Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [324,3,Mod(163,324)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(324, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("324.163");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 324.d (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: | |
Coefficient field: | 6.0.3636603.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
|
Coefficient ring: | |
Coefficient ring index: | |
Twist minimal: | yes |
Sato-Tate group: |
Embedding invariants
Embedding label | 163.4 | ||
Root | of defining polynomial | ||
Character | 324.163 | ||
Dual form | 324.3.d.e.163.3 |
-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of on generators for .
Coefficient data
For each we display the coefficients of the -expansion , the Satake parameters , and the Satake angles .
−0.195350 | + | 1.99044i | −0.0976748 | + | 0.995218i | |||||
0 | 0 | |||||||||
−3.92368 | − | 0.777662i | −0.980919 | − | 0.194416i | |||||
−7.23805 | −1.44761 | −0.723805 | − | 0.690004i | ||||||
−0.723805 | + | 0.690004i | ||||||||
0 | 0 | |||||||||
6.88025i | 0.982893i | 0.870908 | + | 0.491447i | ||||||
−0.870908 | + | 0.491447i | ||||||||
2.31438 | − | 7.65792i | 0.289297 | − | 0.957239i | |||||
0 | 0 | |||||||||
1.41395 | − | 14.4069i | 0.141395 | − | 1.44069i | |||||
− | 17.9526i | − | 1.63206i | −0.578010 | − | 0.816029i | ||||
0.578010 | − | 0.816029i | ||||||||
0 | 0 | |||||||||
7.67526 | 0.590404 | 0.295202 | − | 0.955435i | ||||||
0.295202 | + | 0.955435i | ||||||||
−13.6947 | − | 1.34405i | −0.978193 | − | 0.0960039i | |||||
0 | 0 | |||||||||
14.7905 | + | 6.10259i | 0.924405 | + | 0.381412i | |||||
1.43720 | 0.0845413 | 0.0422707 | − | 0.999106i | ||||||
0.0422707 | + | 0.999106i | ||||||||
0 | 0 | |||||||||
13.8943i | 0.731281i | 0.930756 | + | 0.365641i | ||||||
−0.930756 | + | 0.365641i | ||||||||
28.3998 | + | 5.62876i | 1.41999 | + | 0.281438i | |||||
0 | 0 | |||||||||
35.7336 | + | 3.50704i | 1.62426 | + | 0.159411i | |||||
− | 16.5824i | − | 0.720976i | −0.932764 | − | 0.360488i | ||||
0.932764 | − | 0.360488i | ||||||||
0 | 0 | |||||||||
27.3894 | 1.09558 | |||||||||
−1.49936 | + | 15.2771i | −0.0576676 | + | 0.587581i | |||||
0 | 0 | |||||||||
5.35051 | − | 26.9959i | 0.191090 | − | 0.964139i | |||||
37.5019 | 1.29317 | 0.646584 | − | 0.762843i | ||||||
0.646584 | + | 0.762843i | ||||||||
0 | 0 | |||||||||
− | 53.9918i | − | 1.74167i | −0.491575 | − | 0.870835i | ||||
0.491575 | − | 0.870835i | ||||||||
−15.0361 | + | 28.2474i | −0.469879 | + | 0.882731i | |||||
0 | 0 | |||||||||
−0.280757 | + | 2.86066i | −0.00825756 | + | 0.0841371i | |||||
− | 49.7996i | − | 1.42285i | |||||||
0 | 0 | |||||||||
44.4415 | 1.20112 | 0.600560 | − | 0.799580i | ||||||
0.600560 | + | 0.799580i | ||||||||
−27.6558 | − | 2.71425i | −0.727784 | − | 0.0714277i | |||||
0 | 0 | |||||||||
−16.7516 | + | 55.4284i | −0.418789 | + | 1.38571i | |||||
−56.9911 | −1.39003 | −0.695014 | − | 0.718997i | ||||||
−0.695014 | + | 0.718997i | ||||||||
0 | 0 | |||||||||
− | 67.6185i | − | 1.57252i | −0.617894 | − | 0.786261i | ||||
0.617894 | − | 0.786261i | ||||||||
−13.9611 | + | 70.4404i | −0.317298 | + | 1.60092i | |||||
0 | 0 | |||||||||
33.0063 | + | 3.23938i | 0.717529 | + | 0.0704212i | |||||
9.43453i | 0.200735i | 0.994950 | + | 0.100367i | ||||||
−0.994950 | + | 0.100367i | ||||||||
0 | 0 | |||||||||
1.66212 | 0.0339208 | |||||||||
−5.35051 | + | 54.5169i | −0.107010 | + | 1.09034i | |||||
0 | 0 | |||||||||
−30.1152 | − | 5.96876i | −0.579139 | − | 0.114784i | |||||
7.82662 | 0.147672 | 0.0738360 | − | 0.997270i | ||||||
0.0738360 | + | 0.997270i | ||||||||
0 | 0 | |||||||||
129.942i | 2.36259i | |||||||||
52.6884 | + | 15.9235i | 0.940864 | + | 0.284348i | |||||
0 | 0 | |||||||||
−7.32598 | + | 74.6451i | −0.126310 | + | 1.28698i | |||||
− | 22.4125i | − | 0.379872i | −0.981796 | − | 0.189936i | ||||
0.981796 | − | 0.189936i | ||||||||
0 | 0 | |||||||||
−67.1814 | −1.10133 | −0.550667 | − | 0.834725i | ||||||
−0.550667 | + | 0.834725i | ||||||||
107.467 | + | 10.5473i | 1.73334 | + | 0.170117i | |||||
0 | 0 | |||||||||
−53.2873 | − | 35.4466i | −0.832614 | − | 0.553853i | |||||
−55.5539 | −0.854676 | |||||||||
0 | 0 | |||||||||
− | 69.2040i | − | 1.03290i | −0.856319 | − | 0.516448i | ||||
0.856319 | − | 0.516448i | ||||||||
−5.63912 | − | 1.11766i | −0.0829282 | − | 0.0164362i | |||||
0 | 0 | |||||||||
99.1230 | + | 9.72834i | 1.41604 | + | 0.138976i | |||||
− | 7.14792i | − | 0.100675i | −0.998732 | − | 0.0503375i | ||||
0.998732 | − | 0.0503375i | ||||||||
0 | 0 | |||||||||
−80.4410 | −1.10193 | −0.550965 | − | 0.834528i | ||||||
−0.550965 | + | 0.834528i | ||||||||
−8.68162 | + | 88.4579i | −0.117319 | + | 1.19538i | |||||
0 | 0 | |||||||||
10.8051 | − | 54.5169i | 0.142172 | − | 0.717328i | |||||
123.519 | 1.60414 | |||||||||
0 | 0 | |||||||||
46.8439i | 0.592960i | 0.955039 | + | 0.296480i | ||||||
−0.955039 | + | 0.296480i | ||||||||
−107.054 | − | 44.1709i | −1.33818 | − | 0.552136i | |||||
0 | 0 | |||||||||
11.1332 | − | 113.437i | 0.135771 | − | 1.38338i | |||||
− | 142.199i | − | 1.71324i | −0.515950 | − | 0.856619i | ||||
0.515950 | − | 0.856619i | ||||||||
0 | 0 | |||||||||
−10.4026 | −0.122383 | |||||||||
134.590 | + | 13.2092i | 1.56500 | + | 0.153596i | |||||
0 | 0 | |||||||||
−137.480 | − | 41.5492i | −1.56227 | − | 0.472150i | |||||
−42.1078 | −0.473122 | −0.236561 | − | 0.971617i | ||||||
−0.236561 | + | 0.971617i | ||||||||
0 | 0 | |||||||||
52.8077i | 0.580304i | |||||||||
−12.8955 | + | 65.0642i | −0.140169 | + | 0.707219i | |||||
0 | 0 | |||||||||
−18.7788 | − | 1.84303i | −0.199775 | − | 0.0196067i | |||||
− | 100.568i | − | 1.05861i | |||||||
0 | 0 | |||||||||
62.8955 | 0.648408 | 0.324204 | − | 0.945987i | ||||||
0.324204 | + | 0.945987i | ||||||||
−0.324695 | + | 3.30835i | −0.00331321 | + | 0.0337586i | |||||
0 | 0 | |||||||||
−107.467 | − | 21.2997i | −1.07467 | − | 0.212997i | |||||
−47.6143 | −0.471429 | −0.235715 | − | 0.971822i | ||||||
−0.235715 | + | 0.971822i | ||||||||
0 | 0 | |||||||||
53.7241i | 0.521593i | 0.965394 | + | 0.260797i | ||||||
−0.965394 | + | 0.260797i | ||||||||
