Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [132,4,Mod(25,132)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(132, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 8]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("132.25");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 132.i (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 |
Coefficient field: | |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
|
Coefficient ring: | |
Coefficient ring index: | |
Twist minimal: | yes |
Sato-Tate group: |
Embedding invariants
Embedding label | 37.2 | ||
Root | of defining polynomial | ||
Character | 132.37 | ||
Dual form | 132.4.i.b.25.2 |
-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of on generators for .
Coefficient data
For each we display the coefficients of the -expansion , the Satake parameters , and the Satake angles .
0 | 0 | |||||||||
−0.927051 | + | 2.85317i | −0.178411 | + | 0.549093i | |||||
0 | 0 | |||||||||
1.60477 | − | 1.16593i | 0.143535 | − | 0.104284i | −0.513700 | − | 0.857970i | ||
0.657235 | + | 0.753685i | ||||||||
0 | 0 | |||||||||
3.78898 | + | 11.6613i | 0.204586 | + | 0.629650i | 0.999730 | + | 0.0232301i | ||
−0.795144 | + | 0.606420i | ||||||||
0 | 0 | |||||||||
−7.28115 | − | 5.29007i | −0.269672 | − | 0.195928i | |||||
0 | 0 | |||||||||
−8.21788 | + | 35.5453i | −0.225253 | + | 0.974300i | |||||
0 | 0 | |||||||||
5.26513 | + | 3.82534i | 0.112330 | + | 0.0816123i | 0.642532 | − | 0.766259i | ||
−0.530202 | + | 0.847871i | ||||||||
0 | 0 | |||||||||
1.83890 | + | 5.65957i | 0.0316535 | + | 0.0974196i | |||||
0 | 0 | |||||||||
−62.9784 | + | 45.7565i | −0.898500 | + | 0.652798i | −0.938080 | − | 0.346418i | ||
0.0395805 | + | 0.999216i | ||||||||
0 | 0 | |||||||||
−28.2631 | + | 86.9850i | −0.341264 | + | 1.05030i | 0.622290 | + | 0.782787i | ||
−0.963554 | + | 0.267515i | ||||||||
0 | 0 | |||||||||
−36.7842 | −0.382237 | |||||||||
0 | 0 | |||||||||
−20.2371 | −0.183466 | −0.0917331 | − | 0.995784i | ||||||
−0.0917331 | + | 0.995784i | ||||||||
0 | 0 | |||||||||
−37.4112 | + | 115.140i | −0.299290 | + | 0.921120i | |||||
0 | 0 | |||||||||
21.8435 | − | 15.8702i | 0.155695 | − | 0.113119i | |||||
0 | 0 | |||||||||
−23.5838 | − | 72.5834i | −0.151014 | − | 0.464773i | 0.846721 | − | 0.532036i | ||
−0.997735 | + | 0.0672639i | ||||||||
0 | 0 | |||||||||
92.8764 | + | 67.4787i | 0.538100 | + | 0.390953i | 0.823379 | − | 0.567492i | ||
−0.285279 | + | 0.958445i | ||||||||
0 | 0 | |||||||||
−93.7983 | − | 56.3993i | −0.494794 | − | 0.297511i | |||||
0 | 0 | |||||||||
19.6767 | + | 14.2960i | 0.0950279 | + | 0.0690418i | |||||
0 | 0 | |||||||||
27.6238 | + | 85.0174i | 0.122739 | + | 0.377751i | 0.993482 | − | 0.113987i | ||
−0.870744 | + | 0.491737i | ||||||||
0 | 0 | |||||||||
−15.7954 | + | 11.4760i | −0.0648535 | + | 0.0471189i | |||||
0 | 0 | |||||||||
30.4658 | − | 93.7641i | 0.116048 | − | 0.357159i | −0.876116 | − | 0.482100i | ||
0.992164 | + | 0.124941i | ||||||||
0 | 0 | |||||||||
488.233 | 1.73151 | 0.865753 | − | 0.500471i | ||||||
0.865753 | + | 0.500471i | ||||||||
0 | 0 | |||||||||
−17.8525 | −0.0591397 | |||||||||
0 | 0 | |||||||||
33.0191 | − | 101.622i | 0.102475 | − | 0.315386i | −0.886654 | − | 0.462433i | ||
0.989130 | + | 0.147046i | ||||||||
0 | 0 | |||||||||
155.864 | − | 113.242i | 0.454413 | − | 0.330150i | |||||
0 | 0 | |||||||||
−72.1668 | − | 222.106i | −0.198144 | − | 0.609826i | |||||
0 | 0 | |||||||||
−447.009 | − | 324.771i | −1.15852 | − | 0.841712i | −0.168928 | − | 0.985628i | ||
−0.989590 | + | 0.143916i | ||||||||
0 | 0 | |||||||||
28.2556 | + | 66.6235i | 0.0692725 | + | 0.163337i | |||||
0 | 0 | |||||||||
−221.982 | − | 161.279i | −0.515828 | − | 0.374771i | |||||
0 | 0 | |||||||||
−52.3705 | − | 161.180i | −0.115560 | − | 0.355658i | 0.876503 | − | 0.481396i | ||
−0.992063 | + | 0.125738i | ||||||||
0 | 0 | |||||||||
235.345 | − | 170.988i | 0.493982 | − | 0.358899i | −0.312732 | − | 0.949841i | ||
0.806713 | + | 0.590943i | ||||||||
0 | 0 | |||||||||
34.1008 | − | 104.952i | 0.0681953 | − | 0.209883i | |||||
0 | 0 | |||||||||
12.9094 | 0.0246341 | |||||||||
0 | 0 | |||||||||
107.351 | 0.195747 | 0.0978736 | − | 0.995199i | ||||||
0.0978736 | + | 0.995199i | ||||||||
0 | 0 | |||||||||
18.7608 | − | 57.7398i | 0.0327324 | − | 0.100740i | |||||
0 | 0 | |||||||||
589.515 | − | 428.308i | 0.985389 | − | 0.715927i | 0.0264824 | − | 0.999649i | ||
0.958906 | + | 0.283722i | ||||||||
0 | 0 | |||||||||
110.836 | + | 341.119i | 0.177704 | + | 0.546917i | 0.999747 | − | 0.0225091i | ||
−0.822043 | + | 0.569426i | ||||||||
0 | 0 | |||||||||
−293.832 | − | 213.481i | −0.452383 | − | 0.328676i | |||||
0 | 0 | |||||||||
−445.641 | + | 38.8493i | −0.659552 | + | 0.0574973i | |||||
0 | 0 | |||||||||
413.815 | + | 300.654i | 0.589339 | + | 0.428180i | 0.842079 | − | 0.539354i | ||
−0.252740 | + | 0.967534i | ||||||||
0 | 0 | |||||||||
25.0304 | + | 77.0356i | 0.0343352 | + | 0.105673i | |||||
0 | 0 | |||||||||
515.712 | − | 374.687i | 0.682010 | − | 0.495509i | −0.192014 | − | 0.981392i | ||
0.874024 | + | 0.485883i | ||||||||
0 | 0 | |||||||||
−47.7168 | + | 146.857i | −0.0608896 | + | 0.187399i | |||||
0 | 0 | |||||||||
228.956 | 0.282146 | |||||||||
0 | 0 | |||||||||
−830.847 | −0.989547 | −0.494773 | − | 0.869022i | ||||||
−0.494773 | + | 0.869022i | ||||||||
0 | 0 | |||||||||
−24.6589 | + | 75.8924i | −0.0284061 | + | 0.0874251i | |||||
0 | 0 | |||||||||
−278.629 | + | 202.436i | −0.310672 | + | 0.225717i | |||||
0 | 0 | |||||||||
56.0629 | + | 172.544i | 0.0605467 | + | 0.186344i | |||||
0 | 0 | |||||||||
−642.830 | − | 467.043i | −0.672882 | − | 0.488877i | 0.198107 | − | 0.980180i | ||
−0.870989 | + | 0.491303i | ||||||||
0 | 0 | |||||||||
247.873 | − | 215.337i | 0.251638 | − | 0.218608i | |||||
0 | 0 | |||||||||
381.819 | + | 277.407i | 0.376162 | + | 0.273298i | 0.759762 | − | 0.650202i | ||
−0.383599 | + | 0.923500i | ||||||||
0 | 0 | |||||||||
