Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [54,8,Mod(19,54)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(54, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("54.19");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 54.c (of order , degree , not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | |
Analytic rank: | |
Dimension: | |
Relative dimension: | over |
Coefficient field: | 6.0.14601465675.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
|
Coefficient ring: | |
Coefficient ring index: | |
Twist minimal: | no (minimal twist has level 18) |
Sato-Tate group: |
Embedding invariants
Embedding label | 19.1 | ||
Root | of defining polynomial | ||
Character | 54.19 | ||
Dual form | 54.8.c.a.37.1 |
-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of on generators for .
Coefficient data
For each we display the coefficients of the -expansion , the Satake parameters , and the Satake angles .
4.00000 | − | 6.92820i | 0.353553 | − | 0.612372i | |||||
0 | 0 | |||||||||
−32.0000 | − | 55.4256i | −0.250000 | − | 0.433013i | |||||
−187.789 | − | 325.261i | −0.671855 | − | 1.16369i | −0.977377 | − | 0.211502i | ||
0.305522 | − | 0.952185i | ||||||||
0 | 0 | |||||||||
−528.867 | + | 916.024i | −0.582778 | + | 1.00940i | 0.412371 | + | 0.911016i | ||
−0.995148 | + | 0.0983845i | ||||||||
−512.000 | −0.353553 | |||||||||
0 | 0 | |||||||||
−3004.63 | −0.950147 | |||||||||
849.965 | − | 1472.18i | 0.192542 | − | 0.333493i | −0.753550 | − | 0.657391i | ||
0.946092 | + | 0.323898i | ||||||||
0 | 0 | |||||||||
6256.75 | + | 10837.0i | 0.789854 | + | 1.36807i | 0.926056 | + | 0.377386i | ||
−0.136202 | + | 0.990681i | ||||||||
4230.93 | + | 7328.19i | 0.412086 | + | 0.713754i | |||||
0 | 0 | |||||||||
−2048.00 | + | 3547.24i | −0.125000 | + | 0.216506i | |||||
−16879.9 | −0.833293 | −0.416646 | − | 0.909069i | ||||||
−0.416646 | + | 0.909069i | ||||||||
0 | 0 | |||||||||
−35281.9 | −1.18009 | −0.590044 | − | 0.807371i | ||||||
−0.590044 | + | 0.807371i | ||||||||
−12018.5 | + | 20816.7i | −0.335928 | + | 0.581844i | |||||
0 | 0 | |||||||||
−6799.72 | − | 11777.5i | −0.136148 | − | 0.235815i | |||||
35482.7 | + | 61457.8i | 0.608092 | + | 1.05325i | 0.991555 | + | 0.129690i | ||
−0.383463 | + | 0.923556i | ||||||||
0 | 0 | |||||||||
−31467.1 | + | 54502.6i | −0.402779 | + | 0.697634i | |||||
100108. | 1.11702 | |||||||||
0 | 0 | |||||||||
67694.9 | 0.582778 | |||||||||
−38827.4 | + | 67251.0i | −0.295628 | + | 0.512042i | −0.975131 | − | 0.221631i | ||
0.679503 | + | 0.733673i | ||||||||
0 | 0 | |||||||||
63093.8 | + | 109282.i | 0.380383 | + | 0.658843i | 0.991117 | − | 0.132993i | ||
−0.610734 | + | 0.791836i | ||||||||
16384.0 | + | 28377.9i | 0.0883883 | + | 0.153093i | |||||
0 | 0 | |||||||||
−67519.4 | + | 116947.i | −0.294614 | + | 0.510286i | |||||
397262. | 1.56617 | |||||||||
0 | 0 | |||||||||
−528664. | −1.71583 | −0.857914 | − | 0.513794i | ||||||
−0.857914 | + | 0.513794i | ||||||||
−141128. | + | 244440.i | −0.417224 | + | 0.722654i | |||||
0 | 0 | |||||||||
96148.1 | + | 166533.i | 0.237537 | + | 0.411426i | |||||
−258960. | − | 448533.i | −0.586800 | − | 1.01637i | −0.994648 | − | 0.103318i | ||
0.407849 | − | 0.913050i | ||||||||
0 | 0 | |||||||||
135830. | − | 235264.i | 0.260529 | − | 0.451249i | −0.705854 | − | 0.708358i | ||
0.966383 | + | 0.257109i | ||||||||
−108795. | −0.192542 | |||||||||
0 | 0 | |||||||||
567723. | 0.859972 | |||||||||
−211814. | + | 366873.i | −0.297586 | + | 0.515435i | −0.975583 | − | 0.219630i | ||
0.677997 | + | 0.735065i | ||||||||
0 | 0 | |||||||||
−147628. | − | 255699.i | −0.179260 | − | 0.310487i | |||||
251737. | + | 436021.i | 0.284808 | + | 0.493301i | |||||
0 | 0 | |||||||||
400432. | − | 693568.i | 0.394927 | − | 0.684034i | |||||
−1.24314e6 | −1.14698 | −0.573490 | − | 0.819213i | ||||||
−0.573490 | + | 0.819213i | ||||||||
0 | 0 | |||||||||
−638457. | −0.517443 | |||||||||
270780. | − | 469004.i | 0.206043 | − | 0.356877i | |||||
0 | 0 | |||||||||
310619. | + | 538008.i | 0.209040 | + | 0.362068i | |||||
−1.34086e6 | − | 2.32244e6i | −0.849968 | − | 1.47219i | −0.881236 | − | 0.472677i | ||
0.0312678 | − | 0.999511i | ||||||||
0 | 0 | |||||||||
377040. | − | 653052.i | 0.212683 | − | 0.368378i | −0.739870 | − | 0.672750i | ||
0.952553 | + | 0.304372i | ||||||||
1.00950e6 | 0.537943 | |||||||||
0 | 0 | |||||||||
262144. | 0.125000 | |||||||||
2.34990e6 | − | 4.07014e6i | 1.06133 | − | 1.83829i | |||||
0 | 0 | |||||||||
131285. | + | 227392.i | 0.0533278 | + | 0.0923664i | 0.891457 | − | 0.453105i | ||
−0.838129 | + | 0.545472i | ||||||||
540156. | + | 935577.i | 0.208323 | + | 0.360826i | |||||
0 | 0 | |||||||||
1.58905e6 | − | 2.75231e6i | 0.553724 | − | 0.959079i | |||||
−990913. | −0.328573 | −0.164286 | − | 0.986413i | ||||||
−0.164286 | + | 0.986413i | ||||||||
0 | 0 | |||||||||
−1.04389e6 | −0.314068 | −0.157034 | − | 0.987593i | ||||||
−0.157034 | + | 0.987593i | ||||||||
−2.11466e6 | + | 3.66269e6i | −0.606637 | + | 1.05073i | |||||
0 | 0 | |||||||||
1.12902e6 | + | 1.95552e6i | 0.295022 | + | 0.510993i | |||||
899036. | + | 1.55718e6i | 0.224419 | + | 0.388705i | |||||
0 | 0 | |||||||||
3.66860e6 | − | 6.35419e6i | 0.837153 | − | 1.44999i | −0.0551117 | − | 0.998480i | ||
0.892265 | − | 0.451512i | ||||||||
1.53837e6 | 0.335928 | |||||||||
0 | 0 | |||||||||
−4.14337e6 | −0.829860 | |||||||||
−1.94611e6 | + | 3.37075e6i | −0.373588 | + | 0.647074i | −0.990115 | − | 0.140260i | ||
0.616526 | + | 0.787334i | ||||||||
0 | 0 | |||||||||
3.16986e6 | + | 5.49035e6i | 0.559852 | + | 0.969692i | |||||
−1.08664e6 | − | 1.88211e6i | −0.184222 | − | 0.319081i | |||||
0 | 0 | |||||||||
−435182. | + | 753757.i | −0.0680740 | + | 0.117908i | |||||
−675681. | −0.101596 | −0.0507980 | − | 0.998709i | ||||||
−0.0507980 | + | 0.998709i | ||||||||
0 | 0 | |||||||||
−1.32359e7 | −1.84124 | |||||||||
2.27089e6 | − | 3.93330e6i | 0.304046 | − | 0.526623i | |||||
0 | 0 | |||||||||
1.69452e6 | + | 2.93499e6i | 0.210425 | + | 0.364467i | |||||
6.62556e6 | + | 1.14758e7i | 0.792849 | + | 1.37325i | |||||
0 | 0 | |||||||||
−8.12785e6 | + | 1.40779e7i | −0.904221 | + | 1.56616i | −0.0822619 | + | 0.996611i | ||
−0.821959 | + | 0.569546i | ||||||||
−2.36205e6 | −0.253512 | |||||||||
0 | 0 | |||||||||
4.02779e6 | 0.402779 | |||||||||
−212270. | + | 367662.i | −0.0205005 | + | 0.0355079i | −0.876094 | − | 0.482141i | ||
0.855593 | + | 0.517649i | ||||||||
0 | 0 | |||||||||
2.43167e6 | + | 4.21178e6i | 0.219268 | + | 0.379783i | 0.954584 | − | 0.297941i | ||
−0.735317 | + | 0.677724i | ||||||||
−3.20345e6 | − | 5.54854e6i | −0.279256 | − | 0.483685i | |||||
0 | 0 | |||||||||