17.7634 | − | 58.7765i | 0.170802 | − | 0.565158i | |||||
0 | 0 | |||||||||
−1.52893 | + | 15.5784i | −0.0144238 | + | 0.146966i | |||||
26.4708i | 0.247390i | 0.992320 | + | 0.123695i | ||||||
−0.992320 | + | 0.123695i | ||||||||
0 | 0 | |||||||||
83.0647 | 0.762061 | 0.381031 | − | 0.924562i | ||||||
0.381031 | + | 0.924562i | ||||||||
−258.642 | − | 25.3842i | −2.35129 | − | 0.230765i | |||||
0 | 0 | |||||||||
−41.9874 | + | 101.762i | −0.374887 | + | 0.908592i | |||||
15.5276 | 0.137413 | 0.0687064 | − | 0.997637i | ||||||
0.0687064 | + | 0.997637i | ||||||||
0 | 0 | |||||||||
120.025i | 1.04369i | |||||||||
−147.145 | − | 29.1638i | −1.26849 | − | 0.251412i | |||||
0 | 0 | |||||||||
44.6106 | + | 4.37827i | 0.378056 | + | 0.0371039i | |||||
9.88832i | 0.0830951i | |||||||||
0 | 0 | |||||||||
−201.298 | −1.66362 | |||||||||
13.1239 | − | 133.720i | 0.107573 | − | 1.09607i | |||||
0 | 0 | |||||||||
−41.9874 | + | 211.846i | −0.338608 | + | 1.70844i | |||||
−17.2947 | −0.138358 | |||||||||
0 | 0 | |||||||||
− | 157.463i | − | 1.23987i | −0.784654 | − | 0.619934i | ||||
0.784654 | − | 0.619934i | ||||||||
80.9639 | − | 99.1406i | 0.632530 | − | 0.774536i | |||||
0 | 0 | |||||||||
10.8524 | − | 110.577i | 0.0834803 | − | 0.850589i | |||||
47.0592i | 0.359231i | 0.983737 | + | 0.179615i | ||||||
−0.983737 | + | 0.179615i | ||||||||
0 | 0 | |||||||||
−95.5966 | −0.718771 | |||||||||
137.746 | + | 13.5190i | 1.02796 | + | 0.100888i | |||||
0 | 0 | |||||||||
3.32623 | − | 11.0060i | 0.0244576 | − | 0.0809263i | |||||
−117.497 | −0.857644 | −0.428822 | − | 0.903389i | ||||||
−0.428822 | + | 0.903389i | ||||||||
0 | 0 | |||||||||
− | 39.6959i | − | 0.285582i | −0.989753 | − | 0.142791i | ||||
0.989753 | − | 0.142791i | ||||||||
−38.7273 | + | 195.398i | −0.276624 | + | 1.39570i | |||||
0 | 0 | |||||||||
14.2275 | + | 1.39634i | 0.100194 | + | 0.00983341i | |||||
− | 137.791i | − | 0.963575i | |||||||
0 | 0 | |||||||||
−271.441 | −1.87200 | |||||||||
15.7141 | − | 160.113i | 0.107631 | − | 1.09666i | |||||
0 | 0 | |||||||||
−174.374 | − | 34.5604i | −1.17820 | − | 0.233516i | |||||
114.827 | 0.770652 | 0.385326 | − | 0.922781i | ||||||
0.385326 | + | 0.922781i | ||||||||
0 | 0 | |||||||||
− | 160.122i | − | 1.06041i | −0.847869 | − | 0.530206i | ||||
0.847869 | − | 0.530206i | ||||||||
106.402 | + | 32.1567i | 0.700011 | + | 0.211557i | |||||
0 | 0 | |||||||||
−24.1293 | + | 245.856i | −0.156684 | + | 1.59647i | |||||
390.795i | 2.52126i | |||||||||
0 | 0 | |||||||||
225.337 | 1.43527 | 0.717634 | − | 0.696421i | ||||||
0.717634 | + | 0.696421i | ||||||||
−93.2397 | − | 9.15093i | −0.590125 | − | 0.0579173i | |||||
0 | 0 | |||||||||
108.832 | − | 204.456i | 0.680202 | − | 1.27785i | |||||
114.091 | 0.708643 | |||||||||
0 | 0 | |||||||||
− | 147.165i | − | 0.902850i | −0.892309 | − | 0.451425i | ||||
0.892309 | − | 0.451425i | ||||||||
223.615 | + | 44.3198i | 1.36350 | + | 0.270243i | |||||
0 | 0 | |||||||||
283.038 | + | 27.7785i | 1.70505 | + | 0.167340i | |||||
105.944i | 0.634396i | 0.948359 | + | 0.317198i | ||||||
−0.948359 | + | 0.317198i | ||||||||
0 | 0 | |||||||||
−110.090 | −0.651423 | |||||||||
2.03213 | − | 20.7056i | 0.0119537 | − | 0.121798i | |||||
0 | 0 | |||||||||
−52.5843 | + | 265.313i | −0.305723 | + | 1.54252i | |||||
186.424 | 1.07759 | 0.538797 | − | 0.842436i | ||||||
0.538797 | + | 0.842436i | ||||||||
0 | 0 | |||||||||
188.446i | 1.07683i | |||||||||
109.558 | − | 265.528i | 0.622487 | − | 1.50868i | |||||
0 | 0 | |||||||||
8.22575 | − | 83.8130i | 0.0462121 | − | 0.470859i | |||||
191.597i | 1.07037i | 0.844734 | + | 0.535187i | ||||||
−0.844734 | + | 0.535187i | ||||||||
0 | 0 | |||||||||
204.960 | 1.13237 | 0.566187 | − | 0.824277i | ||||||
0.566187 | + | 0.824277i | ||||||||
−105.110 | − | 10.3160i | −0.577530 | − | 0.0566811i | |||||
0 | 0 | |||||||||
−126.987 | − | 38.3780i | −0.690147 | − | 0.208576i | |||||
−321.670 | −1.73875 | |||||||||
0 | 0 | |||||||||
− | 25.8016i | − | 0.137976i | |||||||
7.33688 | − | 37.0180i | 0.0390259 | − | 0.196904i | |||||
0 | 0 | |||||||||
200.174 | + | 19.6459i | 1.05355 | + | 0.103400i | |||||
− | 89.8155i | − | 0.470238i | −0.971967 | − | 0.235119i | ||||
0.971967 | − | 0.235119i | ||||||||
0 | 0 | |||||||||
167.596 | 0.868374 | 0.434187 | − | 0.900823i | ||||||
0.434187 | + | 0.900823i | ||||||||
−12.2866 | + | 125.190i | −0.0633331 | + | 0.645307i | |||||
0 | 0 | |||||||||
−6.52163 | − | 1.29257i | −0.0332736 | − | 0.00659474i | |||||
−185.277 | −0.940492 | −0.470246 | − | 0.882535i | ||||||
−0.470246 | + | 0.882535i | ||||||||
0 | 0 | |||||||||
− | 137.625i | − | 0.691585i | −0.938311 | − | 0.345793i | ||||
0.938311 | − | 0.345793i | ||||||||
63.3894 | − | 209.746i | 0.316947 | − | 1.04873i | |||||
0 | 0 | |||||||||
9.30144 | − | 94.7733i | 0.0460467 | − | 0.469175i | |||||
258.022i | 1.27105i | |||||||||
0 | 0 | |||||||||
412.505 | 2.01222 | |||||||||
−106.934 | − | 10.4950i | −0.519099 | − | 0.0509465i | |||||
0 | 0 | |||||||||
113.521 | + | 46.8389i | 0.545773 | + | 0.225187i | |||||
249.440 | 1.19349 | |||||||||
0 | 0 | |||||||||
305.254i | 1.44670i | 0.690482 | + | 0.723350i | ||||||
−0.690482 | + | 0.723350i | ||||||||
−30.7091 | − | 6.08647i | −0.144854 | − | 0.0287097i | |||||
0 | 0 | |||||||||
−52.6884 | − | 5.17106i | −0.246207 | − | 0.0241638i | |||||
489.426i | 2.27640i | |||||||||
0 | 0 | |||||||||
371.477 | 1.71188 | |||||||||
−16.2267 | + | 165.335i | −0.0744342 | + | 0.758417i | |||||
0 | 0 | |||||||||
101.051 | − | 509.851i | 0.459323 | − | 2.31751i | |||||
11.0309 | 0.0499136 | |||||||||
0 | 0 | |||||||||
17.2224i | 0.0772303i | 0.999254 | + | 0.0386152i | ||||||
−0.999254 | + | 0.0386152i | ||||||||
−194.349 | − | 103.452i | −0.867630 | − | 0.461841i | |||||
0 | 0 | |||||||||
−3.03332 | + | 30.9068i | −0.0134218 | + | 0.136756i | |||||
− | 40.9846i | − | 0.180549i | −0.995917 | − | 0.0902744i | ||||
0.995917 | − | 0.0902744i | ||||||||
0 | 0 | |||||||||
−133.453 | −0.582763 | −0.291381 | − | 0.956607i | ||||||
−0.291381 | + | 0.956607i | ||||||||
−238.901 | − | 23.4468i | −1.03870 | − | 0.101942i | |||||
0 | 0 | |||||||||
