Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [171,4,Mod(53,171)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(171, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([9, 11]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("171.53");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 171.y (of order , degree , minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | |
Analytic rank: | |
Dimension: | |
Relative dimension: | over |
Twist minimal: | yes |
Sato-Tate group: |
Embedding invariants
Embedding label | 53.16 | ||
Character | 171.53 | ||
Dual form | 171.4.y.a.71.16 |
-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 .
3.36331 | + | 1.22414i | 1.18911 | + | 0.432800i | 0.859410 | − | 0.511286i | ||
0.329698 | + | 0.944086i | ||||||||
0 | 0 | |||||||||
3.68495 | + | 3.09204i | 0.460619 | + | 0.386505i | |||||
−13.3019 | − | 15.8526i | −1.18976 | − | 1.41790i | −0.885079 | − | 0.465440i | ||
−0.304677 | − | 0.952456i | ||||||||
0 | 0 | |||||||||
−7.77429 | + | 13.4655i | −0.419772 | + | 0.727067i | −0.995916 | − | 0.0902812i | ||
0.576144 | + | 0.817348i | ||||||||
−5.70811 | − | 9.88673i | −0.252265 | − | 0.436936i | |||||
0 | 0 | |||||||||
−25.3325 | − | 69.6004i | −0.801084 | − | 2.20096i | |||||
0.507963 | − | 0.293273i | 0.0139233 | − | 0.00803864i | −0.493022 | − | 0.870017i | ||
0.506946 | + | 0.861978i | ||||||||
0 | 0 | |||||||||
−46.3397 | − | 8.17093i | −0.988639 | − | 0.174324i | −0.344131 | − | 0.938922i | ||
−0.644508 | + | 0.764598i | ||||||||
−42.6310 | + | 35.7717i | −0.813830 | + | 0.682884i | |||||
0 | 0 | |||||||||
−13.7778 | − | 78.1379i | −0.215278 | − | 1.22090i | |||||
10.6943 | − | 29.3824i | 0.152574 | − | 0.419193i | −0.839732 | − | 0.543000i | ||
0.992306 | + | 0.123807i | ||||||||
0 | 0 | |||||||||
−31.0413 | − | 76.7818i | −0.374808 | − | 0.927102i | |||||
− | 99.5459i | − | 1.11296i | |||||||
0 | 0 | |||||||||
2.06744 | − | 0.364546i | 0.0200355 | − | 0.00353280i | |||||
−15.0014 | + | 17.8779i | −0.136000 | + | 0.162078i | −0.829746 | − | 0.558141i | ||
0.693746 | + | 0.720220i | ||||||||
0 | 0 | |||||||||
−52.6577 | + | 298.637i | −0.421261 | + | 2.38909i | |||||
−145.852 | − | 84.2078i | −1.10015 | − | 0.635173i | |||||
0 | 0 | |||||||||
−70.2837 | + | 25.5812i | −0.474370 | + | 0.172657i | |||||
267.617 | − | 97.4045i | 1.71363 | − | 0.623709i | 0.716369 | − | 0.697721i | ||
0.997257 | + | 0.0740120i | ||||||||
0 | 0 | |||||||||
86.4832 | + | 49.9311i | 0.501059 | + | 0.289287i | 0.729151 | − | 0.684353i | ||
−0.228092 | + | 0.973640i | ||||||||
33.4537 | − | 189.726i | 0.184808 | − | 1.04810i | |||||
0 | 0 | |||||||||
71.9366 | − | 85.7307i | 0.362854 | − | 0.432432i | |||||
316.875 | − | 55.8736i | 1.53033 | − | 0.269839i | |||||
0 | 0 | |||||||||
− | 53.8378i | − | 0.239213i | −0.992821 | − | 0.119606i | ||||
0.992821 | − | 0.119606i | ||||||||
−10.4094 | − | 296.240i | −0.0444374 | − | 1.26464i | |||||
0 | 0 | |||||||||
−80.8014 | + | 222.000i | −0.319396 | + | 0.877533i | |||||
58.8231 | + | 333.603i | 0.224064 | + | 1.27073i | 0.864466 | + | 0.502691i | ||
−0.640402 | + | 0.768040i | ||||||||
0 | 0 | |||||||||
−199.580 | + | 167.468i | −0.707808 | + | 0.593921i | −0.923983 | − | 0.382433i | ||
0.216175 | + | 0.976355i | ||||||||
2.77863 | + | 0.489948i | 0.00952033 | + | 0.00167869i | |||||
0 | 0 | |||||||||
−72.3393 | + | 41.7651i | −0.231866 | + | 0.133868i | |||||
−210.832 | − | 579.255i | −0.654318 | − | 1.79772i | −0.601147 | − | 0.799138i | ||
−0.0531704 | − | 0.998585i | ||||||||
0 | 0 | |||||||||
50.6207 | + | 87.6777i | 0.147582 | + | 0.255620i | |||||
−542.678 | + | 939.946i | −1.53493 | + | 2.65857i | |||||
0 | 0 | |||||||||
−145.495 | − | 173.394i | −0.388009 | − | 0.462411i | |||||
116.390 | + | 97.6631i | 0.301650 | + | 0.253114i | 0.781031 | − | 0.624493i | ||
−0.479381 | + | 0.877607i | ||||||||
0 | 0 | |||||||||
−11.4060 | − | 4.15144i | −0.0279633 | − | 0.0101778i | |||||
177.506 | 0.423576 | |||||||||
0 | 0 | |||||||||
1019.31 | 2.30763 | |||||||||
−425.794 | − | 154.976i | −0.939554 | − | 0.341970i | −0.173564 | − | 0.984823i | ||
−0.765990 | + | 0.642853i | ||||||||
0 | 0 | |||||||||
−479.767 | − | 402.572i | −1.00701 | − | 0.844985i | −0.0190729 | − | 0.999818i | ||
−0.987941 | + | 0.154833i | ||||||||
229.747 | + | 273.801i | 0.470611 | + | 0.560852i | |||||
0 | 0 | |||||||||
27.3934 | − | 47.4467i | 0.0535027 | − | 0.0926694i | |||||
486.874 | + | 843.291i | 0.929066 | + | 1.60919i | |||||
0 | 0 | |||||||||
−309.378 | − | 850.010i | −0.564128 | − | 1.54993i | −0.813527 | − | 0.581528i | ||
0.249399 | − | 0.968401i | ||||||||
130.260 | − | 75.2055i | 0.232299 | − | 0.134118i | |||||
0 | 0 | |||||||||
1134.14 | + | 199.980i | 1.93652 | + | 0.341460i | |||||
186.080 | − | 156.140i | 0.311037 | − | 0.260991i | −0.473883 | − | 0.880588i | ||
0.784921 | + | 0.619596i | ||||||||
0 | 0 | |||||||||
59.3899 | + | 336.817i | 0.0952200 | + | 0.540020i | 0.994680 | + | 0.103016i | ||
−0.899460 | + | 0.437004i | ||||||||
65.9052 | − | 181.073i | 0.103531 | − | 0.284450i | |||||
0 | 0 | |||||||||
123.027 | − | 378.918i | 0.185686 | − | 0.571906i | |||||
9.11995i | 0.0134976i | |||||||||
0 | 0 | |||||||||
551.538 | − | 97.2510i | 0.785479 | − | 0.138501i | 0.233497 | − | 0.972357i | ||
0.551982 | + | 0.833856i | ||||||||
−1055.41 | + | 1257.79i | −1.47499 | + | 1.75782i | |||||
0 | 0 | |||||||||
−210.537 | + | 1194.02i | −0.283536 | + | 1.60801i | |||||
−518.748 | − | 299.499i | −0.686024 | − | 0.396076i | 0.116097 | − | 0.993238i | ||
−0.802121 | + | 0.597162i | ||||||||
0 | 0 | |||||||||
−608.041 | + | 221.309i | −0.775898 | + | 0.282404i | |||||
−876.255 | + | 318.931i | −1.09871 | + | 0.399898i | |||||
0 | 0 | |||||||||
−5.79902 | − | 3.34806i | −0.00702474 | − | 0.00405574i | |||||
207.685 | − | 1177.84i | 0.247355 | − | 1.40282i | −0.567605 | − | 0.823301i | ||
0.814960 | − | 0.579518i | ||||||||
0 | 0 | |||||||||
470.284 | − | 560.462i | 0.541748 | − | 0.645631i | |||||
−110.559 | + | 19.4944i | −0.125288 | + | 0.0220917i | |||||
0 | 0 | |||||||||
− | 2206.30i | − | 2.42088i | |||||||
−804.281 | + | 1513.42i | −0.868605 | + | 1.63446i | |||||
0 | 0 | |||||||||
71.1316 | − | 195.432i | 0.0744569 | − | 0.204569i | −0.896881 | − | 0.442272i | ||
0.971338 | + | 0.237704i | ||||||||
62.9230 | + | 356.854i | 0.0648590 | + | 0.367834i | |||||
0 | 0 | |||||||||
−1117.44 | + | 937.642i | −1.11744 | + | 0.937642i | |||||
1472.31 | + | 259.609i | 1.45050 | + | 0.255762i | 0.842724 | − | 0.538345i | ||
0.607777 | + | 0.794108i | ||||||||
0 | 0 | |||||||||
−592.237 | + | 341.928i | −0.566552 | + | 0.327099i | −0.755771 | − | 0.654836i | ||
0.189219 | + | 0.981935i | ||||||||
183.728 | + | 504.788i | 0.173231 | + | 0.475948i | |||||
0 | 0 | |||||||||
271.903 | + | 470.949i | 0.249146 | + | 0.431534i | |||||
403.890 | − | 699.557i | 0.364911 | − | 0.632044i | −0.623851 | − | 0.781543i | ||
