Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [538,4,Mod(537,538)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(538, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("538.537");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 538.b (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 | 537.17 | ||
Character | 538.537 | ||
Dual form | 538.4.b.a.537.52 |
-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 .
− | 2.00000i | − | 0.707107i | |||||||
− | 0.122336i | − | 0.0235435i | −0.999931 | − | 0.0117718i | ||||
0.999931 | − | 0.0117718i | ||||||||
−4.00000 | −0.500000 | |||||||||
7.26358 | 0.649674 | 0.324837 | − | 0.945770i | ||||||
0.324837 | + | 0.945770i | ||||||||
−0.244671 | −0.0166478 | |||||||||
31.0626i | 1.67722i | 0.544731 | + | 0.838611i | ||||||
−0.544731 | + | 0.838611i | ||||||||
8.00000i | 0.353553i | |||||||||
26.9850 | 0.999446 | |||||||||
− | 14.5272i | − | 0.459389i | |||||||
−3.20731 | −0.0879126 | −0.0439563 | − | 0.999033i | ||||||
−0.0439563 | + | 0.999033i | ||||||||
0.489343i | 0.0117718i | |||||||||
−10.0275 | −0.213934 | −0.106967 | − | 0.994263i | ||||||
−0.106967 | + | 0.994263i | ||||||||
62.1251 | 1.18597 | |||||||||
− | 0.888595i | − | 0.0152956i | |||||||
16.0000 | 0.250000 | |||||||||
− | 27.1710i | − | 0.387643i | −0.981037 | − | 0.193821i | ||||
0.981037 | − | 0.193821i | ||||||||
− | 53.9701i | − | 0.706715i | |||||||
41.3494i | 0.499273i | 0.968340 | + | 0.249637i | ||||||
−0.968340 | + | 0.249637i | ||||||||
−29.0543 | −0.324837 | |||||||||
3.80006 | 0.0394877 | |||||||||
6.41461i | 0.0621636i | |||||||||
−160.747 | −1.45731 | −0.728654 | − | 0.684882i | ||||||
−0.728654 | + | 0.684882i | ||||||||
0.978685 | 0.00832389 | |||||||||
−72.2404 | −0.577923 | |||||||||
20.0551i | 0.151274i | |||||||||
− | 6.60430i | − | 0.0470740i | |||||||
− | 124.250i | − | 0.838611i | |||||||
265.809i | 1.70205i | 0.525127 | + | 0.851024i | ||||||
−0.525127 | + | 0.851024i | ||||||||
−1.77719 | −0.0108156 | |||||||||
85.9313i | 0.497862i | 0.968521 | + | 0.248931i | ||||||
−0.968521 | + | 0.248931i | ||||||||
− | 32.0000i | − | 0.176777i | |||||||
0.392368i | 0.00206977i | |||||||||
−54.3420 | −0.274105 | |||||||||
225.625i | 1.08965i | |||||||||
−107.940 | −0.499723 | |||||||||
−320.328 | −1.42329 | −0.711644 | − | 0.702541i | ||||||
−0.711644 | + | 0.702541i | ||||||||
82.6987 | 0.353040 | |||||||||
1.22673i | 0.00503676i | |||||||||
58.1086i | 0.229695i | |||||||||
−357.805 | −1.36292 | −0.681460 | − | 0.731856i | ||||||
−0.681460 | + | 0.731856i | ||||||||
− | 7.60012i | − | 0.0279220i | |||||||
263.079 | 0.933004 | 0.466502 | − | 0.884520i | ||||||
0.466502 | + | 0.884520i | ||||||||
12.8292 | 0.0439563 | |||||||||
196.008 | 0.649314 | |||||||||
321.494i | 1.03047i | |||||||||
577.976 | 1.79375 | 0.896877 | − | 0.442280i | ||||||
0.896877 | + | 0.442280i | ||||||||
− | 1.95737i | − | 0.00588588i | |||||||
−621.883 | −1.81307 | |||||||||
144.481i | 0.408653i | |||||||||
−3.32398 | −0.00912648 | |||||||||
40.1102 | 0.106967 | |||||||||
−482.084 | −1.24942 | −0.624711 | − | 0.780856i | ||||||
−0.624711 | + | 0.780856i | ||||||||
−13.2086 | −0.0332863 | |||||||||
−23.2965 | −0.0571146 | |||||||||
−248.501 | −0.592987 | |||||||||
5.05850 | 0.0117546 | |||||||||
531.617 | 1.20353 | |||||||||
− | 377.297i | − | 0.832539i | −0.909241 | − | 0.416270i | ||||
0.909241 | − | 0.416270i | ||||||||
3.55438i | 0.00764781i | |||||||||
695.295 | 1.45940 | 0.729700 | − | 0.683767i | ||||||
0.729700 | + | 0.683767i | ||||||||
171.863 | 0.352041 | |||||||||
838.225i | 1.67629i | |||||||||
−64.0000 | −0.125000 | |||||||||
−72.8359 | −0.138987 | |||||||||
0.784736 | 0.00146355 | |||||||||
383.312 | 0.698940 | 0.349470 | − | 0.936948i | ||||||
0.349470 | + | 0.936948i | ||||||||
108.684i | 0.193821i | |||||||||
19.6651i | 0.0343102i | |||||||||
451.251 | 0.770497 | |||||||||
1054.15i | 1.76204i | 0.473081 | + | 0.881019i | ||||||
−0.473081 | + | 0.881019i | ||||||||
215.880i | 0.353357i | |||||||||
685.580 | 1.09919 | 0.549596 | − | 0.835430i | ||||||
0.549596 | + | 0.835430i | ||||||||
640.656i | 1.00642i | |||||||||
8.83758i | 0.0136063i | |||||||||
− | 165.397i | − | 0.249637i | |||||||
− | 99.6271i | − | 0.147449i | |||||||
2.45345 | 0.00356153 | |||||||||
−707.008 | −1.00689 | −0.503447 | − | 0.864026i | ||||||
−0.503447 | + | 0.864026i | ||||||||
116.217 | 0.162419 | |||||||||
727.788 | 0.998337 | |||||||||
715.609i | 0.963729i | |||||||||
− | 66.6066i | − | 0.0880847i | −0.999030 | − | 0.0440423i | ||||
0.999030 | − | 0.0440423i | ||||||||
−15.2002 | −0.0197438 | |||||||||
− | 197.359i | − | 0.251842i | |||||||
− | 526.158i | − | 0.659734i | |||||||
32.5179 | 0.0400722 | |||||||||
− | 25.6584i | − | 0.0310818i | |||||||
−1138.10 | −1.35549 | −0.677746 | − | 0.735296i | ||||||
−0.677746 | + | 0.735296i | ||||||||
− | 392.016i | − | 0.459134i | |||||||
− | 311.481i | − | 0.358815i | |||||||
642.988 | 0.728654 | |||||||||
10.5125 | 0.0117214 | |||||||||
− | 1155.95i | − | 1.26838i | |||||||
300.344i | 0.324365i | |||||||||
−3.91474 | −0.00416194 | |||||||||
29.1175 | 0.0304787 | 0.0152393 | − | 0.999884i | ||||||
0.0152393 | + | 0.999884i | ||||||||
1243.77i | 1.28203i | |||||||||
−86.5492 | −0.0878639 | |||||||||
288.962 | 0.288962 | |||||||||
691.301i | 0.681059i | 0.940234 | + | 0.340530i | ||||||
−0.940234 | + | 0.340530i | ||||||||
6.64796i | 0.00645339i | |||||||||
495.942 | 0.474433 | 0.237217 | − | 0.971457i | ||||||
0.237217 | + | 0.971457i | ||||||||
− | 80.2204i | − | 0.0756371i | |||||||
27.6020 | 0.0256541 | |||||||||
964.169i | 0.883475i | |||||||||
1846.33i | 1.66814i | 0.551657 | + | 0.834071i | ||||||