−4.97257e6 | + | 8.61275e6i | −0.405519 | + | 0.702379i | |||||
−2.83648e6 | −0.223839 | −0.111920 | − | 0.993717i | ||||||
−0.111920 | + | 0.993717i | ||||||||
0 | 0 | |||||||||
6.31389e6 | 0.466987 | 0.233493 | − | 0.972358i | ||||||
0.233493 | + | 0.972358i | ||||||||
−2.55383e6 | + | 4.42336e6i | −0.182944 | + | 0.316868i | |||||
0 | 0 | |||||||||
−2.16624e6 | − | 3.75203e6i | −0.145694 | − | 0.252350i | |||||
1.07218e7 | + | 1.85708e7i | 0.699029 | + | 1.21075i | 0.968804 | + | 0.247830i | ||
−0.269775 | + | 0.962923i | ||||||||
0 | 0 | |||||||||
1.33265e7 | − | 2.30822e7i | 0.817100 | − | 1.41526i | |||||
4.96990e6 | 0.295628 | |||||||||
0 | 0 | |||||||||
−2.14538e7 | −1.20204 | |||||||||
8.92719e6 | − | 1.54624e7i | 0.485624 | − | 0.841126i | |||||
0 | 0 | |||||||||
8.29871e6 | + | 1.43738e7i | 0.425855 | + | 0.737602i | |||||
−3.01632e6 | − | 5.22442e6i | −0.150390 | − | 0.260483i | |||||
0 | 0 | |||||||||
4.03801e6 | − | 6.99403e6i | 0.190191 | − | 0.329421i | |||||
−5.70534e6 | −0.261274 | |||||||||
0 | 0 | |||||||||
1.35681e7 | 0.587768 | 0.293884 | − | 0.955841i | ||||||
0.293884 | + | 0.955841i | ||||||||
1.04858e6 | − | 1.81619e6i | 0.0441942 | − | 0.0765466i | |||||
0 | 0 | |||||||||
−1.87992e7 | − | 3.25612e7i | −0.750477 | − | 1.29986i | |||||
−1.17657e7 | − | 2.03788e7i | −0.457265 | − | 0.792005i | 0.541551 | − | 0.840668i | ||
−0.998815 | + | 0.0486627i | ||||||||
0 | 0 | |||||||||
1.86594e7 | − | 3.23191e7i | 0.687729 | − | 1.19118i | |||||
2.10056e6 | 0.0754169 | |||||||||
0 | 0 | |||||||||
8.64249e6 | 0.294614 | |||||||||
−1.39952e7 | + | 2.42405e7i | −0.465006 | + | 0.805414i | −0.999202 | − | 0.0399467i | ||
0.534196 | + | 0.845361i | ||||||||
0 | 0 | |||||||||
4.00094e6 | + | 6.92982e6i | 0.126360 | + | 0.218862i | 0.922264 | − | 0.386561i | ||
−0.795904 | + | 0.605423i | ||||||||
−1.27124e7 | − | 2.20185e7i | −0.391542 | − | 0.678171i | |||||
0 | 0 | |||||||||
−3.96365e6 | + | 6.86525e6i | −0.116168 | + | 0.201209i | |||||
2.12721e7 | 0.608322 | |||||||||
0 | 0 | |||||||||
2.91655e7 | 0.794476 | |||||||||
−4.17555e6 | + | 7.23226e6i | −0.111040 | + | 0.192327i | |||||
0 | 0 | |||||||||
1.69172e7 | + | 2.93015e7i | 0.428957 | + | 0.742975i | |||||
−1.35829e7 | − | 2.35262e7i | −0.336387 | − | 0.582639i | 0.647363 | − | 0.762182i | ||
−0.983750 | + | 0.179542i | ||||||||
0 | 0 | |||||||||
−2.09932e7 | + | 3.63612e7i | −0.496202 | + | 0.859447i | −0.999990 | − | 0.00438023i | ||
0.503789 | + | 0.863827i | ||||||||
1.80643e7 | 0.417224 | |||||||||
0 | 0 | |||||||||
1.43846e7 | 0.317376 | |||||||||
2.36967e7 | − | 4.10439e7i | 0.511125 | − | 0.885294i | |||||
0 | 0 | |||||||||
−4.10239e7 | − | 7.10556e7i | −0.846036 | − | 1.46538i | −0.884719 | − | 0.466125i | ||
0.0386831 | − | 0.999252i | ||||||||
−2.93488e7 | − | 5.08336e7i | −0.591957 | − | 1.02530i | |||||
0 | 0 | |||||||||
6.15348e6 | − | 1.06581e7i | 0.118768 | − | 0.205713i | |||||
−7.50625e7 | −1.41753 | |||||||||
0 | 0 | |||||||||
−2.89286e7 | −0.523203 | −0.261602 | − | 0.965176i | ||||||
−0.261602 | + | 0.965176i | ||||||||
−1.65735e7 | + | 2.87061e7i | −0.293400 | + | 0.508184i | |||||
0 | 0 | |||||||||
1.55688e7 | + | 2.69660e7i | 0.264167 | + | 0.457550i | |||||
1.33585e7 | + | 2.31376e7i | 0.221947 | + | 0.384424i | 0.955399 | − | 0.295318i | ||
−0.733452 | + | 0.679741i | ||||||||
0 | 0 | |||||||||
−4.69195e7 | + | 8.12669e7i | −0.747738 | + | 1.29512i | |||||
5.07177e7 | 0.791751 | |||||||||
0 | 0 | |||||||||
−1.73862e7 | −0.260529 | |||||||||
−1.31561e7 | + | 2.27871e7i | −0.193182 | + | 0.334601i | −0.946303 | − | 0.323281i | ||
0.753121 | + | 0.657882i | ||||||||
0 | 0 | |||||||||
−3.32838e7 | − | 5.76492e7i | −0.469461 | − | 0.813131i | |||||
3.48146e6 | + | 6.03006e6i | 0.0481356 | + | 0.0833733i | |||||
0 | 0 | |||||||||
−2.70272e6 | + | 4.68125e6i | −0.0359196 | + | 0.0622146i | |||||
2.19724e7 | 0.286347 | 0.143174 | − | 0.989698i | ||||||
0.143174 | + | 0.989698i | ||||||||
0 | 0 | |||||||||
1.26202e8 | 1.58195 | 0.790975 | − | 0.611849i | ||||||
0.790975 | + | 0.611849i | ||||||||
−5.29437e7 | + | 9.17012e7i | −0.650976 | + | 1.12752i | |||||
0 | 0 | |||||||||
−1.81671e7 | − | 3.14664e7i | −0.214993 | − | 0.372379i | |||||
9.92774e7 | + | 1.71954e8i | 1.15279 | + | 1.99669i | |||||
0 | 0 | |||||||||
−1.43473e7 | + | 2.48502e7i | −0.160444 | + | 0.277898i | |||||
2.71122e7 | 0.297586 | |||||||||
0 | 0 | |||||||||
1.06009e8 | 1.12126 | |||||||||
8.97257e7 | − | 1.55409e8i | 0.931752 | − | 1.61384i | 0.151425 | − | 0.988469i | ||
0.780326 | − | 0.625372i | ||||||||
0 | 0 | |||||||||
1.49157e7 | + | 2.58348e7i | 0.149346 | + | 0.258675i | 0.930986 | − | 0.365055i | ||
−0.781640 | + | 0.623730i | ||||||||
6.50228e7 | + | 1.12623e8i | 0.639381 | + | 1.10744i | |||||
0 | 0 | |||||||||
−9.44820e6 | + | 1.63648e7i | −0.0896299 | + | 0.155243i | |||||
−6.70863e7 | −0.625176 | −0.312588 | − | 0.949889i | ||||||
−0.312588 | + | 0.949889i | ||||||||
0 | 0 | |||||||||
−1.18177e8 | −1.06304 | −0.531519 | − | 0.847046i | ||||||
−0.531519 | + | 0.847046i | ||||||||
1.61112e7 | − | 2.79053e7i | 0.142404 | − | 0.246651i | |||||
0 | 0 | |||||||||
1.69816e6 | + | 2.94130e6i | 0.0144960 | + | 0.0251078i | |||||
−4.10690e7 | − | 7.11336e7i | −0.344570 | − | 0.596813i | |||||
0 | 0 | |||||||||
−9.72600e7 | + | 1.68459e8i | −0.788489 | + | 1.36570i | |||||
3.89067e7 | 0.310091 | |||||||||
0 | 0 | |||||||||
−5.12553e7 | −0.394927 | |||||||||
−2.99884e7 | + | 5.19414e7i | −0.227217 | + | 0.393552i | |||||
0 | 0 | |||||||||
−5.19927e7 | − | 9.00540e7i | −0.381025 | − | 0.659955i | 0.610184 | − | 0.792260i | ||
−0.991209 | + | 0.132305i | ||||||||
3.97806e7 | + | 6.89020e7i | 0.286745 | + | 0.496657i | |||||
0 | 0 | |||||||||
−1.13459e7 | + | 1.96517e7i | −0.0791392 | + | 0.137073i | |||||
−1.02030e8 | −0.700150 | |||||||||
0 | 0 | |||||||||
−1.33473e8 | −0.886715 | |||||||||
2.52556e7 | − | 4.37439e7i | 0.165105 | − | 0.285970i | |||||
0 | 0 | |||||||||
2.04306e7 | + | 3.53869e7i | 0.129361 | + | 0.224059i | |||||
−1.05613e8 | − | 1.82927e8i | −0.658180 | − | 1.14000i | |||||
0 | 0 | |||||||||
8.07648e7 | − | 1.39889e8i | 0.487703 | − | 0.844726i | −0.512197 | − | 0.858868i | ||
0.999900 | + | 0.0141421i | ||||||||
−3.46598e7 | −0.206043 | |||||||||
0 | 0 | |||||||||
1.71550e8 | 0.988576 | |||||||||
1.90267e7 | − | 3.29553e7i | 0.107963 | − | 0.186997i | −0.806982 | − | 0.590576i | ||
0.914945 | + | 0.403579i | ||||||||
0 | 0 | |||||||||
1.44858e8 | + | 2.50901e8i | 0.797110 | + | 1.38064i | 0.921491 | + | 0.388401i | ||
−0.124381 | + | 0.992235i | ||||||||
−1.06612e8 | − | 1.84658e8i | −0.577777 | − | 1.00074i | |||||
0 | 0 | |||||||||
1.98796e7 | − | 3.44325e7i | 0.104520 | − | 0.181034i | |||||
