Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [65,6,Mod(51,65)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(65, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("65.51");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 65.c (of order , degree , minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | |
Analytic rank: | |
Dimension: | |
Coefficient field: | |
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 | 51.7 | ||
Root | of defining polynomial | ||
Character | 65.51 | ||
Dual form | 65.6.c.b.51.8 |
-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 .
− | 1.21921i | − | 0.215528i | −0.994176 | − | 0.107764i | ||||
0.994176 | − | 0.107764i | ||||||||
−11.3769 | −0.729828 | −0.364914 | − | 0.931041i | ||||||
−0.364914 | + | 0.931041i | ||||||||
30.5135 | 0.953548 | |||||||||
25.0000i | 0.447214i | |||||||||
13.8708i | 0.157298i | |||||||||
− | 6.14028i | − | 0.0473634i | −0.999720 | − | 0.0236817i | ||||
0.999720 | − | 0.0236817i | ||||||||
− | 76.2172i | − | 0.421045i | |||||||
−113.566 | −0.467351 | |||||||||
30.4803 | 0.0963871 | |||||||||
391.252i | 0.974933i | 0.873142 | + | 0.487467i | ||||||
−0.873142 | + | 0.487467i | ||||||||
−347.149 | −0.695926 | |||||||||
472.460 | + | 384.804i | 0.775366 | + | 0.631512i | |||||
−7.48630 | −0.0102081 | |||||||||
− | 284.422i | − | 0.326389i | |||||||
883.508 | 0.862801 | |||||||||
1547.69 | 1.29886 | 0.649428 | − | 0.760423i | ||||||
0.649428 | + | 0.760423i | ||||||||
138.461i | 0.100727i | |||||||||
3012.26i | 1.91430i | 0.289601 | + | 0.957148i | ||||||
−0.289601 | + | 0.957148i | ||||||||
762.838i | 0.426439i | |||||||||
69.8572i | 0.0345671i | |||||||||
477.019 | 0.210126 | |||||||||
921.321 | 0.363154 | 0.181577 | − | 0.983377i | ||||||
0.181577 | + | 0.983377i | ||||||||
867.115i | 0.307290i | |||||||||
−625.000 | −0.200000 | |||||||||
469.158 | − | 576.029i | 0.136109 | − | 0.167113i | |||||
4056.62 | 1.07091 | |||||||||
− | 187.361i | − | 0.0451632i | |||||||
−5248.50 | −1.15888 | −0.579442 | − | 0.815013i | ||||||
−0.579442 | + | 0.815013i | ||||||||
−346.771 | −0.0703460 | |||||||||
1749.89i | 0.327045i | 0.986540 | + | 0.163522i | ||||||
−0.986540 | + | 0.163522i | ||||||||
− | 3516.13i | − | 0.607002i | |||||||
− | 4451.23i | − | 0.711534i | |||||||
− | 1886.96i | − | 0.279940i | |||||||
153.507 | 0.0211816 | |||||||||
−3465.31 | −0.445642 | |||||||||
2782.37i | 0.334127i | 0.985946 | + | 0.167063i | ||||||
−0.985946 | + | 0.167063i | ||||||||
3672.59 | 0.412585 | |||||||||
−5375.13 | − | 4377.88i | −0.565884 | − | 0.460895i | |||||
1905.43 | 0.188297 | |||||||||
7301.71i | 0.678368i | 0.940720 | + | 0.339184i | ||||||
−0.940720 | + | 0.339184i | ||||||||
85.1708 | 0.00745019 | |||||||||
−2464.65 | −0.203275 | −0.101638 | − | 0.994821i | ||||||
−0.101638 | + | 0.994821i | ||||||||
11938.5i | 0.929645i | |||||||||
− | 2839.16i | − | 0.209006i | |||||||
− | 1123.29i | − | 0.0782700i | |||||||
