |||||
582518. | 1.35364 | |||||||||
110583.i | 0.256188i | |||||||||
−595733. | −1.37594 | |||||||||
− | 654514.i | − | 1.50712i | −0.657379 | − | 0.753560i | ||||
0.657379 | − | 0.753560i | ||||||||
155216. | + | 81683.2i | 0.356328 | + | 0.187519i | |||||
175823.i | 0.402413i | 0.979549 | + | 0.201206i | ||||||
−0.979549 | + | 0.201206i | ||||||||
188097.i | 0.429205i | |||||||||
−22610.9 | −0.0514387 | |||||||||
− | 479672.i | − | 1.08795i | |||||||
−161570. | + | 307019.i | −0.365357 | + | 0.694260i | |||||
80162.5i | 0.180727i | |||||||||
170204. | − | 382233.i | 0.382576 | − | 0.859166i | |||||
315020.i | 0.705968i | |||||||||
−109093. | −0.243749 | |||||||||
350897. | − | 666783.i | 0.781682 | − | 1.48537i | |||||
387008. | 0.859558 | |||||||||
318894. | 0.706169 | |||||||||
487162.i | 1.07558i | 0.843078 | + | 0.537791i | ||||||
−0.843078 | + | 0.537791i | ||||||||
163405.i | 0.359704i | |||||||||
405841. | − | 278807.i | 0.890736 | − | 0.611922i | |||||
−236194. | −0.516863 | |||||||||
−372718. | −0.813210 | −0.406605 | − | 0.913604i | ||||||
−0.406605 | + | 0.913604i | ||||||||
365.338 | 0.000794758 | |||||||||
−735977. | −1.59634 | |||||||||
56844.7 | − | 108018.i | 0.122934 | − | 0.233602i | |||||
− | 330459.i | − | 0.712564i | |||||||
−219445. | −0.471799 | |||||||||
− | 278036.i | − | 0.596019i | −0.954563 | − | 0.298009i | ||||
0.954563 | − | 0.298009i | ||||||||
− | 85096.4i | − | 0.181886i | |||||||
183622. | + | 96631.6i | 0.391330 | + | 0.205939i | |||||
598822.i | 1.27248i | |||||||||
−477293. | −1.01128 | |||||||||
2277.59 | 0.00481171 | |||||||||
− | 72136.4i | − | 0.151955i | |||||||
350777. | − | 276445.i | 0.736771 | − | 0.580645i | |||||
−335596. | −0.702848 | −0.351424 | − | 0.936216i | ||||||
−0.351424 | + | 0.936216i | ||||||||
− | 162525.i | − | 0.339397i | |||||||
− | 197975.i | − | 0.412234i | |||||||
−213455. | −0.443188 | |||||||||
540272. | + | 284320.i | 1.11852 | + | 0.588624i | |||||
201421. | 0.415801 | |||||||||
−238480. | −0.490892 | |||||||||
453348.i | 0.930510i | |||||||||
−442956. | −0.906580 | |||||||||
−141961. | − | 206644.i | −0.289716 | − | 0.421722i | |||||
− | 220951.i | − | 0.449635i | −0.974401 | − | 0.224817i | ||||
0.974401 | − | 0.224817i | ||||||||
98546.1i | 0.199970i | |||||||||
− | 138001.i | − | 0.279237i | |||||||
29863.0i | 0.0602543i | |||||||||
−383748. | − | 201949.i | −0.772090 | − | 0.406315i | |||||
256533. | 0.514675 | |||||||||
144474. | 0.289036 | |||||||||
− | 234164.i | − | 0.467147i | |||||||
755284.i | 1.50251i | 0.660012 | + | 0.751255i | ||||||
−0.660012 | + | 0.751255i | ||||||||
252657. | − | 480105.i | 0.501204 | − | 0.952400i | |||||
303330.i | 0.600035i | |||||||||
204767. | 0.403924 | |||||||||
−78611.9 | + | 176542.i | −0.154635 | + | 0.347271i | |||||
−209652. | −0.411247 | |||||||||
−67964.5 | − | 35766.6i | −0.132944 | − | 0.0699625i | |||||