7.45094e7 | 0.385892 | 0.192946 | − | 0.981209i | ||||||
0.192946 | + | 0.981209i | ||||||||
0 | 0 | |||||||||
1.59106e8 | 0.799740 | |||||||||
−8.58153e7 | + | 1.48636e8i | −0.424984 | + | 0.736094i | |||||
0 | 0 | |||||||||
−7.14175e7 | − | 1.23699e8i | −0.343388 | − | 0.594766i | |||||
8.98328e7 | + | 1.55595e8i | 0.425640 | + | 0.737230i | 0.996480 | − | 0.0838313i | ||
−0.570840 | + | 0.821061i | ||||||||
0 | 0 | |||||||||
3.04341e7 | − | 5.27134e7i | 0.140056 | − | 0.242583i | −0.787462 | − | 0.616364i | ||
0.927517 | + | 0.373780i | ||||||||
1.32779e8 | 0.602250 | |||||||||
0 | 0 | |||||||||
−4.82611e7 | −0.212683 | |||||||||
−5.54459e7 | + | 9.60352e7i | −0.240873 | + | 0.417205i | |||||
0 | 0 | |||||||||
−2.20750e8 | − | 3.82350e8i | −0.932098 | − | 1.61444i | |||||
−3.23041e7 | − | 5.59523e7i | −0.134486 | − | 0.232936i | |||||
0 | 0 | |||||||||
−2.28213e7 | + | 3.95277e7i | −0.0923743 | + | 0.159997i | |||||
−2.14309e8 | −0.855426 | −0.427713 | − | 0.903915i | ||||||
−0.427713 | + | 0.903915i | ||||||||
0 | 0 | |||||||||
1.20636e8 | 0.468334 | |||||||||
5.42724e7 | − | 9.40025e7i | 0.207807 | − | 0.359933i | |||||
0 | 0 | |||||||||
−8.38861e6 | − | 1.45295e7i | −0.0312500 | − | 0.0541266i | |||||
−2.63538e7 | − | 4.56461e7i | −0.0968450 | − | 0.167740i | 0.813532 | − | 0.581520i | ||
−0.910377 | + | 0.413779i | ||||||||
0 | 0 | |||||||||
2.79593e8 | − | 4.84269e8i | 0.999946 | − | 1.73196i | |||||
−3.00787e8 | −1.06133 | |||||||||
0 | 0 | |||||||||
−1.88251e8 | −0.646670 | |||||||||
2.44289e8 | − | 4.23121e8i | 0.828055 | − | 1.43423i | −0.0715077 | − | 0.997440i | ||
0.899562 | − | 0.436793i | ||||||||
0 | 0 | |||||||||
2.33449e8 | + | 4.04346e8i | 0.770604 | + | 1.33473i | |||||
−1.49275e8 | − | 2.58553e8i | −0.486298 | − | 0.842293i | |||||
0 | 0 | |||||||||
8.40224e6 | − | 1.45531e7i | 0.0266639 | − | 0.0461832i | |||||
1.69083e8 | 0.529622 | 0.264811 | − | 0.964300i | ||||||
0.264811 | + | 0.964300i | ||||||||
0 | 0 | |||||||||
−1.99531e8 | −0.609001 | −0.304501 | − | 0.952512i | ||||||
−0.304501 | + | 0.952512i | ||||||||
3.45700e7 | − | 5.98769e7i | 0.104162 | − | 0.180413i | |||||
0 | 0 | |||||||||
1.11962e8 | + | 1.93924e8i | 0.328809 | + | 0.569514i | |||||
5.34919e7 | + | 9.26506e7i | 0.155104 | + | 0.268648i | |||||
0 | 0 | |||||||||
1.77438e8 | − | 3.07331e8i | 0.501611 | − | 0.868816i | −0.498387 | − | 0.866955i | ||
0.999998 | − | 0.00186126i | ||||||||
6.40150e7 | 0.178700 | |||||||||
0 | 0 | |||||||||
−2.03398e8 | −0.553724 | |||||||||
−1.40245e8 | + | 2.42912e8i | −0.377065 | + | 0.653096i | −0.990634 | − | 0.136545i | ||
0.613569 | + | 0.789641i | ||||||||
0 | 0 | |||||||||
7.95244e7 | + | 1.37740e8i | 0.208568 | + | 0.361251i | 0.951264 | − | 0.308379i | ||
−0.742696 | + | 0.669629i | ||||||||
3.17092e7 | + | 5.49220e7i | 0.0821431 | + | 0.142276i | |||||
0 | 0 | |||||||||
8.50882e7 | − | 1.47377e8i | 0.215074 | − | 0.372519i | |||||
5.47822e8 | 1.36790 | |||||||||
0 | 0 | |||||||||
−1.25409e8 | −0.305623 | |||||||||
1.16662e8 | − | 2.02064e8i | 0.280890 | − | 0.486515i | |||||
0 | 0 | |||||||||
3.34044e7 | + | 5.78581e7i | 0.0785170 | + | 0.135995i | |||||
1.72190e8 | + | 2.98242e8i | 0.399918 | + | 0.692679i | 0.993715 | − | 0.111936i | ||
−0.593797 | + | 0.804615i | ||||||||
0 | 0 | |||||||||
−5.03600e8 | + | 8.72260e8i | −1.14211 | + | 1.97819i | |||||
2.70676e8 | 0.606637 | |||||||||
0 | 0 | |||||||||
−2.17326e8 | −0.475723 | |||||||||
−4.44013e8 | + | 7.69052e8i | −0.960608 | + | 1.66382i | |||||
0 | 0 | |||||||||
1.43672e8 | + | 2.48847e8i | 0.303661 | + | 0.525956i | |||||
1.67945e8 | + | 2.90890e8i | 0.350868 | + | 0.607721i | |||||
0 | 0 | |||||||||
7.22574e7 | − | 1.25153e8i | 0.147511 | − | 0.255497i | |||||
−2.83216e8 | −0.571569 | |||||||||
0 | 0 | |||||||||
5.28744e8 | 1.04294 | 0.521472 | − | 0.853269i | ||||||
0.521472 | + | 0.853269i | ||||||||
5.75383e7 | − | 9.96592e7i | 0.112209 | − | 0.194352i | |||||
0 | 0 | |||||||||
−1.89574e8 | − | 3.28351e8i | −0.361420 | − | 0.625997i | |||||
−1.43382e8 | − | 2.48345e8i | −0.270292 | − | 0.468159i | 0.698645 | − | 0.715469i | ||
−0.968937 | + | 0.247310i | ||||||||
0 | 0 | |||||||||
−1.25124e7 | + | 2.16722e7i | −0.0230641 | + | 0.0399482i | −0.877327 | − | 0.479893i | ||
0.854263 | + | 0.519841i | ||||||||
−6.56383e8 | −1.19648 | |||||||||
0 | 0 | |||||||||
−4.69580e8 | −0.837153 | |||||||||
−2.60137e8 | + | 4.50570e8i | −0.458663 | + | 0.794428i | −0.998891 | − | 0.0470910i | ||
0.540227 | + | 0.841519i | ||||||||
0 | 0 | |||||||||
6.60038e7 | + | 1.14322e8i | 0.113842 | + | 0.197180i | |||||
−4.92278e7 | − | 8.52651e7i | −0.0839819 | − | 0.145461i | |||||
0 | 0 | |||||||||
−3.00250e8 | + | 5.20048e8i | −0.501172 | + | 0.868056i | |||||
5.95554e8 | 0.983359 | |||||||||
0 | 0 | |||||||||
−7.87527e8 | −1.27255 | |||||||||
−1.15714e8 | + | 2.00423e8i | −0.184980 | + | 0.320395i | |||||
0 | 0 | |||||||||
1.32588e8 | + | 2.29649e8i | 0.207465 | + | 0.359340i | |||||
−2.24043e8 | − | 3.88054e8i | −0.346853 | − | 0.600768i | |||||
0 | 0 | |||||||||
2.52520e8 | − | 4.37377e8i | 0.382734 | − | 0.662915i | −0.608718 | − | 0.793387i | ||
0.991452 | + | 0.130472i | ||||||||
2.49102e8 | 0.373588 | |||||||||
0 | 0 | |||||||||
2.13736e8 | 0.313881 | |||||||||
4.93078e7 | − | 8.54037e7i | 0.0716571 | − | 0.124114i | |||||
0 | 0 | |||||||||
9.18750e7 | + | 1.59132e8i | 0.130765 | + | 0.226492i | 0.923972 | − | 0.382461i | ||
−0.793206 | + | 0.608953i | ||||||||
3.75356e8 | + | 6.50135e8i | 0.528731 | + | 0.915789i | |||||
0 | 0 | |||||||||
2.02871e8 | − | 3.51383e8i | 0.279926 | − | 0.484846i | |||||
2.14510e8 | 0.292960 | |||||||||
0 | 0 | |||||||||
−5.58786e8 | −0.747681 | |||||||||
−6.95449e7 | + | 1.20455e8i | −0.0921108 | + | 0.159541i | |||||
0 | 0 | |||||||||
1.05249e8 | + | 1.82296e8i | 0.136600 | + | 0.236598i | |||||
−1.43066e8 | − | 2.47797e8i | −0.183816 | − | 0.318378i | 0.759361 | − | 0.650670i | ||
−0.943177 | + | 0.332291i | ||||||||
0 | 0 | |||||||||
1.83182e7 | − | 3.17281e7i | 0.0230672 | − | 0.0399535i | −0.854261 | − | 0.519844i | ||
0.877329 | + | 0.479890i | ||||||||
−5.32541e8 | −0.663918 | |||||||||
0 | 0 | |||||||||
5.57033e7 | 0.0680740 | |||||||||
2.38469e8 | − | 4.13040e8i | 0.288549 | − | 0.499782i | −0.684914 | − | 0.728624i | ||
0.973464 | + | 0.228841i | ||||||||
0 | 0 | |||||||||
1.86083e8 | + | 3.22305e8i | 0.220753 | + | 0.382356i | |||||
2.16218e7 | + | 3.74500e7i | 0.0253990 | + | 0.0439923i | |||||
0 | 0 | |||||||||
8.78898e7 | − | 1.52230e8i | 0.101239 | − | 0.175351i | |||||
3.73983e8 | 0.426600 | 0.213300 | − | 0.976987i | ||||||
0.213300 | + | 0.976987i | ||||||||
0 | 0 | |||||||||
3.50942e8 | 0.392609 | |||||||||