−0.551657 | + | 0.834071i | ||||||||
26.4172i | 0.0235370i | |||||||||
− | 1176.18i | − | 1.03356i | −0.856118 | − | 0.516780i | ||||
0.856118 | − | 0.516780i | ||||||||
46.5930i | 0.0403861i | |||||||||
39.1876i | 0.0335092i | |||||||||
497.001i | 0.419305i | |||||||||
1643.91i | 1.36855i | 0.729225 | + | 0.684274i | ||||||
−0.729225 | + | 0.684274i | ||||||||
− | 10.1170i | − | 0.00831179i | |||||||
−1167.60 | −0.946776 | |||||||||
− | 1063.23i | − | 0.851024i | |||||||
−270.594 | −0.213815 | |||||||||
−754.593 | −0.588694 | |||||||||
844.000 | 0.650163 | |||||||||
7.10876 | 0.00540782 | |||||||||
−1320.71 | −0.992271 | |||||||||
− | 1390.59i | − | 1.03195i | |||||||
43.7723i | 0.0320879i | |||||||||
− | 343.725i | − | 0.248931i | |||||||
−1432.67 | −1.02514 | |||||||||
1676.45 | 1.18532 | |||||||||
1520.34 | 1.06227 | 0.531136 | − | 0.847287i | ||||||
0.531136 | + | 0.847287i | ||||||||
128.000i | 0.0883883i | |||||||||
− | 32.1840i | − | 0.0219662i | |||||||
145.672i | 0.0982789i | |||||||||
1277.37 | 0.851939 | 0.425969 | − | 0.904738i | ||||||
0.425969 | + | 0.904738i | ||||||||
− | 1.56947i | − | 0.00103489i | |||||||
−1284.42 | −0.837392 | |||||||||
− | 766.623i | − | 0.494225i | |||||||
− | 47.9708i | − | 0.0305828i | |||||||
217.368 | 0.137052 | |||||||||
2021.91i | 1.26090i | 0.776230 | + | 0.630450i | ||||||
−0.776230 | + | 0.630450i | ||||||||
39.3302 | 0.0242609 | |||||||||
− | 269.209i | − | 0.164274i | −0.996621 | − | 0.0821368i | ||||
0.996621 | − | 0.0821368i | ||||||||
− | 902.502i | − | 0.544824i | |||||||
− | 70.7071i | − | 0.0422313i | |||||||
2108.30 | 1.24595 | |||||||||
32.1614 | 0.0188075 | |||||||||
431.761 | 0.249861 | |||||||||
1930.72i | 1.10578i | |||||||||
− | 1371.16i | − | 0.777247i | |||||||
76.0785i | 0.0426861i | |||||||||
1281.31 | 0.711644 | |||||||||
280.768 | 0.154372 | 0.0771860 | − | 0.997017i | ||||||
0.0771860 | + | 0.997017i | ||||||||
17.6752 | 0.00962114 | |||||||||
2271.80 | 1.22435 | 0.612174 | − | 0.790723i | ||||||
0.612174 | + | 0.790723i | ||||||||
−330.795 | −0.176520 | |||||||||
− | 733.210i | − | 0.387428i | |||||||
−199.254 | −0.104262 | |||||||||
624.169i | 0.323448i | |||||||||
− | 4.90691i | − | 0.00251838i | |||||||
− | 162.060i | − | 0.0823808i | −0.999151 | − | 0.0411904i | ||||
0.999151 | − | 0.0411904i | ||||||||
1414.02i | 0.711981i | |||||||||
58.9761i | 0.0294158i | |||||||||
− | 232.435i | − | 0.114847i | |||||||
− | 4993.22i | − | 2.44423i | |||||||
− | 1455.58i | − | 0.705931i | |||||||
− | 2598.91i | − | 1.24885i | −0.781085 | − | 0.624425i | ||||
0.781085 | − | 0.624425i | ||||||||
1431.22 | 0.681460 | |||||||||
2.85000i | 0.00134468i | |||||||||
−133.213 | −0.0622853 | |||||||||
− | 436.551i | − | 0.202283i | −0.994872 | − | 0.101142i | ||||
0.994872 | − | 0.101142i | ||||||||
30.4005i | 0.0139610i | |||||||||
−2096.45 | −0.954232 | |||||||||
−394.717 | −0.178079 | |||||||||
1115.81i | 0.498997i | |||||||||
−1052.32 | −0.466502 | |||||||||
4047.07 | 1.77857 | 0.889286 | − | 0.457351i | ||||||
0.889286 | + | 0.457351i | ||||||||
− | 65.0357i | − | 0.0283353i | |||||||
− | 2243.97i | − | 0.969305i | |||||||
−51.3169 | −0.0219782 | |||||||||
−46.1568 | −0.0196009 | |||||||||
2276.21i | 0.958478i | |||||||||
− | 1628.93i | − | 0.680179i | −0.940393 | − | 0.340089i | ||||
0.940393 | − | 0.340089i | ||||||||
−784.032 | −0.324657 | |||||||||
3241.10i | 1.33099i | 0.746403 | + | 0.665495i | ||||||
−0.746403 | + | 0.665495i | ||||||||
−622.963 | −0.253720 | |||||||||
− | 85.0594i | − | 0.0343594i | |||||||
− | 1285.98i | − | 0.515236i | |||||||
−2326.73 | −0.924673 | |||||||||
− | 21.0249i | − | 0.00828829i | |||||||
87.1456i | 0.0340787i | |||||||||
−2311.90 | −0.896877 | |||||||||
205.146 | 0.0789535 | |||||||||
600.689 | 0.229361 | |||||||||
−3075.70 | −1.16518 | −0.582591 | − | 0.812765i | ||||||
−0.582591 | + | 0.812765i | ||||||||
7.82948i | 0.00294294i | |||||||||
− | 1969.70i | − | 0.734621i | −0.930098 | − | 0.367310i | ||||
0.930098 | − | 0.367310i | ||||||||
− | 58.2350i | − | 0.0215517i | |||||||
8.91043i | 0.00327225i | |||||||||
2487.53 | 0.906535 | |||||||||
1090.38i | 0.394347i | 0.980369 | + | 0.197174i | ||||||
−0.980369 | + | 0.197174i | ||||||||
173.098i | 0.0621292i | |||||||||
1851.20 | 0.659436 | 0.329718 | − | 0.944079i | ||||||
0.329718 | + | 0.944079i | ||||||||
− | 577.923i | − | 0.204327i | |||||||
− | 46.8927i | − | 0.0164555i | |||||||
1382.60 | 0.481582 | |||||||||
−8256.70 | −2.85471 | |||||||||
13.2959 | 0.00456324 | |||||||||
−2598.94 | −0.885454 | |||||||||
− | 991.884i | − | 0.335475i | |||||||
−4337.77 | −1.45650 | |||||||||
−160.441 | −0.0534835 | |||||||||
− | 132.620i | − | 0.0438924i | |||||||
− | 55.2041i | − | 0.0181402i | |||||||
−2123.86 | −0.692952 | −0.346476 | − | 0.938059i | ||||||
−0.346476 | + | 0.938059i | ||||||||
1928.34 | 0.624711 | |||||||||
128.960 | 0.0414846 | |||||||||
3692.65 | 1.17955 | |||||||||
1910.90 | 0.606149 | |||||||||
52.8344 | 0.0166432 | |||||||||
−2669.25 | −0.835024 | |||||||||
−2352.37 | −0.730838 | |||||||||
− | 83.8709i | − | 0.0258789i | |||||||
93.1861 | 0.0285573 | |||||||||
272.458i | 0.0829300i | |||||||||
78.3751 | 0.0236946 | |||||||||
2167.13i | 0.650770i | 0.945582 | + | 0.325385i | ||||||
−0.945582 | + | 0.325385i | ||||||||
994.002 | 0.296494 | |||||||||
−1949.41 | −0.577603 | |||||||||
3287.82 | 0.967709 | |||||||||
4523.56i | 1.32264i | 0.750104 | + | 0.661320i | ||||||
−0.750104 | + | 0.661320i | ||||||||
−20.2340 | −0.00587732 | |||||||||
− | 493.569i | − | 0.142428i | −0.997461 | − | 0.0712139i | ||||
0.997461 | − | 0.0712139i | ||||||||
2335.20i | 0.669471i | |||||||||
−12.1880 | −0.00347147 | |||||||||