0.988762 | + | 0.149499i | ||||||||
0 | 0 | |||||||||
202.419 | + | 241.233i | 0.177873 | + | 0.211981i | 0.847613 | − | 0.530615i | ||
−0.669740 | + | 0.742596i | ||||||||
−33.2799 | − | 27.9251i | −0.0288465 | − | 0.0242051i | |||||
0 | 0 | |||||||||
1159.28 | + | 421.942i | 0.978048 | + | 0.355980i | |||||
−397.509 | −0.330925 | −0.165462 | − | 0.986216i | ||||||
−0.165462 | + | 0.986216i | ||||||||
0 | 0 | |||||||||
482.957 | 0.391617 | |||||||||
1287.33 | + | 468.551i | 1.03040 | + | 0.375033i | |||||
0 | 0 | |||||||||
−1242.36 | − | 1042.47i | −0.969227 | − | 0.813278i | |||||
312.507 | + | 372.432i | 0.240735 | + | 0.286897i | |||||
0 | 0 | |||||||||
−665.328 | + | 1152.38i | −0.499871 | + | 0.865802i | |||||
−1120.80 | − | 1941.28i | −0.831739 | − | 1.44061i | |||||
0 | 0 | |||||||||
164.297 | + | 451.403i | 0.118987 | + | 0.326913i | |||||
3194.40 | − | 1844.29i | 2.28573 | − | 1.31967i | |||||
0 | 0 | |||||||||
1404.21 | + | 247.599i | 0.981127 | + | 0.172999i | 0.641134 | − | 0.767429i | ||
0.339993 | + | 0.940428i | ||||||||
−1030.43 | + | 864.632i | −0.711546 | + | 0.597058i | |||||
0 | 0 | |||||||||
605.198 | + | 3432.25i | 0.408303 | + | 2.31560i | |||||
621.100 | − | 1706.46i | 0.414242 | − | 1.13812i | −0.540670 | − | 0.841235i | ||
0.954913 | − | 0.296887i | ||||||||
0 | 0 | |||||||||
1275.23 | + | 178.939i | 0.831400 | + | 0.116661i | |||||
− | 3237.57i | − | 2.08719i | |||||||
0 | 0 | |||||||||
−351.540 | + | 61.9861i | −0.221650 | + | 0.0390828i | |||||
−71.1041 | + | 84.7386i | −0.0443419 | + | 0.0528446i | −0.787760 | − | 0.615983i | ||
0.743418 | + | 0.668827i | ||||||||
0 | 0 | |||||||||
−307.402 | + | 1743.37i | −0.187579 | + | 1.06382i | 0.735017 | + | 0.678049i | ||
−0.922596 | + | 0.385767i | ||||||||
1340.43 | + | 773.899i | 0.809194 | + | 0.467188i | |||||
0 | 0 | |||||||||
816.982 | − | 297.357i | 0.482814 | − | 0.175730i | |||||
−25.9352 | + | 9.43963i | −0.0151665 | + | 0.00552015i | |||||
0 | 0 | |||||||||
−5103.92 | − | 2946.75i | −2.92315 | − | 1.68768i | |||||
−212.566 | + | 1205.52i | −0.120494 | + | 0.683353i | |||||
0 | 0 | |||||||||
166.469 | − | 198.390i | 0.0924570 | − | 0.110186i | |||||
−1037.46 | + | 182.932i | −0.570417 | + | 0.100580i | −0.451415 | − | 0.892314i | ||
−0.119002 | + | 0.992894i | ||||||||
0 | 0 | |||||||||
− | 1020.14i | − | 0.549789i | −0.961474 | − | 0.274895i | ||||
0.961474 | − | 0.274895i | ||||||||
−581.934 | + | 745.175i | −0.310533 | + | 0.397643i | |||||
0 | 0 | |||||||||
−11.1641 | + | 30.6732i | −0.00584176 | + | 0.0160501i | |||||
−358.853 | − | 2035.16i | −0.185960 | − | 1.05463i | |||||
0 | 0 | |||||||||
2296.68 | − | 1927.14i | 1.16748 | − | 0.979634i | 0.167502 | − | 0.985872i | ||
0.999981 | + | 0.00623754i | ||||||||
1974.04 | + | 348.077i | 0.993963 | + | 0.175263i | |||||
0 | 0 | |||||||||
−3452.63 | + | 1993.38i | −1.70597 | + | 0.984940i | |||||
−124.110 | − | 340.988i | −0.0607529 | − | 0.166917i | |||||
0 | 0 | |||||||||
−773.278 | − | 1339.36i | −0.371582 | − | 0.643599i | 0.618227 | − | 0.785999i | ||
−0.989809 | + | 0.142401i | ||||||||
−814.753 | + | 1411.19i | −0.387936 | + | 0.671925i | |||||
0 | 0 | |||||||||
−1378.08 | − | 1642.33i | −0.644336 | − | 0.767889i | |||||
−3156.36 | − | 2648.50i | −1.46255 | − | 1.22723i | −0.922730 | − | 0.385448i | ||
−0.539822 | − | 0.841779i | ||||||||
0 | 0 | |||||||||
16.0952 | + | 5.85818i | 0.00732600 | + | 0.00266645i | |||||
−2315.94 | −1.04485 | |||||||||
0 | 0 | |||||||||
−1253.26 | −0.555583 | |||||||||
−3385.01 | − | 1232.04i | −1.48761 | − | 0.541448i | −0.534794 | − | 0.844982i | ||
−0.952820 | + | 0.303535i | ||||||||
0 | 0 | |||||||||
−3611.91 | − | 3030.75i | −1.56020 | − | 1.30916i | |||||
−29.9144 | − | 35.6505i | −0.0128118 | − | 0.0152685i | |||||
0 | 0 | |||||||||
2140.36 | − | 3707.20i | 0.901272 | − | 1.56105i | |||||
389.679 | + | 674.943i | 0.162715 | + | 0.281830i | 0.935841 | − | 0.352421i | ||
−0.773127 | + | 0.634252i | ||||||||
0 | 0 | |||||||||
296.501 | + | 814.631i | 0.121761 | + | 0.334536i | 0.985566 | − | 0.169290i | ||
−0.863805 | + | 0.503826i | ||||||||
2267.79 | − | 1309.31i | 0.923627 | − | 0.533256i | |||||
0 | 0 | |||||||||
262.383 | + | 46.2653i | 0.105126 | + | 0.0185365i | |||||
−853.467 | + | 716.144i | −0.339179 | + | 0.284605i | |||||
0 | 0 | |||||||||
−3.18474 | − | 18.0615i | −0.00124541 | − | 0.00706305i | |||||
1014.18 | − | 2786.43i | 0.393438 | − | 1.08096i | |||||
0 | 0 | |||||||||
−4557.69 | + | 4105.56i | −1.74026 | + | 1.56762i | |||||
3746.70i | 1.41938i | 0.704514 | + | 0.709690i | ||||||
−0.704514 | + | 0.709690i | ||||||||
0 | 0 | |||||||||
1602.36 | − | 282.539i | 0.597617 | − | 0.105376i | 0.133347 | − | 0.991069i | ||
0.464271 | + | 0.885693i | ||||||||
478.475 | − | 570.224i | 0.177075 | − | 0.211029i | |||||
0 | 0 | |||||||||
−84.5681 | + | 479.610i | −0.0308193 | + | 0.174785i | |||||
319.858 | + | 184.670i | 0.115680 | + | 0.0667878i | 0.556724 | − | 0.830698i | ||
−0.441044 | + | 0.897486i | ||||||||
0 | 0 | |||||||||
2623.17 | − | 954.754i | 0.934429 | − | 0.340104i | 0.170465 | − | 0.985364i | ||
0.763963 | + | 0.645259i | ||||||||
3253.11 | − | 1184.04i | 1.15015 | − | 0.418620i | |||||
0 | 0 | |||||||||
4634.04 | + | 2675.47i | 1.61411 | + | 0.931907i | |||||
−768.933 | + | 4360.84i | −0.265855 | + | 1.50774i | |||||
0 | 0 | |||||||||
4506.00 | − | 5370.04i | 1.53518 | − | 1.82956i | |||||
−2410.45 | + | 425.027i | −0.815261 | + | 0.143752i | |||||
0 | 0 | |||||||||
3733.46i | 1.24456i | |||||||||
−38.2858 | − | 29.8988i | −0.0126712 | − | 0.00989541i | |||||
0 | 0 | |||||||||
674.084 | − | 1852.03i | 0.219933 | − | 0.604261i | −0.779831 | − | 0.625990i | ||
0.999764 | + | 0.0217291i | ||||||||
126.914 | + | 719.767i | 0.0411156 | + | 0.233178i | |||||
0 | 0 | |||||||||
2214.76 | − | 1858.41i | 0.707468 | − | 0.593636i | |||||
5309.59 | + | 936.224i | 1.68424 | + | 0.296976i | |||||
0 | 0 | |||||||||
−1344.69 | + | 776.358i | −0.420662 | + | 0.242869i | |||||
385.492 | + | 1059.13i | 0.119765 | + | 0.329052i | |||||
0 | 0 | |||||||||
−29.1941 | − | 50.5656i | −0.00894666 | − | 0.0154961i | |||||
−735.653 | + | 1274.19i | −0.223916 | + | 0.387834i | |||||
0 | 0 | |||||||||
3862.31 | + | 4602.93i | 1.15982 | + | 1.38222i | 0.910352 | + | 0.413835i | ||
0.249467 | + | 0.968383i | ||||||||
2294.67 | + | 1925.45i | 0.684459 | + | 0.574329i | |||||
0 | 0 | |||||||||
−1336.95 | − | 486.608i | −0.393506 | − | 0.143224i | |||||
−2018.84 | −0.590287 | −0.295143 | − | 0.955453i | ||||||
−0.295143 | + | 0.955453i | ||||||||
0 | 0 | |||||||||
4532.55 | 1.30794 | 0.653972 | − | 0.756519i | ||||||
0.653972 | + | 0.756519i | ||||||||
1624.33 | + | 591.209i | 0.465675 | + | 0.169492i | |||||
0 | 0 | |||||||||
−2490.60 | − | 2089.86i | −0.704809 | − | 0.591405i | |||||
−2069.78 | − | 2466.67i | −0.581957 | − | 0.693550i | 0.392082 | − | 0.919930i | ||