5.04809e8 | − | 8.74356e8i | 0.559303 | − | 0.968742i | |||||
0 | 0 | |||||||||
4.23550e8 | + | 7.33610e8i | 0.460309 | + | 0.797279i | |||||
1.96031e8 | + | 3.39535e8i | 0.211008 | + | 0.365477i | |||||
0 | 0 | |||||||||
2.91624e8 | − | 5.05107e8i | 0.307958 | − | 0.533399i | −0.669957 | − | 0.742400i | ||
0.977916 | + | 0.209000i | ||||||||
−2.90674e8 | −0.304046 | |||||||||
0 | 0 | |||||||||
1.58844e9 | 1.63029 | |||||||||
6.57457e8 | − | 1.13875e9i | 0.668434 | − | 1.15776i | |||||
0 | 0 | |||||||||
−7.38605e8 | − | 1.27930e9i | −0.736939 | − | 1.27642i | −0.953867 | − | 0.300228i | ||
0.216928 | − | 0.976188i | ||||||||
1.14778e8 | + | 1.98802e8i | 0.113451 | + | 0.196503i | |||||
0 | 0 | |||||||||
1.08449e8 | − | 1.87839e8i | 0.105213 | − | 0.182234i | |||||
−9.71732e8 | −0.934011 | |||||||||
0 | 0 | |||||||||
−6.08958e8 | −0.574580 | −0.287290 | − | 0.957844i | ||||||
−0.287290 | + | 0.957844i | ||||||||
4.24036e8 | − | 7.34452e8i | 0.396424 | − | 0.686627i | |||||
0 | 0 | |||||||||
−7.17806e8 | − | 1.24328e9i | −0.658848 | − | 1.14116i | |||||
−4.24357e8 | − | 7.35008e8i | −0.385954 | − | 0.668492i | 0.605947 | − | 0.795505i | ||
−0.991901 | + | 0.127013i | ||||||||
0 | 0 | |||||||||
3.37659e8 | − | 5.84842e8i | 0.301554 | − | 0.522307i | |||||
2.38651e8 | 0.211207 | |||||||||
0 | 0 | |||||||||
1.04036e9 | 0.904221 | |||||||||
−1.26651e8 | + | 2.19367e8i | −0.109090 | + | 0.188950i | −0.915402 | − | 0.402541i | ||
0.806312 | + | 0.591491i | ||||||||
0 | 0 | |||||||||
−5.98943e8 | − | 1.03740e9i | −0.506719 | − | 0.877662i | |||||
7.55856e7 | + | 1.30918e8i | 0.0633779 | + | 0.109774i | |||||
0 | 0 | |||||||||
−2.68345e8 | + | 4.64788e8i | −0.221033 | + | 0.382841i | |||||
−2.75569e9 | −2.24978 | |||||||||
0 | 0 | |||||||||
9.92215e8 | 0.795865 | 0.397932 | − | 0.917415i | ||||||
0.397932 | + | 0.917415i | ||||||||
−4.72710e8 | + | 8.18758e8i | −0.375841 | + | 0.650975i | |||||
0 | 0 | |||||||||
−1.28889e8 | − | 2.23243e8i | −0.100695 | − | 0.174408i | |||||
−4.74376e8 | − | 8.21644e8i | −0.367382 | − | 0.636324i | 0.621774 | − | 0.783197i | ||
−0.989155 | + | 0.146873i | ||||||||
0 | 0 | |||||||||
−7.89524e8 | + | 1.36750e9i | −0.600894 | + | 1.04078i | |||||
2.71706e7 | 0.0205005 | |||||||||
0 | 0 | |||||||||
−6.57104e8 | −0.487296 | |||||||||
−4.49346e8 | + | 7.78290e8i | −0.330370 | + | 0.572217i | |||||
0 | 0 | |||||||||
−3.88383e8 | − | 6.72699e8i | −0.280691 | − | 0.486171i | 0.690864 | − | 0.722985i | ||
−0.971555 | + | 0.236813i | ||||||||
7.78080e8 | + | 1.34767e9i | 0.557546 | + | 0.965698i | |||||
0 | 0 | |||||||||
1.55627e8 | − | 2.69554e8i | 0.109634 | − | 0.189891i | |||||
2.83655e9 | 1.98137 | |||||||||
0 | 0 | |||||||||
1.46183e9 | 1.00399 | |||||||||
−2.05021e8 | + | 3.55107e8i | −0.139628 | + | 0.241842i | |||||
0 | 0 | |||||||||
2.39907e8 | + | 4.15531e8i | 0.160667 | + | 0.278283i | |||||
−3.14943e8 | − | 5.45498e8i | −0.209162 | − | 0.362280i | 0.742289 | − | 0.670080i | ||
−0.951451 | + | 0.307801i | ||||||||
0 | 0 | |||||||||
−5.52425e8 | + | 9.56829e8i | −0.360816 | + | 0.624952i | −0.988095 | − | 0.153842i | ||
0.627279 | + | 0.778795i | ||||||||
−8.31883e8 | −0.538851 | |||||||||
0 | 0 | |||||||||
6.36490e8 | 0.405519 | |||||||||
5.31160e8 | − | 9.19997e8i | 0.335633 | − | 0.581333i | |||||
0 | 0 | |||||||||
3.98808e8 | + | 6.90755e8i | 0.247894 | + | 0.429365i | |||||
9.07674e7 | + | 1.57214e8i | 0.0559599 | + | 0.0969253i | |||||
0 | 0 | |||||||||
−4.08118e8 | + | 7.06881e8i | −0.247541 | + | 0.428753i | |||||
2.85661e8 | 0.171863 | 0.0859313 | − | 0.996301i | ||||||
0.0859313 | + | 0.996301i | ||||||||
0 | 0 | |||||||||
4.76788e8 | 0.282239 | 0.141120 | − | 0.989993i | ||||||
0.141120 | + | 0.989993i | ||||||||
−5.33892e8 | + | 9.24727e8i | −0.313501 | + | 0.543000i | |||||
0 | 0 | |||||||||
−2.02045e8 | − | 3.49952e8i | −0.116747 | − | 0.202211i | |||||
−1.25190e9 | − | 2.16835e9i | −0.717602 | − | 1.24292i | |||||
0 | 0 | |||||||||
−1.25879e9 | + | 2.18029e9i | −0.710112 | + | 1.22995i | 0.254703 | + | 0.967019i | ||
−0.964815 | + | 0.262931i | ||||||||
3.26890e8 | 0.182944 | |||||||||
0 | 0 | |||||||||
−1.68981e9 | −0.930807 | |||||||||
−2.29324e8 | + | 3.97201e8i | −0.125325 | + | 0.217069i | −0.921860 | − | 0.387523i | ||
0.796535 | + | 0.604592i | ||||||||
0 | 0 | |||||||||
1.26886e8 | + | 2.19772e8i | 0.0682578 | + | 0.118226i | |||||
−6.46118e8 | − | 1.11911e9i | −0.344858 | − | 0.597311i | |||||
0 | 0 | |||||||||
−1.38639e8 | + | 2.40130e8i | −0.0728472 | + | 0.126175i | |||||
1.46433e9 | 0.763444 | 0.381722 | − | 0.924277i | ||||||
0.381722 | + | 0.924277i | ||||||||
0 | 0 | |||||||||
−8.80429e8 | −0.451936 | |||||||||
6.86198e8 | − | 1.18853e9i | 0.349514 | − | 0.605377i | |||||
0 | 0 | |||||||||
−1.52214e8 | − | 2.63642e8i | −0.0763411 | − | 0.132227i | |||||
2.48557e9 | + | 4.30513e9i | 1.23704 | + | 2.14262i | |||||
0 | 0 | |||||||||
−6.98299e8 | + | 1.20949e9i | −0.342243 | + | 0.592783i | −0.984849 | − | 0.173414i | ||
0.642606 | + | 0.766197i | ||||||||
2.31773e9 | 1.12728 | |||||||||
0 | 0 | |||||||||
−1.70580e9 | −0.817100 | |||||||||
−1.98110e9 | + | 3.43137e9i | −0.941789 | + | 1.63123i | −0.179733 | + | 0.983715i | ||
−0.762056 | + | 0.647511i | ||||||||
0 | 0 | |||||||||
9.40813e8 | + | 1.62954e9i | 0.440524 | + | 0.763010i | 0.997728 | − | 0.0673653i | ||
−0.557204 | + | 0.830375i | ||||||||
−1.59037e8 | − | 2.75460e8i | −0.0739069 | − | 0.128011i | |||||
0 | 0 | |||||||||
2.98038e8 | − | 5.16217e8i | 0.136433 | − | 0.236310i | |||||
−9.69518e8 | −0.440501 | −0.220250 | − | 0.975443i | ||||||
−0.220250 | + | 0.975443i | ||||||||
0 | 0 | |||||||||
−2.77729e8 | −0.124313 | |||||||||
6.36424e8 | − | 1.10232e9i | 0.282751 | − | 0.489739i | |||||
0 | 0 | |||||||||
6.86522e8 | + | 1.18909e9i | 0.300509 | + | 0.520497i | |||||
−2.30901e8 | − | 3.99933e8i | −0.100326 | − | 0.173769i | |||||
0 | 0 | |||||||||
1.11022e9 | − | 1.92296e9i | 0.475315 | − | 0.823269i | |||||
−1.14268e9 | −0.485624 | |||||||||
0 | 0 | |||||||||
1.43733e9 | 0.601946 | |||||||||
−1.00435e9 | + | 1.73959e9i | −0.417552 | + | 0.723222i | −0.995693 | − | 0.0927156i | ||
0.578140 | + | 0.815937i | ||||||||
0 | 0 | |||||||||
−3.30772e9 | − | 5.72913e9i | −1.35525 | − | 2.34737i | |||||
−2.43473e8 | − | 4.21707e8i | −0.0990343 | − | 0.171532i | |||||
0 | 0 | |||||||||
5.31117e8 | − | 9.19922e8i | 0.212927 | − | 0.368801i | |||||
6.10529e9 | 2.43002 | |||||||||
0 | 0 | |||||||||
3.02884e9 | 1.18830 | 0.594148 | − | 0.804356i | ||||||
0.594148 | + | 0.804356i | ||||||||
−1.93044e8 | + | 3.34363e8i | −0.0751948 | + | 0.130241i | |||||
0 | 0 | |||||||||
4.43567e8 | + | 7.68281e8i | 0.170323 | + | 0.295008i | |||||
2.25862e9 | + | 3.91204e9i | 0.861107 | + | 1.49148i | 0.870861 | + | 0.491529i | ||