−2126.47 | −0.601765 | |||||||||
−417.669 | −0.117435 | −0.0587177 | − | 0.998275i | ||||||
−0.0587177 | + | 0.998275i | ||||||||
541.188i | 0.151190i | |||||||||
4198.17 | 1.16536 | |||||||||
1509.19i | 0.416270i | |||||||||
86.4923i | 0.0237058i | |||||||||
− | 1688.00i | − | 0.459735i | |||||||
−1920.77 | −0.519850 | −0.259925 | − | 0.965629i | ||||||
−0.259925 | + | 0.965629i | ||||||||
− | 14.2175i | − | 0.00382390i | |||||||
− | 3148.64i | − | 0.841584i | −0.907157 | − | 0.420792i | ||||
0.907157 | − | 0.420792i | ||||||||
2641.43i | 0.701642i | |||||||||
− | 267.350i | − | 0.0705783i | |||||||
−2781.18 | −0.729700 | |||||||||
−4517.10 | −1.17791 | |||||||||
87.5445 | 0.0226896 | |||||||||
− | 414.633i | − | 0.106812i | |||||||
−687.450 | −0.176021 | |||||||||
−8.14837 | −0.00207382 | |||||||||
2865.34i | 0.724881i | |||||||||
1308.03i | 0.328934i | 0.986383 | + | 0.164467i | ||||||
−0.986383 | + | 0.164467i | ||||||||
− | 3352.90i | − | 0.838146i | |||||||
515.565 | 0.128116 | |||||||||
− | 3040.68i | − | 0.751139i | |||||||
−24.1440 | −0.00592924 | |||||||||
256.000 | 0.0625000 | |||||||||
− | 8167.52i | − | 1.98240i | −0.132382 | − | 0.991199i | ||||
0.132382 | − | 0.991199i | ||||||||
−64.3679 | −0.0155325 | |||||||||
− | 9950.22i | − | 2.38717i | |||||||
291.344 | 0.0694937 | |||||||||
7172.85i | 1.70110i | |||||||||
− | 2554.73i | − | 0.602412i | |||||||
−185.643 | −0.0435256 | −0.0217628 | − | 0.999763i | ||||||
−0.0217628 | + | 0.999763i | ||||||||
−3.13894 | −0.000731775 | |||||||||
−3501.66 | −0.811718 | |||||||||
2568.83i | 0.592125i | |||||||||
139.231i | 0.0319131i | |||||||||
−1533.25 | −0.349470 | |||||||||
4197.58 | + | 1358.48i | 0.951416 | + | 0.307910i | |||||
−95.9417 | −0.0216253 | |||||||||
− | 5940.84i | − | 1.33166i | −0.746103 | − | 0.665831i | ||||
0.746103 | − | 0.665831i | ||||||||
− | 434.736i | − | 0.0969107i | |||||||
−38.1053 | −0.00844776 | |||||||||
4043.82 | 0.891591 | |||||||||
231.697 | 0.0508068 | |||||||||
− | 78.6604i | − | 0.0171551i | |||||||
1194.15i | 0.259022i | 0.991578 | + | 0.129511i | ||||||
−0.991578 | + | 0.129511i | ||||||||
−538.418 | −0.116159 | |||||||||
2318.86i | 0.497586i | |||||||||
−1805.00 | −0.385249 | |||||||||
− | 6228.31i | − | 1.32224i | −0.750280 | − | 0.661120i | ||||
0.750280 | − | 0.661120i | ||||||||
−141.414 | −0.0298620 | |||||||||
−5882.70 | −1.23566 | −0.617828 | − | 0.786314i | ||||||
−0.617828 | + | 0.786314i | ||||||||
− | 4216.60i | − | 0.881019i | |||||||
36.7428 | 0.00763669 | |||||||||
− | 64.3228i | − | 0.0132989i | |||||||
− | 11114.3i | − | 2.28592i | |||||||
− | 863.521i | − | 0.176679i | |||||||
4174.74 | 0.849733 | |||||||||
3861.44 | 0.781902 | |||||||||
− | 3.56211i | − | 0.000717575i | |||||||
−2742.32 | −0.549596 | |||||||||
−2627.25 | −0.523841 | −0.261921 | − | 0.965089i | ||||||
−0.261921 | + | 0.965089i | ||||||||
152.157 | 0.0301836 | |||||||||
− | 2740.52i | − | 0.540879i | |||||||
− | 2562.62i | − | 0.503208i | |||||||
21.1820i | 0.00413840i | |||||||||
− | 561.537i | − | 0.109158i | |||||||
1611.90 | 0.311768 | |||||||||
− | 35.3503i | − | 0.00680317i | |||||||
8171.91i | 1.56485i | |||||||||
− | 4543.60i | − | 0.865745i | |||||||
84.5708 | 0.0160345 | |||||||||
661.590i | 0.124818i | |||||||||
5050.33 | 0.948135 | |||||||||
−1466.42 | −0.273953 | |||||||||
2129.41 | 0.395870 | 0.197935 | − | 0.980215i | ||||||
0.197935 | + | 0.980215i | ||||||||
398.509i | 0.0737245i | |||||||||
− | 60.6714i | − | 0.0111698i | |||||||
1248.34 | 0.228712 | |||||||||
− | 6693.56i | − | 1.22044i | −0.792232 | − | 0.610220i | ||||
0.792232 | − | 0.610220i | ||||||||
−9.81382 | −0.00178076 | |||||||||
6519.74 | 1.17737 | 0.588686 | − | 0.808362i | ||||||
0.588686 | + | 0.808362i | ||||||||
−324.120 | −0.0582520 | |||||||||
6088.51i | 1.08904i | |||||||||
2828.03 | 0.503447 | |||||||||
− | 5992.74i | − | 1.06178i | −0.847439 | − | 0.530892i | ||||
0.847439 | − | 0.530892i | ||||||||
117.952 | 0.0208001 | |||||||||
− | 852.529i | − | 0.149632i | |||||||
−464.869 | −0.0812093 | |||||||||
225.872 | 0.0392739 | |||||||||
−9986.44 | −1.72833 | |||||||||
1123.50 | 0.193540 | |||||||||
−2911.15 | −0.499169 | |||||||||
724.394 | 0.123637 | |||||||||
−5197.82 | −0.883070 | |||||||||
−143.889 | −0.0243336 | |||||||||
− | 2862.44i | − | 0.481865i | |||||||
17953.4i | 3.00852i | |||||||||
5.69999 | 0.000950831 | |||||||||
7466.81 | 1.23992 | 0.619959 | − | 0.784634i | ||||||
0.619959 | + | 0.784634i | ||||||||
266.427i | 0.0440423i | |||||||||
−8644.07 | −1.42250 | |||||||||
−873.102 | −0.143036 | |||||||||
2784.21 | 0.454083 | |||||||||
60.8010 | 0.00987192 | |||||||||
308.183i | 0.0498154i | 0.999690 | + | 0.0249077i | ||||||
−0.999690 | + | 0.0249077i | ||||||||
4192.90i | 0.674744i | |||||||||
201.109 | 0.0322204 | |||||||||
789.434i | 0.125921i | |||||||||
− | 275.608i | − | 0.0437683i | |||||||
2231.63 | 0.352844 | |||||||||
− | 8662.83i | − | 1.36370i | |||||||
2104.63i | 0.329867i | |||||||||
142.839i | 0.0222904i | |||||||||
− | 8094.14i | − | 1.25764i | |||||||
2712.41 | 0.419625 | 0.209812 | − | 0.977742i | ||||||
0.209812 | + | 0.977742i | ||||||||
−130.071 | −0.0200361 | |||||||||
−5057.24 | −0.775668 | −0.387834 | − | 0.921729i | ||||||
−0.387834 | + | 0.921729i | ||||||||
−4487.95 | −0.685402 | |||||||||
66.2249i | 0.0100707i | |||||||||
102.634i | 0.0155409i | |||||||||
7714.10 | 1.16312 | 0.581558 | − | 0.813505i | ||||||
0.581558 | + | 0.813505i | ||||||||
92.3137i | 0.0138599i | |||||||||
7656.91i | 1.14475i | |||||||||
4552.42 | 0.677746 | |||||||||
− | 103.251i | − | 0.0153071i | |||||||
−3257.86 | −0.480959 | |||||||||
12270.4i | 1.80392i | 0.431823 | + | 0.901959i | ||||||