− | 22645.6i | − | 1.49533i | −0.664073 | − | 0.747667i | ||||
0.664073 | − | 0.747667i | ||||||||
−10051.6 | −0.629696 | |||||||||
16769.3 | 0.997757 | |||||||||
762.007i | 0.0431056i | |||||||||
−17607.9 | −0.947941 | |||||||||
14416.4 | + | 11741.7i | 0.739349 | + | 0.602177i | |||||
−27383.4 | −1.33905 | −0.669527 | − | 0.742788i | ||||||
−0.669527 | + | 0.742788i | ||||||||
− | 4945.87i | − | 0.230812i | |||||||
−9781.30 | −0.436004 | |||||||||
−467.995 | −0.0199421 | |||||||||
− | 34270.2i | − | 1.39711i | |||||||
6399.03i | 0.249772i | |||||||||
− | 47642.5i | − | 1.78182i | −0.454176 | − | 0.890912i | ||||
0.454176 | − | 0.890912i | ||||||||
− | 8678.73i | − | 0.311227i | |||||||
−25808.7 | −0.888059 | −0.444030 | − | 0.896012i | ||||||
−0.444030 | + | 0.896012i | ||||||||
2133.49 | 0.0704873 | |||||||||
697.329i | 0.0221353i | |||||||||
23985.3 | 0.731974 | |||||||||
−9620.11 | + | 11811.5i | −0.282421 | + | 0.346754i | |||||
−5426.99 | −0.153356 | |||||||||
36207.0i | 0.985384i | 0.870204 | + | 0.492692i | ||||||
−0.870204 | + | 0.492692i | ||||||||
47225.4 | 1.23852 | |||||||||
−10481.8 | −0.265040 | |||||||||
− | 187.157i | − | 0.00456522i | |||||||
25265.2i | 0.594809i | 0.954752 | + | 0.297404i | ||||||
−0.954752 | + | 0.297404i | ||||||||
8655.71i | 0.196776i | |||||||||
− | 60584.3i | − | 1.33062i | −0.746568 | − | 0.665309i | ||||
0.746568 | − | 0.665309i | ||||||||
3392.30 | 0.0720137 | |||||||||
7110.56 | 0.145966 | |||||||||
91914.8i | 1.82537i | |||||||||
2402.40 | 0.0461762 | |||||||||
−5337.56 | + | 6553.42i | −0.0993359 | + | 0.121964i | |||||
87635.7 | 1.57984 | 0.789920 | − | 0.613209i | ||||||
0.789920 | + | 0.613209i | ||||||||
22087.7i | 0.385856i | |||||||||
−18555.1 | −0.314232 | |||||||||
8902.33 | 0.146207 | |||||||||
82465.4i | 1.31394i | 0.753915 | + | 0.656972i | ||||||
−0.753915 | + | 0.656972i | ||||||||
2131.59i | 0.0329614i | |||||||||
38692.2i | 0.580866i | |||||||||
3004.93i | 0.0438116i | |||||||||
59711.6 | 0.845787 | |||||||||
29820.1 | 0.410490 | |||||||||
26062.4i | 0.348771i | 0.984677 | + | 0.174385i | ||||||
−0.984677 | + | 0.174385i | ||||||||
−3461.54 | −0.0450467 | |||||||||
2362.80 | − | 2901.04i | 0.0299105 | − | 0.0367240i | |||||
28112.7 | 0.346285 | |||||||||
− | 19908.3i | − | 0.238686i | |||||||
−27609.7 | −0.322287 | |||||||||
−75306.6 | −0.856099 | |||||||||
40002.7i | 0.443007i | |||||||||
− | 135691.i | − | 1.46427i | −0.681159 | − | 0.732135i | ||||
0.681159 | − | 0.732135i | ||||||||
− | 20445.3i | − | 0.215045i | |||||||
− | 44433.1i | − | 0.455636i | |||||||
−19071.0 | −0.190710 | |||||||||
−144713. | −1.41157 | −0.705787 | − | 0.708424i | ||||||
−0.705787 | + | 0.708424i | ||||||||
21467.7i | 0.204308i | |||||||||
−6472.89 | −0.0601181 | −0.0300590 | − | 0.999548i | ||||||
−0.0300590 | + | 0.999548i | ||||||||
29328.7 | − | 36009.6i | 0.265895 | − | 0.326464i | |||||
−1746.43 | −0.0154589 | |||||||||
33386.2i | 0.288604i | |||||||||