−0.00975413 | + | 0.999952i | ||||||||
0 | 0 | |||||||||
6.55401e8 | − | 1.13519e9i | 0.246344 | − | 0.426681i | |||||
−3.53200e9 | −1.31819 | |||||||||
0 | 0 | |||||||||
−5.16865e8 | −0.190191 | |||||||||
5.24061e8 | − | 9.07700e8i | 0.191485 | − | 0.331661i | |||||
0 | 0 | |||||||||
2.32832e9 | + | 4.03277e9i | 0.838862 | + | 1.45295i | 0.890846 | + | 0.454305i | ||
−0.0519839 | + | 0.998648i | ||||||||
1.82571e8 | + | 3.16222e8i | 0.0653185 | + | 0.113135i | |||||
0 | 0 | |||||||||
−8.57236e8 | + | 1.48478e9i | −0.302439 | + | 0.523840i | |||||
−2.88413e9 | −1.01048 | −0.505239 | − | 0.862980i | ||||||
−0.505239 | + | 0.862980i | ||||||||
0 | 0 | |||||||||
1.59448e8 | 0.0550934 | |||||||||
4.82545e8 | − | 8.35792e8i | 0.165581 | − | 0.286795i | |||||
0 | 0 | |||||||||
−4.34179e8 | − | 7.52020e8i | −0.146942 | − | 0.254511i | |||||
−6.60362e8 | − | 1.14378e9i | −0.221957 | − | 0.384442i | 0.733445 | − | 0.679749i | ||
−0.955402 | + | 0.295307i | ||||||||
0 | 0 | |||||||||
5.52077e8 | − | 9.56225e8i | 0.183032 | − | 0.317020i | |||||
−1.34218e8 | −0.0441942 | |||||||||
0 | 0 | |||||||||
−4.21661e8 | −0.136960 | |||||||||
9.13283e8 | − | 1.58185e9i | 0.294632 | − | 0.510318i | |||||
0 | 0 | |||||||||
3.60070e8 | + | 6.23659e8i | 0.114596 | + | 0.198486i | |||||
−2.23674e9 | − | 3.87415e9i | −0.707069 | − | 1.22468i | |||||
0 | 0 | |||||||||
−1.20315e9 | + | 2.08391e9i | −0.375239 | + | 0.649932i | |||||
−5.14654e9 | −1.59435 | −0.797175 | − | 0.603749i | ||||||
−0.797175 | + | 0.603749i | ||||||||
0 | 0 | |||||||||
−2.17050e9 | −0.663444 | −0.331722 | − | 0.943377i | ||||||
−0.331722 | + | 0.943377i | ||||||||
−7.53004e8 | + | 1.30424e9i | −0.228632 | + | 0.396003i | |||||
0 | 0 | |||||||||
−1.95431e9 | − | 3.38497e9i | −0.585523 | − | 1.01416i | |||||
−1.06502e9 | − | 1.84466e9i | −0.316970 | − | 0.549009i | |||||
0 | 0 | |||||||||
−8.15632e8 | + | 1.41272e9i | −0.239552 | + | 0.414916i | |||||
3.73518e9 | 1.08980 | |||||||||
0 | 0 | |||||||||
−2.38841e9 | −0.687729 | |||||||||
3.24050e9 | − | 5.61271e9i | 0.926972 | − | 1.60556i | |||||
0 | 0 | |||||||||
5.32661e8 | + | 9.22595e8i | 0.150388 | + | 0.260479i | |||||
−6.72180e7 | − | 1.16425e8i | −0.0188542 | − | 0.0326565i | |||||
0 | 0 | |||||||||
6.76330e8 | − | 1.17144e9i | 0.187250 | − | 0.324326i | |||||
−5.01915e8 | −0.138060 | |||||||||
0 | 0 | |||||||||
−9.27955e7 | −0.0251963 | −0.0125981 | − | 0.999921i | ||||||
−0.0125981 | + | 0.999921i | ||||||||
−7.98125e8 | + | 1.38239e9i | −0.215314 | + | 0.372936i | |||||
0 | 0 | |||||||||
−2.76560e8 | − | 4.79015e8i | −0.0736534 | − | 0.127571i | |||||
−1.18568e9 | − | 2.05366e9i | −0.313747 | − | 0.543427i | |||||
0 | 0 | |||||||||
2.73518e9 | − | 4.73747e9i | 0.714547 | − | 1.23763i | −0.248588 | − | 0.968609i | ||
0.963134 | − | 0.269022i | ||||||||
1.79139e9 | 0.465006 | |||||||||
0 | 0 | |||||||||
8.55870e8 | 0.219350 | |||||||||
1.36990e9 | − | 2.37274e9i | 0.348867 | − | 0.604255i | |||||
0 | 0 | |||||||||
3.88039e9 | + | 6.72104e9i | 0.975749 | + | 1.69005i | |||||
−1.41950e9 | − | 2.45865e9i | −0.354693 | − | 0.614346i | |||||
0 | 0 | |||||||||
2.56060e8 | − | 4.43509e8i | 0.0631800 | − | 0.109431i | |||||
−4.50060e9 | −1.10351 | −0.551756 | − | 0.834006i | ||||||
−0.551756 | + | 0.834006i | ||||||||
0 | 0 | |||||||||
3.39941e9 | 0.823119 | |||||||||
−8.13592e8 | + | 1.40918e9i | −0.195771 | + | 0.339086i | |||||
0 | 0 | |||||||||
1.12196e9 | + | 1.94330e9i | 0.266625 | + | 0.461809i | |||||
3.06529e9 | + | 5.30923e9i | 0.723922 | + | 1.25387i | 0.959416 | + | 0.281994i | ||
−0.235494 | + | 0.971876i | ||||||||
0 | 0 | |||||||||
4.02690e9 | − | 6.97479e9i | 0.939292 | − | 1.62690i | |||||
1.27239e9 | 0.294960 | |||||||||
0 | 0 | |||||||||
5.07347e8 | 0.116168 | |||||||||
−1.71059e9 | + | 2.96282e9i | −0.389271 | + | 0.674238i | −0.992352 | − | 0.123443i | ||
0.603080 | + | 0.797680i | ||||||||
0 | 0 | |||||||||
−1.14292e9 | − | 1.97960e9i | −0.256916 | − | 0.444991i | 0.708498 | − | 0.705712i | ||
−0.965414 | + | 0.260721i | ||||||||
−6.80706e8 | − | 1.17902e9i | −0.152080 | − | 0.263411i | |||||
0 | 0 | |||||||||
2.19129e9 | − | 3.79542e9i | 0.483624 | − | 0.837661i | |||||
−4.46615e9 | −0.979706 | |||||||||
0 | 0 | |||||||||
−7.03121e9 | −1.52375 | −0.761877 | − | 0.647722i | ||||||
−0.761877 | + | 0.647722i | ||||||||
−5.01636e8 | + | 8.68859e8i | −0.108054 | + | 0.187155i | |||||
0 | 0 | |||||||||
−9.33295e8 | − | 1.61651e9i | −0.198619 | − | 0.344018i | |||||
−2.05846e9 | − | 3.56536e9i | −0.435438 | − | 0.754200i | |||||
0 | 0 | |||||||||
−1.05663e9 | + | 1.83013e9i | −0.220842 | + | 0.382510i | |||||
5.34470e8 | 0.111040 | |||||||||
0 | 0 | |||||||||
2.75504e9 | 0.565570 | |||||||||
−4.47158e8 | + | 7.74500e8i | −0.0912488 | + | 0.158048i | −0.908037 | − | 0.418890i | ||
0.816788 | + | 0.576938i | ||||||||
0 | 0 | |||||||||
−2.22607e9 | − | 3.85567e9i | −0.448886 | − | 0.777493i | |||||
4.02880e9 | + | 6.97808e9i | 0.807594 | + | 1.39879i | |||||
0 | 0 | |||||||||
1.08270e9 | − | 1.87530e9i | 0.214478 | − | 0.371488i | |||||
8.80907e9 | 1.73476 | 0.867379 | − | 0.497649i | ||||||
0.867379 | + | 0.497649i | ||||||||
0 | 0 | |||||||||
−6.70572e9 | −1.30508 | |||||||||
−8.69302e8 | + | 1.50568e9i | −0.168193 | + | 0.291320i | |||||
0 | 0 | |||||||||
3.55210e9 | + | 6.15242e9i | 0.679252 | + | 1.17650i | |||||
4.91595e8 | + | 8.51468e8i | 0.0934574 | + | 0.161873i | 0.908964 | − | 0.416875i | ||
−0.815506 | + | 0.578748i | ||||||||
0 | 0 | |||||||||
−1.02236e9 | + | 1.77078e9i | −0.192107 | + | 0.332739i | −0.945948 | − | 0.324317i | ||
0.753841 | + | 0.657056i | ||||||||
2.29875e9 | 0.429441 | |||||||||
0 | 0 | |||||||||
2.68712e9 | 0.496202 | |||||||||
3.11682e9 | − | 5.39848e9i | 0.572226 | − | 0.991124i | |||||
0 | 0 | |||||||||
−1.78806e9 | − | 3.09701e9i | −0.324505 | − | 0.562059i | 0.656907 | − | 0.753971i | ||
−0.981412 | + | 0.191913i | ||||||||
−5.78059e8 | − | 1.00123e9i | −0.104306 | − | 0.180663i | |||||
0 | 0 | |||||||||
−1.13286e9 | + | 1.96218e9i | −0.202080 | + | 0.350013i | |||||
−5.30108e9 | −0.940199 | |||||||||
0 | 0 | |||||||||
1.22567e9 | 0.214913 | 0.107457 | − | 0.994210i | ||||||
0.107457 | + | 0.994210i | ||||||||
2.11497e9 | − | 3.66324e9i | 0.368736 | − | 0.638670i | |||||
0 | 0 | |||||||||
−4.60306e8 | − | 7.97274e8i | −0.0793441 | − | 0.137428i | |||||
3.80166e9 | + | 6.58468e9i | 0.651592 | + | 1.12859i | 0.982737 | + | 0.185010i | ||
−0.331145 | + | 0.943580i | ||||||||
0 | 0 | |||||||||
−2.87850e9 | + | 4.98571e9i | −0.487808 | + | 0.844908i | −0.999902 | − | 0.0140213i | ||
0.512094 | + | 0.858930i | ||||||||
−3.03318e9 | −0.511125 | |||||||||
0 | 0 | |||||||||