−0.974039 | + | 0.226381i | ||||||||
0 | 0 | |||||||||
−6378.22 | + | 11047.4i | −1.77051 | + | 3.06661i | |||||
−1089.84 | − | 1887.65i | −0.300603 | − | 0.520660i | |||||
0 | 0 | |||||||||
595.148 | + | 1635.16i | 0.162091 | + | 0.445342i | |||||
−4014.76 | + | 2317.92i | −1.08658 | + | 0.627339i | −0.932664 | − | 0.360745i | ||
−0.153918 | + | 0.988084i | ||||||||
0 | 0 | |||||||||
−6641.51 | − | 1171.08i | −1.77517 | − | 0.313011i | −0.812356 | − | 0.583162i | ||
−0.962818 | + | 0.270151i | ||||||||
−3648.38 | + | 3061.36i | −0.969120 | + | 0.813188i | |||||
0 | 0 | |||||||||
−523.147 | − | 2966.92i | −0.137259 | − | 0.778432i | |||||
716.565 | − | 1968.75i | 0.186856 | − | 0.513382i | |||||
0 | 0 | |||||||||
811.062 | + | 3811.68i | 0.208934 | + | 0.981908i | |||||
− | 1140.05i | − | 0.291908i | |||||||
0 | 0 | |||||||||
13001.4 | − | 2292.50i | 3.28913 | − | 0.579963i | |||||
−2630.37 | + | 3134.75i | −0.661463 | + | 0.788301i | −0.987595 | − | 0.157023i | ||
0.326132 | + | 0.945324i | ||||||||
0 | 0 | |||||||||
−2.37703 | + | 13.4808i | −0.000590683 | + | 0.00334993i | |||||
4419.68 | + | 2551.70i | 1.09179 | + | 0.630347i | |||||
0 | 0 | |||||||||
−4935.94 | + | 1796.54i | −1.20506 | + | 0.438608i | |||||
5250.22 | − | 1910.92i | 1.27432 | − | 0.463814i | 0.385769 | − | 0.922595i | ||
0.888549 | + | 0.458781i | ||||||||
0 | 0 | |||||||||
724.951 | + | 418.551i | 0.173924 | + | 0.100415i | |||||
−813.382 | + | 4612.92i | −0.194015 | + | 1.10031i | |||||
0 | 0 | |||||||||
4177.90 | − | 4979.03i | 0.985158 | − | 1.17407i | |||||
7263.49 | − | 1280.75i | 1.70299 | − | 0.300283i | 0.764251 | − | 0.644918i | ||
0.938737 | + | 0.344636i | ||||||||
0 | 0 | |||||||||
− | 3144.19i | − | 0.728852i | |||||||
4069.93 | + | 2162.89i | 0.938133 | + | 0.498553i | |||||
0 | 0 | |||||||||
1488.22 | − | 4088.86i | 0.339207 | − | 0.931965i | |||||
−177.720 | − | 1007.90i | −0.0402816 | − | 0.228448i | 0.958020 | − | 0.286700i | ||
−0.998302 | + | 0.0582520i | ||||||||
0 | 0 | |||||||||
−4082.96 | + | 3426.01i | −0.915212 | + | 0.767954i | −0.973103 | − | 0.230369i | ||
0.0578917 | + | 0.998323i | ||||||||
−2443.23 | − | 430.807i | −0.544641 | − | 0.0960349i | |||||
0 | 0 | |||||||||
−342.877 | + | 197.960i | −0.0755984 | + | 0.0436468i | |||||
60.8338 | + | 167.140i | 0.0133397 | + | 0.0366505i | |||||
0 | 0 | |||||||||
2776.61 | + | 4809.22i | 0.602274 | + | 1.04317i | 0.992476 | + | 0.122440i | ||
−0.390201 | + | 0.920730i | ||||||||
−3168.02 | + | 5487.17i | −0.683472 | + | 1.18381i | |||||
0 | 0 | |||||||||
−2361.16 | − | 2813.92i | −0.503952 | − | 0.600586i | |||||
5678.68 | + | 4764.98i | 1.20556 | + | 1.01158i | 0.999454 | + | 0.0330525i | ||
0.206104 | + | 0.978530i | ||||||||
0 | 0 | |||||||||
3476.62 | + | 1265.39i | 0.730260 | + | 0.265793i | 0.680275 | − | 0.732957i | ||
0.0499849 | + | 0.998750i | ||||||||
1168.49 | 0.244144 | |||||||||
0 | 0 | |||||||||
−98.7834 | −0.0204237 | |||||||||
−4949.42 | − | 1801.44i | −1.01796 | − | 0.370508i | |||||
0 | 0 | |||||||||
3014.62 | + | 2529.57i | 0.613600 | + | 0.514872i | |||||
−13558.8 | − | 16158.7i | −2.74552 | − | 3.27198i | |||||
0 | 0 | |||||||||
−822.603 | + | 1424.79i | −0.164860 | + | 0.285546i | |||||
158.920 | + | 275.257i | 0.0316867 | + | 0.0548830i | 0.881434 | − | 0.472307i | ||
−0.849747 | + | 0.527190i | ||||||||
0 | 0 | |||||||||
3207.09 | + | 8811.41i | 0.632963 | + | 1.73905i | |||||
−532.280 | + | 307.312i | −0.104521 | + | 0.0603451i | |||||
0 | 0 | |||||||||
−3713.24 | − | 654.744i | −0.721819 | − | 0.127276i | |||||
841.237 | − | 705.882i | 0.162709 | − | 0.136529i | |||||
0 | 0 | |||||||||
−703.437 | − | 3989.39i | −0.134702 | − | 0.763935i | |||||
1248.80 | − | 3431.06i | 0.237949 | − | 0.653759i | |||||
0 | 0 | |||||||||
−5571.89 | + | 3483.38i | −1.05122 | + | 0.657190i | |||||
12960.5i | 2.43317i | |||||||||
0 | 0 | |||||||||
2868.16 | − | 505.735i | 0.533208 | − | 0.0940189i | 0.0994398 | − | 0.995044i | ||
0.433768 | + | 0.901025i | ||||||||
−28.1993 | + | 33.6066i | −0.00521689 | + | 0.00621725i | |||||
0 | 0 | |||||||||
1284.39 | − | 7284.15i | 0.235318 | − | 1.33455i | |||||
−4209.45 | − | 2430.33i | −0.767512 | − | 0.443123i | 0.0644743 | − | 0.997919i | ||
−0.831986 | + | 0.554796i | ||||||||
0 | 0 | |||||||||
−4039.58 | + | 1470.29i | −0.729491 | + | 0.265513i | −0.679950 | − | 0.733259i | ||
−0.0495418 | + | 0.998772i | ||||||||
10083.5 | − | 3670.10i | 1.81225 | − | 0.659605i | |||||
0 | 0 | |||||||||
2333.09 | + | 1347.01i | 0.415338 | + | 0.239795i | |||||
710.113 | − | 4027.25i | 0.125817 | − | 0.713542i | −0.855003 | − | 0.518623i | ||
0.980819 | − | 0.194919i | ||||||||
0 | 0 | |||||||||
107.373 | − | 127.963i | 0.0188456 | − | 0.0224593i | |||||
−1116.54 | + | 196.875i | −0.195051 | + | 0.0343927i | |||||
0 | 0 | |||||||||
− | 1298.78i | − | 0.224776i | |||||||
−2588.00 | + | 90.9378i | −0.445821 | + | 0.0156654i | |||||
0 | 0 | |||||||||
4880.28 | − | 13408.5i | 0.832951 | − | 2.28851i | |||||
−961.207 | − | 5451.27i | −0.163302 | − | 0.926129i | |||||
0 | 0 | |||||||||
2962.47 | − | 2485.81i | 0.498704 | − | 0.418463i | |||||
9439.01 | + | 1664.35i | 1.58173 | + | 0.278902i | |||||
0 | 0 | |||||||||
−4107.97 | + | 2371.74i | −0.682158 | + | 0.393844i | −0.800668 | − | 0.599109i | ||
0.118509 | + | 0.992953i | ||||||||
−985.498 | − | 2707.63i | −0.162910 | − | 0.447592i | |||||
0 | 0 | |||||||||
−7373.65 | − | 12771.5i | −1.20799 | − | 2.09230i | |||||
−9359.52 | + | 16211.2i | −1.52646 | + | 2.64391i | |||||
0 | 0 | |||||||||
3482.36 | + | 4150.11i | 0.562897 | + | 0.670834i | 0.970157 | − | 0.242478i | ||
−0.407260 | + | 0.913312i | ||||||||
46.9619 | + | 39.4057i | 0.00755738 | + | 0.00634139i | |||||
0 | 0 | |||||||||
−2924.90 | − | 1064.58i | −0.466544 | − | 0.169808i | |||||
58.5737 | 0.00930189 | |||||||||
0 | 0 | |||||||||
−6907.33 | −1.08735 | |||||||||
2794.94 | + | 1017.27i | 0.438061 | + | 0.159441i | |||||
0 | 0 | |||||||||
−9876.62 | − | 8287.47i | −1.53460 | − | 1.28768i | |||||
−4198.08 | − | 5003.07i | −0.649466 | − | 0.774003i | 0.336368 | − | 0.941731i | ||
−0.985833 | + | 0.167728i | ||||||||
0 | 0 | |||||||||
2007.68 | − | 3477.41i | 0.307934 | − | 0.533357i | −0.669977 | − | 0.742382i | ||
0.977910 | + | 0.209026i | ||||||||
−8437.88 | − | 14614.8i | −1.28864 | − | 2.23199i | |||||
0 | 0 | |||||||||
−38.6481 | − | 106.185i | −0.00585213 | − | 0.0160786i | |||||
2038.50 | − | 1176.93i | 0.307361 | − | 0.177455i | −0.338384 | − | 0.941008i | ||
0.645745 | + | 0.763553i | ||||||||
0 | 0 | |||||||||
−4950.43 | − | 872.894i | −0.740117 | − | 0.130503i | |||||
4407.24 | − | 3698.12i | 0.656133 | − | 0.550561i | |||||
0 | 0 | |||||||||
484.381 | + | 2747.06i | 0.0715094 | + | 0.405550i | |||||
730.862 | − | 2008.03i | 0.107447 | − | 0.295208i | −0.874304 | − | 0.485378i | ||
0.981751 | + | 0.190170i | ||||||||