89977.4 | 0.759755 | 0.379878 | − | 0.925037i | ||||||
0.379878 | + | 0.925037i | ||||||||
123782. | 1.02117 | |||||||||
36938.6i | 0.297792i | 0.988853 | + | 0.148896i | ||||||
−0.988853 | + | 0.148896i | ||||||||
11925.5i | 0.0939711i | |||||||||
− | 31654.8i | − | 0.243855i | |||||||
− | 5424.98i | − | 0.0408652i | |||||||
27703.8 | 0.204100 | 0.102050 | − | 0.994779i | ||||||
0.102050 | + | 0.994779i | ||||||||
−41782.6 | −0.301116 | |||||||||
23033.0i | 0.162408i | |||||||||
−160150. | −1.10505 | |||||||||
−53655.6 | − | 43700.8i | −0.362368 | − | 0.295138i | |||||
−58086.3 | −0.384033 | |||||||||
− | 9503.22i | − | 0.0615182i | |||||||
−21677.9 | −0.137424 | |||||||||
7972.79 | 0.0495047 | |||||||||
31466.3i | 0.191402i | |||||||||
− | 83070.8i | − | 0.495092i | |||||||
53395.4i | 0.311853i | |||||||||
− | 15625.0i | − | 0.0894427i | |||||||
850.191 | 0.00477079 | |||||||||
198569. | 1.09245 | 0.546226 | − | 0.837638i | ||||||
0.546226 | + | 0.837638i | ||||||||
− | 141759.i | − | 0.764764i | |||||||
28040.1 | 0.148356 | |||||||||
14400.7 | + | 11728.9i | 0.0747353 | + | 0.0608696i | |||||
−102104. | −0.519834 | −0.259917 | − | 0.965631i | ||||||
−0.259917 | + | 0.965631i | ||||||||
− | 135823.i | − | 0.678481i | |||||||
18496.1 | 0.0906675 | |||||||||
44144.0 | 0.212378 | |||||||||
101415.i | 0.478927i | |||||||||
− | 117960.i | − | 0.546876i | |||||||
− | 388748.i | − | 1.76957i | −0.466001 | − | 0.884784i | ||||
0.466001 | − | 0.884784i | ||||||||
12779.5i | 0.0571236i | |||||||||
−245256. | −1.07667 | −0.538334 | − | 0.842732i | ||||||
−0.538334 | + | 0.842732i | ||||||||
4684.04 | 0.0201976 | |||||||||
257636.i | 1.09134i | |||||||||
30803.7 | 0.128198 | |||||||||
−150555. | + | 184851.i | −0.615682 | + | 0.755930i | |||||
−100337. | −0.403231 | |||||||||
− | 131213.i | − | 0.518269i | |||||||
−73865.1 | −0.286786 | |||||||||
−190782. | −0.728191 | |||||||||
84900.0i | 0.318606i | |||||||||
− | 455367.i | − | 1.68034i | −0.542327 | − | 0.840168i | ||||
0.542327 | − | 0.840168i | ||||||||
− | 8669.27i | − | 0.0314597i | |||||||
265698.i | 0.948301i | 0.880444 | + | 0.474150i | ||||||
−0.880444 | + | 0.474150i | ||||||||
229586. | 0.806004 | |||||||||
−175765. | −0.607022 | |||||||||
− | 2929.03i | − | 0.00995226i | |||||||
−43747.3 | −0.146259 | |||||||||
−164014. | − | 133584.i | −0.539597 | − | 0.439485i | |||||
160333. | 0.519127 | 0.259564 | − | 0.965726i | ||||||
0.259564 | + | 0.965726i | ||||||||
− | 106846.i | − | 0.340500i | |||||||
311538. | 0.977279 | |||||||||
87903.3 | 0.271460 | |||||||||
− | 5657.16i | − | 0.0172002i | |||||||
22622.5i | 0.0677258i | |||||||||
417031.i | 1.22942i | 0.788755 | + | 0.614708i | ||||||
−0.788755 | + | 0.614708i | ||||||||
222801.i | 0.646856i | |||||||||
111281. | 0.318208 | |||||||||
100543. | 0.283192 | |||||||||
84930.5i | 0.235653i | 0.993034 | + | 0.117826i | ||||||
−0.993034 | + | 0.117826i | ||||||||
5324.32 | 0.0145543 | |||||||||