−0.431823 | + | 0.901959i | ||||||||
1568.06i | 0.229567i | |||||||||
5149.23 | 0.750726 | |||||||||
6482.20 | 0.941151 | |||||||||
161.570i | 0.0233616i | |||||||||
1245.93i | 0.179407i | |||||||||
4979.76 | 0.714117 | |||||||||
−170.119 | −0.0242958 | |||||||||
2970.62i | 0.422520i | 0.977430 | + | 0.211260i | ||||||
−0.977430 | + | 0.211260i | ||||||||
−2571.95 | −0.364327 | |||||||||
−9655.37 | −1.36216 | |||||||||
4653.46i | 0.653843i | |||||||||
− | 14974.8i | − | 2.09556i | |||||||
−42.0498 | −0.00586071 | |||||||||
9243.34i | 1.28312i | 0.767075 | + | 0.641558i | ||||||
−0.767075 | + | 0.641558i | ||||||||
174.291 | 0.0240973 | |||||||||
175.267i | 0.0241353i | |||||||||
4623.81i | 0.634188i | |||||||||
− | 2665.41i | − | 0.364126i | |||||||
− | 410.293i | − | 0.0558285i | |||||||
− | 13810.3i | − | 1.87174i | −0.352349 | − | 0.935869i | ||||
0.352349 | − | 0.935869i | ||||||||
− | 1201.38i | − | 0.162183i | |||||||
− | 185.992i | − | 0.0250096i | |||||||
6151.40i | 0.823908i | |||||||||
13891.0i | 1.85326i | 0.375975 | + | 0.926630i | ||||||
−0.375975 | + | 0.926630i | ||||||||
15.6590 | 0.00208097 | |||||||||
− | 723.650i | − | 0.0957938i | |||||||
−3939.39 | −0.519455 | |||||||||
7099.20 | 0.932487 | |||||||||
−116.470 | −0.0152393 | |||||||||
−7854.08 | −1.02370 | −0.511848 | − | 0.859076i | ||||||
−0.511848 | + | 0.859076i | ||||||||
17.8209 | 0.00231383 | |||||||||
4367.66i | 0.564915i | |||||||||
− | 4975.07i | − | 0.641017i | |||||||
− | 156.267i | − | 0.0200576i | |||||||
2180.76 | 0.278846 | |||||||||
−5135.41 | −0.654153 | |||||||||
346.197 | 0.0439319 | |||||||||
9957.88i | 1.25887i | 0.777053 | + | 0.629436i | ||||||
−0.777053 | + | 0.629436i | ||||||||
− | 3702.39i | − | 0.466292i | |||||||
157.130i | 0.0197151i | |||||||||
−1155.85 | −0.144481 | |||||||||
− | 8394.48i | − | 1.04539i | −0.852520 | − | 0.522694i | ||||
0.852520 | − | 0.522694i | ||||||||
−93.7854 | −0.0116358 | |||||||||
− | 861.680i | − | 0.106510i | |||||||
− | 2765.20i | − | 0.340530i | |||||||
5286.35 | 0.648594 | |||||||||
16513.4i | 2.01859i | |||||||||
1027.39 | 0.125125 | |||||||||
− | 26.5918i | − | 0.00322670i | |||||||
− | 3999.23i | − | 0.483495i | −0.970339 | − | 0.241747i | ||||
0.970339 | − | 0.241747i | ||||||||
5197.88i | 0.626110i | |||||||||
247.351 | 0.0296860 | |||||||||
−1983.77 | −0.237217 | |||||||||
11719.8 | 1.39635 | |||||||||
8675.53i | 1.02990i | |||||||||
− | 483.803i | − | 0.0572264i | |||||||
320.882i | 0.0378185i | |||||||||
−32.9339 | −0.00386758 | |||||||||
−265.240 | −0.0310366 | |||||||||
12862.8 | 1.49974 | 0.749870 | − | 0.661585i | ||||||
0.749870 | + | 0.661585i | ||||||||
−110.408 | −0.0128271 | |||||||||
6298.92 | 0.729194 | 0.364597 | − | 0.931165i | ||||||
0.364597 | + | 0.931165i | ||||||||
4247.73i | 0.489991i | |||||||||
15596.7 | 1.79276 | |||||||||
− | 3856.68i | − | 0.441738i | |||||||
1962.84i | 0.224028i | |||||||||
− | 257.921i | − | 0.0293340i | |||||||
21597.7i | 2.44774i | |||||||||
− | 7385.31i | − | 0.834071i | |||||||
− | 3.93449i | − | 0.000442795i | |||||||
− | 3821.79i | − | 0.428612i | |||||||
− | 6881.85i | − | 0.769112i | −0.923102 | − | 0.384556i | ||||
0.923102 | − | 0.384556i | ||||||||
− | 105.669i | − | 0.0117685i | |||||||
−8331.33 | −0.924661 | −0.462330 | − | 0.886708i | ||||||
−0.462330 | + | 0.886708i | ||||||||
5338.49i | 0.590451i | |||||||||
236.196 | 0.0260339 | |||||||||
4704.74i | 0.516780i | |||||||||
− | 6646.79i | − | 0.727595i | |||||||
−167.742 | −0.0182991 | |||||||||
16612.5 | 1.80609 | 0.903045 | − | 0.429545i | ||||||
0.903045 | + | 0.429545i | ||||||||
− | 186.372i | − | 0.0201931i | |||||||
−16781.5 | −1.81207 | |||||||||
544.917 | 0.0586404 | |||||||||
− | 4223.25i | − | 0.452941i | −0.974018 | − | 0.226470i | ||||
0.974018 | − | 0.226470i | ||||||||
− | 156.750i | − | 0.0167546i | |||||||
−8266.71 | −0.880629 | |||||||||
4334.26 | 0.460164 | |||||||||
− | 34.3480i | − | 0.00363446i | |||||||
− | 1988.00i | − | 0.209653i | |||||||
−7728.23 | −0.812289 | −0.406145 | − | 0.913809i | ||||||
−0.406145 | + | 0.913809i | ||||||||
3898.82i | 0.408427i | |||||||||
1147.59 | 0.119818 | |||||||||
− | 6575.63i | − | 0.684274i | |||||||
− | 277.922i | − | 0.0288255i | |||||||
9047.13 | 0.935248 | |||||||||
− | 2262.47i | − | 0.233113i | |||||||
40.4680i | 0.00415590i | |||||||||
17690.5 | 1.81078 | 0.905388 | − | 0.424586i | ||||||
0.905388 | + | 0.424586i | ||||||||
−987.138 | −0.100712 | |||||||||
−179.445 | −0.0182479 | |||||||||
4670.40 | 0.473388 | |||||||||
− | 7931.13i | − | 0.801279i | −0.916236 | − | 0.400639i | ||||
0.916236 | − | 0.400639i | ||||||||
24.3759i | 0.00245470i | |||||||||
427.435i | 0.0429040i | 0.999770 | + | 0.0214520i | ||||||
−0.999770 | + | 0.0214520i | ||||||||
4252.94i | 0.425512i | |||||||||
76.3581 | 0.00761510 | |||||||||
835.339i | 0.0830393i | |||||||||
13725.1i | 1.36000i | 0.733212 | + | 0.680000i | ||||||
−0.733212 | + | 0.680000i | ||||||||
1082.38 | 0.106908 | |||||||||
11906.6i | 1.17228i | |||||||||
− | 8396.35i | − | 0.824031i | |||||||
−19.8257 | −0.00193953 | |||||||||
3018.37 | 0.294347 | |||||||||
−843.775 | −0.0820229 | |||||||||
172.985 | 0.0167625 | |||||||||
− | 2987.09i | − | 0.288542i | |||||||
−3376.00 | −0.325081 | |||||||||
−13009.1 | −1.24873 | |||||||||
3841.54i | 0.367590i | |||||||||
− | 7925.52i | − | 0.756005i | −0.925805 | − | 0.378002i | ||||
0.925805 | − | 0.378002i | ||||||||
−28.4350 | −0.00270391 | |||||||||
3212.11 | 0.304489 | |||||||||
−6297.28 | −0.595090 | |||||||||
−610.849 | −0.0575457 | |||||||||
5282.85 | 0.496136 | |||||||||
211.497 | 0.0198012 | |||||||||
−534.701 | −0.0499064 | |||||||||