86.7935 | − | 287.186i | 0.374110 | − | 1.23787i | |||||
368.345 | 1.58088 | 0.790441 | − | 0.612539i | ||||||
0.790441 | + | 0.612539i | ||||||||
0 | 0 | |||||||||
− | 68.2876i | − | 0.290586i | |||||||
−17.4293 | + | 87.9393i | −0.0738531 | + | 0.372624i | |||||
0 | 0 | |||||||||
−19.6821 | − | 1.93168i | −0.0826978 | − | 0.00811630i | |||||
288.560i | 1.20737i | 0.797225 | + | 0.603683i | ||||||
−0.797225 | + | 0.603683i | ||||||||
0 | 0 | |||||||||
−102.987 | −0.427333 | −0.213667 | − | 0.976907i | ||||||
−0.213667 | + | 0.976907i | ||||||||
39.3234 | − | 400.670i | 0.162493 | − | 1.65566i | |||||
0 | 0 | |||||||||
263.598 | + | 52.2444i | 1.08032 | + | 0.214116i | |||||
−12.0305 | −0.0491042 | |||||||||
0 | 0 | |||||||||
106.643i | 0.431751i | |||||||||
−413.464 | − | 124.957i | −1.66720 | − | 0.503860i | |||||
0 | 0 | |||||||||
3.37852 | − | 34.4241i | 0.0135141 | − | 0.137696i | |||||
− | 69.9866i | − | 0.278831i | −0.990234 | − | 0.139416i | ||||
0.990234 | − | 0.139416i | ||||||||
0 | 0 | |||||||||
−297.699 | −1.17668 | |||||||||
313.421 | + | 30.7604i | 1.23394 | + | 0.121104i | |||||
0 | 0 | |||||||||
181.517 | + | 180.521i | 0.709050 | + | 0.705158i | |||||
−97.0819 | −0.377751 | −0.188875 | − | 0.982001i | ||||||
−0.188875 | + | 0.982001i | ||||||||
0 | 0 | |||||||||
305.768i | 1.18057i | |||||||||
217.976 | + | 43.2022i | 0.838368 | + | 0.166162i | |||||
0 | 0 | |||||||||
−93.6684 | − | 9.19301i | −0.357513 | − | 0.0350878i | |||||
8.40472i | 0.0319571i | 0.999872 | + | 0.0159785i | ||||||
−0.999872 | + | 0.0159785i | ||||||||
0 | 0 | |||||||||
−56.6495 | −0.213772 | |||||||||
18.6748 | − | 190.279i | 0.0702058 | − | 0.715334i | |||||
0 | 0 | |||||||||
−53.8174 | + | 271.534i | −0.200811 | + | 1.01319i | |||||
−281.198 | −1.04535 | −0.522673 | − | 0.852533i | ||||||
−0.522673 | + | 0.852533i | ||||||||
0 | 0 | |||||||||
− | 369.456i | − | 1.36331i | −0.731675 | − | 0.681654i | ||||
0.731675 | − | 0.681654i | ||||||||
21.2569 | + | 8.77066i | 0.0781505 | + | 0.0322451i | |||||
0 | 0 | |||||||||
22.9530 | − | 233.871i | 0.0837702 | − | 0.853543i | |||||
− | 491.713i | − | 1.78805i | |||||||
0 | 0 | |||||||||
132.909 | 0.479817 | 0.239908 | − | 0.970796i | ||||||
0.239908 | + | 0.970796i | ||||||||
79.0123 | + | 7.75459i | 0.284217 | + | 0.0278942i | |||||
0 | 0 | |||||||||
−381.361 | − | 115.255i | −1.36200 | − | 0.411625i | |||||
−37.3154 | −0.132795 | −0.0663974 | − | 0.997793i | ||||||
−0.0663974 | + | 0.997793i | ||||||||
0 | 0 | |||||||||
156.168i | 0.551832i | 0.961182 | + | 0.275916i | ||||||
−0.961182 | + | 0.275916i | ||||||||
−5.55867 | + | 28.0461i | −0.0195728 | + | 0.0987540i | |||||
0 | 0 | |||||||||
274.265 | + | 26.9175i | 0.958967 | + | 0.0941170i | |||||
− | 392.113i | − | 1.36625i | |||||||
0 | 0 | |||||||||
−286.934 | −0.992853 | |||||||||
53.0258 | − | 540.285i | 0.182848 | − | 1.86305i | |||||
0 | 0 | |||||||||
315.624 | + | 62.5559i | 1.08091 | + | 0.214232i | |||||
−25.9762 | −0.0886561 | −0.0443280 | − | 0.999017i | ||||||
−0.0443280 | + | 0.999017i | ||||||||
0 | 0 | |||||||||
162.223i | 0.549907i | |||||||||
102.854 | − | 340.329i | 0.347481 | − | 1.14976i | |||||
0 | 0 | |||||||||
−22.4314 | + | 228.556i | −0.0752733 | + | 0.766967i | |||||
− | 127.275i | − | 0.425667i | |||||||
0 | 0 | |||||||||
465.232 | 1.54562 | |||||||||
318.713 | + | 31.2798i | 1.05534 | + | 0.103575i | |||||
0 | 0 | |||||||||
−84.7915 | + | 205.504i | −0.278919 | + | 0.676000i | |||||
486.262 | 1.59430 | |||||||||
0 | 0 | |||||||||
− | 111.670i | − | 0.363745i | −0.983322 | − | 0.181872i | ||||
0.983322 | − | 0.181872i | ||||||||
−484.648 | − | 96.0559i | −1.57353 | − | 0.311870i | |||||
0 | 0 | |||||||||
−777.854 | − | 76.3417i | −2.50920 | − | 0.246264i | |||||
323.742i | 1.04097i | 0.853871 | + | 0.520485i | ||||||
−0.853871 | + | 0.520485i | ||||||||
0 | 0 | |||||||||
−366.181 | −1.16991 | −0.584953 | − | 0.811067i | ||||||
−0.584953 | + | 0.811067i | ||||||||
−44.0195 | + | 448.519i | −0.140189 | + | 1.42840i | |||||
0 | 0 | |||||||||
36.4287 | − | 183.800i | 0.115281 | − | 0.581646i | |||||
−65.0029 | −0.205056 | −0.102528 | − | 0.994730i | ||||||
−0.102528 | + | 0.994730i | ||||||||
0 | 0 | |||||||||
− | 673.258i | − | 2.11053i | |||||||
385.696 | + | 256.564i | 1.20530 | + | 0.801764i | |||||
0 | 0 | |||||||||
−22.2877 | + | 227.092i | −0.0692165 | + | 0.705254i | |||||
19.9690i | 0.0618235i | |||||||||
0 | 0 | |||||||||
210.221 | 0.646833 | |||||||||
292.922 | + | 28.7485i | 0.898533 | + | 0.0881857i | |||||
0 | 0 | |||||||||
−131.899 | + | 436.433i | −0.402131 | + | 1.33059i | |||||
−64.9119 | −0.197301 | |||||||||
0 | 0 | |||||||||
− | 439.440i | − | 1.32761i | −0.747904 | − | 0.663807i | ||||
0.747904 | − | 0.663807i | ||||||||
−110.583 | + | 557.942i | −0.333080 | + | 1.68055i | |||||
0 | 0 | |||||||||
−210.875 | − | 20.6962i | −0.631363 | − | 0.0619645i | |||||
500.902i | 1.49523i | |||||||||
0 | 0 | |||||||||
−374.818 | −1.11222 | −0.556109 | − | 0.831109i | ||||||
−0.556109 | + | 0.831109i | ||||||||
21.5061 | − | 219.128i | 0.0636276 | − | 0.648308i | |||||
0 | 0 | |||||||||
40.8163 | + | 8.08967i | 0.120048 | + | 0.0237931i | |||||
−969.295 | −2.84251 | |||||||||
0 | 0 | |||||||||
348.568i | 1.01623i | |||||||||
−517.816 | − | 156.495i | −1.50528 | − | 0.454926i | |||||
0 | 0 | |||||||||
−36.4178 | + | 371.065i | −0.105254 | + | 1.07244i | |||||
− | 329.030i | − | 0.948213i | −0.880467 | − | 0.474107i | ||||
0.880467 | − | 0.474107i | ||||||||
0 | 0 | |||||||||
372.506 | 1.06735 | 0.533676 | − | 0.845689i | ||||||
0.533676 | + | 0.845689i | ||||||||
−375.090 | − | 36.8129i | −1.07169 | − | 0.105180i | |||||
0 | 0 | |||||||||
507.115 | + | 269.938i | 1.44067 | + | 0.766871i | |||||
−217.758 | −0.616879 | −0.308440 | − | 0.951244i | ||||||
−0.308440 | + | 0.951244i | ||||||||
0 | 0 | |||||||||
51.7370i | 0.145738i | |||||||||
165.218 | + | 32.7457i | 0.464094 | + | 0.0919822i | |||||
0 | 0 | |||||||||
−381.361 | − | 37.4284i | −1.06526 | − | 0.104549i | |||||
− | 145.576i | − | 0.405505i | −0.979230 | − | 0.202753i | ||||
0.979230 | − | 0.202753i | ||||||||
0 | 0 | |||||||||