571.034 | + | 1757.46i | 0.546268 | + | 1.68124i | 0.717955 | + | 0.696090i | ||
−0.171686 | + | 0.985152i | ||||||||
0 | 0 | |||||||||
−59.0302 | + | 42.8880i | −0.0548644 | + | 0.0398613i | |||||
0 | 0 | |||||||||
−287.507 | + | 884.855i | −0.259760 | + | 0.799460i | 0.733094 | + | 0.680127i | ||
−0.992854 | + | 0.119332i | ||||||||
0 | 0 | |||||||||
433.332 | 0.380786 | 0.190393 | − | 0.981708i | ||||||
0.190393 | + | 0.981708i | ||||||||
0 | 0 | |||||||||
−268.178 | −0.229318 | |||||||||
0 | 0 | |||||||||
−520.776 | + | 1602.78i | −0.433544 | + | 1.33431i | 0.461026 | + | 0.887386i | ||
−0.894571 | + | 0.446926i | ||||||||
0 | 0 | |||||||||
−32.4759 | + | 23.5951i | −0.0263338 | + | 0.0191327i | |||||
0 | 0 | |||||||||
−18.0999 | − | 55.7058i | −0.0143020 | − | 0.0440171i | |||||
0 | 0 | |||||||||
−772.203 | − | 561.038i | −0.594855 | − | 0.432187i | |||||
0 | 0 | |||||||||
−1195.93 | − | 584.214i | −0.898522 | − | 0.438928i | |||||
0 | 0 | |||||||||
239.282 | + | 173.848i | 0.175409 | + | 0.127442i | |||||
0 | 0 | |||||||||
150.830 | + | 464.208i | 0.107925 | + | 0.332160i | |||||
0 | 0 | |||||||||
−100.382 | + | 72.9320i | −0.0701377 | + | 0.0509580i | −0.622302 | − | 0.782778i | ||
0.552164 | + | 0.833736i | ||||||||
0 | 0 | |||||||||
−452.617 | + | 1393.01i | −0.308920 | + | 0.950758i | |||||
0 | 0 | |||||||||
−140.240 | −0.0935328 | −0.0467664 | − | 0.998906i | ||||||
−0.0467664 | + | 0.998906i | ||||||||
0 | 0 | |||||||||
−1121.45 | −0.731140 | |||||||||
0 | 0 | |||||||||
16.5501 | − | 50.9361i | 0.0105512 | − | 0.0324732i | |||||
0 | 0 | |||||||||
610.321 | − | 443.424i | 0.380608 | − | 0.276528i | −0.380988 | − | 0.924580i | ||
0.761596 | + | 0.648052i | ||||||||
0 | 0 | |||||||||
−367.333 | − | 1130.53i | −0.224149 | − | 0.689861i | −0.998377 | − | 0.0569534i | ||
0.774227 | − | 0.632907i | ||||||||
0 | 0 | |||||||||
259.336 | + | 188.418i | 0.154894 | + | 0.112537i | |||||
0 | 0 | |||||||||
−179.241 | + | 155.714i | −0.104817 | + | 0.0910594i | |||||
0 | 0 | |||||||||
−122.474 | − | 88.9827i | −0.0701443 | − | 0.0509628i | |||||
0 | 0 | |||||||||
178.604 | + | 549.686i | 0.100211 | + | 0.308417i | |||||
0 | 0 | |||||||||
1173.73 | − | 852.763i | 0.645339 | − | 0.468866i | −0.216341 | − | 0.976318i | ||
0.861680 | + | 0.507452i | ||||||||
0 | 0 | |||||||||
−870.060 | + | 2677.77i | −0.468904 | + | 1.44314i | 0.385102 | + | 0.922874i | ||
−0.854006 | + | 0.520263i | ||||||||
0 | 0 | |||||||||
700.610 | 0.370202 | |||||||||
0 | 0 | |||||||||
227.721 | 0.118006 | |||||||||
0 | 0 | |||||||||
742.481 | − | 2285.12i | 0.377429 | − | 1.16161i | −0.564396 | − | 0.825504i | ||
0.941825 | − | 0.336104i | ||||||||
0 | 0 | |||||||||
1341.03 | − | 974.314i | 0.668871 | − | 0.485963i | |||||
0 | 0 | |||||||||
−76.6779 | − | 235.990i | −0.0375346 | − | 0.115520i | |||||
0 | 0 | |||||||||
−1694.23 | − | 1230.93i | −0.814123 | − | 0.591495i | 0.100900 | − | 0.994897i | ||
−0.915023 | + | 0.403402i | ||||||||
0 | 0 | |||||||||
−216.283 | + | 18.8547i | −0.102046 | + | 0.00889598i | |||||
0 | 0 | |||||||||
3089.83 | + | 2244.90i | 1.43173 | + | 1.04021i | 0.989692 | + | 0.143214i | ||
0.442036 | + | 0.896997i | ||||||||
0 | 0 | |||||||||
−665.822 | − | 2049.19i | −0.303060 | − | 0.932722i | |||||
0 | 0 | |||||||||
665.945 | − | 483.837i | 0.297813 | − | 0.216374i | |||||
0 | 0 | |||||||||
−611.373 | + | 1881.61i | −0.268681 | + | 0.826916i | 0.722141 | + | 0.691746i | ||
−0.990822 | + | 0.135170i | ||||||||
0 | 0 | |||||||||
−1484.43 | −0.641214 | |||||||||
0 | 0 | |||||||||
508.424 | 0.215907 | |||||||||
0 | 0 | |||||||||
818.393 | − | 2518.76i | 0.341729 | − | 1.05174i | −0.621582 | − | 0.783349i | ||
0.963311 | − | 0.268386i | ||||||||
0 | 0 | |||||||||
3446.85 | − | 2504.29i | 1.41548 | − | 1.02841i | 0.422988 | − | 0.906135i | ||
0.992496 | − | 0.122274i | ||||||||
0 | 0 | |||||||||
269.682 | + | 829.995i | 0.108937 | + | 0.335273i | |||||
0 | 0 | |||||||||
143.455 | + | 104.226i | 0.0570108 | + | 0.0414208i | |||||
0 | 0 | |||||||||
−1108.88 | − | 2614.60i | −0.433632 | − | 1.02245i | |||||
0 | 0 | |||||||||
267.831 | + | 194.591i | 0.103079 | + | 0.0748910i | |||||
0 | 0 | |||||||||
−407.397 | − | 1253.84i | −0.154336 | − | 0.474998i | 0.843757 | − | 0.536726i | ||
−0.998093 | + | 0.0617276i | ||||||||
0 | 0 | |||||||||
2230.05 | − | 1620.23i | 0.831724 | − | 0.604283i | −0.0883223 | − | 0.996092i | ||
0.920047 | + | 0.391809i | ||||||||
0 | 0 | |||||||||
−11.9677 | + | 36.8328i | −0.00439500 | + | 0.0135264i | |||||
0 | 0 | |||||||||
1901.61 | 0.687738 | 0.343869 | − | 0.939018i | ||||||
0.343869 | + | 0.939018i | ||||||||
0 | 0 | |||||||||
−3994.66 | −1.42299 | −0.711493 | − | 0.702693i | ||||||
−0.711493 | + | 0.702693i | ||||||||
0 | 0 | |||||||||
−99.5203 | + | 306.292i | −0.0349235 | + | 0.107483i | |||||
0 | 0 | |||||||||
757.058 | − | 550.034i | 0.261749 | − | 0.190172i | |||||
0 | 0 | |||||||||
−60.4322 | − | 185.991i | −0.0205891 | − | 0.0633668i | |||||
0 | 0 | |||||||||
147.349 | + | 107.056i | 0.0494758 | + | 0.0359462i | |||||
0 | 0 | |||||||||
−2859.64 | − | 1719.45i | −0.946438 | − | 0.569077i | |||||
0 | 0 | |||||||||
−417.464 | − | 303.305i | −0.136206 | − | 0.0989592i | 0.517596 | − | 0.855625i | ||
−0.653802 | + | 0.756666i | ||||||||
0 | 0 | |||||||||
675.525 | + | 2079.05i | 0.217306 | + | 0.668799i | |||||
0 | 0 | |||||||||
783.502 | − | 569.247i | 0.248532 | − | 0.180569i | |||||
0 | 0 | |||||||||
−434.981 | + | 1338.73i | −0.136076 | + | 0.418798i | |||||
0 | 0 | |||||||||
−1076.02 | −0.332013 | |||||||||
0 | 0 | |||||||||
−506.624 | −0.154204 | |||||||||
0 | 0 | |||||||||
−271.131 | + | 834.455i | −0.0814182 | + | 0.250579i | −0.983477 | − | 0.181034i | ||
0.902059 | + | 0.431614i | ||||||||
0 | 0 | |||||||||
881.495 | − | 640.444i | 0.261184 | − | 0.189761i | |||||
0 | 0 | |||||||||
−1238.72 | − | 3812.39i | −0.362189 | − | 1.11470i | −0.951723 | − | 0.306959i | ||
0.589534 | − | 0.807743i | ||||||||
0 | 0 | |||||||||
−1386.93 | − | 1007.66i | −0.400222 | − | 0.290779i | 0.369409 | − | 0.929267i | ||