−2.29411e9 | −0.382250 | |||||||||
3.57345e8 | − | 6.18940e8i | 0.0592079 | − | 0.102551i | |||||
0 | 0 | |||||||||
3.52977e9 | + | 6.11374e9i | 0.578317 | + | 1.00167i | |||||
1.00099e8 | + | 1.73377e8i | 0.0163088 | + | 0.0282476i | |||||
0 | 0 | |||||||||
−2.62553e9 | + | 4.54756e9i | −0.423018 | + | 0.732688i | |||||
8.92377e9 | 1.42979 | |||||||||
0 | 0 | |||||||||
−2.41912e9 | −0.383313 | −0.191657 | − | 0.981462i | ||||||
−0.191657 | + | 0.981462i | ||||||||
−1.87832e9 | + | 3.25335e9i | −0.295978 | + | 0.512650i | |||||
0 | 0 | |||||||||
2.08109e9 | + | 3.60456e9i | 0.324324 | + | 0.561746i | |||||
−2.54794e9 | − | 4.41316e9i | −0.394895 | − | 0.683978i | |||||
0 | 0 | |||||||||
1.84734e9 | − | 3.19969e9i | 0.283178 | − | 0.490479i | |||||
1.05606e9 | 0.160997 | |||||||||
0 | 0 | |||||||||
−7.87645e8 | −0.118768 | |||||||||
−3.95891e9 | + | 6.85703e9i | −0.593707 | + | 1.02833i | 0.400021 | + | 0.916506i | ||
−0.993728 | + | 0.111825i | ||||||||
0 | 0 | |||||||||
5.35854e9 | + | 9.28126e9i | 0.794891 | + | 1.37679i | 0.922908 | + | 0.385020i | ||
−0.128017 | + | 0.991772i | ||||||||
2.40200e9 | + | 4.16038e9i | 0.354382 | + | 0.613808i | |||||
0 | 0 | |||||||||
2.38222e9 | − | 4.12612e9i | 0.347670 | − | 0.602182i | |||||
−8.06643e9 | −1.17089 | −0.585446 | − | 0.810712i | ||||||
−0.585446 | + | 0.810712i | ||||||||
0 | 0 | |||||||||
−4.55875e9 | −0.654620 | |||||||||
−3.15011e9 | + | 5.45614e9i | −0.449913 | + | 0.779272i | |||||
0 | 0 | |||||||||
9.25715e8 | + | 1.60338e9i | 0.130801 | + | 0.226554i | |||||
5.00680e9 | + | 8.67202e9i | 0.703661 | + | 1.21878i | 0.967172 | + | 0.254121i | ||
−0.263511 | + | 0.964656i | ||||||||
0 | 0 | |||||||||
−4.41894e9 | + | 7.65382e9i | −0.614431 | + | 1.06423i | |||||
2.12140e9 | 0.293400 | |||||||||
0 | 0 | |||||||||
−3.58469e9 | −0.490525 | |||||||||
7.05570e9 | − | 1.22208e10i | 0.960376 | − | 1.66342i | 0.238821 | − | 0.971064i | ||
0.721555 | − | 0.692357i | ||||||||
0 | 0 | |||||||||
−4.81075e9 | − | 8.33246e9i | −0.647899 | − | 1.12219i | −0.983624 | − | 0.180234i | ||
0.335725 | − | 0.941960i | ||||||||
−2.02016e9 | − | 3.49902e9i | −0.270634 | − | 0.468752i | |||||
0 | 0 | |||||||||
9.96406e8 | − | 1.72583e9i | 0.132083 | − | 0.228775i | |||||
−1.40162e10 | −1.84822 | |||||||||
0 | 0 | |||||||||
−5.51080e9 | −0.719075 | |||||||||
8.54943e8 | − | 1.48080e9i | 0.110974 | − | 0.192212i | |||||
0 | 0 | |||||||||
−3.94463e8 | − | 6.83230e8i | −0.0506692 | − | 0.0877617i | |||||
−6.40941e8 | − | 1.11014e9i | −0.0819011 | − | 0.141857i | |||||
0 | 0 | |||||||||
−5.84290e9 | + | 1.01202e10i | −0.738884 | + | 1.27978i | 0.214115 | + | 0.976808i | ||
−0.952998 | + | 0.302975i | ||||||||
1.47000e9 | 0.184930 | |||||||||
0 | 0 | |||||||||
6.00569e9 | 0.747738 | |||||||||
−5.55719e9 | + | 9.62534e9i | −0.688327 | + | 1.19222i | 0.284051 | + | 0.958809i | ||
−0.972379 | + | 0.233409i | ||||||||
0 | 0 | |||||||||
−8.59710e9 | − | 1.48906e10i | −1.05392 | − | 1.82544i | |||||
−1.62297e9 | − | 2.81106e9i | −0.197938 | − | 0.342838i | |||||
0 | 0 | |||||||||
8.58041e8 | − | 1.48617e9i | 0.103577 | − | 0.179400i | |||||
1.61450e10 | 1.93894 | 0.969472 | − | 0.245201i | ||||||
0.969472 | + | 0.245201i | ||||||||
0 | 0 | |||||||||
1.05126e10 | 1.24967 | |||||||||
−2.23515e9 | + | 3.87139e9i | −0.264345 | + | 0.457859i | |||||
0 | 0 | |||||||||
5.56359e8 | + | 9.63642e8i | 0.0651322 | + | 0.112812i | |||||
−7.77803e9 | − | 1.34719e10i | −0.905946 | − | 1.56915i | |||||
0 | 0 | |||||||||
6.98902e8 | − | 1.21053e9i | 0.0805829 | − | 0.139574i | −0.822918 | − | 0.568161i | ||
0.903500 | + | 0.428587i | ||||||||
1.68398e9 | 0.193182 | |||||||||
0 | 0 | |||||||||
−2.28905e9 | −0.259955 | |||||||||
1.50267e9 | − | 2.60269e9i | 0.169791 | − | 0.294087i | |||||
0 | 0 | |||||||||
4.37122e9 | + | 7.57117e9i | 0.488976 | + | 0.846931i | |||||
−1.46546e8 | − | 2.53825e8i | −0.0163110 | − | 0.0282514i | |||||
0 | 0 | |||||||||
−2.13016e9 | + | 3.68955e9i | −0.234731 | + | 0.406565i | |||||
1.34244e9 | 0.147191 | 0.0735956 | − | 0.997288i | ||||||
0.0735956 | + | 0.997288i | ||||||||
0 | 0 | |||||||||
1.86523e10 | 2.02483 | |||||||||
2.22813e8 | − | 3.85924e8i | 0.0240678 | − | 0.0416867i | |||||
0 | 0 | |||||||||
−1.90775e9 | − | 3.30432e9i | −0.204035 | − | 0.353399i | |||||
−2.24525e8 | − | 3.88889e8i | −0.0238944 | − | 0.0413864i | |||||
0 | 0 | |||||||||
7.93153e9 | − | 1.37378e10i | 0.835786 | − | 1.44762i | −0.0576025 | − | 0.998340i | ||
0.893389 | − | 0.449285i | ||||||||
2.97732e9 | 0.312192 | |||||||||
0 | 0 | |||||||||
3.45949e8 | 0.0359196 | |||||||||
−4.47748e9 | + | 7.75522e9i | −0.462616 | + | 0.801274i | |||||
0 | 0 | |||||||||
−3.99466e9 | − | 6.91896e9i | −0.408704 | − | 0.707896i | |||||
−7.03118e8 | − | 1.21784e9i | −0.0715868 | − | 0.123992i | |||||
0 | 0 | |||||||||
1.49593e9 | − | 2.59103e9i | 0.150826 | − | 0.261238i | |||||
−2.14766e9 | −0.215483 | −0.107742 | − | 0.994179i | ||||||
−0.107742 | + | 0.994179i | ||||||||
0 | 0 | |||||||||
−5.14412e9 | −0.511137 | |||||||||
1.40377e9 | − | 2.43140e9i | 0.138808 | − | 0.240423i | |||||
0 | 0 | |||||||||
−4.03848e9 | − | 6.99485e9i | −0.395487 | − | 0.685004i | |||||
−2.44357e9 | − | 4.23239e9i | −0.238145 | − | 0.412480i | |||||
0 | 0 | |||||||||
5.14336e9 | − | 8.90856e9i | 0.496451 | − | 0.859879i | −0.503540 | − | 0.863972i | ||
0.999992 | + | 0.00409288i | ||||||||
6.77680e9 | 0.650976 | |||||||||
0 | 0 | |||||||||
3.13649e9 | 0.298411 | |||||||||
−2.29279e9 | + | 3.97123e9i | −0.217097 | + | 0.376023i | |||||
0 | 0 | |||||||||
1.60210e9 | + | 2.77493e9i | 0.150254 | + | 0.260248i | 0.931321 | − | 0.364200i | ||
−0.781067 | + | 0.624448i | ||||||||
−2.33299e9 | − | 4.04086e9i | −0.217759 | − | 0.377170i | |||||
0 | 0 | |||||||||
−1.16270e9 | + | 2.01385e9i | −0.107496 | + | 0.186189i | |||||
4.46351e8 | 0.0410715 | |||||||||
0 | 0 | |||||||||
1.29766e10 | 1.18279 | 0.591394 | − | 0.806383i | ||||||
0.591394 | + | 0.806383i | ||||||||
6.35375e9 | − | 1.10050e10i | 0.576394 | − | 0.998343i | |||||
0 | 0 | |||||||||
−5.25966e9 | − | 9.10999e9i | −0.472654 | − | 0.818661i | |||||
3.62353e9 | + | 6.27614e9i | 0.324094 | + | 0.561348i | 0.981329 | − | 0.192339i | ||
−0.657234 | + | 0.753686i | ||||||||
0 | 0 | |||||||||
−5.10143e9 | + | 8.83593e9i | −0.452007 | + | 0.782898i | |||||
−1.18177e10 | −1.04219 | |||||||||
0 | 0 | |||||||||
1.83645e9 | 0.160444 | |||||||||
1.50012e9 | − | 2.59828e9i | 0.130449 | − | 0.225944i | |||||
0 | 0 | |||||||||
4.47123e9 | + | 7.74440e9i | 0.385201 | + | 0.667188i | 0.991797 | − | 0.127822i | ||
−0.606596 | + | 0.795010i | ||||||||
−8.67592e8 | − | 1.50271e9i | −0.0743966 | − | 0.128859i | |||||
0 | 0 | |||||||||