167.947 | 0.465228 | |||||||||
−40.0388 | + | 407.959i | −0.110604 | + | 1.12696i | |||||
0 | 0 | |||||||||
41.0666 | − | 207.200i | 0.112820 | − | 0.569232i | |||||
582.236 | 1.59517 | |||||||||
0 | 0 | |||||||||
53.4769i | 0.145714i | 0.997342 | + | 0.0728568i | ||||||
−0.997342 | + | 0.0728568i | ||||||||
101.196 | − | 245.262i | 0.274989 | − | 0.666474i | |||||
0 | 0 | |||||||||
62.8380 | − | 640.263i | 0.169833 | − | 1.73044i | |||||
53.8491i | 0.145146i | |||||||||
0 | 0 | |||||||||
−341.504 | −0.915561 | −0.457781 | − | 0.889065i | ||||||
−0.457781 | + | 0.889065i | ||||||||
51.3565 | + | 5.04033i | 0.137317 | + | 0.0134768i | |||||
0 | 0 | |||||||||
72.2488 | + | 21.8350i | 0.192151 | + | 0.0580719i | |||||
287.837 | 0.763492 | |||||||||
0 | 0 | |||||||||
220.189i | 0.580972i | 0.956879 | + | 0.290486i | ||||||
−0.956879 | + | 0.290486i | ||||||||
−78.2079 | + | 394.596i | −0.205810 | + | 1.03841i | |||||
0 | 0 | |||||||||
178.772 | + | 17.5454i | 0.467990 | + | 0.0459304i | |||||
− | 671.073i | − | 1.75215i | −0.482175 | − | 0.876075i | ||||
0.482175 | − | 0.876075i | ||||||||
0 | 0 | |||||||||
−894.035 | −2.32217 | |||||||||
−32.7399 | + | 333.590i | −0.0848183 | + | 0.864222i | |||||
0 | 0 | |||||||||
−246.782 | − | 48.9115i | −0.636036 | − | 0.126061i | |||||
−484.924 | −1.24659 | −0.623296 | − | 0.781986i | ||||||
−0.623296 | + | 0.781986i | ||||||||
0 | 0 | |||||||||
− | 23.8323i | − | 0.0609523i | |||||||
3.84677 | − | 12.7284i | 0.00981320 | − | 0.0324704i | |||||
0 | 0 | |||||||||
36.1938 | − | 368.782i | 0.0918624 | − | 0.935995i | |||||
− | 339.058i | − | 0.858376i | |||||||
0 | 0 | |||||||||
−279.373 | −0.703711 | −0.351855 | − | 0.936054i | ||||||
−0.351855 | + | 0.936054i | ||||||||
273.935 | + | 26.8851i | 0.688278 | + | 0.0675505i | |||||
0 | 0 | |||||||||
405.103 | + | 167.146i | 1.01276 | + | 0.417866i | |||||
582.199 | 1.45187 | 0.725934 | − | 0.687765i | ||||||
0.725934 | + | 0.687765i | ||||||||
0 | 0 | |||||||||
− | 414.401i | − | 1.02829i | |||||||
186.823 | + | 37.0279i | 0.462434 | + | 0.0916531i | |||||
0 | 0 | |||||||||
−513.577 | − | 50.4046i | −1.26497 | − | 0.124149i | |||||
− | 797.842i | − | 1.96030i | |||||||
0 | 0 | |||||||||
−436.661 | −1.06763 | −0.533815 | − | 0.845601i | ||||||
−0.533815 | + | 0.845601i | ||||||||
−80.5827 | + | 821.065i | −0.196543 | + | 2.00260i | |||||
0 | 0 | |||||||||
41.7792 | − | 210.796i | 0.101406 | − | 0.511641i | |||||
154.203 | 0.373374 | |||||||||
0 | 0 | |||||||||
1029.24i | 2.48010i | |||||||||
−115.406 | + | 216.806i | −0.277419 | + | 0.521168i | |||||
0 | 0 | |||||||||
−48.7281 | + | 496.495i | −0.116574 | + | 1.18779i | |||||
758.271i | 1.80972i | 0.425714 | + | 0.904858i | ||||||
−0.425714 | + | 0.904858i | ||||||||
0 | 0 | |||||||||
523.348 | 1.24311 | 0.621553 | − | 0.783372i | ||||||
0.621553 | + | 0.783372i | ||||||||
−607.588 | − | 59.6312i | −1.43978 | − | 0.141306i | |||||
0 | 0 | |||||||||
18.1137 | − | 59.9356i | 0.0427211 | − | 0.141358i | |||||
39.3641 | 0.0926215 | |||||||||
0 | 0 | |||||||||
− | 462.225i | − | 1.08249i | |||||||
20.5853 | − | 103.863i | 0.0480965 | − | 0.242670i | |||||
0 | 0 | |||||||||
−974.171 | − | 95.6092i | −2.26551 | − | 0.222347i | |||||
729.146i | 1.69176i | 0.533377 | + | 0.845878i | ||||||
−0.533377 | + | 0.845878i | ||||||||
0 | 0 | |||||||||
−491.219 | −1.13445 | −0.567227 | − | 0.823561i | ||||||
−0.567227 | + | 0.823561i | ||||||||
−72.5679 | + | 739.402i | −0.167207 | + | 1.70369i | |||||
0 | 0 | |||||||||
−325.919 | − | 64.5963i | −0.747521 | − | 0.148157i | |||||
230.402 | 0.527236 | |||||||||
0 | 0 | |||||||||
188.693i | 0.429825i | 0.976633 | + | 0.214913i | ||||||
−0.976633 | + | 0.214913i | ||||||||
995.087 | + | 300.735i | 2.26156 | + | 0.683489i | |||||
0 | 0 | |||||||||
−2.15488 | + | 21.9563i | −0.00487530 | + | 0.0496749i | |||||
− | 413.208i | − | 0.932749i | −0.884587 | − | 0.466375i | ||||
0.884587 | − | 0.466375i | ||||||||
0 | 0 | |||||||||
304.779 | 0.684896 | |||||||||
−34.2800 | − | 3.36438i | −0.0768610 | − | 0.00754346i | |||||
0 | 0 | |||||||||
243.882 | − | 366.630i | 0.544378 | − | 0.818371i | |||||
638.253 | 1.42150 | 0.710749 | − | 0.703446i | ||||||
0.710749 | + | 0.703446i | ||||||||
0 | 0 | |||||||||
1023.14i | 2.26861i | |||||||||
−60.9255 | − | 12.0753i | −0.134791 | − | 0.0267152i | |||||
0 | 0 | |||||||||
81.5772 | + | 8.00633i | 0.179686 | + | 0.0176351i | |||||
− | 382.225i | − | 0.840055i | |||||||
0 | 0 | |||||||||
−230.687 | −0.504786 | −0.252393 | − | 0.967625i | ||||||
−0.252393 | + | 0.967625i | ||||||||
26.0699 | − | 265.629i | 0.0569213 | − | 0.579976i | |||||
0 | 0 | |||||||||
93.3386 | − | 470.938i | 0.202910 | − | 1.02378i | |||||
400.188 | 0.868088 | 0.434044 | − | 0.900892i | ||||||
0.434044 | + | 0.900892i | ||||||||
0 | 0 | |||||||||
296.656i | 0.640727i | 0.947295 | + | 0.320363i | ||||||
−0.947295 | + | 0.320363i | ||||||||
554.671 | + | 228.859i | 1.19541 | + | 0.493230i | |||||
0 | 0 | |||||||||
−71.9561 | + | 733.168i | −0.154412 | + | 1.57332i | |||||
− | 127.057i | − | 0.272070i | −0.990704 | − | 0.136035i | ||||
0.990704 | − | 0.136035i | ||||||||
0 | 0 | |||||||||
476.141 | 1.01523 | |||||||||
135.922 | + | 13.3400i | 0.289196 | + | 0.0283829i | |||||
0 | 0 | |||||||||
−171.633 | − | 51.8709i | −0.363629 | − | 0.109896i | |||||
−1213.93 | −2.56645 | |||||||||
0 | 0 | |||||||||
380.558i | 0.801174i | |||||||||
7.68977 | − | 38.7986i | 0.0161550 | − | 0.0815096i | |||||
0 | 0 | |||||||||
−574.361 | − | 56.3701i | −1.20159 | − | 0.117929i | |||||
12.3150i | 0.0257098i | 0.999917 | + | 0.0128549i | ||||||
−0.999917 | + | 0.0128549i | ||||||||
0 | 0 | |||||||||
341.100 | 0.709147 | |||||||||
20.1185 | − | 204.990i | 0.0417397 | − | 0.425290i | |||||
0 | 0 | |||||||||
789.827 | + | 156.542i | 1.63187 | + | 0.323433i | |||||
−455.241 | −0.938642 | |||||||||
0 | 0 | |||||||||
− | 181.054i | − | 0.371773i | −0.982571 | − | 0.185887i | ||||
0.982571 | − | 0.185887i | ||||||||
−155.483 | + | 514.469i | −0.318613 | + | 1.05424i | |||||
0 | 0 | |||||||||
2.35016 | − | 23.9460i | 0.00479624 | − | 0.0488694i | |||||