0 | 0 | |||||||||
−4931.88 | + | 4766.81i | −0.719038 | + | 0.694971i | |||||
3102.81i | 0.450498i | |||||||||
0 | 0 | |||||||||
3465.94 | − | 611.139i | 0.499079 | − | 0.0880011i | |||||
4549.41 | − | 5421.78i | 0.652403 | − | 0.777504i | |||||
0 | 0 | |||||||||
548.074 | − | 3108.28i | 0.0779543 | − | 0.442101i | −0.920701 | − | 0.390268i | ||
0.998656 | − | 0.0518331i | ||||||||
1603.63 | + | 925.856i | 0.227160 | + | 0.131151i | |||||
0 | 0 | |||||||||
−3747.13 | + | 1363.85i | −0.526498 | + | 0.191630i | |||||
−2219.93 | + | 807.989i | −0.310655 | + | 0.113069i | |||||
0 | 0 | |||||||||
−6283.68 | − | 3627.89i | −0.872270 | − | 0.503605i | −0.00416822 | − | 0.999991i | ||
−0.868102 | + | 0.496386i | ||||||||
11.3987 | − | 64.6451i | 0.00157597 | − | 0.00893775i | |||||
0 | 0 | |||||||||
−4523.49 | + | 5390.88i | −0.620428 | + | 0.739398i | |||||
−13197.2 | + | 2327.01i | −1.80289 | + | 0.317897i | |||||
0 | 0 | |||||||||
5263.86i | 0.713420i | 0.934215 | + | 0.356710i | ||||||
−0.934215 | + | 0.356710i | ||||||||
−7643.31 | + | 3090.03i | −1.03182 | + | 0.417145i | |||||
0 | 0 | |||||||||
−4586.50 | + | 12601.3i | −0.614308 | + | 1.68780i | |||||
−976.746 | − | 5539.40i | −0.130312 | − | 0.739035i | −0.978010 | − | 0.208556i | ||
0.847699 | − | 0.530478i | ||||||||
0 | 0 | |||||||||
144.575 | − | 121.312i | 0.0191382 | − | 0.0160588i | |||||
5735.09 | + | 1011.25i | 0.756239 | + | 0.133345i | |||||
0 | 0 | |||||||||
866.401 | − | 500.217i | 0.113363 | − | 0.0654502i | |||||
−2418.52 | − | 6644.84i | −0.315229 | − | 0.866084i | −0.991579 | − | 0.129504i | ||
0.676350 | − | 0.736580i | ||||||||
0 | 0 | |||||||||
364.867 | + | 631.968i | 0.0471921 | + | 0.0817392i | |||||
577.897 | − | 1000.95i | 0.0744597 | − | 0.128968i | |||||
0 | 0 | |||||||||
849.717 | + | 1012.65i | 0.108650 | + | 0.129484i | |||||
−8878.16 | − | 7449.66i | −1.13091 | − | 0.948945i | |||||
0 | 0 | |||||||||
9183.64 | + | 3342.57i | 1.16099 | + | 0.422566i | 0.849452 | − | 0.527667i | ||
0.311540 | + | 0.950233i | ||||||||
9991.27 | 1.25833 | |||||||||
0 | 0 | |||||||||
24060.3 | 3.00754 | |||||||||
4793.19 | + | 1744.58i | 0.596909 | + | 0.217257i | 0.622765 | − | 0.782409i | ||
−0.0258567 | + | 0.999666i | ||||||||
0 | 0 | |||||||||
−3599.62 | − | 3020.44i | −0.444937 | − | 0.373347i | |||||
4622.68 | + | 5509.10i | 0.569275 | + | 0.678435i | |||||
0 | 0 | |||||||||
−7924.45 | + | 13725.5i | −0.968679 | + | 1.67780i | |||||
−15.7892 | − | 27.3476i | −0.00192295 | − | 0.00333064i | |||||
0 | 0 | |||||||||
−16.0667 | − | 44.1429i | −0.00194242 | − | 0.00533674i | 0.938718 | − | 0.344687i | ||
−0.940660 | + | 0.339350i | ||||||||
21728.7 | − | 12545.1i | 2.61733 | − | 1.51112i | |||||
0 | 0 | |||||||||
−3239.62 | − | 571.233i | −0.387390 | − | 0.0683073i | |||||
5397.08 | − | 4528.69i | 0.643034 | − | 0.539569i | |||||
0 | 0 | |||||||||
2152.49 | + | 12207.4i | 0.254607 | + | 1.44395i | |||||
−3100.47 | + | 8518.47i | −0.365416 | + | 1.00397i | |||||
0 | 0 | |||||||||
−92.1666 | − | 147.426i | −0.0107847 | − | 0.0172508i | |||||
− | 4773.84i | − | 0.556605i | −0.960494 | − | 0.278302i | ||||
0.960494 | − | 0.278302i | ||||||||
0 | 0 | |||||||||
864.150 | − | 152.373i | 0.100038 | − | 0.0176394i | −0.123405 | − | 0.992356i | ||
0.223443 | + | 0.974717i | ||||||||
4534.31 | − | 5403.78i | 0.523049 | − | 0.623345i | |||||
0 | 0 | |||||||||
301.200 | − | 1708.19i | 0.0344990 | − | 0.195653i | |||||
8211.53 | + | 4740.93i | 0.937218 | + | 0.541103i | |||||
0 | 0 | |||||||||
9150.67 | − | 3330.57i | 1.03708 | − | 0.377465i | |||||
3651.37 | − | 1328.99i | 0.412373 | − | 0.150092i | |||||
0 | 0 | |||||||||
16711.7 | + | 9648.51i | 1.87421 | + | 1.08208i | |||||
−592.556 | + | 3360.55i | −0.0662237 | + | 0.375573i | 0.933626 | + | 0.358249i | ||
−0.999850 | + | 0.0173246i | ||||||||
0 | 0 | |||||||||
5080.87 | − | 6055.15i | 0.563905 | − | 0.672036i | −0.406463 | − | 0.913667i | ||
0.970368 | + | 0.241631i | ||||||||
−5472.98 | + | 965.035i | −0.605326 | + | 0.106735i | |||||
0 | 0 | |||||||||
1514.82i | 0.166392i | |||||||||
1838.36 | + | 596.878i | 0.201237 | + | 0.0653376i | |||||
0 | 0 | |||||||||
5891.95 | − | 16188.0i | 0.640564 | − | 1.75994i | −0.00938327 | − | 0.999956i | ||
0.649947 | − | 0.759979i | ||||||||
24.0624 | + | 136.465i | 0.00260712 | + | 0.0147857i | |||||
0 | 0 | |||||||||
−4034.02 | + | 3384.94i | −0.434115 | + | 0.364265i | |||||
6847.95 | + | 1207.48i | 0.734438 | + | 0.129501i | 0.528343 | − | 0.849031i | ||
0.206095 | + | 0.978532i | ||||||||
0 | 0 | |||||||||
−21434.4 | + | 12375.2i | −2.28334 | + | 1.31829i | |||||
7355.50 | + | 20209.1i | 0.780926 | + | 2.14558i | |||||
0 | 0 | |||||||||
425.928 | + | 737.730i | 0.0449179 | + | 0.0778001i | |||||
−1530.82 | + | 2651.46i | −0.160899 | + | 0.278686i | −0.935192 | − | 0.354142i | ||
0.774292 | + | 0.632828i | ||||||||
0 | 0 | |||||||||
127.717 | + | 152.207i | 0.0133347 | + | 0.0158916i | |||||
−1464.80 | − | 1229.11i | −0.152430 | − | 0.127904i | |||||
0 | 0 | |||||||||
−6789.98 | − | 2471.35i | −0.701915 | − | 0.255476i | |||||
−15140.4 | −1.55999 | |||||||||
0 | 0 | |||||||||
−13086.6 | −1.33953 | −0.669766 | − | 0.742572i | ||||||
−0.669766 | + | 0.742572i | ||||||||
15244.3 | + | 5548.49i | 1.55529 | + | 0.566078i | |||||
0 | 0 | |||||||||
1779.67 | + | 1493.32i | 0.180386 | + | 0.151362i | |||||
6745.89 | + | 8039.44i | 0.681535 | + | 0.812221i | 0.990304 | − | 0.138916i | ||
−0.308770 | + | 0.951137i | ||||||||
0 | 0 | |||||||||
7339.34 | − | 12712.1i | 0.736691 | − | 1.27599i | −0.217286 | − | 0.976108i | ||
0.953977 | − | 0.299878i | ||||||||
−11298.2 | − | 19569.0i | −1.13040 | − | 1.95790i | |||||
0 | 0 | |||||||||
−3941.76 | − | 10829.9i | −0.391842 | − | 1.07658i | |||||
−4543.90 | + | 2623.42i | −0.450250 | + | 0.259952i | −0.707936 | − | 0.706277i | ||
0.257686 | + | 0.966229i | ||||||||
0 | 0 | |||||||||
13851.0 | + | 2442.30i | 1.36371 | + | 0.240458i | |||||
−34975.5 | + | 29347.9i | −3.43255 | + | 2.88025i | |||||
0 | 0 | |||||||||
898.269 | + | 5094.33i | 0.0875978 | + | 0.496792i | |||||
−52.2658 | + | 143.599i | −0.00508073 | + | 0.0139592i | |||||
0 | 0 | |||||||||
24564.4 | − | 5226.90i | 2.37283 | − | 0.504898i | |||||
2338.68i | 0.225196i | |||||||||
0 | 0 | |||||||||
−16340.3 | + | 2881.24i | −1.56358 | + | 0.275701i | |||||
3625.56 | − | 4320.77i | 0.345837 | − | 0.412153i | −0.564887 | − | 0.825169i | ||
0.910724 | + | 0.413016i | ||||||||
0 | 0 | |||||||||
−439.905 | + | 2494.83i | −0.0417005 | + | 0.236495i | |||||
−20903.9 | − | 12068.8i | −1.97540 | − | 1.14050i | |||||
0 | 0 | |||||||||
−6014.91 | + | 2189.25i | −0.564887 | + | 0.205602i | |||||
−4044.29 | + | 1472.00i | −0.378642 | + | 0.137815i | |||||
0 | 0 | |||||||||
7501.19 | + | 4330.81i | 0.697970 | + | 0.402973i | 0.806591 | − | 0.591110i | ||
−0.108621 | + | 0.994083i | ||||||||