−0.769632 | + | 0.638488i | ||||||||
0 | 0 | |||||||||
302.288 | − | 1307.50i | 0.0861000 | − | 0.372413i | |||||
0 | 0 | |||||||||
5121.82 | + | 3721.22i | 1.44009 | + | 1.04629i | 0.988023 | + | 0.154305i | ||
0.452068 | + | 0.891983i | ||||||||
0 | 0 | |||||||||
−65.4970 | − | 201.579i | −0.0181811 | − | 0.0559556i | |||||
0 | 0 | |||||||||
−1241.44 | + | 901.962i | −0.340255 | + | 0.247210i | |||||
0 | 0 | |||||||||
−1863.05 | + | 5733.87i | −0.504228 | + | 1.55185i | 0.297837 | + | 0.954617i | ||
−0.802065 | + | 0.597237i | ||||||||
0 | 0 | |||||||||
2528.58 | 0.675852 | 0.337926 | − | 0.941173i | ||||||
0.337926 | + | 0.941173i | ||||||||
0 | 0 | |||||||||
−243.000 | −0.0641500 | |||||||||
0 | 0 | |||||||||
118.093 | − | 363.454i | 0.0307947 | − | 0.0947763i | |||||
0 | 0 | |||||||||
−481.557 | + | 349.871i | −0.124051 | + | 0.0901287i | |||||
0 | 0 | |||||||||
590.954 | + | 1818.77i | 0.150402 | + | 0.462891i | |||||
0 | 0 | |||||||||
−2313.85 | − | 1681.11i | −0.581867 | − | 0.422751i | 0.257530 | − | 0.966270i | ||
−0.839397 | + | 0.543519i | ||||||||
0 | 0 | |||||||||
166.306 | − | 719.333i | 0.0413263 | − | 0.178751i | |||||
0 | 0 | |||||||||
−374.773 | − | 272.288i | −0.0920360 | − | 0.0668681i | |||||
0 | 0 | |||||||||
1454.89 | + | 4477.69i | 0.353127 | + | 1.08681i | 0.957088 | + | 0.289798i | ||
−0.603961 | + | 0.797014i | ||||||||
0 | 0 | |||||||||
−886.746 | + | 644.259i | −0.212740 | + | 0.154565i | |||||
0 | 0 | |||||||||
−212.254 | + | 653.251i | −0.0503379 | + | 0.154924i | |||||
0 | 0 | |||||||||
−1322.27 | −0.310018 | −0.155009 | − | 0.987913i | ||||||
−0.155009 | + | 0.987913i | ||||||||
0 | 0 | |||||||||
−1096.01 | −0.254065 | |||||||||
0 | 0 | |||||||||
770.238 | − | 2370.55i | 0.176546 | − | 0.543353i | |||||
0 | 0 | |||||||||
−4208.37 | + | 3057.56i | −0.953863 | + | 0.693022i | −0.951717 | − | 0.306976i | ||
−0.00214547 | + | 0.999998i | ||||||||
0 | 0 | |||||||||
1664.83 | + | 5123.81i | 0.373177 | + | 1.14852i | 0.944700 | + | 0.327935i | ||
−0.571523 | + | 0.820586i | ||||||||
0 | 0 | |||||||||
−193.674 | − | 140.712i | −0.0429365 | − | 0.0311952i | |||||
0 | 0 | |||||||||
−3785.24 | − | 2276.00i | −0.830031 | − | 0.499083i | |||||
0 | 0 | |||||||||
2523.21 | + | 1833.22i | 0.547310 | + | 0.397644i | 0.826793 | − | 0.562507i | ||
−0.279483 | + | 0.960151i | ||||||||
0 | 0 | |||||||||
−319.281 | − | 982.645i | −0.0685120 | − | 0.210858i | |||||
0 | 0 | |||||||||
5524.63 | − | 4013.88i | 1.17285 | − | 0.852127i | 0.181505 | − | 0.983390i | ||
0.991348 | + | 0.131263i | ||||||||
0 | 0 | |||||||||
−2827.14 | + | 8701.05i | −0.593838 | + | 1.82765i | −0.0334114 | + | 0.999442i | ||
−0.560427 | + | 0.828204i | ||||||||
0 | 0 | |||||||||
−544.271 | −0.113122 | |||||||||
0 | 0 | |||||||||
1208.84 | 0.248627 | |||||||||
0 | 0 | |||||||||
354.420 | − | 1090.79i | 0.0721391 | − | 0.222021i | |||||
0 | 0 | |||||||||
1928.49 | − | 1401.13i | 0.388488 | − | 0.282253i | |||||
0 | 0 | |||||||||
1000.77 | + | 3080.04i | 0.199541 | + | 0.614123i | 0.999894 | + | 0.0145935i | ||
−0.800353 | + | 0.599529i | ||||||||
0 | 0 | |||||||||
−271.968 | − | 197.596i | −0.0536766 | − | 0.0389983i | |||||
0 | 0 | |||||||||
384.604 | + | 906.851i | 0.0751413 | + | 0.177175i | |||||
0 | 0 | |||||||||
−106.551 | − | 77.4138i | −0.0206087 | − | 0.0149731i | |||||
0 | 0 | |||||||||
1849.90 | + | 5693.42i | 0.354242 | + | 1.09024i | |||||
0 | 0 | |||||||||
−1145.46 | + | 832.222i | −0.217177 | + | 0.157789i | |||||
0 | 0 | |||||||||
178.314 | − | 548.794i | 0.0334762 | − | 0.103029i | |||||
0 | 0 | |||||||||
−3909.16 | −0.726735 | −0.363367 | − | 0.931646i | ||||||
−0.363367 | + | 0.931646i | ||||||||
0 | 0 | |||||||||
−5543.71 | −1.02062 | |||||||||
0 | 0 | |||||||||
−2705.87 | + | 8327.83i | −0.493364 | + | 1.51842i | 0.326128 | + | 0.945326i | ||
−0.819491 | + | 0.573091i | ||||||||
0 | 0 | |||||||||
4483.78 | − | 3257.66i | 0.809707 | − | 0.588286i | −0.104039 | − | 0.994573i | ||
0.913746 | + | 0.406287i | ||||||||
0 | 0 | |||||||||
−67.6426 | − | 208.183i | −0.0120991 | − | 0.0372373i | |||||
0 | 0 | |||||||||
−6558.45 | − | 4765.00i | −1.16202 | − | 0.844255i | −0.171985 | − | 0.985099i | ||
−0.990032 | + | 0.140845i | ||||||||
0 | 0 | |||||||||
2773.81 | − | 241.810i | 0.486844 | − | 0.0424413i | |||||
0 | 0 | |||||||||
−2258.11 | − | 1640.61i | −0.392633 | − | 0.285265i | |||||
0 | 0 | |||||||||
−2200.16 | − | 6771.39i | −0.379010 | − | 1.16647i | |||||
0 | 0 | |||||||||
−637.425 | + | 463.116i | −0.108794 | + | 0.0790433i | |||||
0 | 0 | |||||||||
−401.721 | + | 1236.37i | −0.0679365 | + | 0.209087i | |||||
0 | 0 | |||||||||
1310.16 | 0.219548 | |||||||||
0 | 0 | |||||||||
2603.54 | 0.432336 | 0.216168 | − | 0.976356i | ||||||
0.216168 | + | 0.976356i | ||||||||
0 | 0 | |||||||||
248.614 | − | 765.156i | 0.0409129 | − | 0.125917i | |||||
0 | 0 | |||||||||
172.274 | − | 125.165i | 0.0280966 | − | 0.0204134i | |||||
0 | 0 | |||||||||
−238.684 | − | 734.594i | −0.0385814 | − | 0.118741i | 0.929911 | − | 0.367785i | ||
−0.968492 | + | 0.249044i | ||||||||
0 | 0 | |||||||||
−4090.23 | − | 2971.73i | −0.655312 | − | 0.476112i | |||||
0 | 0 | |||||||||
−3161.80 | + | 2746.79i | −0.502114 | + | 0.436208i | |||||
0 | 0 | |||||||||
5313.56 | + | 3860.53i | 0.836458 | + | 0.607722i | |||||
0 | 0 | |||||||||
−37.2141 | − | 114.533i | −0.00580735 | − | 0.0178732i | |||||
0 | 0 | |||||||||
3408.56 | − | 2476.46i | 0.527323 | − | 0.383123i | −0.292032 | − | 0.956408i | ||
0.819355 | + | 0.573286i | ||||||||
0 | 0 | |||||||||
1483.19 | − | 4564.79i | 0.227488 | − | 0.700137i | −0.770541 | − | 0.637390i | ||
0.998029 | − | 0.0627467i | ||||||||
0 | 0 | |||||||||
175.718 | 0.0267211 | |||||||||
0 | 0 | |||||||||
−448.615 | −0.0676412 | −0.0338206 | − | 0.999428i | ||||||
−0.0338206 | + | 0.999428i | ||||||||
0 | 0 | |||||||||
446.658 | − | 1374.67i | 0.0667779 | − | 0.205521i | |||||
0 | 0 | |||||||||
2316.61 | − | 1683.11i | 0.343440 | − | 0.249523i | |||||