21429.7 | 1.99399 | 0.996993 | − | 0.0774867i | ||||||
0.996993 | + | 0.0774867i | ||||||||
5562.36i | 0.515976i | |||||||||
−317.940 | −0.0294023 | |||||||||
9034.20i | 0.832905i | |||||||||
−5643.24 | −0.518688 | −0.259344 | − | 0.965785i | ||||||
−0.259344 | + | 0.965785i | ||||||||
− | 175.089i | − | 0.0160440i | |||||||
7222.28 | 0.659787 | |||||||||
−829.265 | −0.0755271 | |||||||||
−628.657 | −0.0570829 | |||||||||
1374.90i | 0.124465i | |||||||||
−32744.6 | −2.95533 | |||||||||
16.2967i | 0.00146641i | |||||||||
19020.6i | 1.70637i | 0.521604 | + | 0.853187i | ||||||
−0.521604 | + | 0.853187i | ||||||||
5730.69 | 0.512568 | |||||||||
−53.4058 | −0.00476246 | |||||||||
2616.07 | 0.232591 | |||||||||
− | 10333.1i | − | 0.915965i | −0.888961 | − | 0.457982i | ||||
0.888961 | − | 0.457982i | ||||||||
−6705.80 | −0.592659 | |||||||||
5021.32i | 0.442467i | |||||||||
− | 1031.13i | − | 0.0905915i | |||||||
256.470i | 0.0224660i | |||||||||
−6081.36 | −0.531136 | |||||||||
11741.1i | 1.02243i | 0.859453 | + | 0.511215i | ||||||
−0.859453 | + | 0.511215i | ||||||||
48.2880i | 0.00419260i | |||||||||
21295.9i | 1.84359i | |||||||||
− | 512.000i | − | 0.0441942i | |||||||
273.083 | 0.0235028 | |||||||||
−16335.0 | −1.40177 | |||||||||
3602.31 | 0.308227 | |||||||||
128.736i | 0.0109831i | |||||||||
−1853.74 | −0.157694 | |||||||||
−19900.4 | −1.68798 | |||||||||
− | 495.101i | − | 0.0418739i | |||||||
− | 582.687i | − | 0.0491395i | |||||||
− | 23455.7i | − | 1.97238i | −0.165605 | − | 0.986192i | ||||
0.165605 | − | 0.986192i | ||||||||
14345.7 | 1.20286 | |||||||||
− | 4737.20i | − | 0.396067i | −0.980195 | − | 0.198034i | ||||
0.980195 | − | 0.198034i | ||||||||
−5109.46 | −0.425969 | |||||||||
−274.518 | −0.0228208 | |||||||||
371.286i | 0.0307772i | |||||||||
2334.84 | 0.192993 | |||||||||
6.27789i | 0.000517443i | |||||||||
13672.6 | 1.12375 | |||||||||
7003.32i | 0.573971i | |||||||||
− | 10181.4i | − | 0.832078i | |||||||
5137.67 | 0.418696 | |||||||||
3587.90 | 0.291575 | |||||||||
278.462 | 0.0225659 | |||||||||
13410.9i | 1.08375i | |||||||||
3066.49i | 0.247112i | |||||||||
−199.276 | −0.0160138 | |||||||||
2716.95 | − | 8395.15i | 0.217725 | − | 0.672752i | |||||
1994.57 | 0.159392 | |||||||||
191.883i | 0.0152914i | |||||||||
− | 16504.9i | − | 1.31165i | −0.754915 | − | 0.655823i | ||||
0.754915 | − | 0.655823i | ||||||||
−11881.7 | −0.941627 | |||||||||
396.502 | 0.0313362 | |||||||||
−869.471 | −0.0685262 | |||||||||
− | 8543.31i | − | 0.671478i | |||||||
76.2106i | 0.00597347i | |||||||||
2430.36 | 0.189972 | 0.0949861 | − | 0.995479i | ||||||
0.0949861 | + | 0.995479i | ||||||||
− | 8087.63i | − | 0.630450i | |||||||
18762.6 | 1.45859 | |||||||||
− | 463.394i | − | 0.0359258i | |||||||
−10991.0 | −0.849787 | |||||||||
−157.321 | −0.0121305 | |||||||||
− | 21961.5i | − | 1.68878i | |||||||
2388.29 | 0.183157 | |||||||||
284.642i | 0.0217701i | |||||||||
1076.84i | 0.0821368i | |||||||||
19699.4i | 1.49854i | 0.662263 | + | 0.749272i | ||||||
−0.662263 | + | 0.749272i | ||||||||
4637.72 | 0.351846 | |||||||||
−2638.04 | −0.199601 | |||||||||
3610.01i | 0.272412i | |||||||||
10.6610 | 0.000802333 | |||||||||
−12456.6 | −0.934965 | |||||||||
−10922.1 | −0.817606 | −0.408803 | − | 0.912623i | ||||||
−0.408803 | + | 0.912623i | ||||||||
282.828i | 0.0211156i | |||||||||
11940.7i | 0.889110i | |||||||||
11765.4i | 0.873740i | |||||||||
22607.0i | 1.67443i | |||||||||
−8433.21 | −0.622975 | |||||||||
− | 2918.32i | − | 0.215013i | −0.994204 | − | 0.107506i | ||||
0.994204 | − | 0.107506i | ||||||||
− | 73.4857i | − | 0.00539996i | |||||||
− | 7609.77i | − | 0.557722i | −0.960332 | − | 0.278861i | ||||
0.960332 | − | 0.278861i | ||||||||
−128.646 | −0.00940375 | |||||||||
376.268i | 0.0274325i | |||||||||
−22228.7 | −1.61639 | |||||||||
11612.4 | 0.842212 | |||||||||
−1727.04 | −0.124931 | |||||||||
16744.6i | 1.20813i | 0.796937 | + | 0.604063i | ||||||
−0.796937 | + | 0.604063i | ||||||||
− | 8349.48i | − | 0.600852i | |||||||
−240.964 | −0.0172956 | |||||||||
− | 7722.89i | − | 0.552889i | |||||||
2068.97 | 0.147737 | |||||||||
−7.12421 | −0.000507402 | |||||||||
1546.19 | 0.109840 | |||||||||
5484.64i | 0.388623i | |||||||||
−1965.48 | −0.138910 | |||||||||
5254.50i | 0.370412i | |||||||||
6105.40 | 0.429296 | 0.214648 | − | 0.976691i | ||||||
0.214648 | + | 0.976691i | ||||||||
− | 304.314i | − | 0.0213430i | |||||||
−3553.20 | −0.248569 | |||||||||
−5481.05 | −0.382460 | |||||||||
133.392 | 0.00928432 | |||||||||
−5125.25 | −0.355822 | |||||||||
−24079.3 | −1.66749 | −0.833743 | − | 0.552152i | ||||||
−0.833743 | + | 0.552152i | ||||||||
42.3640 | 0.00292629 | |||||||||
6130.46 | 0.422394 | |||||||||
−1123.07 | −0.0771860 | |||||||||
− | 226.467i | − | 0.0155254i | |||||||
− | 3223.80i | − | 0.220453i | |||||||
−13036.2 | −0.889224 | −0.444612 | − | 0.895723i | ||||||
−0.444612 | + | 0.895723i | ||||||||
−70.7006 | −0.00481057 | |||||||||
23316.0i | 1.58250i | 0.611495 | + | 0.791248i | ||||||
−0.611495 | + | 0.791248i | ||||||||
16343.8 | 1.10652 | |||||||||
10343.7 | 0.698552 | |||||||||
−9087.20 | −0.612174 | |||||||||
−9593.11 | −0.644653 | |||||||||
− | 169.142i | − | 0.0113381i | |||||||
− | 5393.06i | − | 0.360622i | −0.983610 | − | 0.180311i | ||||
0.983610 | − | 0.180311i | ||||||||
1323.18 | 0.0882599 | |||||||||
1010.09i | 0.0672099i | |||||||||
− | 10100.7i | − | 0.670433i | |||||||
−5795.68 | −0.383745 | |||||||||
2932.84i | 0.193714i | |||||||||
3038.78i | 0.200221i | 0.994976 | + | 0.100110i | ||||||
−0.994976 | + | 0.100110i | ||||||||
− | 4258.82i | − | 0.279922i | |||||||
317.943i | 0.0208467i | |||||||||