−1241.56 | + | 7041.25i | −0.115170 | + | 0.653160i | |||||
0 | 0 | |||||||||
4820.06 | − | 5744.32i | 0.444384 | − | 0.529596i | |||||
−13111.7 | + | 2311.95i | −1.20514 | + | 0.212499i | −0.739920 | − | 0.672695i | ||
−0.465222 | + | 0.885194i | ||||||||
0 | 0 | |||||||||
− | 8904.90i | − | 0.813502i | |||||||
−1938.19 | + | 13812.7i | −0.176525 | + | 1.25802i | |||||
0 | 0 | |||||||||
2709.96 | − | 7445.56i | 0.245324 | − | 0.674023i | |||||
655.854 | + | 3719.53i | 0.0591933 | + | 0.335702i | |||||
0 | 0 | |||||||||
−6868.77 | + | 5763.59i | −0.616209 | + | 0.517061i | −0.896609 | − | 0.442822i | ||
0.280400 | + | 0.959883i | ||||||||
17473.8 | + | 3081.11i | 1.56291 | + | 0.275583i | |||||
0 | 0 | |||||||||
−12684.1 | + | 7323.17i | −1.12773 | + | 0.651094i | |||||
−732.241 | − | 2011.81i | −0.0649085 | − | 0.178335i | 0.902998 | − | 0.429644i | ||
−0.967907 | + | 0.251309i | ||||||||
0 | 0 | |||||||||
−15469.1 | − | 26793.2i | −1.36310 | − | 2.36095i | |||||
−24.4971 | + | 42.4303i | −0.00215223 | + | 0.00372778i | |||||
0 | 0 | |||||||||
4408.84 | + | 5254.25i | 0.385060 | + | 0.458897i | |||||
16941.6 | + | 14215.7i | 1.47529 | + | 1.23792i | 0.911042 | + | 0.412315i | ||
0.564251 | + | 0.825603i | ||||||||
0 | 0 | |||||||||
−4997.11 | − | 1818.80i | −0.432601 | − | 0.157454i | |||||
−8039.28 | −0.693925 | |||||||||
0 | 0 | |||||||||
19997.4 | 1.71604 | |||||||||
13298.3 | + | 4840.19i | 1.13785 | + | 0.414144i | |||||
0 | 0 | |||||||||
−276.974 | − | 232.409i | −0.0235615 | − | 0.0197705i | |||||
1925.87 | + | 2295.16i | 0.163355 | + | 0.194679i | |||||
0 | 0 | |||||||||
5558.26 | − | 9627.19i | 0.468742 | − | 0.811885i | |||||
−1634.47 | − | 2830.98i | −0.137442 | − | 0.238057i | 0.789086 | − | 0.614283i | ||
−0.926528 | + | 0.376227i | ||||||||
0 | 0 | |||||||||
−2224.28 | − | 6111.15i | −0.185967 | − | 0.510941i | 0.811316 | − | 0.584608i | ||
−0.997283 | + | 0.0736677i | ||||||||
7565.16 | − | 4367.75i | 0.630698 | − | 0.364134i | |||||
0 | 0 | |||||||||
25997.2 | + | 4584.00i | 2.15500 | + | 0.379985i | |||||
2391.98 | − | 2007.11i | 0.197716 | − | 0.165903i | |||||
0 | 0 | |||||||||
2018.20 | + | 11445.8i | 0.165875 | + | 0.940722i | |||||
3848.94 | − | 10574.9i | 0.315447 | − | 0.866684i | |||||
0 | 0 | |||||||||
4145.86 | + | 4602.43i | 0.337868 | + | 0.375077i | |||||
− | 15939.7i | − | 1.29535i | |||||||
0 | 0 | |||||||||
−16462.3 | + | 2902.74i | −1.33033 | + | 0.234573i | |||||
−6637.85 | + | 7910.69i | −0.534910 | + | 0.637481i | |||||
0 | 0 | |||||||||
636.086 | − | 3607.42i | 0.0509733 | − | 0.289084i | |||||
51.4270 | + | 29.6914i | 0.00410968 | + | 0.00237272i | |||||
0 | 0 | |||||||||
20922.5 | − | 7615.15i | 1.66271 | − | 0.605178i | 0.671926 | − | 0.740618i | ||
0.990785 | + | 0.135441i | ||||||||
−17926.2 | + | 6524.60i | −1.42066 | + | 0.517077i | |||||
0 | 0 | |||||||||
−5216.83 | − | 3011.94i | −0.411158 | − | 0.237382i | |||||
1131.62 | − | 6417.71i | 0.0889415 | − | 0.504412i | |||||
0 | 0 | |||||||||
−2657.93 | + | 3167.60i | −0.207761 | + | 0.247599i | −0.859855 | − | 0.510538i | ||
0.652094 | + | 0.758138i | ||||||||
−524.030 | + | 92.4007i | −0.0408494 | + | 0.00720285i | |||||
0 | 0 | |||||||||
636.611i | 0.0493549i | |||||||||
−15786.1 | − | 17524.5i | −1.22052 | − | 1.35494i | |||||
0 | 0 | |||||||||
−2978.29 | + | 8182.77i | −0.229023 | + | 0.629235i | |||||
3451.40 | + | 19573.9i | 0.264686 | + | 1.50111i | |||||
0 | 0 | |||||||||
−6523.32 | + | 5473.72i | −0.497573 | + | 0.417513i | |||||
−3266.41 | − | 575.957i | −0.248478 | − | 0.0438134i | 0.0480217 | − | 0.998846i | ||
−0.296500 | + | 0.955033i | ||||||||
0 | 0 | |||||||||
10616.9 | − | 6129.65i | 0.803301 | − | 0.463786i | |||||
−8731.69 | − | 23990.1i | −0.658895 | − | 1.81030i | |||||
0 | 0 | |||||||||
13266.1 | + | 22977.6i | 0.995725 | + | 1.72465i | |||||
−8843.07 | + | 15316.6i | −0.661973 | + | 1.14657i | 0.318123 | + | 0.948049i | ||
−0.980096 | + | 0.198522i | ||||||||
0 | 0 | |||||||||
5287.62 | + | 6301.54i | 0.393720 | + | 0.469217i | |||||
10143.9 | + | 8511.76i | 0.753323 | + | 0.632113i | |||||
0 | 0 | |||||||||
−2605.88 | − | 948.462i | −0.192500 | − | 0.0700644i | |||||
10925.5 | 0.804959 | 0.402480 | − | 0.915429i | ||||||
0.402480 | + | 0.915429i | ||||||||
0 | 0 | |||||||||
−13116.4 | −0.961305 | −0.480652 | − | 0.876911i | ||||||
−0.480652 | + | 0.876911i | ||||||||
−124.758 | − | 45.4080i | −0.00911954 | − | 0.00331924i | |||||
0 | 0 | |||||||||
−14441.2 | − | 12117.6i | −1.05011 | − | 0.881149i | |||||
−4549.06 | − | 5421.36i | −0.329929 | − | 0.393194i | |||||
0 | 0 | |||||||||
−4494.99 | + | 7785.54i | −0.324313 | + | 0.561727i | −0.981373 | − | 0.192111i | ||
0.657060 | + | 0.753838i | ||||||||
7042.54 | + | 12198.0i | 0.506801 | + | 0.877805i | |||||
0 | 0 | |||||||||
−9696.22 | − | 26640.1i | −0.694161 | − | 1.90719i | |||||
8065.80 | − | 4656.79i | 0.575948 | − | 0.332524i | |||||
0 | 0 | |||||||||
87.7639 | + | 15.4751i | 0.00623467 | + | 0.00109934i | |||||
2991.01 | − | 2509.76i | 0.211933 | − | 0.177833i | |||||
0 | 0 | |||||||||
197.542 | + | 1120.32i | 0.0139256 | + | 0.0789758i | |||||
6445.89 | − | 17709.9i | 0.453237 | − | 1.24526i | −0.477196 | − | 0.878797i | ||
0.930433 | − | 0.366462i | ||||||||
0 | 0 | |||||||||
1149.25 | − | 8190.26i | 0.0803974 | − | 0.572960i | |||||
33561.4i | 2.34187i | |||||||||
0 | 0 | |||||||||
−4206.77 | + | 741.768i | −0.292056 | + | 0.0514974i | |||||
5754.77 | − | 6858.27i | 0.398516 | − | 0.474933i | −0.529051 | − | 0.848590i | ||
0.927567 | + | 0.373657i | ||||||||
0 | 0 | |||||||||
1747.06 | − | 9908.08i | 0.120374 | − | 0.682675i | |||||
−4388.63 | − | 2533.78i | −0.301620 | − | 0.174140i | |||||
0 | 0 | |||||||||
3693.44 | − | 1344.30i | 0.252568 | − | 0.0919274i | |||||
−9574.28 | + | 3484.75i | −0.653079 | + | 0.237701i | −0.647246 | − | 0.762281i | ||
−0.00583382 | + | 0.999983i | ||||||||
0 | 0 | |||||||||
−1647.80 | − | 951.360i | −0.111839 | − | 0.0645704i | 0.443037 | − | 0.896503i | ||
−0.554876 | + | 0.831933i | ||||||||
2517.71 | − | 14278.6i | 0.170456 | − | 0.966701i | |||||
0 | 0 | |||||||||
3154.33 | − | 3759.18i | 0.212496 | − | 0.253243i | |||||
27118.3 | − | 4781.69i | 1.82234 | − | 0.321328i | |||||
0 | 0 | |||||||||
3728.13i | 0.249292i | 0.992201 | + | 0.124646i | ||||||
−0.992201 | + | 0.124646i | ||||||||
−15605.9 | + | 3320.68i | −1.04096 | + | 0.221499i | |||||
0 | 0 | |||||||||
−15865.5 | + | 43590.1i | −1.05307 | + | 2.89330i | |||||
5036.81 | + | 28565.2i | 0.333498 | + | 1.89136i | |||||
0 | 0 | |||||||||
−3839.31 | + | 3221.57i | −0.252966 | + | 0.212264i | −0.760448 | − | 0.649398i | ||
0.507482 | + | 0.861662i | ||||||||
10265.6 | + | 1810.10i | 0.674733 | + | 0.118974i | |||||
0 | 0 | |||||||||
90.1665 | − | 52.0577i | 0.00589759 | − | 0.00340497i | |||||
−7116.73 | − | 19553.0i | −0.464358 | − | 1.27581i | −0.922178 | − | 0.386767i | ||