−462501. | −0.902165 | |||||||||
198627.i | 0.386367i | |||||||||
1.18957e6 | 2.30750 | |||||||||
−68333.1 | −0.132182 | −0.0660912 | − | 0.997814i | ||||||
−0.0660912 | + | 0.997814i | ||||||||
−243187. | − | 127978.i | −0.469110 | − | 0.246871i | |||||
−294478. | −0.566478 | |||||||||
− | 220941.i | − | 0.423841i | |||||||
−416176. | −0.796160 | |||||||||
− | 509019.i | − | 0.971084i | |||||||
−279920. | − | 407461.i | −0.532546 | − | 0.775193i | |||||
3765.36 | 0.00714387 | |||||||||
−343164. | −0.649281 | −0.324640 | − | 0.945838i | ||||||
−0.324640 | + | 0.945838i | ||||||||
−44728.6 | −0.0843961 | |||||||||
−524944. | −0.987775 | |||||||||
352001. | + | 185242.i | 0.660539 | + | 0.347611i | |||||
−932.433 | −0.00174495 | |||||||||
−184051. | −0.343491 | |||||||||
449850. | 0.837259 | 0.418630 | − | 0.908157i | ||||||
0.418630 | + | 0.908157i | ||||||||
931216.i | 1.72846i | |||||||||
−12116.6 | + | 23024.3i | −0.0224288 | + | 0.0426197i | |||||
−475939. | − | 211929.i | −0.878609 | − | 0.391233i | |||||
− | 740186.i | − | 1.36272i | |||||||
309663.i | 0.568561i | |||||||||
321903. | 0.589435 | 0.294717 | − | 0.955584i | ||||||
0.294717 | + | 0.955584i | ||||||||
88250.1 | + | 46441.9i | 0.161158 | + | 0.0848100i | |||||
− | 50543.8i | − | 0.0920517i | |||||||
− | 668862.i | − | 1.21487i | |||||||
−725883. | −1.31489 | −0.657445 | − | 0.753503i | ||||||
−0.657445 | + | 0.753503i | ||||||||
−93030.1 | −0.168065 | |||||||||
1215.72 | − | 2310.14i | 0.00219039 | − | 0.00416222i | |||||
− | 774960.i | − | 1.39252i | |||||||
442111. | 0.792301 | |||||||||
134515.i | 0.240419i | |||||||||
88369.1 | 0.157520 | |||||||||
−61862.4 | − | 524027.i | −0.109978 | − | 0.931603i | |||||
− | 943161.i | − | 1.67227i | −0.548525 | − | 0.836134i | ||||
0.548525 | − | 0.836134i | ||||||||
812341.i | 1.43649i | |||||||||
−146642. | −0.258623 | |||||||||
98939.4 | 0.174031 | |||||||||
−615961. | − | 324152.i | −1.08059 | − | 0.568663i | |||||
316017.i | 0.552926i | |||||||||
534635. | 0.932965 | 0.466483 | − | 0.884530i | ||||||
0.466483 | + | 0.884530i | ||||||||
735187. | 1.27956 | |||||||||
178470. | − | 400799.i | 0.309801 | − | 0.695733i | |||||
241460. | + | 127069.i | 0.418040 | + | 0.219995i | |||||
150078. | 0.259148 | 0.129574 | − | 0.991570i | ||||||
0.129574 | + | 0.991570i | ||||||||
567675.i | 0.977665i | |||||||||
− | 178521.i | − | 0.306648i | |||||||
− | 410825.i | − | 0.703834i | |||||||
99559.2 | + | 52393.4i | 0.170121 | + | 0.0895269i | |||||
− | 607841.i | − | 1.03594i | |||||||
102533.i | 0.174291i | |||||||||
− | 546351.i | − | 0.926296i | |||||||
238646.i | 0.403553i | 0.979432 | + | 0.201777i | ||||||
−0.979432 | + | 0.201777i | ||||||||
−630179. | − | 331634.i | −1.06288 | − | 0.559342i | |||||
611934. | 1.02943 | |||||||||
− | 193307.i | − | 0.324349i | |||||||
197164. | 0.329965 | 0.164983 | − | 0.986296i | ||||||