797.017 | 0.0521311 | |||||||||
13293.5 | 0.867385 | 0.433692 | − | 0.901061i | ||||||
0.433692 | + | 0.901061i | ||||||||
−121.343 | −0.00789826 | |||||||||
7323.81 | 0.475555 | 0.237778 | − | 0.971320i | ||||||
0.237778 | + | 0.971320i | ||||||||
− | 2496.67i | − | 0.161724i | |||||||
1061.62i | 0.0686013i | |||||||||
−13387.1 | −0.862982 | |||||||||
− | 35352.5i | − | 2.27346i | |||||||
19.6276i | 0.00125919i | |||||||||
−1376.27 | −0.0880814 | |||||||||
− | 13039.5i | − | 0.832527i | |||||||
−16.2242 | −0.00103338 | |||||||||
648.240i | 0.0411904i | |||||||||
8703.63i | 0.551727i | |||||||||
12177.0 | 0.770070 | |||||||||
−10301.6 | −0.649922 | −0.324961 | − | 0.945727i | ||||||
−0.324961 | + | 0.945727i | ||||||||
− | 5656.06i | − | 0.355991i | |||||||
259.824i | 0.0163145i | |||||||||
−11985.5 | −0.750795 | |||||||||
11043.1 | 0.690130 | |||||||||
− | 235.905i | − | 0.0147079i | |||||||
6235.97 | 0.387877 | |||||||||
−1705.06 | −0.105805 | |||||||||
28446.3i | 1.76106i | |||||||||
929.738i | 0.0574236i | |||||||||
−28814.6 | −1.77552 | −0.887761 | − | 0.460304i | ||||||
−0.887761 | + | 0.460304i | ||||||||
− | 451.743i | − | 0.0277709i | |||||||
21689.4 | 1.33024 | 0.665121 | − | 0.746736i | ||||||
0.665121 | + | 0.746736i | ||||||||
19972.9i | 1.22211i | |||||||||
− | 233.771i | − | 0.0142709i | |||||||
− | 2247.00i | − | 0.136853i | |||||||
8098.38i | 0.492087i | 0.969259 | + | 0.246044i | ||||||
−0.969259 | + | 0.246044i | ||||||||
5822.30i | 0.352966i | |||||||||
1210.11i | 0.0731907i | |||||||||
− | 1448.79i | − | 0.0874249i | |||||||
326.544i | 0.0196594i | |||||||||
10395.6i | 0.624425i | |||||||||
−8898.08 | −0.533244 | −0.266622 | − | 0.963801i | ||||||
−0.266622 | + | 0.963801i | ||||||||
287.779i | 0.0172065i | |||||||||
9278.25 | 0.553483 | |||||||||
−5724.87 | −0.340730 | |||||||||
18500.4 | 1.09858 | |||||||||
35906.8 | 2.12735 | |||||||||
29685.7 | 1.75477 | 0.877383 | − | 0.479790i | ||||||
0.877383 | + | 0.479790i | ||||||||
− | 11.4000i | − | 0.000672339i | |||||||
− | 20652.3i | − | 1.21525i | −0.794224 | − | 0.607625i | ||||
0.794224 | − | 0.607625i | ||||||||
− | 14933.6i | − | 0.876755i | |||||||
33.3314 | 0.00195246 | |||||||||
532.853 | 0.0311426 | |||||||||
−9329.47 | −0.544032 | |||||||||
17288.1i | 1.00586i | |||||||||
− | 42727.9i | − | 2.48041i | |||||||
1746.20i | 0.101142i | |||||||||
265.117 | 0.0153214 | |||||||||
− | 5568.43i | − | 0.321085i | |||||||
−2230.02 | −0.128300 | |||||||||
− | 121.602i | − | 0.00698050i | |||||||
− | 10310.0i | − | 0.590525i | −0.955416 | − | 0.295262i | ||||
0.955416 | − | 0.295262i | ||||||||
616.366 | 0.0352248 | |||||||||
477.097i | 0.0272051i | |||||||||
8385.79 | 0.477116 | |||||||||
− | 23022.6i | − | 1.30699i | −0.756932 | − | 0.653494i | ||||
0.756932 | − | 0.653494i | ||||||||
− | 402.217i | − | 0.0227833i | |||||||
904.464i | 0.0511195i | |||||||||
1578.87 | 0.0890395 | |||||||||
553.393 | 0.0311396 | |||||||||
−551.216 | −0.0309489 | |||||||||
16684.0i | 0.934691i | 0.884075 | + | 0.467346i | ||||||
−0.884075 | + | 0.467346i | ||||||||
− | 4463.25i | − | 0.249498i | |||||||
14686.3i | 0.819174i | |||||||||
−17325.7 | −0.964281 | |||||||||
−60.3811 | −0.00335325 | |||||||||
4209.27 | 0.233251 | |||||||||
4834.13 | 0.267294 | |||||||||
285.678 | 0.0157617 | |||||||||
− | 778.602i | − | 0.0428645i | −0.999770 | − | 0.0214323i | ||||
0.999770 | − | 0.0214323i | ||||||||
−16188.3 | −0.889286 | |||||||||
− | 2688.44i | − | 0.147367i | |||||||
− | 5424.82i | − | 0.296719i | |||||||
− | 1955.42i | − | 0.106724i | |||||||
260.143i | 0.0141677i | |||||||||
9721.90i | 0.528326i | |||||||||
10114.5i | 0.548480i | |||||||||
51.0959i | 0.00276484i | |||||||||
8975.89i | 0.484653i | |||||||||
− | 15688.2i | − | 0.845271i | −0.906300 | − | 0.422636i | ||||
0.906300 | − | 0.422636i | ||||||||
132.450 | 0.00712108 | |||||||||
− | 13245.4i | − | 0.710609i | |||||||
205.268 | 0.0109891 | |||||||||
− | 513.586i | − | 0.0274366i | |||||||
− | 15428.2i | − | 0.822448i | |||||||
−21473.6 | −1.14229 | |||||||||
184.627 | 0.00980045 | |||||||||
20712.4i | 1.09714i | 0.836106 | + | 0.548568i | ||||||
−0.836106 | + | 0.548568i | ||||||||
15313.8 | 0.809461 | |||||||||
−19078.6 | −1.00634 | |||||||||
− | 9104.84i | − | 0.479239i | |||||||
− | 13813.2i | − | 0.725538i | |||||||
−206.503 | −0.0108238 | |||||||||
233.607 | 0.0122187 | |||||||||
6515.72i | 0.340089i | |||||||||
234.979i | 0.0122391i | |||||||||
24540.8 | 1.27556 | |||||||||
− | 17274.8i | − | 0.896024i | −0.894028 | − | 0.448012i | ||||
0.894028 | − | 0.448012i | ||||||||
3136.13 | 0.162329 | |||||||||
15405.2i | 0.795729i | |||||||||
− | 10298.5i | − | 0.530844i | |||||||
−385.191 | −0.0198138 | |||||||||
− | 12964.4i | − | 0.665495i | |||||||
− | 19202.1i | − | 0.983653i | |||||||
323.141 | 0.0165191 | |||||||||
−9015.71 | −0.459937 | −0.229968 | − | 0.973198i | ||||||
−0.229968 | + | 0.973198i | ||||||||
2491.85 | 0.126860 | |||||||||
19617.6 | 0.996676 | |||||||||
− | 9959.53i | − | 0.504957i | |||||||
− | 7148.12i | − | 0.361673i | |||||||
340.238i | 0.0171797i | |||||||||
19576.5i | 0.986458i | 0.869899 | + | 0.493229i | ||||||
−0.869899 | + | 0.493229i | ||||||||
5941.23 | 0.298767 | |||||||||
552.602i | 0.0277320i | |||||||||
5143.91i | 0.257618i | |||||||||
−1229.40 | −0.0614456 | |||||||||
19310.7i | 0.963195i | |||||||||
− | 3744.57i | − | 0.186396i | −0.995648 | − | 0.0931978i | ||||
0.995648 | − | 0.0931978i | ||||||||
9306.92 | 0.462337 | |||||||||
−50.7244 | −0.00251472 | |||||||||
−29949.6 | −1.48178 | |||||||||
33774.0 | 1.66763 | 0.833814 | − | 0.552046i | ||||||
0.833814 | + | 0.552046i | ||||||||
84.0997i | 0.00414414i | |||||||||