0.457820 | − | 0.889045i | ||||||||
0 | 0 | |||||||||
6410.57 | + | 11103.4i | 0.416256 | + | 0.720977i | 0.995559 | − | 0.0941351i | ||
−0.579303 | + | 0.815112i | ||||||||
4970.43 | − | 8609.04i | 0.321964 | − | 0.557657i | |||||
0 | 0 | |||||||||
−11182.6 | − | 13326.9i | −0.720871 | − | 0.859101i | |||||
14245.6 | + | 11953.5i | 0.916111 | + | 0.768708i | |||||
0 | 0 | |||||||||
−36108.8 | − | 13142.5i | −2.31096 | − | 0.841122i | |||||
−15386.2 | −0.982359 | |||||||||
0 | 0 | |||||||||
14421.9 | 0.916398 | |||||||||
−1581.88 | − | 575.759i | −0.100276 | − | 0.0364976i | |||||
0 | 0 | |||||||||
18059.7 | + | 15153.9i | 1.13937 | + | 0.956047i | 0.999418 | − | 0.0341111i | ||
0.139954 | + | 0.990158i | ||||||||
−4109.73 | − | 4897.79i | −0.258665 | − | 0.308265i | |||||
0 | 0 | |||||||||
7318.26 | − | 12675.6i | 0.458431 | − | 0.794025i | |||||
−14753.5 | − | 25553.8i | −0.922007 | − | 1.59696i | |||||
0 | 0 | |||||||||
−1629.34 | − | 4476.57i | −0.101345 | − | 0.278443i | |||||
517.774 | − | 298.937i | 0.0321299 | − | 0.0185502i | |||||
0 | 0 | |||||||||
27413.3 | + | 4833.70i | 1.69313 | + | 0.298545i | |||||
6448.66 | − | 5411.07i | 0.397358 | − | 0.333423i | −0.422113 | − | 0.906543i | ||
0.819472 | + | 0.573120i | ||||||||
0 | 0 | |||||||||
−525.679 | − | 2981.27i | −0.0322407 | − | 0.182846i | 0.964435 | − | 0.264321i | ||
−0.996675 | + | 0.0814754i | ||||||||
597.012 | − | 1640.28i | 0.0365304 | − | 0.100366i | |||||
0 | 0 | |||||||||
−8815.56 | − | 2862.23i | −0.536909 | − | 0.174324i | |||||
8844.45i | 0.537421i | 0.963221 | + | 0.268710i | ||||||
−0.963221 | + | 0.268710i | ||||||||
0 | 0 | |||||||||
−261.738 | + | 46.1515i | −0.0158307 | + | 0.00279138i | |||||
32827.8 | − | 39122.6i | 1.98094 | − | 2.36079i | |||||
0 | 0 | |||||||||
1291.86 | − | 7326.48i | 0.0775966 | − | 0.440072i | |||||
−5428.18 | − | 3133.96i | −0.325300 | − | 0.187812i | 0.328452 | − | 0.944521i | ||
−0.653753 | + | 0.756708i | ||||||||
0 | 0 | |||||||||
−35313.5 | + | 12853.1i | −2.10659 | + | 0.766734i | |||||
25256.6 | − | 9192.63i | 1.50321 | − | 0.547122i | |||||
0 | 0 | |||||||||
29708.9 | + | 17152.4i | 1.76014 | + | 1.01622i | |||||
1752.32 | − | 9937.90i | 0.103582 | − | 0.587444i | −0.888195 | − | 0.459467i | ||
0.991777 | − | 0.127977i | ||||||||
0 | 0 | |||||||||
−6084.26 | + | 7250.94i | −0.358019 | + | 0.426670i | −0.914749 | − | 0.404024i | ||
0.556730 | + | 0.830694i | ||||||||
−16719.7 | + | 2948.14i | −0.981616 | + | 0.173085i | |||||
0 | 0 | |||||||||
6838.30i | 0.399665i | |||||||||
−14126.3 | − | 22595.8i | −0.823749 | − | 1.31764i | |||||
0 | 0 | |||||||||
−2273.22 | + | 6245.63i | −0.131963 | + | 0.362566i | |||||
−3441.76 | − | 19519.2i | −0.199350 | − | 1.13057i | |||||
0 | 0 | |||||||||
−51323.7 | + | 43065.7i | −2.95942 | + | 2.48324i | |||||
−361.767 | − | 63.7893i | −0.0208135 | − | 0.00366998i | |||||
0 | 0 | |||||||||
−2930.86 | + | 1692.13i | −0.167870 | + | 0.0969196i | −0.581581 | − | 0.813489i | ||
0.413711 | + | 0.910408i | ||||||||
6631.91 | + | 18221.0i | 0.379008 | + | 1.04132i | |||||
0 | 0 | |||||||||
41.1964 | + | 71.3542i | 0.00234390 | + | 0.00405975i | |||||
−6198.39 | + | 10735.9i | −0.351881 | + | 0.609476i | −0.986579 | − | 0.163284i | ||
0.634698 | + | 0.772760i | ||||||||
0 | 0 | |||||||||
2078.59 | + | 2477.17i | 0.117480 | + | 0.140007i | |||||
5658.78 | + | 4748.28i | 0.319124 | + | 0.267777i | |||||
0 | 0 | |||||||||
197.001 | + | 71.7027i | 0.0110610 | + | 0.00402586i | |||||
18080.6 | 1.01293 | 0.506466 | − | 0.862260i | ||||||
0.506466 | + | 0.862260i | ||||||||
0 | 0 | |||||||||
2289.14 | 0.127684 | |||||||||
−23231.5 | − | 8455.56i | −1.29298 | − | 0.470605i | |||||
0 | 0 | |||||||||
15835.4 | + | 13287.5i | 0.877497 | + | 0.736307i | |||||
−4595.49 | − | 5476.69i | −0.254099 | − | 0.302823i | |||||
0 | 0 | |||||||||
9026.08 | − | 15633.6i | 0.496915 | − | 0.860682i | −0.503079 | − | 0.864241i | ||
0.999994 | + | 0.00355848i | ||||||||
−8664.06 | − | 15006.6i | −0.475951 | − | 0.824372i | |||||
0 | 0 | |||||||||
−7994.94 | − | 21965.9i | −0.437297 | − | 1.20146i | |||||
31725.8 | − | 18316.9i | 1.73155 | − | 0.999713i | |||||
0 | 0 | |||||||||
10431.1 | + | 1839.29i | 0.566868 | + | 0.0999541i | |||||
11009.3 | − | 9237.90i | 0.597003 | − | 0.500945i | |||||
0 | 0 | |||||||||
−3938.50 | − | 22336.3i | −0.212659 | − | 1.20605i | |||||
5123.61 | − | 14077.0i | 0.276057 | − | 0.758460i | −0.721743 | − | 0.692161i | ||
0.997800 | − | 0.0662989i | ||||||||
0 | 0 | |||||||||
−4133.76 | + | 1671.19i | −0.221775 | + | 0.0896589i | |||||
− | 32.1349i | − | 0.00172036i | |||||||
0 | 0 | |||||||||
8296.84 | − | 1462.96i | 0.442289 | − | 0.0779874i | |||||
−14941.9 | + | 17807.1i | −0.794837 | + | 0.947250i | |||||
0 | 0 | |||||||||
4549.43 | − | 25801.1i | 0.240984 | − | 1.36669i | −0.588654 | − | 0.808385i | ||
0.829638 | − | 0.558302i | ||||||||
−15581.3 | − | 8995.85i | −0.823598 | − | 0.475505i | |||||
0 | 0 | |||||||||
−12830.5 | + | 4669.91i | −0.675341 | + | 0.245804i | |||||
−2190.03 | + | 797.105i | −0.115031 | + | 0.0418679i | |||||
0 | 0 | |||||||||
494.629 | + | 285.574i | 0.0258714 | + | 0.0149369i | |||||
−651.005 | + | 3692.04i | −0.0339794 | + | 0.192706i | |||||
0 | 0 | |||||||||
4916.23 | − | 5858.93i | 0.255532 | − | 0.304531i | |||||
25947.0 | − | 4575.16i | 1.34584 | − | 0.237308i | 0.546135 | − | 0.837697i | ||
0.799708 | + | 0.600389i | ||||||||
0 | 0 | |||||||||
− | 10633.0i | − | 0.549229i | |||||||
−22422.7 | + | 9994.90i | −1.15580 | + | 0.515196i | |||||
0 | 0 | |||||||||
−1426.28 | + | 3918.67i | −0.0732144 | + | 0.201155i | |||||
14996.5 | + | 85049.2i | 0.768214 | + | 4.35676i | |||||
0 | 0 | |||||||||
−2045.11 | + | 1716.05i | −0.104331 | + | 0.0875443i | −0.693461 | − | 0.720494i | ||
0.589130 | + | 0.808038i | ||||||||
−8225.57 | − | 1450.39i | −0.418763 | − | 0.0738393i | |||||
0 | 0 | |||||||||
21938.1 | − | 12666.0i | 1.11228 | − | 0.642176i | |||||
2786.23 | + | 7655.11i | 0.140975 | + | 0.387325i | |||||
0 | 0 | |||||||||
−13594.0 | − | 23545.5i | −0.685002 | − | 1.18646i | −0.973436 | − | 0.228959i | ||
0.288434 | − | 0.957500i | ||||||||
5648.32 | − | 9783.18i | 0.284037 | − | 0.491967i | |||||
0 | 0 | |||||||||
2890.05 | + | 3444.22i | 0.144740 | + | 0.172494i | |||||
−406.438 | − | 341.042i | −0.0203139 | − | 0.0170454i | |||||
0 | 0 | |||||||||
−1733.94 | − | 631.102i | −0.0863111 | − | 0.0314147i | 0.298504 | − | 0.954408i | ||
−0.384815 | + | 0.922994i | ||||||||
−5359.33 | −0.266234 | |||||||||
0 | 0 | |||||||||
−8455.41 | −0.418339 | |||||||||
−25271.5 | − | 9198.07i | −1.24781 | − | 0.454165i | −0.368148 | − | 0.929767i | ||
−0.879660 | + | 0.475602i | ||||||||
0 | 0 | |||||||||
16700.1 | + | 14013.1i | 0.821269 | + | 0.689126i | |||||
−16692.9 | − | 19893.8i | −0.819264 | − | 0.976360i | |||||
0 | 0 | |||||||||
44.1114 | − | 76.4033i | 0.00215625 | − | 0.00373473i | |||||