0.164983 | + | 0.986296i | ||||||||
1210.75i | 0.00202104i | |||||||||
129286. | + | 188194.i | 0.215253 | + | 0.313330i | |||||
578821.i | 0.961215i | |||||||||
152686.i | 0.252905i | |||||||||
−606619. | −1.00220 | |||||||||
− | 533092.i | − | 0.878471i | |||||||
32322.1 | + | 17009.6i | 0.0531264 | + | 0.0279580i | |||||
− | 532958.i | − | 0.873758i | |||||||
312898. | + | 139330.i | 0.511670 | + | 0.227840i | |||||
623125.i | 1.01637i | |||||||||
48739.1 | 0.0792950 | |||||||||
−1.02642e6 | − | 540159.i | −1.66566 | − | 0.876562i | |||||
−141552. | −0.229124 | |||||||||
103089. | 0.166441 | 0.0832206 | − | 0.996531i | ||||||
0.0832206 | + | 0.996531i | ||||||||
119973.i | 0.193210i | |||||||||
− | 145387.i | − | 0.233546i | |||||||
965539. | + | 508119.i | 1.54709 | + | 0.814162i | |||||
−512.992 | −0.000819894 | |||||||||
−155700. | −0.248221 | |||||||||
80590.3 | 0.128155 | |||||||||
−491608. | −0.779791 | |||||||||
226739. | − | 430855.i | 0.358750 | − | 0.681705i | |||||
− | 376867.i | − | 0.594788i | |||||||
−1.05340e6 | −1.65835 | −0.829174 | − | 0.558990i | ||||||
−0.829174 | + | 0.558990i | ||||||||
− | 468651.i | − | 0.735943i | |||||||
− | 332568.i | − | 0.520938i | |||||||
−507351. | + | 348542.i | −0.792736 | + | 0.544598i | |||||
188732.i | 0.294159i | |||||||||
1.15265e6 | 1.79205 | |||||||||
390752. | 0.605996 | |||||||||
352013.i | 0.544561i | |||||||||
−492546. | + | 388173.i | −0.760073 | + | 0.599009i | |||||
−45697.1 | −0.0703426 | |||||||||
800899.i | 1.22979i | |||||||||
− | 113624.i | − | 0.174040i | |||||||
−280562. | −0.428679 | −0.214340 | − | 0.976759i | ||||||
−0.214340 | + | 0.976759i | ||||||||
−149433. | + | 283957.i | −0.227760 | + | 0.432795i | |||||
−977553. | −1.48627 | −0.743137 | − | 0.669140i | ||||||
−0.743137 | + | 0.669140i | ||||||||
317278. | 0.481203 | |||||||||
753607.i | 1.14015i | |||||||||
283258. | 0.427497 | |||||||||
−343689. | + | 653086.i | −0.517429 | + | 0.983231i | |||||
285881.i | 0.429344i | |||||||||
− | 2084.34i | − | 0.00312266i | |||||||
− | 456739.i | − | 0.682592i | |||||||
− | 41226.1i | − | 0.0614616i | |||||||
340905. | + | 179403.i | 0.506997 | + | 0.266809i | |||||
240514. | 0.356824 | 0.178412 | − | 0.983956i | ||||||
0.178412 | + | 0.983956i | ||||||||
−280291. | −0.414825 | |||||||||
− | 148476.i | − | 0.219208i | −0.993975 | − | 0.109604i | ||||
0.993975 | − | 0.109604i | ||||||||
231597.i | 0.341098i | |||||||||
−293515. | − | 427252.i | −0.431244 | − | 0.627734i | |||||
950707.i | 1.39343i | |||||||||
−186234. | −0.272301 | −0.136150 | − | 0.990688i | ||||||
−0.136150 | + | 0.990688i | ||||||||
62570.8 | − | 140518.i | 0.0912664 | − | 0.204961i | |||||
601485. | 0.875217 | 0.437608 | − | 0.899166i | ||||||
0.437608 | + | 0.899166i | ||||||||
740595. | − | 1.40730e6i | 1.07504 | − | 2.04282i | |||||
−83318.9 | −0.120654 | |||||||||