−3.88693e9 | + | 6.73236e9i | −0.330223 | + | 0.571962i | |||||
1.57692e10 | 1.33350 | |||||||||
0 | 0 | |||||||||
1.36108e10 | 1.14037 | 0.570187 | − | 0.821515i | ||||||
0.570187 | + | 0.821515i | ||||||||
−2.43583e9 | + | 4.21899e9i | −0.203145 | + | 0.351857i | |||||
0 | 0 | |||||||||
−3.39229e9 | − | 5.87562e9i | −0.280314 | − | 0.485519i | |||||
−1.10122e10 | − | 1.90738e10i | −0.905794 | − | 1.56888i | −0.819848 | − | 0.572582i | ||
−0.0859464 | − | 0.996300i | ||||||||
0 | 0 | |||||||||
−3.33921e9 | + | 5.78368e9i | −0.272149 | + | 0.471377i | |||||
−1.14849e10 | −0.931752 | |||||||||
0 | 0 | |||||||||
−6.78971e9 | −0.545821 | |||||||||
1.67789e10 | − | 2.90619e10i | 1.34270 | − | 2.32563i | |||||
0 | 0 | |||||||||
−5.17112e9 | − | 8.95663e9i | −0.410055 | − | 0.710236i | 0.584840 | − | 0.811148i | ||
−0.994895 | + | 0.100912i | ||||||||
−2.70127e9 | − | 4.67873e9i | −0.213231 | − | 0.369327i | |||||
0 | 0 | |||||||||
9.54605e8 | − | 1.65342e9i | 0.0746729 | − | 0.129337i | |||||
−3.65169e9 | −0.284358 | −0.142179 | − | 0.989841i | ||||||
−0.142179 | + | 0.989841i | ||||||||
0 | 0 | |||||||||
−7.94152e9 | −0.612841 | |||||||||
4.16146e9 | − | 7.20786e9i | 0.319690 | − | 0.553720i | |||||
0 | 0 | |||||||||
1.01321e9 | + | 1.75493e9i | 0.0771385 | + | 0.133608i | |||||
9.13662e9 | + | 1.58251e10i | 0.692476 | + | 1.19940i | |||||
0 | 0 | |||||||||
−8.42241e8 | + | 1.45880e9i | −0.0632642 | + | 0.109577i | |||||
−9.58309e9 | −0.716608 | |||||||||
0 | 0 | |||||||||
1.20937e9 | 0.0896299 | |||||||||
−1.54077e10 | + | 2.66869e10i | −1.13683 | + | 1.96904i | |||||
0 | 0 | |||||||||
−1.19537e10 | − | 2.07044e10i | −0.874158 | − | 1.51409i | −0.857657 | − | 0.514222i | ||
−0.0165008 | − | 0.999864i | ||||||||
2.14676e9 | + | 3.71830e9i | 0.156294 | + | 0.270709i | |||||
0 | 0 | |||||||||
−1.10228e10 | + | 1.90920e10i | −0.795419 | + | 1.37771i | |||||
−2.26817e10 | −1.62951 | |||||||||
0 | 0 | |||||||||
9.43617e9 | 0.671954 | |||||||||
3.96886e9 | − | 6.87427e9i | 0.281381 | − | 0.487366i | |||||
0 | 0 | |||||||||
3.78168e9 | + | 6.55006e9i | 0.265760 | + | 0.460309i | |||||
1.36082e10 | + | 2.35700e10i | 0.952128 | + | 1.64913i | 0.740807 | + | 0.671718i | ||
0.211321 | + | 0.977417i | ||||||||
0 | 0 | |||||||||
3.57540e9 | − | 6.19277e9i | 0.247977 | − | 0.429508i | |||||
−2.06223e9 | −0.142404 | |||||||||
0 | 0 | |||||||||
−7.59002e9 | −0.519556 | |||||||||
−8.87267e8 | + | 1.53679e9i | −0.0604714 | + | 0.104740i | |||||
0 | 0 | |||||||||
1.40959e10 | + | 2.44149e10i | 0.952375 | + | 1.64956i | |||||
6.31619e9 | + | 1.09400e10i | 0.424896 | + | 0.735942i | |||||
0 | 0 | |||||||||
1.08682e8 | − | 1.88243e8i | 0.00724801 | − | 0.0125539i | |||||
2.09999e10 | 1.39443 | 0.697216 | − | 0.716861i | ||||||
0.697216 | + | 0.716861i | ||||||||
0 | 0 | |||||||||
−1.21414e10 | −0.799276 | −0.399638 | − | 0.916673i | ||||||
−0.399638 | + | 0.916673i | ||||||||
−2.62842e9 | + | 4.55255e9i | −0.172285 | + | 0.298407i | |||||
0 | 0 | |||||||||
3.59477e9 | + | 6.22632e9i | 0.233607 | + | 0.404619i | |||||
5.43248e9 | + | 9.40933e9i | 0.351517 | + | 0.608845i | |||||
0 | 0 | |||||||||
−4.79234e9 | + | 8.30057e9i | −0.307447 | + | 0.532514i | |||||
−6.21413e9 | −0.396957 | |||||||||
0 | 0 | |||||||||
1.24493e10 | 0.788489 | |||||||||
−5.66101e9 | + | 9.80516e9i | −0.357020 | + | 0.618377i | −0.987462 | − | 0.157860i | ||
0.630441 | + | 0.776237i | ||||||||
0 | 0 | |||||||||
2.91399e9 | + | 5.04718e9i | 0.182217 | + | 0.315609i | 0.942635 | − | 0.333825i | ||
−0.760418 | + | 0.649434i | ||||||||
−1.24502e9 | − | 2.15643e9i | −0.0775228 | − | 0.134273i | |||||
0 | 0 | |||||||||
1.13462e10 | − | 1.96522e10i | 0.700520 | − | 1.21334i | |||||
−2.11794e10 | −1.30210 | −0.651050 | − | 0.759034i | ||||||
−0.651050 | + | 0.759034i | ||||||||
0 | 0 | |||||||||
−1.77492e10 | −1.08203 | −0.541013 | − | 0.841014i | ||||||
−0.541013 | + | 0.841014i | ||||||||
5.84733e9 | − | 1.01279e10i | 0.354964 | − | 0.614815i | |||||
0 | 0 | |||||||||
1.64017e9 | + | 2.84085e9i | 0.0987317 | + | 0.171008i | |||||
2.49194e9 | + | 4.31617e9i | 0.149376 | + | 0.258727i | |||||
0 | 0 | |||||||||
5.01716e9 | − | 8.68997e9i | 0.298233 | − | 0.516554i | |||||
3.83851e9 | 0.227217 | |||||||||
0 | 0 | |||||||||
−5.03909e9 | −0.295800 | |||||||||
−1.31911e10 | + | 2.28476e10i | −0.771104 | + | 1.33559i | 0.165855 | + | 0.986150i | ||
−0.936959 | + | 0.349441i | ||||||||
0 | 0 | |||||||||
5.60981e9 | + | 9.71647e9i | 0.325209 | + | 0.563278i | |||||
4.41940e9 | + | 7.65463e9i | 0.255136 | + | 0.441908i | |||||
0 | 0 | |||||||||
−3.32753e9 | + | 5.76345e9i | −0.190513 | + | 0.329977i | |||||
3.52439e10 | 2.00949 | |||||||||
0 | 0 | |||||||||
−1.75556e10 | −0.992715 | |||||||||
2.54596e9 | − | 4.40973e9i | 0.143372 | − | 0.248328i | |||||
0 | 0 | |||||||||
−4.24928e9 | − | 7.35997e9i | −0.237328 | − | 0.411065i | |||||
−1.87584e10 | − | 3.24905e10i | −1.04338 | − | 1.80719i | |||||
0 | 0 | |||||||||
−1.33903e10 | + | 2.31927e10i | −0.738701 | + | 1.27947i | 0.214379 | + | 0.976750i | ||
−0.953080 | + | 0.302717i | ||||||||
6.38092e9 | 0.350575 | |||||||||
0 | 0 | |||||||||
1.45228e9 | 0.0791392 | |||||||||
6.44399e9 | − | 1.11613e10i | 0.349721 | − | 0.605735i | −0.636479 | − | 0.771294i | ||
0.986200 | + | 0.165560i | ||||||||
0 | 0 | |||||||||
−2.13794e9 | − | 3.70302e9i | −0.115085 | − | 0.199333i | 0.802729 | − | 0.596344i | ||
−0.917814 | + | 0.397011i | ||||||||
3.26495e9 | + | 5.65505e9i | 0.175038 | + | 0.303174i | |||||
0 | 0 | |||||||||
1.14265e9 | − | 1.97912e9i | 0.0607626 | − | 0.105244i | |||||
2.63998e10 | 1.39818 | 0.699089 | − | 0.715035i | ||||||
0.699089 | + | 0.715035i | ||||||||
0 | 0 | |||||||||
9.88231e9 | 0.519161 | |||||||||
1.90715e9 | − | 3.30328e9i | 0.0997867 | − | 0.172836i | |||||
0 | 0 | |||||||||
4.27113e9 | + | 7.39782e9i | 0.221679 | + | 0.383959i | |||||
−6.23635e9 | − | 1.08017e10i | −0.322375 | − | 0.558370i | |||||
0 | 0 | |||||||||
−1.64283e9 | + | 2.84547e9i | −0.0842423 | + | 0.145912i | |||||
−3.23271e9 | −0.165105 | |||||||||
0 | 0 | |||||||||
−2.00304e10 | −1.01484 | |||||||||
3.01736e9 | − | 5.22622e9i | 0.152265 | − | 0.263730i | |||||
0 | 0 | |||||||||
−7.19624e9 | − | 1.24642e10i | −0.360252 | − | 0.623975i | 0.627750 | − | 0.778415i | ||
−0.988002 | + | 0.154440i | ||||||||
1.00703e10 | + | 1.74423e10i | 0.502125 | + | 0.869706i | |||||
0 | 0 | |||||||||
1.30756e9 | − | 2.26476e9i | 0.0646803 | − | 0.112030i | |||||
−2.86878e10 | −1.41345 | −0.706727 | − | 0.707487i | ||||||
−0.706727 | + | 0.707487i | ||||||||
0 | 0 | |||||||||
1.10176e10 | 0.538550 | 0.269275 | − | 0.963063i | ||||||
0.269275 | + | 0.963063i | ||||||||
−6.75923e9 | + | 1.17073e10i | −0.329090 | + | 0.570000i | |||||