6279.91 | + | 10877.1i | 0.306359 | + | 0.530630i | |||||
0 | 0 | |||||||||
−5931.55 | − | 16296.8i | −0.288209 | − | 0.791849i | −0.996317 | − | 0.0857445i | ||
0.708108 | − | 0.706104i | ||||||||
−42357.0 | + | 24454.8i | −2.05399 | + | 1.18587i | |||||
0 | 0 | |||||||||
−47234.7 | − | 8328.75i | −2.28141 | − | 0.402275i | |||||
−16171.9 | + | 13569.8i | −0.779544 | + | 0.654115i | |||||
0 | 0 | |||||||||
−1788.97 | − | 10145.7i | −0.0858931 | − | 0.487124i | −0.997160 | − | 0.0753083i | ||
0.911267 | − | 0.411816i | ||||||||
−6443.72 | + | 17704.0i | −0.308768 | + | 0.848334i | |||||
0 | 0 | |||||||||
19553.7 | − | 687.085i | 0.933275 | − | 0.0327937i | |||||
− | 22833.9i | − | 1.08769i | −0.839187 | − | 0.543843i | ||||
0.839187 | − | 0.543843i | ||||||||
0 | 0 | |||||||||
−4821.98 | + | 850.246i | −0.228791 | + | 0.0403420i | |||||
−11584.9 | + | 13806.4i | −0.548598 | + | 0.653793i | |||||
0 | 0 | |||||||||
3495.93 | − | 19826.4i | 0.164899 | − | 0.935191i | |||||
18464.9 | + | 10660.7i | 0.869266 | + | 0.501871i | |||||
0 | 0 | |||||||||
23430.0 | − | 8527.84i | 1.09871 | − | 0.399898i | 0.271870 | − | 0.962334i | ||
0.826841 | + | 0.562436i | ||||||||
634.753 | − | 231.031i | 0.0297077 | − | 0.0108127i | |||||
0 | 0 | |||||||||
6778.23 | + | 3913.41i | 0.316002 | + | 0.182444i | |||||
−340.976 | + | 1933.77i | −0.0158655 | + | 0.0899779i | −0.991712 | − | 0.128478i | ||
0.975847 | + | 0.218456i | ||||||||
0 | 0 | |||||||||
−19465.3 | + | 23197.8i | −0.902210 | + | 1.07521i | |||||
−2338.21 | + | 412.290i | −0.108166 | + | 0.0190726i | |||||
0 | 0 | |||||||||
− | 25309.2i | − | 1.16630i | |||||||
23788.7 | − | 14872.0i | 1.09412 | − | 0.684011i | |||||
0 | 0 | |||||||||
48.7304 | − | 133.886i | 0.00223266 | − | 0.00613419i | |||||
453.540 | + | 2572.15i | 0.0207398 | + | 0.117622i | |||||
0 | 0 | |||||||||
6153.51 | − | 5163.41i | 0.280317 | − | 0.235214i | |||||
−61100.2 | − | 10773.6i | −2.77804 | − | 0.489843i | |||||
0 | 0 | |||||||||
−23562.3 | + | 13603.7i | −1.06723 | + | 0.616163i | −0.927422 | − | 0.374016i | ||
−0.139803 | + | 0.990179i | ||||||||
607.653 | + | 1669.51i | 0.0274705 | + | 0.0754746i | |||||
0 | 0 | |||||||||
−20740.5 | − | 35923.7i | −0.934070 | − | 1.61786i | |||||
3090.35 | − | 5352.65i | 0.138913 | − | 0.240605i | |||||
0 | 0 | |||||||||
18942.8 | + | 22575.2i | 0.848272 | + | 1.01093i | |||||
26795.6 | + | 22484.2i | 1.19766 | + | 1.00495i | |||||
0 | 0 | |||||||||
12618.4 | + | 4592.71i | 0.561868 | + | 0.204503i | |||||
13880.4 | 0.616899 | 0.308449 | − | 0.951241i | ||||||
0.308449 | + | 0.951241i | ||||||||
0 | 0 | |||||||||
−19274.6 | −0.853425 | |||||||||
54897.4 | + | 19981.0i | 2.42615 | + | 0.883045i | |||||
0 | 0 | |||||||||
13985.3 | + | 11735.1i | 0.615760 | + | 0.516684i | |||||
128.947 | + | 153.673i | 0.00566681 | + | 0.00675344i | |||||
0 | 0 | |||||||||
−3754.65 | + | 6503.24i | −0.164390 | + | 0.284732i | |||||
−8409.17 | − | 14565.1i | −0.367494 | − | 0.636519i | |||||
0 | 0 | |||||||||
−5837.44 | − | 16038.2i | −0.254159 | − | 0.698296i | |||||
−9580.31 | + | 5531.20i | −0.416348 | + | 0.240379i | −0.693514 | − | 0.720443i | ||
0.277165 | + | 0.960822i | ||||||||
0 | 0 | |||||||||
6132.92 | + | 1081.40i | 0.265544 | + | 0.0468225i | 0.304835 | − | 0.952405i | ||
−0.0392909 | + | 0.999228i | ||||||||
−16317.4 | + | 13691.9i | −0.705206 | + | 0.591738i | |||||
0 | 0 | |||||||||
−19.6264 | − | 111.307i | −0.000845091 | − | 0.00479275i | |||||
−10946.2 | + | 30074.4i | −0.470464 | + | 1.29259i | |||||
0 | 0 | |||||||||
19053.7 | + | 10125.7i | 0.815918 | + | 0.433604i | |||||
− | 168.134i | − | 0.00718665i | |||||||
0 | 0 | |||||||||
33208.8 | − | 5855.60i | 1.41427 | − | 0.249374i | |||||
9106.86 | − | 10853.1i | 0.387128 | − | 0.461361i | −0.536923 | − | 0.843631i | ||
0.924050 | + | 0.382271i | ||||||||
0 | 0 | |||||||||
973.517 | − | 5521.09i | 0.0412329 | − | 0.233843i | −0.957226 | − | 0.289342i | ||
0.998459 | + | 0.0554984i | ||||||||
6761.11 | + | 3903.53i | 0.285843 | + | 0.165031i | |||||
0 | 0 | |||||||||
23695.8 | − | 8624.57i | 0.998163 | − | 0.363301i | |||||
13477.3 | − | 4905.34i | 0.566690 | − | 0.206258i | −0.0427566 | − | 0.999086i | ||
0.609446 | + | 0.792827i | ||||||||
0 | 0 | |||||||||
17268.0 | + | 9969.69i | 0.723453 | + | 0.417686i | 0.816022 | − | 0.578020i | ||
−0.0925691 | + | 0.995706i | ||||||||
−7704.11 | + | 43692.2i | −0.322185 | + | 1.82720i | |||||
0 | 0 | |||||||||
−1657.08 | + | 1974.84i | −0.0690494 | + | 0.0822898i | |||||
3117.54 | − | 549.706i | 0.129671 | − | 0.0228646i | |||||
0 | 0 | |||||||||
85266.3i | 3.53385i | |||||||||
−48.6332 | − | 228.557i | −0.00201198 | − | 0.00945551i | |||||
0 | 0 | |||||||||
5843.87 | − | 16055.9i | 0.240899 | − | 0.661864i | |||||
−6999.02 | − | 39693.4i | −0.288001 | − | 1.63334i | −0.694364 | − | 0.719624i | ||
0.406362 | − | 0.913712i | ||||||||
0 | 0 | |||||||||
43448.0 | − | 36457.2i | 1.78146 | − | 1.49482i | |||||
3092.93 | + | 545.367i | 0.126591 | + | 0.0223214i | |||||
0 | 0 | |||||||||
8210.53 | − | 4740.35i | 0.334855 | − | 0.193329i | |||||
−121.230 | − | 333.075i | −0.00493541 | − | 0.0135599i | |||||
0 | 0 | |||||||||
−10344.9 | − | 17917.9i | −0.419664 | − | 0.726879i | |||||
6027.58 | − | 10440.1i | 0.244090 | − | 0.422776i | |||||
0 | 0 | |||||||||
21814.3 | + | 25997.3i | 0.880264 | + | 1.04906i | |||||
962.508 | + | 807.640i | 0.0387713 | + | 0.0325329i | |||||
0 | 0 | |||||||||
−21299.9 | − | 7752.55i | −0.854978 | − | 0.311187i | −0.122910 | − | 0.992418i | ||
−0.732068 | + | 0.681231i | ||||||||
34853.6 | 1.39656 | |||||||||
0 | 0 | |||||||||
−9221.78 | −0.368217 | |||||||||
9943.89 | + | 3619.28i | 0.396355 | + | 0.144262i | 0.532505 | − | 0.846427i | ||
−0.136150 | + | 0.990688i | ||||||||
0 | 0 | |||||||||
9275.48 | + | 7783.06i | 0.368423 | + | 0.309144i | 0.808137 | − | 0.588994i | ||
−0.439714 | + | 0.898138i | ||||||||
16670.7 | + | 19867.4i | 0.661009 | + | 0.787759i | |||||
0 | 0 | |||||||||
−6106.74 | + | 10577.2i | −0.241295 | + | 0.417936i | |||||
873.926 | + | 1513.68i | 0.0344714 | + | 0.0597062i | 0.882746 | − | 0.469850i | ||
−0.848275 | + | 0.529556i | ||||||||
0 | 0 | |||||||||
25495.9 | + | 70049.5i | 1.00218 | + | 2.75347i | |||||
24500.9 | − | 14145.6i | 0.961402 | − | 0.555066i | |||||
0 | 0 | |||||||||
−7355.65 | − | 1297.00i | −0.287635 | − | 0.0507178i | |||||
251.640 | − | 211.151i | 0.00982313 | − | 0.00824258i | |||||
0 | 0 | |||||||||
7391.11 | + | 41917.1i | 0.287530 | + | 1.63066i | |||||
1229.58 | − | 3378.25i | 0.0477510 | − | 0.131195i | |||||
0 | 0 | |||||||||
5452.30 | + | 4257.90i | 0.211015 | + | 0.164789i | |||||
57352.2i | 2.21584i | |||||||||
0 | 0 | |||||||||
−38701.9 | + | 6824.19i | −1.49016 | + | 0.262755i | −0.858630 | − | 0.512596i | ||
−0.631530 | + | 0.775351i | ||||||||
39632.9 | − | 47232.7i | 1.52340 | − | 1.81552i | |||||