− | 497.080i | − | 1.01238i | −0.862421 | − | 0.506191i | ||||
0.862421 | − | 0.506191i | ||||||||
0 | 0 | |||||||||
53.8978 | 0.109326 | |||||||||
−212.265 | − | 20.8326i | −0.429687 | − | 0.0421712i | |||||
0 | 0 | |||||||||
329.490 | − | 798.565i | 0.664294 | − | 1.61001i | |||||
49.1795 | 0.0989527 | |||||||||
0 | 0 | |||||||||
− | 762.567i | − | 1.52819i | −0.645103 | − | 0.764096i | ||||
0.645103 | − | 0.764096i | ||||||||
67.8589 | + | 13.4495i | 0.135718 | + | 0.0268989i | |||||
0 | 0 | |||||||||
139.304 | + | 13.6719i | 0.277498 | + | 0.0272348i | |||||
− | 994.596i | − | 1.97733i | −0.150146 | − | 0.988664i | ||||
0.150146 | − | 0.988664i | ||||||||
0 | 0 | |||||||||
344.635 | 0.682446 | |||||||||
58.1554 | − | 592.551i | 0.114932 | − | 1.17105i | |||||
0 | 0 | |||||||||
−122.453 | + | 617.835i | −0.241050 | + | 1.21621i | |||||
−53.7310 | −0.105562 | −0.0527810 | − | 0.998606i | ||||||
−0.0527810 | + | 0.998606i | ||||||||
0 | 0 | |||||||||
− | 553.454i | − | 1.08308i | |||||||
−394.774 | + | 326.033i | −0.771043 | + | 0.636783i | |||||
0 | 0 | |||||||||
18.9649 | − | 193.235i | 0.0368967 | − | 0.375944i | |||||
− | 388.858i | − | 0.755064i | |||||||
0 | 0 | |||||||||
169.375 | 0.327611 | |||||||||
−608.613 | − | 59.7318i | −1.17493 | − | 0.115312i | |||||
0 | 0 | |||||||||
−128.573 | + | 425.427i | −0.247255 | + | 0.818129i | |||||
−616.206 | −1.18274 | −0.591369 | − | 0.806401i | ||||||
−0.591369 | + | 0.806401i | ||||||||
0 | 0 | |||||||||
− | 683.938i | − | 1.30772i | −0.756615 | − | 0.653860i | ||||
0.756615 | − | 0.653860i | ||||||||
36.5962 | − | 184.645i | 0.0698401 | − | 0.352376i | |||||
0 | 0 | |||||||||
−16.7291 | − | 1.64186i | −0.0318043 | − | 0.00312140i | |||||
− | 77.5971i | − | 0.147243i | |||||||
0 | 0 | |||||||||
254.022 | 0.480194 | |||||||||
11.0665 | − | 112.757i | 0.0208801 | − | 0.212749i | |||||
0 | 0 | |||||||||
375.090 | + | 74.3418i | 0.705057 | + | 0.139740i | |||||
−437.421 | −0.820678 | |||||||||
0 | 0 | |||||||||
− | 191.597i | − | 0.358125i | |||||||
−529.959 | − | 160.164i | −0.988729 | − | 0.298814i | |||||
0 | 0 | |||||||||
54.9320 | − | 559.707i | 0.102104 | − | 1.04035i | |||||
− | 29.8395i | − | 0.0553608i | |||||||
0 | 0 | |||||||||
518.000 | 0.957486 | 0.478743 | − | 0.877955i | ||||||
0.478743 | + | 0.877955i | ||||||||
735.379 | + | 72.1731i | 1.35679 | + | 0.133161i | |||||
0 | 0 | |||||||||
−21.6100 | + | 40.5972i | −0.0397242 | + | 0.0746272i | |||||
−601.227 | −1.10317 | |||||||||
0 | 0 | |||||||||
294.263i | 0.537957i | 0.963146 | + | 0.268979i | ||||||
−0.963146 | + | 0.268979i | ||||||||
461.021 | + | 91.3732i | 0.841280 | + | 0.166739i | |||||
0 | 0 | |||||||||
978.723 | + | 96.0559i | 1.77950 | + | 0.174647i | |||||
521.064i | 0.945669i | |||||||||
0 | 0 | |||||||||
−322.298 | −0.582817 | |||||||||
−25.9638 | + | 264.547i | −0.0468660 | + | 0.477522i | |||||
0 | 0 | |||||||||
−30.8700 | + | 155.754i | −0.0555216 | + | 0.280133i | |||||
−395.706 | −0.710424 | −0.355212 | − | 0.934786i | ||||||
−0.355212 | + | 0.934786i | ||||||||
0 | 0 | |||||||||
− | 518.989i | − | 0.928424i | |||||||
303.907 | − | 736.561i | 0.542691 | − | 1.31529i | |||||
0 | 0 | |||||||||
7.28954 | − | 74.2739i | 0.0129707 | − | 0.132160i | |||||
259.253i | 0.460484i | 0.973133 | + | 0.230242i | ||||||
−0.973133 | + | 0.230242i | ||||||||
0 | 0 | |||||||||
−112.390 | −0.198920 | |||||||||
−310.843 | − | 30.5074i | −0.549193 | − | 0.0539001i | |||||
0 | 0 | |||||||||
−54.7382 | − | 16.5430i | −0.0963700 | − | 0.0291250i | |||||
247.188 | 0.434426 | 0.217213 | − | 0.976124i | ||||||
0.217213 | + | 0.976124i | ||||||||
0 | 0 | |||||||||
− | 601.307i | − | 1.05308i | −0.850151 | − | 0.526539i | ||||
0.850151 | − | 0.526539i | ||||||||
−107.155 | + | 540.648i | −0.187334 | + | 0.945189i | |||||
0 | 0 | |||||||||
780.477 | + | 76.5992i | 1.35972 | + | 0.133448i | |||||
− | 454.184i | − | 0.789885i | |||||||
0 | 0 | |||||||||
−754.648 | −1.30788 | −0.653941 | − | 0.756545i | ||||||
−0.653941 | + | 0.756545i | ||||||||
56.0525 | − | 571.125i | 0.0969767 | − | 0.988105i | |||||
0 | 0 | |||||||||
1065.05 | + | 211.089i | 1.83628 | + | 0.363947i | |||||
978.363 | 1.68393 | |||||||||
0 | 0 | |||||||||
− | 140.509i | − | 0.241010i | |||||||
−186.171 | + | 616.010i | −0.318785 | + | 1.05481i | |||||
0 | 0 | |||||||||
5.07445 | − | 51.7040i | 0.00865946 | − | 0.0882321i | |||||
243.805i | 0.415342i | 0.978199 | + | 0.207671i | ||||||
−0.978199 | + | 0.207671i | ||||||||
0 | 0 | |||||||||
750.180 | 1.27365 | |||||||||
−322.894 | − | 31.6901i | −0.547278 | − | 0.0537121i | |||||
0 | 0 | |||||||||
657.311 | + | 271.208i | 1.11032 | + | 0.458122i | |||||
1091.73 | 1.84103 | 0.920516 | − | 0.390704i | ||||||
0.920516 | + | 0.390704i | ||||||||
0 | 0 | |||||||||
− | 71.5722i | − | 0.120289i | |||||||
−450.545 | − | 89.2967i | −0.755947 | − | 0.149827i | |||||
0 | 0 | |||||||||
253.332 | + | 24.8630i | 0.423632 | + | 0.0415770i | |||||
− | 940.721i | − | 1.57049i | −0.619188 | − | 0.785243i | ||||
0.619188 | − | 0.785243i | ||||||||
0 | 0 | |||||||||
1052.23 | 1.75079 | 0.875396 | − | 0.483406i | ||||||
0.875396 | + | 0.483406i | ||||||||
−90.8829 | + | 926.015i | −0.150968 | + | 1.53823i | |||||
0 | 0 | |||||||||
−124.521 | + | 628.267i | −0.206160 | + | 1.04018i | |||||
1457.00 | 2.40827 | |||||||||
0 | 0 | |||||||||
439.798i | 0.724544i | 0.932072 | + | 0.362272i | ||||||
−0.932072 | + | 0.362272i | ||||||||
−392.479 | − | 208.917i | −0.645524 | − | 0.343614i | |||||
0 | 0 | |||||||||
−94.9912 | + | 967.875i | −0.155723 | + | 1.58668i | |||||
72.4124i | 0.118515i | |||||||||
0 | 0 | |||||||||
449.866 | 0.733876 | 0.366938 | − | 0.930245i | ||||||
0.366938 | + | 0.930245i | ||||||||
222.271 | + | 21.8146i | 0.362005 | + | 0.0355287i | |||||
0 | 0 | |||||||||
285.869 | − | 945.896i | 0.464073 | − | 1.53555i | |||||
−848.536 | −1.37526 | −0.687630 | − | 0.726061i | ||||||
−0.687630 | + | 0.726061i | ||||||||
0 | 0 | |||||||||
539.918i | 0.872242i | 0.899888 | + | 0.436121i | ||||||
−0.899888 | + | 0.436121i | ||||||||
303.907 | − | 1533.35i | 0.490172 | − | 2.47315i | |||||
0 | 0 | |||||||||
−644.387 | − | 63.2428i | −1.03599 | − | 0.101677i | |||||