2039.38 | 0.100292 | |||||||||
18486.7 | 0.907300 | |||||||||
− | 1797.38i | − | 0.0880359i | |||||||
− | 348.582i | − | 0.0170394i | |||||||
−57351.7 | −2.79784 | |||||||||
350.534 | 0.0170662 | |||||||||
−8064.59 | −0.391852 | −0.195926 | − | 0.980619i | ||||||
−0.195926 | + | 0.980619i | ||||||||
9247.61 | 0.448438 | |||||||||
160.019 | 0.00774426 | |||||||||
−5330.82 | −0.257476 | |||||||||
16501.4 | 0.795428 | |||||||||
−820.586 | −0.0394767 | |||||||||
− | 5247.19i | − | 0.251932i | −0.992035 | − | 0.125966i | ||||
0.992035 | − | 0.125966i | ||||||||
−27620.6 | −1.32352 | |||||||||
− | 63.0720i | − | 0.00301630i | |||||||
−2402.75 | −0.114680 | |||||||||
− | 26230.0i | − | 1.24946i | −0.780842 | − | 0.624729i | ||||
0.780842 | − | 0.624729i | ||||||||
−371.984 | −0.0176845 | |||||||||
36535.3 | 1.73351 | |||||||||
12302.8 | 0.582591 | |||||||||
− | 5325.73i | − | 0.251702i | |||||||
27782.1 | 1.31045 | |||||||||
3783.36i | 0.178108i | |||||||||
− | 31.3179i | − | 0.00147147i | |||||||
−22118.8 | −1.03722 | −0.518611 | − | 0.855010i | ||||||
−0.518611 | + | 0.855010i | ||||||||
−1447.30 | −0.0677364 | |||||||||
−999.180 | −0.0466726 | |||||||||
7878.78i | 0.367310i | |||||||||
14551.5 | 0.677076 | 0.338538 | − | 0.940953i | ||||||
0.338538 | + | 0.940953i | ||||||||
− | 14198.4i | − | 0.659368i | |||||||
− | 6207.71i | − | 0.287726i | |||||||
232.940i | 0.0107758i | |||||||||
−1217.27 | −0.0562023 | |||||||||
15708.2i | 0.723862i | |||||||||
− | 14795.0i | − | 0.680469i | |||||||
− | 35.6417i | − | 0.00163613i | |||||||
− | 3380.98i | − | 0.154905i | |||||||
8735.31 | 0.399455 | |||||||||
1755.48 | 0.0801222 | |||||||||
−9950.13 | −0.453268 | |||||||||
− | 1177.14i | − | 0.0535207i | |||||||
−312.535 | −0.0141829 | |||||||||
−15917.0 | −0.720940 | −0.360470 | − | 0.932771i | ||||||
−0.360470 | + | 0.932771i | ||||||||
− | 4361.52i | − | 0.197174i | |||||||
22.7108i | 0.00102475i | |||||||||
10270.8i | 0.462556i | |||||||||
−51064.0 | −2.29536 | |||||||||
− | 692.394i | − | 0.0310646i | |||||||
−6972.10 | −0.312215 | |||||||||
19915.8 | 0.890156 | |||||||||
428.378i | 0.0191107i | |||||||||
−7404.79 | −0.329718 | |||||||||
− | 27816.6i | − | 1.23628i | −0.786068 | − | 0.618140i | ||||
0.786068 | − | 0.618140i | ||||||||
314.260 | 0.0139407 | |||||||||
− | 15704.2i | − | 0.695336i | |||||||
2311.69i | 0.102163i | |||||||||
−30711.8 | −1.35474 | |||||||||
−16789.0 | −0.739201 | |||||||||
−2198.86 | −0.0966329 | |||||||||
187.571i | 0.00822775i | |||||||||
− | 36268.6i | − | 1.58795i | |||||||
−1723.36 | −0.0753136 | |||||||||
166.190 | − | 513.513i | 0.00724928 | − | 0.0223997i | |||||
−5530.41 | −0.240791 | |||||||||
− | 125.653i | − | 0.00546073i | −0.999996 | − | 0.00273037i | ||||
0.999996 | − | 0.00273037i | ||||||||
− | 10572.7i | − | 0.458625i | |||||||
−23561.6 | −1.02017 | −0.510086 | − | 0.860123i | ||||||
−0.510086 | + | 0.860123i | ||||||||
33026.8 | 1.42736 | |||||||||
−726.777 | −0.0313520 | |||||||||
− | 2054.78i | − | 0.0884767i | |||||||
− | 18877.4i | − | 0.811345i | |||||||
−53.1837 | −0.00228162 | |||||||||
10878.2i | 0.465824i | |||||||||
−7998.47 | −0.341882 | |||||||||
− | 8405.34i | − | 0.358616i | |||||||
10395.8 | 0.442727 | |||||||||
−13635.4 | −0.579631 | −0.289816 | − | 0.957083i | ||||||
−0.289816 | + | 0.957083i | ||||||||
− | 494.703i | − | 0.0209912i | |||||||
10832.5 | 0.458804 | 0.229402 | − | 0.973332i | ||||||
0.229402 | + | 0.973332i | ||||||||
3967.54i | 0.167737i | |||||||||
− | 28.3448i | − | 0.00119617i | |||||||
− | 23439.6i | − | 0.987371i | |||||||
−32051.0 | −1.34767 | −0.673835 | − | 0.738882i | ||||||
−0.673835 | + | 0.738882i | ||||||||
17351.1 | 0.728250 | |||||||||
8792.02i | 0.368347i | 0.982894 | + | 0.184173i | ||||||
−0.982894 | + | 0.184173i | ||||||||
−967.605 | −0.0404651 | |||||||||
146.087 | 0.00609830 | |||||||||
641.763 | 0.0267417 | |||||||||
16897.2i | 0.702824i | |||||||||
65.8678i | 0.00273479i | |||||||||
− | 3170.92i | − | 0.131418i | |||||||
530.480i | 0.0219462i | |||||||||
567.515 | 0.0234363 | |||||||||
− | 25725.7i | − | 1.06048i | |||||||
− | 20675.3i | − | 0.850765i | −0.905014 | − | 0.425382i | ||||
0.905014 | − | 0.425382i | ||||||||
220.816i | 0.00907011i | |||||||||
−46265.2 | −1.89697 | |||||||||
− | 12597.8i | − | 0.515618i | |||||||
−761.944 | −0.0311302 | |||||||||
8495.46 | 0.346476 | |||||||||
−15227.7 | −0.619940 | |||||||||
− | 31193.4i | − | 1.26767i | |||||||
− | 41024.7i | − | 1.66426i | |||||||
−7713.35 | −0.312356 | |||||||||
719.665i | 0.0290917i | |||||||||
3925.68 | 0.158412 | |||||||||
51491.8 | 2.07417 | |||||||||
−515.841 | −0.0207423 | |||||||||
− | 31131.7i | − | 1.24962i | −0.780776 | − | 0.624811i | ||||
0.780776 | − | 0.624811i | ||||||||
43195.3 | 1.73081 | |||||||||
8104.80i | 0.324185i | |||||||||
−14770.6 | −0.589777 | |||||||||
44684.1i | 1.78107i | 0.454910 | + | 0.890537i | ||||||
−0.454910 | + | 0.890537i | ||||||||
−7.86898 | −0.000313103 | |||||||||
30638.1 | 1.21695 | 0.608474 | − | 0.793574i | ||||||
0.608474 | + | 0.793574i | ||||||||
−7643.58 | −0.303075 | |||||||||
−1359.68 | −0.0538185 | |||||||||
−13763.7 | −0.543844 | |||||||||
26688.4 | 1.05271 | 0.526353 | − | 0.850266i | ||||||
0.526353 | + | 0.850266i | ||||||||
−211.337 | −0.00832158 | |||||||||
29396.2 | 1.15549 | |||||||||
16662.7i | 0.653834i | |||||||||
− | 510.719i | − | 0.0200057i | |||||||
10677.0 | 0.417512 | |||||||||
2267.59 | 0.0885186 | |||||||||
− | 472.392i | − | 0.0184087i | |||||||
−3843.68 | −0.149527 | |||||||||
9409.48 | 0.365419 | |||||||||
785.736 | 0.0304618 | |||||||||
−13293.6 | −0.514487 | |||||||||
− | 44502.5i | − | 1.71938i | |||||||