75144.3 | + | 363609.i | 0.202386 | + | 0.979306i | |||||
47173.9 | 0.125193 | |||||||||
− | 342092.i | − | 0.894648i | |||||||
−75205.2 | −0.193833 | |||||||||
−122126. | −0.310236 | −0.155118 | − | 0.987896i | ||||||
−0.155118 | + | 0.987896i | ||||||||
− | 72801.1i | − | 0.182291i | |||||||
3837.67i | 0.00947268i | |||||||||
345674.i | 0.841173i | |||||||||
542024.i | 1.30043i | |||||||||
31775.6 | 0.0751699 | |||||||||
459412. | 1.07169 | 0.535846 | − | 0.844316i | ||||||
0.535846 | + | 0.844316i | ||||||||
− | 86632.7i | − | 0.199297i | |||||||
334446. | 0.758804 | 0.379402 | − | 0.925232i | ||||||
0.379402 | + | 0.925232i | ||||||||
−3536.98 | − | 2880.76i | −0.00791505 | − | 0.00644657i | |||||
293623. | 0.648130 | |||||||||
− | 70220.5i | − | 0.152904i | |||||||
−69559.3 | −0.149426 | |||||||||
−24272.5 | −0.0514436 | |||||||||
605536.i | 1.26630i | |||||||||
− | 690996.i | − | 1.42587i | |||||||
− | 24908.7i | − | 0.0507221i | |||||||
91814.7i | 0.184513i | |||||||||
−51647.5 | −0.102439 | −0.0512195 | − | 0.998687i | ||||||
−0.0512195 | + | 0.998687i | ||||||||
−272879. | −0.534215 | |||||||||
661873.i | 1.27903i | 0.768778 | + | 0.639516i | ||||||
−0.768778 | + | 0.639516i | ||||||||
−165436. | −0.315592 | |||||||||
109447. | − | 134378.i | 0.206118 | − | 0.253071i | |||||
511690. | 0.951409 | |||||||||
− | 418033.i | − | 0.767442i | −0.923449 | − | 0.383721i | ||||
0.923449 | − | 0.383721i | ||||||||
−54173.3 | −0.0982025 | |||||||||
846082. | 1.51454 | 0.757268 | − | 0.653104i | ||||||
0.757268 | + | 0.653104i | ||||||||
47635.8i | 0.0842089i | |||||||||
− | 411923.i | − | 0.719161i | |||||||
176436.i | 0.304234i | |||||||||
32227.2i | 0.0548887i | |||||||||
−537278. | −0.903907 | |||||||||
−182543. | −0.303375 | |||||||||
7891.82i | 0.0129571i | |||||||||
−104631. | −0.169721 | |||||||||
417422. | + | 339978.i | 0.668986 | + | 0.544869i | |||||
−1.17855e6 | −1.86631 | |||||||||
2129.27i | 0.00333183i | |||||||||
469546. | 0.726059 | 0.363029 | − | 0.931778i | ||||||
0.363029 | + | 0.931778i | ||||||||
−835565. | −1.27685 | |||||||||
− | 287440.i | − | 0.434108i | |||||||
− | 109701.i | − | 0.163749i | |||||||
− | 61616.3i | − | 0.0909075i | |||||||
− | 309184.i | − | 0.450903i | |||||||
10744.8 | 0.0154899 | |||||||||
45035.9 | 0.0641827 | |||||||||
689261.i | 0.971122i | |||||||||
−298462. | −0.415750 | |||||||||
731220. | + | 595556.i | 1.00709 | + | 0.820242i | |||||
−38593.8 | −0.0525576 | |||||||||
− | 739991.i | − | 0.996470i | −0.867042 | − | 0.498235i | ||||
0.867042 | − | 0.498235i | ||||||||
−21590.0 | −0.0287497 | |||||||||
70979.0 | 0.0934703 | |||||||||
− | 33776.8i | − | 0.0439894i | |||||||
− | 102602.i | − | 0.132157i | −0.997814 | − | 0.0660786i | ||||
0.997814 | − | 0.0660786i | ||||||||
− | 1.04570e6i | − | 1.33221i | |||||||
82633.6i | 0.104128i | 0.998644 | + | 0.0520640i | ||||||
−0.998644 | + | 0.0520640i | ||||||||
28082.1 | 0.0350034 | |||||||||