− | 289.713i | − | 0.465028i | |||||||
0 | 0 | |||||||||
−559.555 | −0.895288 | |||||||||
71.5332 | − | 728.859i | 0.114270 | − | 1.16431i | |||||
0 | 0 | |||||||||
−884.150 | − | 175.236i | −1.40788 | − | 0.279038i | |||||
63.8714 | 0.101544 | |||||||||
0 | 0 | |||||||||
43.6036i | 0.0691024i | 0.999403 | + | 0.0345512i | ||||||
−0.999403 | + | 0.0345512i | ||||||||
358.726 | + | 108.414i | 0.567605 | + | 0.171542i | |||||
0 | 0 | |||||||||
12.6983 | − | 129.384i | 0.0200288 | − | 0.204076i | |||||
1139.73i | 1.79485i | |||||||||
0 | 0 | |||||||||
12.7572 | 0.0200270 | |||||||||
1340.08 | + | 131.521i | 2.10043 | + | 0.206145i | |||||
0 | 0 | |||||||||
−586.021 | + | 717.585i | −0.915657 | + | 1.12123i | |||||
−167.263 | −0.260940 | −0.130470 | − | 0.991452i | ||||||
−0.130470 | + | 0.991452i | ||||||||
0 | 0 | |||||||||
745.770i | 1.15983i | 0.814678 | + | 0.579914i | ||||||
−0.814678 | + | 0.579914i | ||||||||
−447.658 | − | 88.7246i | −0.695121 | − | 0.137771i | |||||
0 | 0 | |||||||||
−39.7470 | − | 3.90093i | −0.0615279 | − | 0.00603860i | |||||
596.836i | 0.922467i | 0.887279 | + | 0.461233i | ||||||
−0.887279 | + | 0.461233i | ||||||||
0 | 0 | |||||||||
−402.363 | −0.619974 | |||||||||
−41.0666 | + | 418.431i | −0.0631793 | + | 0.643740i | |||||
0 | 0 | |||||||||
−114.444 | + | 577.426i | −0.175528 | + | 0.885623i | |||||
−790.871 | −1.21113 | −0.605567 | − | 0.795794i | ||||||
−0.605567 | + | 0.795794i | ||||||||
0 | 0 | |||||||||
− | 340.617i | − | 0.520026i | |||||||
−842.926 | − | 347.793i | −1.28495 | − | 0.530173i | |||||
0 | 0 | |||||||||
12.6805 | − | 129.203i | 0.0192713 | − | 0.196357i | |||||
402.569i | 0.610878i | 0.952212 | + | 0.305439i | ||||||
−0.952212 | + | 0.305439i | ||||||||
0 | 0 | |||||||||
486.544 | 0.736072 | 0.368036 | − | 0.929811i | ||||||
0.368036 | + | 0.929811i | ||||||||
874.678 | + | 85.8445i | 1.32127 | + | 0.129674i | |||||
0 | 0 | |||||||||
−1088.95 | − | 329.101i | −1.63998 | − | 0.495634i | |||||
691.933 | 1.04050 | |||||||||
0 | 0 | |||||||||
− | 621.873i | − | 0.932343i | |||||||
82.3888 | − | 415.691i | 0.123337 | − | 0.622292i | |||||
0 | 0 | |||||||||
−997.015 | − | 97.8511i | −1.48808 | − | 0.146046i | |||||
1206.08i | 1.79744i | |||||||||
0 | 0 | |||||||||
−171.727 | −0.255167 | −0.127583 | − | 0.991828i | ||||||
−0.127583 | + | 0.991828i | ||||||||
73.2205 | − | 746.051i | 0.108636 | − | 1.10690i | |||||
0 | 0 | |||||||||
431.959 | + | 85.6132i | 0.638993 | + | 0.126647i | |||||
213.095 | 0.314763 | 0.157382 | − | 0.987538i | ||||||
0.157382 | + | 0.987538i | ||||||||
0 | 0 | |||||||||
432.737i | 0.637316i | |||||||||
−24.0754 | + | 79.6619i | −0.0354050 | + | 0.117150i | |||||
0 | 0 | |||||||||
189.352 | − | 1929.32i | 0.277642 | − | 2.82892i | |||||
602.265i | 0.881794i | 0.897558 | + | 0.440897i | ||||||
−0.897558 | + | 0.440897i | ||||||||
0 | 0 | |||||||||
850.451 | 1.24153 | |||||||||
−693.803 | − | 68.0927i | −1.01137 | − | 0.0992605i | |||||
0 | 0 | |||||||||
412.648 | − | 1000.11i | 0.599779 | − | 1.45365i | |||||
60.0713 | 0.0871862 | |||||||||
0 | 0 | |||||||||
− | 1227.31i | − | 1.77614i | −0.459705 | − | 0.888071i | ||||
0.459705 | − | 0.888071i | ||||||||
−731.466 | − | 144.975i | −1.05703 | − | 0.209501i | |||||
0 | 0 | |||||||||
654.913 | + | 64.2759i | 0.943679 | + | 0.0926166i | |||||
287.321i | 0.413412i | |||||||||
0 | 0 | |||||||||
−81.9078 | −0.117515 | |||||||||
−72.7689 | + | 741.449i | −0.104253 | + | 1.06225i | |||||
0 | 0 | |||||||||
146.547 | − | 739.402i | 0.209353 | − | 1.05629i | |||||
−133.314 | −0.190176 | −0.0950882 | − | 0.995469i | ||||||
−0.0950882 | + | 0.995469i | ||||||||
0 | 0 | |||||||||
617.485i | 0.878357i | |||||||||
−636.360 | + | 956.649i | −0.903921 | + | 1.35888i | |||||
0 | 0 | |||||||||
42.5390 | − | 433.434i | 0.0602536 | − | 0.613929i | |||||
− | 327.599i | − | 0.463364i | |||||||
0 | 0 | |||||||||
−610.256 | −0.860728 | −0.430364 | − | 0.902655i | ||||||
−0.430364 | + | 0.902655i | ||||||||
−102.979 | − | 10.1068i | −0.145041 | − | 0.0142349i | |||||
0 | 0 | |||||||||
−97.4534 | + | 322.458i | −0.136873 | + | 0.452891i | |||||
−895.316 | −1.25570 | |||||||||
0 | 0 | |||||||||
997.340i | 1.39488i | |||||||||
148.998 | − | 751.764i | 0.208097 | − | 1.04995i | |||||
0 | 0 | |||||||||
289.761 | + | 28.4383i | 0.403566 | + | 0.0396077i | |||||
967.279i | 1.34531i | 0.739956 | + | 0.672656i | ||||||
−0.739956 | + | 0.672656i | ||||||||
0 | 0 | |||||||||
−369.635 | −0.512671 | |||||||||
−32.8084 | + | 334.289i | −0.0454411 | + | 0.463004i | |||||
0 | 0 | |||||||||
−804.196 | − | 159.389i | −1.11077 | − | 0.220151i | |||||
1027.15 | 1.41676 | |||||||||
0 | 0 | |||||||||
1396.59i | 1.92103i | 0.278220 | + | 0.960517i | ||||||
−0.278220 | + | 0.960517i | ||||||||
404.397 | + | 122.217i | 0.555490 | + | 0.167880i | |||||
0 | 0 | |||||||||
−113.740 | + | 1158.90i | −0.155808 | + | 1.58754i | |||||
− | 97.1814i | − | 0.132943i | |||||||
0 | 0 | |||||||||
−306.229 | −0.417775 | −0.208888 | − | 0.977940i | ||||||
−0.208888 | + | 0.977940i | ||||||||
−106.442 | − | 10.4467i | −0.145017 | − | 0.0142325i | |||||
0 | 0 | |||||||||
468.411 | + | 249.336i | 0.636428 | + | 0.338772i | |||||
−1242.40 | −1.68575 | |||||||||
0 | 0 | |||||||||
− | 463.182i | − | 0.626769i | −0.949626 | − | 0.313384i | ||||
0.949626 | − | 0.313384i | ||||||||
1262.13 | + | 250.150i | 1.70558 | + | 0.338041i | |||||
0 | 0 | |||||||||
−107.183 | − | 10.5194i | −0.144452 | − | 0.0141771i | |||||
810.697i | 1.09111i | 0.838074 | + | 0.545557i | ||||||
−0.838074 | + | 0.545557i | ||||||||
0 | 0 | |||||||||
−831.125 | −1.11560 | |||||||||
66.7128 | − | 679.743i | 0.0894273 | − | 0.911183i | |||||
0 | 0 | |||||||||
−20.0649 | + | 101.237i | −0.0268248 | + | 0.135344i | |||||
−182.126 | −0.243158 | |||||||||
0 | 0 | |||||||||
990.928i | 1.31948i | 0.751495 | + | 0.659739i | ||||||
−0.751495 | + | 0.659739i | ||||||||
−57.5751 | + | 139.541i | −0.0765626 | + | 0.185560i | |||||
0 | 0 | |||||||||
−56.2288 | + | 572.920i | −0.0745739 | + | 0.759841i | |||||
1158.97i | 1.53506i | |||||||||
0 | 0 | |||||||||
−320.001 | −0.422723 | −0.211361 | − | 0.977408i | ||||||