0 | 0 | |||||||||
−3435.35 | − | 10572.9i | −0.505045 | − | 1.55437i | −0.800695 | − | 0.599072i | ||
0.295651 | − | 0.955296i | ||||||||
0 | 0 | |||||||||
−1218.54 | − | 885.320i | −0.177655 | − | 0.129074i | |||||
0 | 0 | |||||||||
2775.55 | − | 2870.60i | 0.401319 | − | 0.415062i | |||||
0 | 0 | |||||||||
575.589 | + | 418.190i | 0.0825417 | + | 0.0599700i | |||||
0 | 0 | |||||||||
3149.15 | + | 9692.08i | 0.447913 | + | 1.37854i | 0.879257 | + | 0.476348i | ||
−0.431344 | + | 0.902188i | ||||||||
0 | 0 | |||||||||
−717.845 | + | 521.545i | −0.101272 | + | 0.0735787i | |||||
0 | 0 | |||||||||
2093.54 | − | 6443.25i | 0.292968 | − | 0.901663i | |||||
0 | 0 | |||||||||
11174.0 | 1.55112 | 0.775560 | − | 0.631274i | ||||||
0.775560 | + | 0.631274i | ||||||||
0 | 0 | |||||||||
−1464.29 | −0.201642 | |||||||||
0 | 0 | |||||||||
153.485 | − | 472.377i | 0.0209678 | − | 0.0645323i | |||||
0 | 0 | |||||||||
7717.65 | − | 5607.20i | 1.04599 | − | 0.759954i | 0.0745413 | − | 0.997218i | ||
0.971445 | + | 0.237264i | ||||||||
0 | 0 | |||||||||
−115.028 | − | 354.019i | −0.0154673 | − | 0.0476036i | |||||
0 | 0 | |||||||||
9441.77 | + | 6859.85i | 1.25967 | + | 0.915201i | 0.998741 | − | 0.0501584i | ||
0.260925 | + | 0.965359i | ||||||||
0 | 0 | |||||||||
−669.856 | + | 581.932i | −0.0886728 | + | 0.0770338i | |||||
0 | 0 | |||||||||
−3554.90 | − | 2582.78i | −0.466939 | − | 0.339251i | |||||
0 | 0 | |||||||||
−3268.87 | − | 10060.6i | −0.426063 | − | 1.31129i | −0.901973 | − | 0.431793i | ||
0.475910 | − | 0.879494i | ||||||||
0 | 0 | |||||||||
1274.50 | − | 925.977i | 0.164844 | − | 0.119766i | |||||
0 | 0 | |||||||||
130.009 | − | 400.128i | 0.0166873 | − | 0.0513582i | |||||
0 | 0 | |||||||||
1014.62 | 0.129243 | |||||||||
0 | 0 | |||||||||
−337.577 | −0.0426763 | −0.0213381 | − | 0.999772i | ||||||
−0.0213381 | + | 0.999772i | ||||||||
0 | 0 | |||||||||
1039.64 | − | 3199.67i | 0.130443 | − | 0.401464i | |||||
0 | 0 | |||||||||
−4762.00 | + | 3459.79i | −0.593024 | + | 0.430857i | −0.843396 | − | 0.537292i | ||
0.250372 | + | 0.968150i | ||||||||
0 | 0 | |||||||||
230.878 | + | 710.569i | 0.0285381 | + | 0.0878311i | |||||
0 | 0 | |||||||||
129.986 | + | 94.4407i | 0.0159483 | + | 0.0115872i | |||||
0 | 0 | |||||||||
−3248.98 | + | 283.233i | −0.395690 | + | 0.0344947i | |||||
0 | 0 | |||||||||
−10318.7 | − | 7496.99i | −1.24750 | − | 0.906363i | −0.249427 | − | 0.968394i | ||
−0.998074 | + | 0.0620309i | ||||||||
0 | 0 | |||||||||
699.366 | + | 2152.43i | 0.0839347 | + | 0.258325i | |||||
0 | 0 | |||||||||
1681.13 | − | 1221.41i | 0.200298 | − | 0.145525i | |||||
0 | 0 | |||||||||
390.740 | − | 1202.57i | 0.0462185 | − | 0.142246i | |||||
0 | 0 | |||||||||
3566.14 | 0.418788 | |||||||||
0 | 0 | |||||||||
4686.15 | 0.546380 | 0.273190 | − | 0.961960i | ||||||
0.273190 | + | 0.961960i | ||||||||
0 | 0 | |||||||||
−479.525 | + | 1475.83i | −0.0555121 | + | 0.170849i | −0.974968 | − | 0.222344i | ||
0.919456 | + | 0.393192i | ||||||||
0 | 0 | |||||||||
−778.007 | + | 565.255i | −0.0894279 | + | 0.0649732i | |||||
0 | 0 | |||||||||
−2912.30 | − | 8963.13i | −0.332393 | − | 1.02300i | |||||
0 | 0 | |||||||||
2885.66 | + | 2096.56i | 0.327042 | + | 0.237610i | |||||
0 | 0 | |||||||||
−278.114 | − | 655.760i | −0.0312994 | − | 0.0738005i | |||||
0 | 0 | |||||||||
9433.01 | + | 6853.48i | 1.05423 | + | 0.765941i | 0.973012 | − | 0.230756i | ||
0.0812156 | + | 0.996697i | ||||||||
0 | 0 | |||||||||
785.662 | + | 2418.02i | 0.0871975 | + | 0.268366i | 0.985142 | − | 0.171743i | ||
−0.897944 | + | 0.440109i | ||||||||
0 | 0 | |||||||||
367.422 | − | 266.948i | 0.0404978 | − | 0.0294234i | |||||
0 | 0 | |||||||||
571.963 | − | 1760.32i | 0.0626103 | − | 0.192695i | |||||
0 | 0 | |||||||||
−5101.99 | −0.554681 | −0.277340 | − | 0.960772i | ||||||
−0.277340 | + | 0.960772i | ||||||||
0 | 0 | |||||||||
−1733.92 | −0.187228 | |||||||||
0 | 0 | |||||||||
846.872 | − | 2606.40i | 0.0908264 | − | 0.279535i | −0.895317 | − | 0.445429i | ||
0.986144 | + | 0.165894i | ||||||||
0 | 0 | |||||||||
−1333.32 | + | 968.714i | −0.142035 | + | 0.103194i | |||||
0 | 0 | |||||||||
1344.97 | + | 4139.40i | 0.142315 | + | 0.438002i | |||||
0 | 0 | |||||||||
−8818.11 | − | 6406.73i | −0.926843 | − | 0.673391i | 0.0183750 | − | 0.999831i | ||
−0.945218 | + | 0.326440i | ||||||||
0 | 0 | |||||||||
3082.51 | + | 1853.46i | 0.321840 | + | 0.193517i | |||||
0 | 0 | |||||||||
−6833.54 | − | 4964.86i | −0.708758 | − | 0.514943i | |||||
0 | 0 | |||||||||
48.9136 | + | 150.541i | 0.00503979 | + | 0.0155109i | |||||
0 | 0 | |||||||||
−11106.2 | + | 8069.11i | −1.13682 | + | 0.825946i | −0.986673 | − | 0.162718i | ||
−0.150144 | + | 0.988664i | ||||||||
0 | 0 | |||||||||
−649.501 | + | 1998.96i | −0.0660482 | + | 0.203275i | |||||
0 | 0 | |||||||||
3104.40 | 0.313636 | 0.156818 | − | 0.987628i | ||||||
0.156818 | + | 0.987628i | ||||||||
0 | 0 | |||||||||
3771.28 | 0.378545 | 0.189272 | − | 0.981925i | ||||||
0.189272 | + | 0.981925i | ||||||||
0 | 0 | |||||||||
−211.109 | + | 649.727i | −0.0210537 | + | 0.0647965i | |||||
0 | 0 | |||||||||
−9914.73 | + | 7203.47i | −0.982439 | + | 0.713784i | −0.958252 | − | 0.285924i | ||
−0.0241865 | + | 0.999707i | ||||||||
0 | 0 | |||||||||
406.753 | + | 1251.86i | 0.0400471 | + | 0.123252i | |||||
0 | 0 | |||||||||
5831.52 | + | 4236.85i | 0.570493 | + | 0.414487i | |||||
0 | 0 | |||||||||
−4012.24 | + | 17354.4i | −0.390027 | + | 1.68701i | |||||
0 | 0 | |||||||||
−8958.09 | − | 6508.43i | −0.865316 | − | 0.628689i | |||||
0 | 0 | |||||||||
1536.68 | + | 4729.42i | 0.147505 | + | 0.453973i | |||||
0 | 0 | |||||||||
843.488 | − | 612.830i | 0.0804592 | − | 0.0584570i | −0.546828 | − | 0.837245i | ||
0.627288 | + | 0.778788i | ||||||||
0 | 0 | |||||||||
−179.778 | + | 553.298i | −0.0170419 | + | 0.0524496i | |||||
0 | 0 | |||||||||
744.405 | 0.0701275 | |||||||||
0 | 0 | |||||||||
−1576.14 | −0.147564 | |||||||||
0 | 0 | |||||||||