6218.65i | 0.00898358i | |||||||||
−19953.5 | −0.0287561 | |||||||||
−824702. | −1.18567 | |||||||||
433565. | − | 823871.i | 0.621844 | − | 1.18164i | |||||
−300692. | −0.430239 | |||||||||
− | 287802.i | − | 0.410812i | |||||||
−317325. | −0.451872 | |||||||||
− | 335094.i | − | 0.476039i | −0.971260 | − | 0.238020i | ||||
0.971260 | − | 0.238020i | ||||||||
−267154. | − | 140591.i | −0.378619 | − | 0.199250i | |||||
−81669.6 | −0.115470 | |||||||||
−620184. | −0.874775 | |||||||||
−947528. | −1.33333 | |||||||||
348827. | 0.489694 | |||||||||
617717. | + | 325076.i | 0.865120 | + | 0.455272i | |||||
−431835. | −0.603361 | |||||||||
−5287.16 | −0.00736980 | |||||||||
−912059. | −1.26833 | |||||||||
19839.9i | 0.0275248i | |||||||||
333550. | − | 229144.i | 0.461661 | − | 0.317154i | |||||
101472. | − | 227879.i | 0.140115 | − | 0.314663i | |||||
253461.i | 0.349165i | |||||||||
− | 374862.i | − | 0.515197i | −0.966252 | − | 0.257598i | ||||
0.966252 | − | 0.257598i | ||||||||
747248. | 1.02459 | |||||||||
−117119. | + | 222552.i | −0.160212 | + | 0.304439i | |||||
− | 69499.3i | − | 0.0948490i | |||||||
− | 141026.i | − | 0.192017i | −0.995381 | − | 0.0960083i | ||||
0.995381 | − | 0.0960083i | ||||||||
103745. | 0.140926 | |||||||||
413213. | 0.560000 | 0.280000 | − | 0.960000i | ||||||
0.280000 | + | 0.960000i | ||||||||
1332.91 | + | 701.447i | 0.00180220 | + | 0.000948414i | |||||
589818.i | 0.795632i | |||||||||
−1.00014e6 | −1.34601 | |||||||||
− | 166710.i | − | 0.223841i | −0.993717 | − | 0.111920i | ||||
0.993717 | − | 0.111920i | ||||||||
775885. | 1.03937 | |||||||||
−223685. | + | 425051.i | −0.298954 | + | 0.568079i | |||||
1.14312e6i | 1.52424i | |||||||||
453274.i | 0.603008i | |||||||||
−146541. | −0.194500 | |||||||||
1.07183e6 | 1.41934 | |||||||||
590943. | + | 310986.i | 0.780741 | + | 0.410868i | |||||
− | 154136.i | − | 0.203173i | |||||||
−140401. | −0.184645 | |||||||||
−533496. | −0.700007 | |||||||||
−311454. | + | 699446.i | −0.407729 | + | 0.915654i | |||||
86864.6 | + | 735817.i | 0.113456 | + | 0.961067i | |||||
−185831. | −0.242164 | |||||||||
− | 543966.i | − | 0.707249i | −0.935387 | − | 0.353625i | ||||
0.935387 | − | 0.353625i | ||||||||
− | 1.39584e6i | − | 1.81070i | |||||||
661551.i | 0.856220i | |||||||||
−452216. | + | 859312.i | −0.583957 | + | 1.10965i | |||||
173103.i | 0.223025i | 0.993763 | + | 0.111512i | ||||||
−0.993763 | + | 0.111512i | ||||||||
25909.4i | 0.0333059i | |||||||||
350410.i | 0.449423i | 0.974425 | + | 0.224712i | ||||||
−0.974425 | + | 0.224712i | ||||||||
28011.3i | 0.0358450i | |||||||||
−322282. | + | 612408.i | −0.411481 | + | 0.781906i | |||||
−611605. | −0.779118 | |||||||||
735051.i | 0.934266i | 0.884187 | + | 0.467133i | ||||||
−0.884187 | + | 0.467133i | ||||||||
120083. | 0.152284 | |||||||||
− | 797106.i | − | 1.00859i | |||||||
600760. | + | 316152.i | 0.758439 | + | 0.399131i | |||||