−0.211361 | + | 0.977408i | ||||||||
−438.271 | − | 43.0137i | −0.578194 | − | 0.0567464i | |||||
0 | 0 | |||||||||
−770.141 | − | 232.752i | −1.01334 | − | 0.306253i | |||||
635.976 | 0.835710 | 0.417855 | − | 0.908514i | ||||||
0.417855 | + | 0.908514i | ||||||||
0 | 0 | |||||||||
571.506i | 0.749025i | |||||||||
−69.8461 | + | 352.407i | −0.0914217 | + | 0.461266i | |||||
0 | 0 | |||||||||
1335.73 | + | 131.094i | 1.74377 | + | 0.171141i | |||||
− | 172.021i | − | 0.224278i | |||||||
0 | 0 | |||||||||
305.852 | 0.397727 | 0.198864 | − | 0.980027i | ||||||
0.198864 | + | 0.980027i | ||||||||
174.649 | − | 1779.52i | 0.226818 | − | 2.31107i | |||||
0 | 0 | |||||||||
−657.593 | − | 130.333i | −0.851805 | − | 0.168825i | |||||
−187.263 | −0.242255 | −0.121128 | − | 0.992637i | ||||||
−0.121128 | + | 0.992637i | ||||||||
0 | 0 | |||||||||
− | 1478.80i | − | 1.90813i | |||||||
145.564 | − | 481.649i | 0.187582 | − | 0.620681i | |||||
0 | 0 | |||||||||
94.7298 | − | 965.211i | 0.121761 | − | 1.24063i | |||||
− | 791.854i | − | 1.01650i | |||||||
0 | 0 | |||||||||
−128.324 | −0.164307 | |||||||||
47.4368 | + | 4.65564i | 0.0606608 | + | 0.00595350i | |||||
0 | 0 | |||||||||
24.5836 | + | 10.1432i | 0.0313566 | + | 0.0129378i | |||||
−1631.00 | −2.07771 | |||||||||
0 | 0 | |||||||||
185.475i | 0.235674i | 0.993033 | + | 0.117837i | ||||||
−0.993033 | + | 0.117837i | ||||||||
726.967 | + | 144.083i | 0.922547 | + | 0.182846i | |||||
0 | 0 | |||||||||
674.874 | + | 66.2349i | 0.854271 | + | 0.0838417i | |||||
106.834i | 0.135062i | |||||||||
0 | 0 | |||||||||
−515.634 | −0.650232 | |||||||||
54.5754 | − | 556.075i | 0.0687348 | − | 0.700346i | |||||
0 | 0 | |||||||||
−107.026 | + | 539.998i | −0.134455 | + | 0.678389i | |||||
1092.40 | 1.37064 | 0.685322 | − | 0.728240i | ||||||
0.685322 | + | 0.728240i | ||||||||
0 | 0 | |||||||||
13.5593i | 0.0169704i | |||||||||
−411.831 | + | 773.679i | −0.514789 | + | 0.967099i | |||||
0 | 0 | |||||||||
−113.732 | + | 1158.83i | −0.141811 | + | 1.44493i | |||||
1444.13i | 1.79842i | |||||||||
0 | 0 | |||||||||
−825.800 | −1.02584 | |||||||||
824.838 | + | 80.9530i | 1.02337 | + | 0.100438i | |||||
0 | 0 | |||||||||
−110.197 | + | 364.627i | −0.136383 | + | 0.451270i | |||||
51.1143 | 0.0631821 | 0.0315911 | − | 0.999501i | ||||||
0.0315911 | + | 0.999501i | ||||||||
0 | 0 | |||||||||
680.159i | 0.838667i | 0.907832 | + | 0.419333i | ||||||
−0.907832 | + | 0.419333i | ||||||||
200.654 | − | 1012.40i | 0.247111 | − | 1.24679i | |||||
0 | 0 | |||||||||
1588.05 | + | 155.858i | 1.95093 | + | 0.191472i | |||||
1065.19i | 1.30698i | |||||||||
0 | 0 | |||||||||
939.514 | 1.14996 | |||||||||
85.3016 | − | 869.146i | 0.104281 | − | 1.06253i | |||||
0 | 0 | |||||||||
−1618.54 | − | 320.789i | −1.97382 | − | 0.391207i | |||||
124.267 | 0.151361 | 0.0756805 | − | 0.997132i | ||||||
0.0756805 | + | 0.997132i | ||||||||
0 | 0 | |||||||||
− | 1107.83i | − | 1.34609i | −0.739602 | − | 0.673044i | ||||
0.739602 | − | 0.673044i | ||||||||
411.415 | + | 124.338i | 0.499290 | + | 0.150895i | |||||
0 | 0 | |||||||||
−30.1236 | + | 306.932i | −0.0364692 | + | 0.371588i | |||||
− | 856.831i | − | 1.03607i | −0.855359 | − | 0.518036i | ||||
0.855359 | − | 0.518036i | ||||||||
0 | 0 | |||||||||
−59.5071 | −0.0717818 | −0.0358909 | − | 0.999356i | ||||||
−0.0358909 | + | 0.999356i | ||||||||
−2048.64 | − | 201.062i | −2.46824 | − | 0.242243i | |||||
0 | 0 | |||||||||
−408.994 | − | 272.062i | −0.491579 | − | 0.326997i | |||||
2.38881 | 0.00286771 | |||||||||
0 | 0 | |||||||||
− | 766.830i | − | 0.918359i | |||||||
−978.723 | − | 193.980i | −1.17072 | − | 0.232034i | |||||
0 | 0 | |||||||||
−1509.29 | − | 148.128i | −1.80106 | − | 0.176764i | |||||
464.691i | 0.553863i | 0.960890 | + | 0.276932i | ||||||
−0.960890 | + | 0.276932i | ||||||||
0 | 0 | |||||||||
565.391 | 0.672284 | |||||||||
−102.236 | + | 1041.69i | −0.121420 | + | 1.23716i | |||||
0 | 0 | |||||||||
237.384 | − | 1197.72i | 0.281261 | − | 1.41910i | |||||
796.840 | 0.943006 | |||||||||
0 | 0 | |||||||||
− | 1384.98i | − | 1.63516i | |||||||
115.759 | + | 47.7627i | 0.136509 | + | 0.0563239i | |||||
0 | 0 | |||||||||
−7.68977 | + | 78.3518i | −0.00904679 | + | 0.0921786i | |||||
− | 736.948i | − | 0.865979i | |||||||
0 | 0 | |||||||||
−1366.33 | −1.60179 | −0.800896 | − | 0.598803i | ||||||
−0.800896 | + | 0.598803i | ||||||||
920.029 | + | 90.2955i | 1.07732 | + | 0.105732i | |||||
0 | 0 | |||||||||
202.711 | + | 61.2633i | 0.236812 | + | 0.0715693i | |||||
1677.60 | 1.95752 | 0.978762 | − | 0.205000i | ||||||
0.978762 | + | 0.205000i | ||||||||
0 | 0 | |||||||||
1645.03i | 1.91505i | 0.288355 | + | 0.957524i | ||||||
−0.288355 | + | 0.957524i | ||||||||
380.608 | − | 1920.35i | 0.442568 | − | 2.23296i | |||||
0 | 0 | |||||||||
−1451.32 | − | 142.439i | −1.68367 | − | 0.165242i | |||||
− | 294.311i | − | 0.341033i | −0.985355 | − | 0.170516i | ||||
0.985355 | − | 0.170516i | ||||||||
0 | 0 | |||||||||
−1349.34 | −1.55994 | |||||||||
95.9594 | − | 977.740i | 0.110808 | − | 1.12903i | |||||
0 | 0 | |||||||||
−1457.56 | − | 288.884i | −1.67921 | − | 0.332815i | |||||
840.971 | 0.967746 | |||||||||
0 | 0 | |||||||||
− | 531.159i | − | 0.609826i | |||||||
192.243 | − | 636.102i | 0.220462 | − | 0.729475i | |||||
0 | 0 | |||||||||
−45.0090 | + | 458.601i | −0.0514977 | + | 0.524715i | |||||
− | 118.992i | − | 0.135991i | |||||||
0 | 0 | |||||||||
719.169 | 0.820033 | 0.410016 | − | 0.912078i | ||||||
0.410016 | + | 0.912078i | ||||||||
−375.582 | − | 36.8612i | −0.427770 | − | 0.0419831i | |||||
0 | 0 | |||||||||
−792.984 | + | 1921.91i | −0.901118 | + | 2.18399i | |||||
16.3083 | 0.0185112 | 0.00925559 | − | 0.999957i | ||||||
0.00925559 | + | 0.999957i | ||||||||
0 | 0 | |||||||||
− | 1190.35i | − | 1.34807i | −0.738698 | − | 0.674036i | ||||
0.738698 | − | 0.674036i | ||||||||
−43.2817 | − | 8.57831i | −0.0489612 | − | 0.00970398i | |||||
0 | 0 | |||||||||
822.464 | + | 80.7200i | 0.928289 | + | 0.0911061i | |||||
− | 400.666i | − | 0.451709i | −0.974161 | − | 0.225855i | ||||
0.974161 | − | 0.225855i | ||||||||
0 | 0 | |||||||||