536.464 | − | 1651.07i | 0.0499169 | − | 0.153628i | −0.922991 | − | 0.384822i | ||
0.972908 | + | 0.231193i | ||||||||
0 | 0 | |||||||||
5082.68 | − | 3692.78i | 0.470034 | − | 0.341500i | |||||
0 | 0 | |||||||||
3489.83 | + | 10740.6i | 0.320761 | + | 0.987202i | 0.973318 | + | 0.229462i | ||
−0.652556 | + | 0.757740i | ||||||||
0 | 0 | |||||||||
4806.43 | + | 3492.07i | 0.439089 | + | 0.319016i | |||||
0 | 0 | |||||||||
146.709 | − | 634.570i | 0.0133214 | − | 0.0576198i | |||||
0 | 0 | |||||||||
7228.28 | + | 5251.66i | 0.652380 | + | 0.473982i | |||||
0 | 0 | |||||||||
−4140.83 | − | 12744.2i | −0.371481 | − | 1.14330i | −0.945822 | − | 0.324686i | ||
0.574341 | − | 0.818616i | ||||||||
0 | 0 | |||||||||
−9269.50 | + | 6734.69i | −0.826608 | + | 0.600566i | |||||
0 | 0 | |||||||||
2410.37 | − | 7418.36i | 0.213664 | − | 0.657591i | −0.785582 | − | 0.618758i | ||
0.999246 | − | 0.0388326i | ||||||||
0 | 0 | |||||||||
936.171 | 0.0824932 | |||||||||
0 | 0 | |||||||||
6463.94 | 0.566220 | |||||||||
0 | 0 | |||||||||
−6733.56 | + | 20723.8i | −0.586365 | + | 1.80465i | 0.00735129 | + | 0.999973i | ||
−0.593717 | + | 0.804674i | ||||||||
0 | 0 | |||||||||
−3557.93 | + | 2584.99i | −0.308011 | + | 0.223783i | |||||
0 | 0 | |||||||||
763.105 | + | 2348.60i | 0.0656762 | + | 0.202131i | |||||
0 | 0 | |||||||||
2965.46 | + | 2154.54i | 0.253736 | + | 0.184350i | |||||
0 | 0 | |||||||||
3340.85 | + | 2008.80i | 0.284198 | + | 0.170883i | |||||
0 | 0 | |||||||||
−4801.79 | − | 3488.70i | −0.406118 | − | 0.295062i | |||||
0 | 0 | |||||||||
−258.126 | − | 794.431i | −0.0217058 | − | 0.0668036i | 0.939617 | − | 0.342228i | ||
−0.961323 | + | 0.275425i | ||||||||
0 | 0 | |||||||||
−664.886 | + | 483.068i | −0.0555898 | + | 0.0403883i | −0.615233 | − | 0.788345i | ||
0.559643 | + | 0.828734i | ||||||||
0 | 0 | |||||||||
1376.14 | − | 4235.33i | 0.114400 | − | 0.352086i | |||||
0 | 0 | |||||||||
−8936.79 | −0.738696 | |||||||||
0 | 0 | |||||||||
−11757.5 | −0.966340 | |||||||||
0 | 0 | |||||||||
−471.335 | + | 1450.62i | −0.0385201 | + | 0.118553i | |||||
0 | 0 | |||||||||
519.087 | − | 377.138i | 0.0421841 | − | 0.0306486i | |||||
0 | 0 | |||||||||
570.300 | + | 1755.20i | 0.0460864 | + | 0.141839i | |||||
0 | 0 | |||||||||
6427.74 | + | 4670.03i | 0.516532 | + | 0.375282i | |||||
0 | 0 | |||||||||
2744.33 | + | 6470.82i | 0.219308 | + | 0.517102i | |||||
0 | 0 | |||||||||
−16604.9 | − | 12064.2i | −1.31960 | − | 0.958744i | −0.999937 | − | 0.0112114i | ||
−0.319660 | − | 0.947532i | ||||||||
0 | 0 | |||||||||
3949.74 | + | 12156.1i | 0.312154 | + | 0.960712i | |||||
0 | 0 | |||||||||
695.399 | − | 505.237i | 0.0546562 | − | 0.0397101i | |||||
0 | 0 | |||||||||
1843.40 | − | 5673.41i | 0.144092 | − | 0.443469i | −0.852801 | − | 0.522236i | ||
0.996893 | + | 0.0787666i | ||||||||
0 | 0 | |||||||||
−2618.12 | −0.203532 | |||||||||
0 | 0 | |||||||||
6980.22 | 0.539687 | |||||||||
0 | 0 | |||||||||
−1938.08 | + | 5964.79i | −0.149033 | + | 0.458677i | |||||
0 | 0 | |||||||||
−430.364 | + | 312.678i | −0.0329152 | + | 0.0239143i | |||||
0 | 0 | |||||||||
−451.401 | − | 1389.27i | −0.0343383 | − | 0.105683i | 0.932418 | − | 0.361381i | ||
−0.966757 | + | 0.255698i | ||||||||
0 | 0 | |||||||||
2570.61 | + | 1867.66i | 0.194499 | + | 0.141312i | |||||
0 | 0 | |||||||||
8487.89 | − | 739.943i | 0.638786 | − | 0.0556870i | |||||
0 | 0 | |||||||||
20000.9 | + | 14531.5i | 1.49723 | + | 1.08780i | 0.971469 | + | 0.237167i | ||
0.525759 | + | 0.850633i | ||||||||
0 | 0 | |||||||||
1033.02 | + | 3179.29i | 0.0769191 | + | 0.236733i | |||||
0 | 0 | |||||||||
−803.494 | + | 583.773i | −0.0595125 | + | 0.0432384i | |||||
0 | 0 | |||||||||
7905.61 | − | 24331.0i | 0.582461 | − | 1.79263i | −0.0267756 | − | 0.999641i | ||
0.609236 | − | 0.792989i | ||||||||
0 | 0 | |||||||||
−8840.84 | −0.647947 | −0.323973 | − | 0.946066i | ||||||
−0.323973 | + | 0.946066i | ||||||||
0 | 0 | |||||||||
3955.09 | 0.288353 | |||||||||
0 | 0 | |||||||||
757.094 | − | 2330.10i | 0.0549096 | − | 0.168994i | |||||
0 | 0 | |||||||||
−14479.3 | + | 10519.8i | −1.04468 | + | 0.759003i | −0.971193 | − | 0.238293i | ||
−0.0734847 | + | 0.997296i | ||||||||
0 | 0 | |||||||||
2555.41 | + | 7864.76i | 0.183419 | + | 0.564505i | |||||
0 | 0 | |||||||||
6323.36 | + | 4594.19i | 0.451527 | + | 0.328053i | |||||
0 | 0 | |||||||||
15217.6 | − | 13220.1i | 1.08104 | − | 0.939146i | |||||
0 | 0 | |||||||||
−93.9956 | − | 68.2918i | −0.00664314 | − | 0.00482653i | |||||
0 | 0 | |||||||||
−8445.52 | − | 25992.6i | −0.593840 | − | 1.82765i | −0.560419 | − | 0.828209i | ||
−0.0334206 | − | 0.999441i | ||||||||
0 | 0 | |||||||||
−8494.61 | + | 6171.70i | −0.594252 | + | 0.431749i | |||||
0 | 0 | |||||||||
−1762.89 | + | 5425.63i | −0.122700 | + | 0.377632i | |||||
0 | 0 | |||||||||
−389.353 | −0.0269626 | −0.0134813 | − | 0.999909i | ||||||
−0.0134813 | + | 0.999909i | ||||||||
0 | 0 | |||||||||
−1893.34 | −0.130453 | |||||||||
0 | 0 | |||||||||
3703.26 | − | 11397.5i | 0.253876 | − | 0.781351i | |||||
0 | 0 | |||||||||
−20429.9 | + | 14843.2i | −1.39356 | + | 1.01248i | −0.398096 | + | 0.917344i | ||
−0.995464 | + | 0.0951368i | ||||||||
0 | 0 | |||||||||
−2181.63 | − | 6714.37i | −0.148071 | − | 0.455715i | 0.849322 | − | 0.527875i | ||
−0.997393 | + | 0.0721596i | ||||||||
0 | 0 | |||||||||
−781.642 | − | 567.896i | −0.0527876 | − | 0.0383524i | |||||
0 | 0 | |||||||||
−2600.35 | + | 456.850i | −0.174743 | + | 0.0307002i | |||||
0 | 0 | |||||||||
−12283.3 | − | 8924.34i | −0.821357 | − | 0.596751i | 0.0957435 | − | 0.995406i | ||
−0.917101 | + | 0.398655i | ||||||||
0 | 0 | |||||||||
867.511 | + | 2669.92i | 0.0577230 | + | 0.177653i | |||||
0 | 0 | |||||||||
562.591 | − | 408.746i | 0.0372504 | − | 0.0270640i | |||||
0 | 0 | |||||||||
4796.66 | − | 14762.6i | 0.316044 | − | 0.972685i | −0.659278 | − | 0.751899i | ||
0.975322 | − | 0.220785i | ||||||||
0 | 0 | |||||||||
586.688 | 0.0384676 | |||||||||
0 | 0 | |||||||||