315216.i | 0.397058i | |||||||||
135148.i | 0.169856i | |||||||||
743414. | 0.932240 | |||||||||
3526.33i | 0.00441212i | |||||||||
1.20958e6 | + | 636544.i | 1.51004 | + | 0.794662i | |||||
804883.i | 1.00257i | |||||||||
37164.5 | − | 83461.9i | 0.0461896 | − | 0.103730i | |||||
1.27835e6i | 1.58525i | |||||||||
−288951. | −0.357523 | |||||||||
−102905. | − | 149792.i | −0.127043 | − | 0.184928i | |||||
373392. | 0.459955 | |||||||||
1.09421e6 | 1.34489 | |||||||||
2306.13i | 0.00282819i | |||||||||
403.451i | 0.000493689i | |||||||||
−700568. | + | 1.33124e6i | −0.855369 | + | 1.62539i | |||||
940238. | 1.14546 | |||||||||
281974. | 0.342763 | 0.171381 | − | 0.985205i | ||||||
0.171381 | + | 0.985205i | ||||||||
−409387. | −0.496549 | |||||||||
104727. | 0.126745 | |||||||||
−131228. | − | 69059.2i | −0.158469 | − | 0.0833947i | |||||
− | 1.44668e6i | − | 1.74315i | −0.490260 | − | 0.871576i | ||||
0.490260 | − | 0.871576i | ||||||||
−639053. | −0.768329 | |||||||||
− | 1.56222e6i | − | 1.87413i | |||||||
910396.i | 1.08978i | |||||||||
481348. | + | 253311.i | 0.574932 | + | 0.302560i | |||||
591290.i | 0.704709i | |||||||||
198761. | 0.236370 | |||||||||
−510093. | −0.605291 | |||||||||
− | 86628.3i | − | 0.102572i | −0.998684 | − | 0.0512860i | ||||
0.998684 | − | 0.0512860i | ||||||||
305285. | + | 387371.i | 0.360686 | + | 0.457668i | |||||
−548169. | −0.646243 | |||||||||
194997.i | 0.229385i | |||||||||
− | 110983.i | − | 0.130272i | |||||||
332689. | 0.389667 | |||||||||
−166882. | − | 242919.i | −0.195041 | − | 0.283908i | |||||
777780. | 0.907058 | |||||||||
−213462. | −0.248405 | |||||||||
− | 778981.i | − | 0.904547i | |||||||
169901. | 0.196863 | 0.0984316 | − | 0.995144i | ||||||
0.0984316 | + | 0.995144i | ||||||||
−272938. | − | 143635.i | −0.315572 | − | 0.166071i | |||||
− | 44603.6i | − | 0.0514601i | |||||||
548753.i | 0.631749i | |||||||||
− | 681796.i | − | 0.783233i | |||||||
− | 1.96487e6i | − | 2.25237i | |||||||
185135. | − | 351797.i | 0.211770 | − | 0.402410i | |||||
−32422.9 | −0.0370084 | |||||||||
1.28498e6 | 1.46358 | 0.731792 | − | 0.681529i | ||||||
0.731792 | + | 0.681529i | ||||||||
− | 1.42917e6i | − | 1.62435i | |||||||
− | 67168.3i | − | 0.0761786i | |||||||
−250183. | + | 475403.i | −0.283140 | + | 0.538030i | |||||
942315.i | 1.06418i | 0.846687 | + | 0.532092i | ||||||
−0.846687 | + | 0.532092i | ||||||||
1.56679e6 | 1.76567 | |||||||||
391979. | − | 880283.i | 0.440798 | − | 0.989918i | |||||
1.29638e6 | 1.45475 | |||||||||
434938. | − | 826479.i | 0.487039 | − | 0.925483i | |||||
4278.26 | 0.00478062 | |||||||||
− | 819939.i | − | 0.914285i | −0.889394 | − | 0.457142i | ||||
0.889394 | − | 0.457142i | ||||||||
−509735. | −0.567189 | |||||||||
81369.7 | 0.0903505 | |||||||||
512223. | + | 745610.i | 0.567560 | + | 0.826160i | |||||
−715837. | −0.791504 | |||||||||