0 | 0 | |||||||||
1.83459e9 | + | 3.17761e9i | 0.0886180 | + | 0.153491i | |||||
8.77534e9 | + | 1.51993e10i | 0.422213 | + | 0.731294i | 0.996156 | − | 0.0876014i | ||
−0.573943 | + | 0.818895i | ||||||||
0 | 0 | |||||||||
−7.17571e9 | + | 1.24287e10i | −0.342538 | + | 0.593293i | |||||
2.03017e9 | 0.0965311 | |||||||||
0 | 0 | |||||||||
−1.03379e10 | −0.487703 | |||||||||
7.47322e9 | − | 1.29440e10i | 0.351178 | − | 0.608259i | |||||
0 | 0 | |||||||||
−4.12619e9 | − | 7.14677e9i | −0.192384 | − | 0.333218i | |||||
1.10911e9 | + | 1.92104e9i | 0.0515108 | + | 0.0892193i | |||||
0 | 0 | |||||||||
5.85733e9 | − | 1.01452e10i | 0.269918 | − | 0.467512i | |||||
−9.79907e9 | −0.449807 | |||||||||
0 | 0 | |||||||||
2.09841e10 | 0.955770 | |||||||||
−3.52172e9 | + | 6.09979e9i | −0.159783 | + | 0.276753i | |||||
0 | 0 | |||||||||
−5.48959e9 | − | 9.50824e9i | −0.247144 | − | 0.428066i | |||||
−2.36994e10 | − | 4.10486e10i | −1.06284 | − | 1.84089i | |||||
0 | 0 | |||||||||
8.42225e9 | − | 1.45878e10i | 0.374803 | − | 0.649177i | −0.615495 | − | 0.788141i | ||
0.990297 | + | 0.138964i | ||||||||
−2.43542e9 | −0.107963 | |||||||||
0 | 0 | |||||||||
3.97691e10 | 1.74945 | |||||||||
7.36357e9 | − | 1.27541e10i | 0.322682 | − | 0.558901i | −0.658359 | − | 0.752704i | ||
0.981040 | + | 0.193803i | ||||||||
0 | 0 | |||||||||
3.30824e9 | + | 5.73005e9i | 0.143863 | + | 0.249178i | |||||
5.58639e9 | + | 9.67592e9i | 0.242003 | + | 0.419161i | |||||
0 | 0 | |||||||||
9.27091e9 | − | 1.60577e10i | 0.398555 | − | 0.690318i | |||||
2.48899e10 | 1.06593 | |||||||||
0 | 0 | |||||||||
7.11506e9 | 0.302395 | 0.151197 | − | 0.988504i | ||||||
0.151197 | + | 0.988504i | ||||||||
−6.82319e9 | + | 1.18181e10i | −0.288888 | + | 0.500369i | |||||
0 | 0 | |||||||||
1.58488e10 | + | 2.74510e10i | 0.665946 | + | 1.15345i | |||||
−6.19989e9 | − | 1.07385e10i | −0.259524 | − | 0.449509i | |||||
0 | 0 | |||||||||
1.66355e10 | − | 2.88136e10i | 0.691099 | − | 1.19702i | |||||
1.50530e10 | 0.622995 | |||||||||
0 | 0 | |||||||||
−2.54459e9 | −0.104520 | |||||||||
−1.69702e10 | + | 2.93933e10i | −0.694437 | + | 1.20280i | 0.275933 | + | 0.961177i | ||
−0.970370 | + | 0.241624i | ||||||||
0 | 0 | |||||||||
5.20860e9 | + | 9.02156e9i | 0.211542 | + | 0.366402i | |||||
−2.38430e9 | − | 4.12973e9i | −0.0964730 | − | 0.167096i | |||||
0 | 0 | |||||||||
−3.87807e9 | + | 6.71702e9i | −0.155741 | + | 0.269751i | |||||
1.07771e10 | 0.431181 | |||||||||
0 | 0 | |||||||||
−3.78364e10 | −1.50252 | −0.751261 | − | 0.660005i | ||||||
−0.751261 | + | 0.660005i | ||||||||
−1.11092e9 | + | 1.92416e9i | −0.0439513 | + | 0.0761258i | |||||
0 | 0 | |||||||||
−5.09139e9 | − | 8.81854e9i | −0.199935 | − | 0.346298i | |||||
8.44461e9 | + | 1.46265e10i | 0.330382 | + | 0.572238i | 0.982587 | − | 0.185805i | ||
−0.652205 | + | 0.758043i | ||||||||
0 | 0 | |||||||||
1.83772e10 | − | 3.18303e10i | 0.713657 | − | 1.23609i | |||||
1.09844e10 | 0.424984 | |||||||||
0 | 0 | |||||||||
−3.69442e9 | −0.141882 | |||||||||
5.84561e9 | − | 1.01249e10i | 0.223668 | − | 0.387405i | −0.732251 | − | 0.681035i | ||
0.955919 | + | 0.293630i | ||||||||
0 | 0 | |||||||||
−6.53134e9 | − | 1.13126e10i | −0.248068 | − | 0.429666i | |||||
−8.88176e9 | − | 1.53837e10i | −0.336098 | − | 0.582139i | |||||
0 | 0 | |||||||||
−4.57072e9 | + | 7.91672e9i | −0.171694 | + | 0.297383i | |||||
−5.10551e10 | −1.91079 | −0.955397 | − | 0.295323i | ||||||
−0.955397 | + | 0.295323i | ||||||||
0 | 0 | |||||||||
−6.73981e10 | −2.50401 | |||||||||
5.74930e9 | − | 9.95808e9i | 0.212820 | − | 0.368615i | |||||
0 | 0 | |||||||||
8.03480e9 | + | 1.39167e10i | 0.295254 | + | 0.511395i | |||||
−1.48032e10 | − | 2.56400e10i | −0.541990 | − | 0.938755i | |||||
0 | 0 | |||||||||
5.79464e9 | − | 1.00366e10i | 0.210618 | − | 0.364800i | |||||
−5.29235e10 | −1.91662 | |||||||||
0 | 0 | |||||||||
−3.89556e9 | −0.140056 | |||||||||
5.60202e9 | − | 9.70298e9i | 0.200678 | − | 0.347584i | |||||
0 | 0 | |||||||||
4.34365e9 | + | 7.52343e9i | 0.154476 | + | 0.267561i | 0.932868 | − | 0.360218i | ||
−0.778392 | + | 0.627779i | ||||||||
−4.24894e9 | − | 7.35937e9i | −0.150562 | − | 0.260782i | |||||
0 | 0 | |||||||||
2.44212e10 | − | 4.22987e10i | 0.859143 | − | 1.48808i | |||||
−3.91347e10 | −1.37181 | −0.685906 | − | 0.727690i | ||||||
−0.685906 | + | 0.727690i | ||||||||
0 | 0 | |||||||||
−8.46384e9 | −0.294559 | |||||||||
1.21153e10 | − | 2.09844e10i | 0.420126 | − | 0.727679i | |||||
0 | 0 | |||||||||
1.54436e9 | + | 2.67490e9i | 0.0531708 | + | 0.0920945i | |||||
−1.36255e10 | − | 2.36001e10i | −0.467437 | − | 0.809624i | 0.531871 | − | 0.846825i | ||
−0.999308 | + | 0.0372010i | ||||||||
0 | 0 | |||||||||
−5.74305e8 | + | 9.94725e8i | −0.0195615 | + | 0.0338816i | |||||
7.09708e9 | 0.240873 | |||||||||
0 | 0 | |||||||||
3.61379e10 | 1.21779 | |||||||||
3.56677e9 | − | 6.17782e9i | 0.119767 | − | 0.207443i | −0.799908 | − | 0.600122i | ||
0.919675 | + | 0.392680i | ||||||||
0 | 0 | |||||||||
1.25981e10 | + | 2.18205e10i | 0.420028 | + | 0.727509i | |||||
−5.24321e9 | − | 9.08150e9i | −0.174192 | − | 0.301709i | |||||
0 | 0 | |||||||||
−1.41280e10 | + | 2.44704e10i | −0.466049 | + | 0.807220i | |||||
1.92784e10 | 0.633702 | |||||||||
0 | 0 | |||||||||
−1.99378e10 | −0.650760 | −0.325380 | − | 0.945583i | ||||||
−0.325380 | + | 0.945583i | ||||||||
−2.06746e9 | + | 3.58094e9i | −0.0672428 | + | 0.116468i | |||||
0 | 0 | |||||||||
−4.19249e9 | − | 7.26160e9i | −0.135400 | − | 0.234520i | |||||
2.21925e10 | + | 3.84385e10i | 0.714208 | + | 1.23704i | |||||
0 | 0 | |||||||||
6.37020e9 | − | 1.10335e10i | 0.203573 | − | 0.352598i | −0.746104 | − | 0.665829i | ||
0.949677 | + | 0.313231i | ||||||||
3.72531e10 | 1.18633 | |||||||||
0 | 0 |
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 54.8.c.a.19.1 | 6 | ||
3.2 | odd | 2 | 18.8.c.a.7.2 | ✓ | 6 | ||
4.3 | odd | 2 | 432.8.i.a.289.1 | 6 | |||
9.2 | odd | 6 | 162.8.a.f.1.1 | 3 | |||
9.4 | even | 3 | inner | 54.8.c.a.37.1 | 6 | ||
9.5 | odd | 6 | 18.8.c.a.13.2 | yes | 6 | ||
9.7 | even | 3 | 162.8.a.e.1.3 | 3 | |||
12.11 | even | 2 | 144.8.i.a.97.2 | 6 | |||
36.23 | even | 6 | 144.8.i.a.49.2 | 6 | |||
36.31 | odd | 6 | 432.8.i.a.145.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
18.8.c.a.7.2 | ✓ | 6 | 3.2 | odd | 2 | ||
18.8.c.a.13.2 | yes | 6 | 9.5 | odd | 6 | ||
54.8.c.a.19.1 | 6 | 1.1 | even | 1 | trivial | ||
54.8.c.a.37.1 | 6 | 9.4 | even | 3 | inner | ||
144.8.i.a.49.2 | 6 | 36.23 | even | 6 | |||
144.8.i.a.97.2 | 6 | 12.11 | even | 2 | |||
162.8.a.e.1.3 | 3 | 9.7 | even | 3 | |||
162.8.a.f.1.1 | 3 | 9.2 | odd | 6 | |||
432.8.i.a.145.1 | 6 | 36.31 | odd | 6 | |||
432.8.i.a.289.1 | 6 | 4.3 | odd | 2 |