27430.4 | 1.78980 | 0.894899 | − | 0.446269i | ||||||
0.894899 | + | 0.446269i | ||||||||
0 | 0 | |||||||||
6668.83 | − | 20524.5i | 0.433025 | − | 1.33272i | −0.462071 | − | 0.886843i | ||
0.895097 | − | 0.445872i | ||||||||
0 | 0 | |||||||||
−442.048 | + | 321.167i | −0.0285648 | + | 0.0207536i | |||||
0 | 0 | |||||||||
−3148.07 | − | 9688.75i | −0.202447 | − | 0.623068i | |||||
0 | 0 | |||||||||
−11459.7 | − | 8325.96i | −0.733421 | − | 0.532862i | |||||
0 | 0 | |||||||||
7556.93 | − | 6565.02i | 0.481331 | − | 0.418153i | |||||
0 | 0 | |||||||||
−5629.80 | − | 4090.29i | −0.356875 | − | 0.259285i | |||||
0 | 0 | |||||||||
−2320.52 | − | 7141.83i | −0.146400 | − | 0.450573i | 0.850788 | − | 0.525509i | ||
−0.997188 | + | 0.0749353i | ||||||||
0 | 0 | |||||||||
1252.39 | − | 909.916i | 0.0786384 | − | 0.0571341i | |||||
0 | 0 | |||||||||
−76.0566 | + | 234.078i | −0.00475310 | + | 0.0146285i | |||||
0 | 0 | |||||||||
1253.83 | 0.0779883 | |||||||||
0 | 0 | |||||||||
−6558.13 | −0.406003 | |||||||||
0 | 0 | |||||||||
−2424.82 | + | 7462.83i | −0.149414 | + | 0.459850i | −0.997552 | − | 0.0699253i | ||
0.848138 | + | 0.529776i | ||||||||
0 | 0 | |||||||||
706.659 | − | 513.418i | 0.0433404 | − | 0.0314887i | −0.565904 | − | 0.824471i | ||
0.609245 | + | 0.792982i | ||||||||
0 | 0 | |||||||||
897.813 | + | 2763.18i | 0.0548083 | + | 0.168683i | |||||
0 | 0 | |||||||||
20663.0 | + | 15012.6i | 1.25556 | + | 0.912217i | 0.998531 | − | 0.0541866i | ||
0.257028 | + | 0.966404i | ||||||||
0 | 0 | |||||||||
6159.56 | − | 536.967i | 0.372548 | − | 0.0324774i | |||||
0 | 0 | |||||||||
−3416.39 | − | 2482.15i | −0.205682 | − | 0.149436i | |||||
0 | 0 | |||||||||
−3190.62 | − | 9819.73i | −0.191208 | − | 0.588477i | −1.00000 | 0.000382475i | |||
0.808792 | − | 0.588095i | ||||||||
0 | 0 | |||||||||
−225.053 | + | 163.510i | −0.0134252 | + | 0.00975401i | |||||
0 | 0 | |||||||||
997.526 | − | 3070.07i | 0.0592347 | − | 0.182306i | |||||
0 | 0 | |||||||||
−28905.7 | −1.70866 | −0.854329 | − | 0.519733i | ||||||
−0.854329 | + | 0.519733i | ||||||||
0 | 0 | |||||||||
28041.5 | 1.65006 | 0.825028 | − | 0.565092i | ||||||
0.825028 | + | 0.565092i | ||||||||
0 | 0 | |||||||||
469.666 | − | 1445.48i | 0.0275118 | − | 0.0846726i | |||||
0 | 0 | |||||||||
−1799.66 | + | 1307.53i | −0.104944 | + | 0.0762465i | |||||
0 | 0 | |||||||||
477.267 | + | 1468.88i | 0.0277059 | + | 0.0852701i | |||||
0 | 0 | |||||||||
−2129.49 | − | 1547.16i | −0.123065 | − | 0.0894123i | |||||
0 | 0 | |||||||||
4143.79 | + | 9770.57i | 0.238404 | + | 0.562129i | |||||
0 | 0 | |||||||||
−7569.87 | − | 5499.83i | −0.433576 | − | 0.315012i | 0.349501 | − | 0.936936i | ||
−0.783077 | + | 0.621924i | ||||||||
0 | 0 | |||||||||
1010.10 | + | 3108.78i | 0.0575984 | + | 0.177270i | |||||
0 | 0 | |||||||||
18651.9 | − | 13551.4i | 1.05886 | − | 0.769309i | 0.0849856 | − | 0.996382i | ||
0.973878 | + | 0.227073i | ||||||||
0 | 0 | |||||||||
3010.66 | − | 9265.84i | 0.170160 | − | 0.523697i | |||||
0 | 0 | |||||||||
12025.8 | 0.676693 | |||||||||
0 | 0 | |||||||||
18443.9 | 1.03329 | 0.516645 | − | 0.856200i | ||||||
0.516645 | + | 0.856200i | ||||||||
0 | 0 | |||||||||
462.422 | − | 1423.19i | 0.0257931 | − | 0.0793829i | |||||
0 | 0 | |||||||||
4160.79 | − | 3022.99i | 0.231068 | − | 0.167881i | |||||
0 | 0 | |||||||||
−1111.20 | − | 3419.93i | −0.0614418 | − | 0.189098i | |||||
0 | 0 | |||||||||
20208.4 | + | 14682.3i | 1.11254 | + | 0.808306i | 0.983061 | − | 0.183276i | ||
0.129476 | + | 0.991582i | ||||||||
0 | 0 | |||||||||
3450.30 | + | 2074.60i | 0.189128 | + | 0.113720i | |||||
0 | 0 | |||||||||
−1907.61 | − | 1385.96i | −0.104115 | − | 0.0756440i | |||||
0 | 0 | |||||||||
2371.63 | + | 7299.12i | 0.128884 | + | 0.396663i | |||||
0 | 0 | |||||||||
−15365.5 | + | 11163.7i | −0.831437 | + | 0.604075i | |||||
0 | 0 | |||||||||
7753.13 | − | 23861.7i | 0.417734 | − | 1.28565i | −0.492048 | − | 0.870568i | ||
0.909782 | − | 0.415086i | ||||||||
0 | 0 | |||||||||
−8175.97 | −0.438638 | |||||||||
0 | 0 | |||||||||
635.858 | 0.0339685 | |||||||||
0 | 0 | |||||||||
−1788.22 | + | 5503.59i | −0.0951246 | + | 0.292763i | |||||
0 | 0 | |||||||||
12414.6 | − | 9019.76i | 0.657604 | − | 0.477777i | −0.208249 | − | 0.978076i | ||
0.865853 | + | 0.500298i | ||||||||
0 | 0 | |||||||||
−1422.57 | − | 4378.22i | −0.0750359 | − | 0.230937i | |||||
0 | 0 | |||||||||
−1879.55 | − | 1365.57i | −0.0987232 | − | 0.0717266i | |||||
0 | 0 | |||||||||
−106.088 | + | 458.869i | −0.00554891 | + | 0.0240010i | |||||
0 | 0 | |||||||||
−14632.6 | − | 10631.2i | −0.762152 | − | 0.553736i | |||||
0 | 0 | |||||||||
−9216.75 | − | 28366.3i | −0.478063 | − | 1.47133i | −0.841783 | − | 0.539817i | ||
0.363720 | − | 0.931508i | ||||||||
0 | 0 | |||||||||
−18330.6 | + | 13318.0i | −0.946835 | + | 0.687916i | |||||
0 | 0 | |||||||||
−2344.13 | + | 7214.48i | −0.120580 | + | 0.371106i | |||||
0 | 0 | |||||||||
9239.55 | 0.473308 | |||||||||
0 | 0 | |||||||||
−19398.7 | −0.989626 | −0.494813 | − | 0.869000i | ||||||
−0.494813 | + | 0.869000i | ||||||||
0 | 0 | |||||||||
225.273 | − | 693.320i | 0.0114451 | − | 0.0352243i | |||||
0 | 0 | |||||||||
−30748.1 | + | 22339.8i | −1.55576 | + | 1.13032i | |||||
0 | 0 | |||||||||
10180.5 | + | 31332.4i | 0.512996 | + | 1.57884i | 0.786900 | + | 0.617081i | ||
−0.273904 | + | 0.961757i | ||||||||
0 | 0 | |||||||||
927.516 | + | 673.880i | 0.0465469 | + | 0.0338183i | |||||
0 | 0 | |||||||||
−882.201 | + | 3815.84i | −0.0440927 | + | 0.190717i | |||||
0 | 0 | |||||||||
5707.17 | + | 4146.50i | 0.284089 | + | 0.206403i | 0.720699 | − | 0.693248i | ||
−0.436610 | + | 0.899651i | ||||||||
0 | 0 | |||||||||
−551.815 | − | 1698.31i | −0.0273568 | − | 0.0841957i | |||||
0 | 0 | |||||||||
−4025.05 | + | 2924.37i | −0.198741 | + | 0.144394i | −0.682705 | − | 0.730694i | ||
0.483964 | + | 0.875088i | ||||||||
0 | 0 | |||||||||
889.298 | − | 2736.98i | 0.0437334 | − | 0.134598i | |||||
0 | 0 | |||||||||
−5737.10 | −0.281003 | |||||||||
0 | 0 | |||||||||