− | 231524.i | − | 0.255459i | |||||||
143611. | 0.158125 | 0.0790625 | − | 0.996870i | ||||||
0.0790625 | + | 0.996870i | ||||||||
− | 484845.i | − | 0.532729i | |||||||
−565423. | + | 1.07443e6i | −0.619964 | + | 1.17807i | |||||
246067. | 0.269239 | |||||||||
655998. | 0.716273 | |||||||||
678192. | 0.738961 | |||||||||
393573. | 0.427945 | |||||||||
−19546.4 | + | 37142.6i | −0.0212092 | + | 0.0403023i | |||||
−790063. | −0.855491 | |||||||||
58985.4 | 0.0637374 | |||||||||
64057.1 | 0.0690740 | |||||||||
515577.i | 0.554803i | |||||||||
−266050. | + | 505555.i | −0.285699 | + | 0.542893i | |||||
344596. | − | 773874.i | 0.369280 | − | 0.829309i | |||||
− | 1.68061e6i | − | 1.79728i | −0.438691 | − | 0.898638i | ||||
0.438691 | − | 0.898638i | ||||||||
4158.17i | 0.00443764i | |||||||||
261624. | 0.278632 | |||||||||
−893676. | + | 1.69819e6i | −0.949810 | + | 1.80485i | |||||
1.16288e6i | 1.23338i | 0.787207 | + | 0.616689i | ||||||
−0.787207 | + | 0.616689i | ||||||||
389901.i | 0.412688i | |||||||||
1.15801e6 | 1.22317 | |||||||||
−1.64784e6 | −1.73699 | |||||||||
−61121.4 | − | 88970.5i | −0.0642960 | − | 0.0935915i | |||||
− | 1.01895e6i | − | 1.06967i | |||||||
997.036 | 0.00104453 | 0.000522266 | − | 1.00000i | ||||||
0.000522266 | 1.00000i | |||||||||
− | 996909.i | − | 1.04226i | |||||||
666895. | 0.695812 | |||||||||
28523.4 | + | 15010.6i | 0.0296995 | + | 0.0156295i | |||||
− | 129407.i | − | 0.134468i | |||||||
− | 359866.i | − | 0.373180i | |||||||
597261. | 0.618097 | 0.309049 | − | 0.951046i | ||||||
0.309049 | + | 0.951046i | ||||||||
463872. | 0.479080 | |||||||||
165120. | − | 313765.i | 0.170187 | − | 0.323394i | |||||
512129.i | 0.526775i | |||||||||
−822521. | −0.844331 | |||||||||
−62615.8 | −0.0641461 | |||||||||
1532.60 | − | 3441.82i | 0.00156688 | − | 0.00351881i | |||||
−456805. | − | 240395.i | −0.466080 | − | 0.245276i | |||||
307119. | 0.312722 | 0.156361 | − | 0.987700i | ||||||
0.156361 | + | 0.987700i | ||||||||
359788.i | 0.365614i | |||||||||
259703.i | 0.263377i | |||||||||
− | 1.02905e6i | − | 1.04151i | |||||||
−518686. | + | 985619.i | −0.523912 | + | 0.995550i | |||||
742950.i | 0.748930i | |||||||||
− | 1.32569e6i | − | 1.33368i | −0.745202 | − | 0.666839i | ||||
0.745202 | − | 0.666839i | ||||||||
320475.i | 0.321761i | |||||||||
371493.i | 0.372237i |
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 115.5.c.c.114.12 | yes | 44 | |
5.4 | even | 2 | inner | 115.5.c.c.114.33 | yes | 44 | |
23.22 | odd | 2 | inner | 115.5.c.c.114.11 | ✓ | 44 | |
115.114 | odd | 2 | inner | 115.5.c.c.114.34 | yes | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
115.5.c.c.114.11 | ✓ | 44 | 23.22 | odd | 2 | inner | |
115.5.c.c.114.12 | yes | 44 | 1.1 | even | 1 | trivial | |
115.5.c.c.114.33 | yes | 44 | 5.4 | even | 2 | inner | |
115.5.c.c.114.34 | yes | 44 | 115.114 | odd | 2 | inner |