0 | 0 | |||||||||
−167.235 | + | 948.438i | −0.00640625 | + | 0.0363316i | |||||
−34092.5 | − | 19683.3i | −1.30375 | − | 0.752722i | −0.322707 | − | 0.946499i | ||
−0.981046 | + | 0.193777i | ||||||||
0 | 0 | |||||||||
11453.2 | − | 4168.64i | 0.436503 | − | 0.158874i | −0.114416 | − | 0.993433i | ||
0.550919 | + | 0.834559i | ||||||||
−6650.69 | + | 2420.65i | −0.253040 | + | 0.0920988i | |||||
0 | 0 | |||||||||
21553.6 | + | 12444.0i | 0.817278 | + | 0.471856i | |||||
1295.85 | − | 7349.15i | 0.0490535 | − | 0.278196i | −0.950408 | − | 0.311006i | ||
0.999462 | + | 0.0328091i | ||||||||
0 | 0 | |||||||||
−14250.7 | + | 16983.4i | −0.537632 | + | 0.640725i | |||||
−87239.4 | + | 15382.7i | −3.28570 | + | 0.579357i | |||||
0 | 0 | |||||||||
28904.0i | 1.08495i | |||||||||
−37931.7 | + | 34168.8i | −1.42143 | + | 1.28042i | |||||
0 | 0 | |||||||||
5516.12 | − | 15155.4i | 0.206015 | − | 0.566022i | |||||
−3631.83 | − | 20597.1i | −0.135414 | − | 0.767970i | |||||
0 | 0 | |||||||||
−8394.38 | + | 7043.72i | −0.311942 | + | 0.261751i | |||||
28007.9 | + | 4938.54i | 1.03906 | + | 0.183214i | |||||
0 | 0 | |||||||||
4114.29 | − | 2375.39i | 0.152128 | − | 0.0878309i | |||||
243.227 | + | 668.261i | 0.00897847 | + | 0.0246681i | |||||
0 | 0 | |||||||||
2269.02 | + | 3930.07i | 0.0834808 | + | 0.144593i | |||||
8969.96 | − | 15536.4i | 0.329471 | − | 0.570661i | |||||
0 | 0 | |||||||||
−14099.2 | − | 16802.7i | −0.516158 | − | 0.615133i | 0.443510 | − | 0.896270i | ||
−0.959668 | + | 0.281136i | ||||||||
−7439.32 | − | 6242.33i | −0.271897 | − | 0.228149i | |||||
0 | 0 | |||||||||
−50921.9 | − | 18534.0i | −1.85499 | − | 0.675162i | |||||
24183.3 | 0.879505 | 0.439752 | − | 0.898119i | ||||||
0.439752 | + | 0.898119i | ||||||||
0 | 0 | |||||||||
−351.340 | −0.0127357 | |||||||||
−44014.3 | − | 16019.9i | −1.59285 | − | 0.579750i | |||||
0 | 0 | |||||||||
16702.2 | + | 14014.8i | 0.602464 | + | 0.505527i | |||||
18149.6 | + | 21629.9i | 0.653603 | + | 0.778934i | |||||
0 | 0 | |||||||||
24138.2 | − | 41808.5i | 0.866425 | − | 1.50069i | 0.000800280 | − | 1.00000i | ||
0.865625 | − | 0.500693i | ||||||||
−2756.77 | − | 4774.86i | −0.0987913 | − | 0.171112i | |||||
0 | 0 | |||||||||
12847.1 | + | 35297.0i | 0.458889 | + | 1.26079i | |||||
−9898.70 | + | 5715.02i | −0.353001 | + | 0.203805i | |||||
0 | 0 | |||||||||
16077.9 | + | 2834.97i | 0.571502 | + | 0.100771i | |||||
40245.9 | − | 33770.3i | 1.42825 | − | 1.19845i | |||||
0 | 0 | |||||||||
−9527.35 | − | 54032.3i | −0.337016 | − | 1.91131i | |||||
−12132.2 | + | 33333.0i | −0.428466 | + | 1.17720i | 0.518278 | + | 0.855212i | ||
−0.946744 | + | 0.321988i | ||||||||
0 | 0 | |||||||||
5160.72 | − | 6608.38i | 0.181671 | − | 0.232632i | |||||
− | 15489.4i | − | 0.544392i | |||||||
0 | 0 | |||||||||
−18494.0 | + | 3260.99i | −0.647903 | + | 0.114243i | |||||
−243.959 | + | 290.739i | −0.00853295 | + | 0.0101692i | |||||
0 | 0 | |||||||||
5916.58 | − | 33554.6i | 0.206282 | − | 1.16988i | −0.689128 | − | 0.724640i | ||
0.895410 | − | 0.445243i | ||||||||
43595.4 | + | 25169.8i | 1.51753 | + | 0.876144i | |||||
0 | 0 | |||||||||
−57662.4 | + | 20987.4i | −2.00079 | + | 0.728227i | |||||
18113.4 | − | 6592.72i | 0.627501 | − | 0.228392i | −0.00864207 | − | 0.999963i | ||
0.636143 | + | 0.771571i | ||||||||
0 | 0 | |||||||||
−6846.55 | − | 3952.86i | −0.236431 | − | 0.136503i | |||||
−6243.02 | + | 35405.9i | −0.215247 | + | 1.22072i | |||||
0 | 0 | |||||||||
−351.572 | + | 418.987i | −0.0120831 | + | 0.0144000i | |||||
−33803.9 | + | 5960.54i | −1.15996 | + | 0.204532i | −0.720319 | − | 0.693643i | ||
−0.439638 | + | 0.898175i | ||||||||
0 | 0 | |||||||||
− | 16093.2i | − | 0.550484i | |||||||
89016.1 | + | 12490.7i | 3.04007 | + | 0.426580i | |||||
0 | 0 | |||||||||
1898.31 | − | 5215.55i | 0.0646265 | − | 0.177560i | |||||
160.465 | + | 910.044i | 0.00545434 | + | 0.0309331i | 0.987413 | − | 0.158160i | ||
−0.981959 | + | 0.189093i | ||||||||
0 | 0 | |||||||||
59394.7 | − | 49838.1i | 2.01253 | − | 1.68872i | |||||
−21961.3 | − | 3872.37i | −0.742970 | − | 0.131006i | |||||
0 | 0 | |||||||||
17483.1 | − | 10093.9i | 0.589618 | − | 0.340416i | |||||
−588.261 | − | 1616.23i | −0.0198081 | − | 0.0544222i | |||||
0 | 0 | |||||||||
−9909.27 | − | 17163.4i | −0.332626 | − | 0.576126i | |||||
−4533.56 | + | 7852.36i | −0.151942 | + | 0.263171i | |||||
0 | 0 | |||||||||
−20852.6 | − | 24851.2i | −0.696698 | − | 0.830293i | |||||
−25793.3 | − | 21643.2i | −0.860431 | − | 0.721988i | |||||
0 | 0 | |||||||||
24660.1 | + | 8975.53i | 0.820077 | + | 0.298483i | 0.717780 | − | 0.696270i | ||
0.102297 | + | 0.994754i | ||||||||
15191.1 | 0.504400 | |||||||||
0 | 0 | |||||||||
−15404.1 | −0.509893 | |||||||||
18612.1 | + | 6774.26i | 0.615131 | + | 0.223889i | 0.630747 | − | 0.775989i | ||
−0.0156160 | + | 0.999878i | ||||||||
0 | 0 | |||||||||
−21085.4 | − | 17692.8i | −0.694725 | − | 0.582943i | |||||
19927.3 | + | 23748.4i | 0.655555 | + | 0.781260i | |||||
0 | 0 | |||||||||
−24846.0 | + | 43034.5i | −0.814857 | + | 1.41137i | |||||
−9613.30 | − | 16650.7i | −0.314797 | − | 0.545245i | 0.664597 | − | 0.747202i | ||
−0.979394 | + | 0.201957i | ||||||||
0 | 0 | |||||||||
−239.932 | − | 659.208i | −0.00783276 | − | 0.0215203i | |||||
8727.95 | − | 5039.09i | 0.284494 | − | 0.164253i | |||||
0 | 0 | |||||||||
−46929.0 | − | 8274.85i | −1.52501 | − | 0.268901i | |||||
−31572.8 | + | 26492.7i | −1.02443 | + | 0.859601i | −0.990178 | − | 0.139813i | ||
−0.0342541 | + | 0.999413i | ||||||||
0 | 0 | |||||||||
−1327.22 | − | 7527.02i | −0.0429326 | − | 0.243483i | |||||
10900.9 | − | 29949.9i | 0.352084 | − | 0.967343i | |||||
0 | 0 | |||||||||
−8797.14 | + | 16553.7i | −0.283274 | + | 0.533039i | |||||
− | 6080.33i | − | 0.195494i | |||||||
0 | 0 | |||||||||
−3507.79 | + | 618.518i | −0.112441 | + | 0.0198263i | −0.229585 | − | 0.973289i | ||
0.117145 | + | 0.993115i | ||||||||
12366.4 | − | 14737.7i | 0.395800 | − | 0.471696i | |||||
0 | 0 | |||||||||
−2347.40 | + | 13312.8i | −0.0749046 | + | 0.424805i | |||||
−50028.3 | − | 28883.9i | −1.59397 | − | 0.920282i | |||||
0 | 0 | |||||||||
448.486 | − | 163.236i | 0.0142464 | − | 0.00518528i | −0.334887 | − | 0.942258i | ||
0.349134 | + | 0.937073i | ||||||||
−30157.3 | + | 10976.3i | −0.956524 | + | 0.348146i | |||||
0 | 0 |
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 171.4.y.a.53.16 | yes | 120 | |
3.2 | odd | 2 | inner | 171.4.y.a.53.5 | ✓ | 120 | |
19.14 | odd | 18 | inner | 171.4.y.a.71.5 | yes | 120 | |
57.14 | even | 18 | inner | 171.4.y.a.71.16 | yes | 120 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
171.4.y.a.53.5 | ✓ | 120 | 3.2 | odd | 2 | inner | |
171.4.y.a.53.16 | yes | 120 | 1.1 | even | 1 | trivial | |
171.4.y.a.71.5 | yes | 120 | 19.14 | odd | 18 | inner | |
171.4.y.a.71.16 | yes | 120 | 57.14 | even | 18 | inner |