−11407.9 | −0.556523 | |||||||||
0 | 0 | |||||||||
10127.4 | − | 31168.8i | 0.492081 | − | 1.51447i | −0.329376 | − | 0.944199i | ||
0.821457 | − | 0.570270i | ||||||||
0 | 0 | |||||||||
6941.54 | − | 5043.32i | 0.335941 | − | 0.244076i | |||||
0 | 0 | |||||||||
1725.86 | + | 5311.64i | 0.0831925 | + | 0.256040i | |||||
0 | 0 | |||||||||
25632.9 | + | 18623.4i | 1.23070 | + | 0.894158i | 0.996943 | − | 0.0781357i | ||
0.233761 | + | 0.972294i | ||||||||
0 | 0 | |||||||||
1898.20 | + | 1141.36i | 0.0907779 | + | 0.0545832i | |||||
0 | 0 | |||||||||
16845.6 | + | 12239.0i | 0.802432 | + | 0.583001i | 0.911627 | − | 0.411019i | ||
−0.109195 | + | 0.994020i | ||||||||
0 | 0 | |||||||||
1641.89 | + | 5053.21i | 0.0779035 | + | 0.239762i | |||||
0 | 0 | |||||||||
1124.32 | − | 816.865i | 0.0531370 | − | 0.0386063i | |||||
0 | 0 | |||||||||
340.831 | − | 1048.97i | 0.0160452 | − | 0.0493821i | |||||
0 | 0 | |||||||||
−15356.6 | −0.720123 | −0.360062 | − | 0.932929i | ||||||
−0.360062 | + | 0.932929i | ||||||||
0 | 0 | |||||||||
−14124.4 | −0.659762 | |||||||||
0 | 0 | |||||||||
−7407.09 | + | 22796.7i | −0.344650 | + | 1.06072i | 0.617121 | + | 0.786868i | ||
−0.961771 | + | 0.273855i | ||||||||
0 | 0 | |||||||||
−11244.1 | + | 8169.33i | −0.521162 | + | 0.378646i | |||||
0 | 0 | |||||||||
−1016.12 | − | 3127.30i | −0.0469152 | − | 0.144390i | |||||
0 | 0 | |||||||||
7295.01 | + | 5300.14i | 0.335521 | + | 0.243770i | |||||
0 | 0 | |||||||||
10379.8 | + | 24474.3i | 0.475566 | + | 1.12133i | |||||
0 | 0 | |||||||||
−1667.07 | − | 1211.19i | −0.0760869 | − | 0.0552804i | |||||
0 | 0 | |||||||||
−1472.79 | − | 4532.78i | −0.0669632 | − | 0.206092i | |||||
0 | 0 | |||||||||
−20832.6 | + | 15135.7i | −0.943584 | + | 0.685554i | −0.949281 | − | 0.314430i | ||
0.00569705 | + | 0.999984i | ||||||||
0 | 0 | |||||||||
1225.81 | − | 3772.67i | 0.0553107 | − | 0.170229i | |||||
0 | 0 | |||||||||
−20663.7 | −0.928847 | |||||||||
0 | 0 | |||||||||
1893.21 | 0.0847793 | |||||||||
0 | 0 | |||||||||
1016.06 | − | 3127.10i | 0.0453281 | − | 0.139505i | |||||
0 | 0 | |||||||||
−18104.8 | + | 13153.9i | −0.804651 | + | 0.584613i | −0.912275 | − | 0.409579i | ||
0.107624 | + | 0.994192i | ||||||||
0 | 0 | |||||||||
2570.39 | + | 7910.86i | 0.113810 | + | 0.350270i | |||||
0 | 0 | |||||||||
6049.53 | + | 4395.24i | 0.266853 | + | 0.193880i | |||||
0 | 0 | |||||||||
−13036.0 | + | 1136.43i | −0.572890 | + | 0.0499424i | |||||
0 | 0 | |||||||||
−398.200 | − | 289.309i | −0.0174344 | − | 0.0126668i | |||||
0 | 0 | |||||||||
−4822.37 | − | 14841.7i | −0.210354 | − | 0.647402i | |||||
0 | 0 | |||||||||
327.625 | − | 238.034i | 0.0142382 | − | 0.0103446i | −0.580643 | − | 0.814158i | ||
0.594882 | + | 0.803813i | ||||||||
0 | 0 | |||||||||
−1964.56 | + | 6046.29i | −0.0850616 | + | 0.261793i | −0.984536 | − | 0.175180i | ||
0.899475 | + | 0.436973i | ||||||||
0 | 0 | |||||||||
−16162.5 | −0.697224 | |||||||||
0 | 0 | |||||||||
−4154.03 | −0.178539 | |||||||||
0 | 0 | |||||||||
−13799.0 | + | 42468.9i | −0.590900 | + | 1.81860i | |||||
0 | 0 | |||||||||
581.021 | − | 422.137i | 0.0247894 | − | 0.0180106i | |||||
0 | 0 | |||||||||
−13029.9 | − | 40102.0i | −0.553895 | − | 1.70471i | −0.698844 | − | 0.715274i | ||
0.144949 | − | 0.989439i | ||||||||
0 | 0 | |||||||||
12019.8 | + | 8732.87i | 0.509092 | + | 0.369877i | 0.812479 | − | 0.582991i | ||
−0.303387 | + | 0.952867i | ||||||||
0 | 0 | |||||||||
10002.9 | − | 8689.96i | 0.422130 | − | 0.366722i | |||||
0 | 0 | |||||||||
296.623 | + | 215.509i | 0.0124723 | + | 0.00906167i | 0.594004 | − | 0.804462i | ||
−0.581532 | + | 0.813524i | ||||||||
0 | 0 | |||||||||
9464.11 | + | 29127.5i | 0.396504 | + | 1.22032i | 0.927784 | + | 0.373118i | ||
−0.531279 | + | 0.847197i | ||||||||
0 | 0 | |||||||||
−7569.62 | + | 5499.65i | −0.315989 | + | 0.229580i | |||||
0 | 0 | |||||||||
−4634.50 | + | 14263.5i | −0.192768 | + | 0.593280i | |||||
0 | 0 | |||||||||
7575.88 | 0.313981 | |||||||||
0 | 0 | |||||||||
3099.64 | 0.128004 | |||||||||
0 | 0 | |||||||||
6047.10 | − | 18611.1i | 0.248831 | − | 0.765822i | −0.746152 | − | 0.665776i | ||
0.994983 | − | 0.100047i | ||||||||
0 | 0 | |||||||||
15019.0 | − | 10911.9i | 0.615809 | − | 0.447411i | |||||
0 | 0 | |||||||||
6330.66 | + | 19483.8i | 0.258647 | + | 0.796034i | |||||
0 | 0 | |||||||||
−3457.71 | − | 2512.18i | −0.140768 | − | 0.102274i | |||||
0 | 0 | |||||||||
2281.32 | − | 16159.7i | 0.0925466 | − | 0.655553i | |||||
0 | 0 | |||||||||
−22204.7 | − | 16132.6i | −0.897600 | − | 0.652144i | |||||
0 | 0 | |||||||||
−559.025 | − | 1720.50i | −0.0225184 | − | 0.0693045i | |||||
0 | 0 | |||||||||
6707.36 | − | 4873.18i | 0.269233 | − | 0.195609i | −0.444975 | − | 0.895543i | ||
0.714207 | + | 0.699934i | ||||||||
0 | 0 | |||||||||
504.567 | − | 1552.90i | 0.0201822 | − | 0.0621145i | |||||
0 | 0 | |||||||||
36841.7 | 1.46848 | 0.734240 | − | 0.678890i | ||||||
0.734240 | + | 0.678890i | ||||||||
0 | 0 | |||||||||
24003.0 | 0.953400 | 0.476700 | − | 0.879066i | ||||||
0.476700 | + | 0.879066i | ||||||||
0 | 0 | |||||||||
−1120.66 | + | 3449.04i | −0.0443577 | + | 0.136519i | |||||
0 | 0 | |||||||||
−15761.4 | + | 11451.3i | −0.621697 | + | 0.451689i | −0.853514 | − | 0.521070i | ||
0.231817 | + | 0.972759i | ||||||||
0 | 0 | |||||||||
1212.72 | + | 3732.38i | 0.0476692 | + | 0.146711i | |||||
0 | 0 | |||||||||
2783.65 | + | 2022.44i | 0.109040 | + | 0.0792222i | |||||
0 | 0 | |||||||||
−14087.5 | + | 12238.4i | −0.549927 | + | 0.477745i | |||||
0 | 0 | |||||||||
565.220 | + | 410.656i | 0.0219882 | + | 0.0159754i | |||||
0 | 0 | |||||||||
2209.85 | + | 6801.23i | 0.0856726 | + | 0.263673i | |||||
0 | 0 | |||||||||
−4841.76 | + | 3517.75i | −0.187065 | + | 0.135910i | |||||
0 | 0 | |||||||||
761.474 | − | 2343.58i | 0.0293194 | − | 0.0902360i | −0.935326 | − | 0.353787i | ||
0.964645 | + | 0.263551i | ||||||||
0 | 0 | |||||||||
−9715.64 | −0.372810 | |||||||||
0 | 0 | |||||||||
12953.1 | 0.495349 | 0.247675 | − | 0.968843i | ||||||