335.484i | 0.0129394i | |||||||||
−22694.3 | −0.873809 | −0.436905 | − | 0.899508i | ||||||
−0.436905 | + | 0.899508i | ||||||||
− | 33225.1i | − | 1.27710i | |||||||
321.406i | 0.0123331i | |||||||||
−372.744 | −0.0142786 | |||||||||
− | 8706.87i | − | 0.332965i | −0.986044 | − | 0.166482i | ||||
0.986044 | − | 0.166482i | ||||||||
33563.1i | 1.28132i | |||||||||
21582.4i | 0.822543i | 0.911513 | + | 0.411272i | ||||||
−0.911513 | + | 0.411272i | ||||||||
− | 1089.83i | − | 0.0414650i | |||||||
−335.264 | −0.0127342 | |||||||||
−8446.50 | −0.320277 | |||||||||
15786.3 | 0.597579 | 0.298790 | − | 0.954319i | ||||||
0.298790 | + | 0.954319i | ||||||||
−313.500 | −0.0118473 | |||||||||
47225.7i | 1.78166i | |||||||||
16533.4i | 0.622699i | |||||||||
−2334.24 | −0.0877665 | |||||||||
− | 8668.52i | − | 0.325385i | |||||||
23898.9i | 0.895573i | |||||||||
−68.6960 | −0.00256995 | |||||||||
− | 11831.9i | − | 0.441895i | |||||||
−3976.01 | −0.148247 | |||||||||
− | 197.193i | − | 0.00734011i | |||||||
15456.5i | 0.574375i | |||||||||
−22841.3 | −0.847385 | |||||||||
7797.64 | 0.288801 | |||||||||
13098.7i | 0.484330i | |||||||||
− | 2295.18i | − | 0.0847240i | |||||||
999.717 | 0.0368422 | |||||||||
−13151.3 | −0.483855 | |||||||||
23542.0i | 0.864709i | |||||||||
−555.845 | −0.0203827 | |||||||||
9745.82 | 0.356786 | 0.178393 | − | 0.983959i | ||||||
0.178393 | + | 0.983959i | ||||||||
− | 18094.3i | − | 0.661320i | |||||||
18654.8i | 0.680682i | |||||||||
−4524.94 | −0.164836 | |||||||||
646.928i | 0.0235276i | 0.999931 | + | 0.0117638i | ||||||
−0.999931 | + | 0.0117638i | ||||||||
80.9360 | 0.00293866 | |||||||||
213.628i | 0.00774376i | |||||||||
− | 35380.9i | − | 1.28041i | |||||||
− | 617.836i | − | 0.0223224i | |||||||
1974.28i | 0.0712139i | |||||||||
39678.3i | 1.42889i | |||||||||
358.890i | 0.0129032i | |||||||||
10915.2i | 0.391795i | 0.980624 | + | 0.195897i | ||||||
−0.980624 | + | 0.195897i | ||||||||
− | 9340.79i | − | 0.334736i | |||||||
− | 260.503i | − | 0.00932016i | |||||||
−15862.3 | −0.566590 | |||||||||
− | 10570.6i | − | 0.376960i | |||||||
48.7518 | 0.00173573 | |||||||||
23140.6 | 0.822551 | |||||||||
854.869 | 0.0303377 | |||||||||
13383.0 | 0.474170 | |||||||||
8505.87 | 0.300882 | |||||||||
31007.7i | 1.09508i | 0.836780 | + | 0.547540i | ||||||
−0.836780 | + | 0.547540i | ||||||||
− | 152.716i | − | 0.00538469i | |||||||
− | 25714.5i | − | 0.905218i | |||||||
1670.68 | 0.0587177 | |||||||||
−818.861 | −0.0287335 | |||||||||
27450.1 | 0.961665 | |||||||||
632.989i | 0.0221401i | |||||||||
− | 2164.75i | − | 0.0755952i | |||||||
8644.64i | 0.301396i | 0.988580 | + | 0.150698i | ||||||
−0.988580 | + | 0.150698i | ||||||||
23813.3 | 0.828925 | |||||||||
− | 797.596i | − | 0.0277195i | |||||||
−16792.7 | −0.582678 | |||||||||
18563.7i | 0.643102i | 0.946892 | + | 0.321551i | ||||||
−0.946892 | + | 0.321551i | ||||||||
39.6514i | 0.00137146i | |||||||||
57516.0 | 1.98619 | |||||||||
− | 6036.74i | − | 0.208135i | |||||||
1490.10 | 0.0512940 | |||||||||
1687.55i | 0.0579989i | |||||||||
56236.7i | 1.92972i | 0.262758 | + | 0.964862i | ||||||
−0.262758 | + | 0.964862i | ||||||||
− | 345.969i | − | 0.0118529i | |||||||
−6874.69 | −0.235155 | |||||||||
−5974.19 | −0.204030 | |||||||||
−733.126 | −0.0249981 | |||||||||
6752.00i | 0.229867i | |||||||||
− | 18539.4i | − | 0.630169i | −0.949064 | − | 0.315084i | ||||
0.949064 | − | 0.315084i | ||||||||
26018.1i | 0.882985i | |||||||||
−22340.6 | −0.756989 | |||||||||
7683.08 | 0.259925 | |||||||||
−104.295 | −0.00352285 | |||||||||
−15851.0 | −0.534576 | |||||||||
−62805.6 | −2.11481 | |||||||||
56.8701i | 0.00191195i | |||||||||
22406.8 | 0.752134 | |||||||||
− | 6424.21i | − | 0.215307i | |||||||
49823.2i | 1.66722i | |||||||||
12594.6i | 0.420792i | |||||||||
− | 14307.0i | − | 0.477264i | |||||||
1221.70i | 0.0406910i | |||||||||
39149.7i | 1.30193i | 0.759106 | + | 0.650967i | ||||||
−0.759106 | + | 0.650967i | ||||||||
− | 10565.7i | − | 0.350821i | |||||||
− | 137.444i | − | 0.00455661i | |||||||
− | 422.994i | − | 0.0140016i | |||||||
−32454.4 | −1.07262 | −0.536308 | − | 0.844022i | ||||||
−0.536308 | + | 0.844022i | ||||||||
1069.40i | 0.0352892i | |||||||||
8362.33 | 0.275523 | |||||||||
− | 42859.4i | − | 1.40996i | |||||||
− | 88.6193i | − | 0.00291086i | |||||||
11124.7 | 0.364850 | |||||||||
22864.2 | 0.748712 | 0.374356 | − | 0.927285i | ||||||
0.374356 | + | 0.927285i | ||||||||
635.879i | 0.0207906i | |||||||||
3650.25 | 0.119165 | |||||||||
18068.4 | 0.588953 | |||||||||
− | 31739.4i | − | 1.03299i | |||||||
11286.5i | 0.366768i | |||||||||
25559.0 | 0.829304 | 0.414652 | − | 0.909980i | ||||||
0.414652 | + | 0.909980i | ||||||||
−350.178 | −0.0113448 | |||||||||
7920.06i | 0.256197i | |||||||||
− | 14444.6i | − | 0.466540i | |||||||
2196.34 | 0.0708312 | |||||||||
1658.53i | 0.0534058i | |||||||||
−42289.2 | −1.35967 | |||||||||
1257.31i | 0.0403637i | |||||||||
8692.11i | 0.278622i | 0.990249 | + | 0.139311i | ||||||
−0.990249 | + | 0.139311i | ||||||||
2749.80 | 0.0880103 | |||||||||
− | 913.457i | − | 0.0291920i | |||||||
65489.3i | 2.08973i | |||||||||
13446.3 | 0.428419 | |||||||||
32.5935 | 0.00103691 | |||||||||
−12135.9 | −0.385505 | −0.192752 | − | 0.981247i | ||||||
−0.192752 | + | 0.981247i | ||||||||
38041.3 | 1.20659 | |||||||||
2115.54i | 0.0669998i |
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 538.4.b.a.537.17 | ✓ | 68 | |
269.268 | even | 2 | inner | 538.4.b.a.537.52 | yes | 68 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
538.4.b.a.537.17 | ✓ | 68 | 1.1 | even | 1 | trivial | |
538.4.b.a.537.52 | yes | 68 | 269.268 | even | 2 | inner |