1083.39 | 1.21866 | |||||||||
−59.5384 | + | 606.643i | −0.0668971 | + | 0.681621i | |||||
0 | 0 | |||||||||
13.3932 | − | 67.5750i | 0.0150148 | − | 0.0757567i | |||||
−131.087 | −0.146793 | |||||||||
0 | 0 | |||||||||
− | 1386.79i | − | 1.54948i | |||||||
682.112 | + | 557.052i | 0.761286 | + | 0.621710i | |||||
0 | 0 | |||||||||
−124.682 | + | 1270.40i | −0.138845 | + | 1.41470i | |||||
− | 2024.79i | − | 2.25227i | |||||||
0 | 0 | |||||||||
11.2484 | 0.0124844 | |||||||||
−2036.50 | − | 199.870i | −2.25776 | − | 0.221586i | |||||
0 | 0 | |||||||||
35.9368 | − | 118.909i | 0.0397531 | − | 0.131537i | |||||
−1483.51 | −1.63924 | |||||||||
0 | 0 | |||||||||
1260.24i | 1.38946i | 0.719270 | + | 0.694731i | ||||||
−0.719270 | + | 0.694731i | ||||||||
−31.8722 | + | 160.810i | −0.0351015 | + | 0.177104i | |||||
0 | 0 | |||||||||
760.795 | + | 74.6675i | 0.836038 | + | 0.0820522i | |||||
964.398i | 1.05862i | 0.848430 | + | 0.529308i | ||||||
−0.848430 | + | 0.529308i | ||||||||
0 | 0 | |||||||||
−2552.84 | −2.79610 | |||||||||
45.0646 | − | 459.168i | 0.0493048 | − | 0.502372i | |||||
0 | 0 | |||||||||
523.625 | + | 103.781i | 0.571643 | + | 0.113298i | |||||
−323.779 | −0.353086 | |||||||||
0 | 0 | |||||||||
− | 424.406i | − | 0.461813i | −0.972976 | − | 0.230906i | ||||
0.972976 | − | 0.230906i | ||||||||
919.139 | + | 277.782i | 0.999064 | + | 0.301937i | |||||
0 | 0 | |||||||||
−78.1767 | + | 796.550i | −0.0847903 | + | 0.863937i | |||||
− | 54.8621i | − | 0.0594389i | |||||||
0 | 0 | |||||||||
1217.23 | 1.31592 | |||||||||
−590.476 | − | 57.9517i | −0.637663 | − | 0.0625829i | |||||
0 | 0 | |||||||||
−563.883 | + | 1059.33i | −0.607633 | + | 1.14152i | |||||
−858.458 | −0.924067 | −0.462033 | − | 0.886862i | ||||||
−0.462033 | + | 0.886862i | ||||||||
0 | 0 | |||||||||
23.0941i | 0.0248057i | |||||||||
−1445.27 | − | 286.448i | −1.55072 | − | 0.307348i | |||||
0 | 0 | |||||||||
252.898 | + | 24.8205i | 0.270769 | + | 0.0265744i | |||||
186.753i | 0.199736i | |||||||||
0 | 0 | |||||||||
858.258 | 0.915964 | 0.457982 | − | 0.888962i | ||||||
0.457982 | + | 0.888962i | ||||||||
−93.0140 | + | 947.729i | −0.0991621 | + | 1.01037i | |||||
0 | 0 | |||||||||
−53.1047 | + | 267.939i | −0.0564944 | + | 0.285041i | |||||
−937.106 | −0.995862 | −0.497931 | − | 0.867217i | ||||||
−0.497931 | + | 0.867217i | ||||||||
0 | 0 | |||||||||
945.052i | 1.00218i | |||||||||
136.774 | − | 331.491i | 0.144888 | − | 0.351156i | |||||
0 | 0 | |||||||||
237.141 | − | 2416.25i | 0.250677 | − | 2.55418i | |||||
− | 887.159i | − | 0.936810i | −0.883514 | − | 0.468405i | ||||
0.883514 | − | 0.468405i | ||||||||
0 | 0 | |||||||||
−617.405 | −0.650585 | |||||||||
−757.476 | − | 74.3418i | −0.797344 | − | 0.0782546i | |||||
0 | 0 | |||||||||
75.7239 | + | 22.8853i | 0.0795419 | + | 0.0240392i | |||||
1078.46 | 1.13164 | 0.565821 | − | 0.824528i | ||||||
0.565821 | + | 0.824528i | ||||||||
0 | 0 | |||||||||
650.090i | 0.680722i | |||||||||
224.402 | − | 1132.22i | 0.234731 | − | 1.18433i | |||||
0 | 0 | |||||||||
−24.5122 | − | 2.40573i | −0.0255868 | − | 0.00251120i | |||||
− | 808.411i | − | 0.842973i | |||||||
0 | 0 | |||||||||
−1954.11 | −2.03342 | |||||||||
−66.6337 | + | 678.937i | −0.0692658 | + | 0.705756i | |||||
0 | 0 | |||||||||
404.089 | + | 80.0894i | 0.419180 | + | 0.0830803i | |||||
−1213.07 | −1.25707 | |||||||||
0 | 0 | |||||||||
− | 119.065i | − | 0.123128i | −0.998103 | − | 0.0615640i | ||||
0.998103 | − | 0.0615640i | ||||||||
−465.878 | + | 1541.52i | −0.481279 | + | 1.59248i | |||||
0 | 0 | |||||||||
88.9312 | − | 906.129i | 0.0916817 | − | 0.934154i | |||||
1516.56i | 1.56185i | 0.624624 | + | 0.780926i | ||||||
−0.624624 | + | 0.780926i | ||||||||
0 | 0 | |||||||||
273.118 | 0.280697 | |||||||||
360.376 | + | 35.3687i | 0.369996 | + | 0.0363129i | |||||
0 | 0 | |||||||||
−993.645 | − | 409.980i | −1.01808 | − | 0.420062i | |||||
1578.30 | 1.61546 | 0.807729 | − | 0.589555i | ||||||
0.807729 | + | 0.589555i | ||||||||
0 | 0 | |||||||||
755.947i | 0.772162i | |||||||||
47.2039 | + | 9.35568i | 0.0481672 | + | 0.00954661i | |||||
0 | 0 | |||||||||
989.406 | + | 97.1044i | 1.00754 | + | 0.0988843i | |||||
− | 592.742i | − | 0.602993i | −0.953467 | − | 0.301497i | ||||
0.953467 | − | 0.301497i | ||||||||
0 | 0 | |||||||||
1341.04 | 1.36147 | |||||||||
−10.5289 | + | 107.280i | −0.0106784 | + | 0.108803i | |||||
0 | 0 | |||||||||
82.9319 | − | 418.431i | 0.0839392 | − | 0.423513i | |||||
−1121.28 | −1.13375 | |||||||||
0 | 0 | |||||||||
1896.17i | 1.91339i | 0.291098 | + | 0.956693i | ||||||
−0.291098 | + | 0.956693i | ||||||||
1525.13 | + | 811.828i | 1.53743 | + | 0.818375i | |||||
0 | 0 | |||||||||
−9.60720 | + | 97.8887i | −0.00966519 | + | 0.0984796i | |||||
996.141i | 1.00115i | |||||||||
0 | 0 | |||||||||
69.7126 | 0.0699224 | 0.0349612 | − | 0.999389i | ||||||
0.0349612 | + | 0.999389i | ||||||||
1517.84 | + | 148.967i | 1.52088 | + | 0.149266i | |||||
0 | 0 |
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 324.3.d.e.163.4 | yes | 6 | |
3.2 | odd | 2 | 324.3.d.f.163.3 | yes | 6 | ||
4.3 | odd | 2 | inner | 324.3.d.e.163.3 | ✓ | 6 | |
9.2 | odd | 6 | 324.3.f.q.271.1 | 12 | |||
9.4 | even | 3 | 324.3.f.r.55.2 | 12 | |||
9.5 | odd | 6 | 324.3.f.q.55.5 | 12 | |||
9.7 | even | 3 | 324.3.f.r.271.6 | 12 | |||
12.11 | even | 2 | 324.3.d.f.163.4 | yes | 6 | ||
36.7 | odd | 6 | 324.3.f.r.271.2 | 12 | |||
36.11 | even | 6 | 324.3.f.q.271.5 | 12 | |||
36.23 | even | 6 | 324.3.f.q.55.1 | 12 | |||
36.31 | odd | 6 | 324.3.f.r.55.6 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
324.3.d.e.163.3 | ✓ | 6 | 4.3 | odd | 2 | inner | |
324.3.d.e.163.4 | yes | 6 | 1.1 | even | 1 | trivial | |
324.3.d.f.163.3 | yes | 6 | 3.2 | odd | 2 | ||
324.3.d.f.163.4 | yes | 6 | 12.11 | even | 2 | ||
324.3.f.q.55.1 | 12 | 36.23 | even | 6 | |||
324.3.f.q.55.5 | 12 | 9.5 | odd | 6 | |||
324.3.f.q.271.1 | 12 | 9.2 | odd | 6 | |||
324.3.f.q.271.5 | 12 | 36.11 | even | 6 | |||
324.3.f.r.55.2 | 12 | 9.4 | even | 3 | |||
324.3.f.r.55.6 | 12 | 36.31 | odd | 6 | |||
324.3.f.r.271.2 | 12 | 36.7 | odd | 6 | |||
324.3.f.r.271.6 | 12 | 9.7 | even | 3 |