0.247675 | + | 0.968843i | ||||||||
0 | 0 | |||||||||
3138.31 | − | 9658.74i | 0.119607 | − | 0.368111i | −0.873273 | − | 0.487231i | ||
0.992880 | + | 0.119119i | ||||||||
0 | 0 | |||||||||
815.904 | − | 592.789i | 0.0309902 | − | 0.0225157i | |||||
0 | 0 | |||||||||
−3710.82 | − | 11420.7i | −0.140470 | − | 0.432323i | 0.855930 | − | 0.517091i | ||
−0.996401 | + | 0.0847679i | ||||||||
0 | 0 | |||||||||
−1230.83 | − | 894.248i | −0.0464349 | − | 0.0337369i | |||||
0 | 0 | |||||||||
−2943.95 | + | 256.642i | −0.110691 | + | 0.00964965i | |||||
0 | 0 | |||||||||
7906.41 | + | 5744.34i | 0.296280 | + | 0.215260i | |||||
0 | 0 | |||||||||
−1623.37 | − | 4996.22i | −0.0606294 | − | 0.186598i | |||||
0 | 0 | |||||||||
319.653 | − | 232.241i | 0.0118984 | − | 0.00864472i | |||||
0 | 0 | |||||||||
2707.46 | − | 8332.69i | 0.100444 | − | 0.309133i | |||||
0 | 0 | |||||||||
43012.3 | 1.59040 | |||||||||
0 | 0 | |||||||||
−17959.2 | −0.661845 | |||||||||
0 | 0 | |||||||||
2611.58 | − | 8037.61i | 0.0959247 | − | 0.295226i | |||||
0 | 0 | |||||||||
−5268.47 | + | 3827.77i | −0.192874 | + | 0.140131i | −0.680031 | − | 0.733183i | ||
0.487157 | + | 0.873314i | ||||||||
0 | 0 | |||||||||
−1312.58 | − | 4039.69i | −0.0478937 | − | 0.147402i | |||||
0 | 0 | |||||||||
−13675.2 | − | 9935.64i | −0.497345 | − | 0.361342i | 0.310657 | − | 0.950522i | ||
−0.808002 | + | 0.589180i | ||||||||
0 | 0 | |||||||||
9080.29 | + | 21410.3i | 0.329150 | + | 0.776097i | |||||
0 | 0 | |||||||||
1400.50 | + | 1017.52i | 0.0506000 | + | 0.0367631i | |||||
0 | 0 | |||||||||
−531.366 | − | 1635.38i | −0.0191355 | − | 0.0588930i | |||||
0 | 0 | |||||||||
27195.5 | − | 19758.7i | 0.976166 | − | 0.709226i | 0.0193174 | − | 0.999813i | ||
0.956848 | + | 0.290587i | ||||||||
0 | 0 | |||||||||
3623.99 | − | 11153.5i | 0.129658 | − | 0.399045i | |||||
0 | 0 | |||||||||
4742.30 | 0.169117 | |||||||||
0 | 0 | |||||||||
−10822.3 | −0.384688 | |||||||||
0 | 0 | |||||||||
5139.31 | − | 15817.2i | 0.182089 | − | 0.560414i | |||||
0 | 0 | |||||||||
14105.6 | − | 10248.3i | 0.498160 | − | 0.361934i | −0.310154 | − | 0.950686i | ||
0.808314 | + | 0.588752i | ||||||||
0 | 0 | |||||||||
5445.12 | + | 16758.4i | 0.191683 | + | 0.589939i | |||||
0 | 0 | |||||||||
−21252.2 | − | 15440.6i | −0.745730 | − | 0.541805i | |||||
0 | 0 | |||||||||
−4827.95 | − | 2902.96i | −0.168867 | − | 0.101537i | |||||
0 | 0 | |||||||||
−32056.6 | − | 23290.5i | −1.11766 | − | 0.812024i | −0.133804 | − | 0.991008i | ||
−0.983852 | + | 0.178983i | ||||||||
0 | 0 | |||||||||
5137.95 | + | 15813.0i | 0.178563 | + | 0.549561i | |||||
0 | 0 | |||||||||
1854.88 | − | 1347.65i | 0.0642586 | − | 0.0466866i | −0.555192 | − | 0.831722i | ||
0.619451 | + | 0.785035i | ||||||||
0 | 0 | |||||||||
−616.539 | + | 1897.51i | −0.0212909 | + | 0.0655265i | |||||
0 | 0 | |||||||||
656.688 | 0.0226054 | |||||||||
0 | 0 | |||||||||
22750.9 | 0.780680 | 0.390340 | − | 0.920671i | ||||||
0.390340 | + | 0.920671i | ||||||||
0 | 0 | |||||||||
−721.329 | + | 2220.02i | −0.0246737 | + | 0.0759378i | |||||
0 | 0 | |||||||||
19675.4 | − | 14295.0i | 0.670891 | − | 0.487431i | |||||
0 | 0 | |||||||||
−12914.9 | − | 39747.8i | −0.438985 | − | 1.35106i | −0.888947 | − | 0.458010i | ||
0.449961 | − | 0.893048i | ||||||||
0 | 0 | |||||||||
−2115.67 | − | 1537.13i | −0.0716875 | − | 0.0520840i | |||||
0 | 0 | |||||||||
−1881.54 | + | 8138.31i | −0.0635542 | + | 0.274895i | |||||
0 | 0 | |||||||||
7483.39 | + | 5437.00i | 0.251983 | + | 0.183076i | |||||
0 | 0 | |||||||||
−5133.26 | − | 15798.6i | −0.172309 | − | 0.530313i | |||||
0 | 0 | |||||||||
6774.32 | − | 4921.84i | 0.226687 | − | 0.164698i | |||||
0 | 0 | |||||||||
1689.65 | − | 5200.19i | 0.0563644 | − | 0.173472i | |||||
0 | 0 | |||||||||
−17075.1 | −0.567836 | −0.283918 | − | 0.958849i | ||||||
−0.283918 | + | 0.958849i | ||||||||
0 | 0 | |||||||||
21359.6 | 0.708121 | |||||||||
0 | 0 | |||||||||
−5934.01 | + | 18263.0i | −0.196119 | + | 0.603592i | 0.803843 | + | 0.594842i | ||
−0.999962 | + | 0.00875008i | ||||||||
0 | 0 | |||||||||
11791.7 | − | 8567.15i | 0.388513 | − | 0.282271i | |||||
0 | 0 | |||||||||
−730.424 | − | 2248.01i | −0.0239921 | − | 0.0738401i | |||||
0 | 0 | |||||||||
−27764.0 | − | 20171.8i | −0.909161 | − | 0.660544i | 0.0316416 | − | 0.999499i | ||
−0.940803 | + | 0.338955i | ||||||||
0 | 0 | |||||||||
6827.81 | − | 29532.7i | 0.222899 | − | 0.964116i | |||||
0 | 0 | |||||||||
−3155.16 | − | 2292.36i | −0.102688 | − | 0.0746069i | |||||
0 | 0 | |||||||||
1435.17 | + | 4416.99i | 0.0465664 | + | 0.143317i | 0.971636 | − | 0.236480i | ||
−0.925070 | + | 0.379797i | ||||||||
0 | 0 | |||||||||
3051.66 | − | 2217.16i | 0.0987146 | − | 0.0717203i | |||||
0 | 0 | |||||||||
−1214.58 | + | 3738.10i | −0.0391698 | + | 0.120552i | |||||
0 | 0 | |||||||||
−9880.40 | −0.317673 | |||||||||
0 | 0 | |||||||||
−14255.1 | −0.456941 | −0.228471 | − | 0.973551i | ||||||
−0.228471 | + | 0.973551i | ||||||||
0 | 0 | |||||||||
−2413.61 | + | 7428.33i | −0.0771335 | + | 0.237393i | |||||
0 | 0 | |||||||||
−6410.52 | + | 4657.52i | −0.204248 | + | 0.148395i | |||||
0 | 0 | |||||||||
−4467.91 | − | 13750.8i | −0.141926 | − | 0.436803i | 0.854677 | − | 0.519160i | ||
−0.996603 | + | 0.0823571i | ||||||||
0 | 0 | |||||||||
1952.64 | + | 1418.68i | 0.0618407 | + | 0.0449299i |
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 132.4.i.b.37.2 | yes | 8 | |
3.2 | odd | 2 | 396.4.j.b.37.1 | 8 | |||
11.3 | even | 5 | inner | 132.4.i.b.25.2 | ✓ | 8 | |
11.5 | even | 5 | 1452.4.a.o.1.2 | 4 | |||
11.6 | odd | 10 | 1452.4.a.p.1.2 | 4 | |||
33.14 | odd | 10 | 396.4.j.b.289.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
132.4.i.b.25.2 | ✓ | 8 | 11.3 | even | 5 | inner | |
132.4.i.b.37.2 | yes | 8 | 1.1 | even | 1 | trivial | |
396.4.j.b.37.1 | 8 | 3.2 | odd | 2 | |||
396.4.j.b.289.1 | 8 | 33.14 | odd | 10 | |||
1452.4.a.o.1.2 | 4 | 11.5 | even | 5 | |||
1452.4.a.p.1.2 | 4 | 11.6 | odd | 10 |