−27331.8 | −0.0337006 | |||||||||
400026.i | 0.487942i | |||||||||
−145160. | −0.175169 | −0.0875846 | − | 0.996157i | ||||||
−0.0875846 | + | 0.996157i | ||||||||
−53280.5 | + | 65417.5i | −0.0636105 | + | 0.0781006i | |||||
566139. | 0.668734 | |||||||||
− | 1.45374e6i | − | 1.69905i | |||||||
−997022. | −1.15301 | |||||||||
−11586.4 | −0.0132589 | |||||||||
305532.i | 0.345989i | 0.984923 | + | 0.172994i | ||||||
−0.984923 | + | 0.172994i | ||||||||
− | 251289.i | − | 0.281609i | |||||||
− | 1.35283e6i | − | 1.50037i | −0.661226 | − | 0.750187i | ||||
0.661226 | − | 0.750187i | ||||||||
− | 9720.52i | − | 0.0106697i | |||||||
−774659. | −0.841579 | |||||||||
−787515. | −0.846807 | |||||||||
419232.i | 0.446210i | |||||||||
−101281. | −0.106706 | |||||||||
−1.15913e6 | + | 1.42317e6i | −1.20890 | + | 1.48428i | |||||
133372. | 0.137700 | |||||||||
− | 938200.i | − | 0.958952i | |||||||
−19050.2 | −0.0192774 | |||||||||
275636. | 0.276155 | 0.138077 | − | 0.990421i | ||||||
0.138077 | + | 0.990421i | ||||||||
21278.0i | 0.0211071i | |||||||||
360469.i | 0.354051i | |||||||||
− | 242098.i | − | 0.235454i | |||||||
− | 440197.i | − | 0.423932i | |||||||
594696. | 0.567146 | |||||||||
611818. | 0.577816 | 0.288908 | − | 0.957357i | ||||||
0.288908 | + | 0.957357i | ||||||||
− | 34186.8i | − | 0.0319749i | |||||||
17084.5 | 0.0158254 | |||||||||
−293543. | + | 360411.i | −0.269302 | + | 0.330647i | |||||
596053. | 0.541606 | |||||||||
124487.i | 0.112039i | |||||||||
−505146. | −0.450327 | −0.225163 | − | 0.974321i | ||||||
−0.225163 | + | 0.974321i | ||||||||
−339261. | −0.299587 | |||||||||
− | 684586.i | − | 0.598843i | |||||||
− | 22550.7i | − | 0.0195414i | |||||||
− | 296509.i | − | 0.254543i | |||||||
1.10480e6i | 0.939610i | |||||||||
325423. | 0.274200 | 0.137100 | − | 0.990557i | ||||||
0.137100 | + | 0.990557i | ||||||||
123647. | 0.103222 | |||||||||
314685.i | 0.260288i | 0.991495 | + | 0.130144i | ||||||
−0.991495 | + | 0.130144i | ||||||||
1.36739e6 | 1.12065 | |||||||||
−26881.4 | + | 33004.8i | −0.0218295 | + | 0.0268022i | |||||
−473967. | −0.381392 | |||||||||
− | 244533.i | − | 0.194987i | |||||||
−319836. | −0.252728 | |||||||||
−1.70118e6 | −1.33214 | −0.666072 | − | 0.745887i | ||||||
−0.666072 | + | 0.745887i | ||||||||
299018.i | 0.232052i | |||||||||
− | 198729.i | − | 0.152845i | |||||||
− | 11699.9i | − | 0.00891838i | |||||||
− | 973161.i | − | 0.735222i | −0.929980 | − | 0.367611i | ||||
0.929980 | − | 0.367611i | ||||||||
314113. | 0.235214 | |||||||||
855504. | 0.634974 | 0.317487 | − | 0.948263i | ||||||
0.317487 | + | 0.948263i | ||||||||
770931.i | 0.567178i | |||||||||
856755. | 0.624805 | |||||||||
225373. | + | 183559.i | 0.162924 | + | 0.132697i | |||||
44834.5 | 0.0321298 | |||||||||
399315.i | 0.283683i | |||||||||
975477. | 0.687025 | |||||||||
−159976. | −0.111702 | |||||||||
1.54374e6i | 1.06867i | |||||||||
− | 1.84864e6i | − | 1.26881i | |||||||
− | 434109.i | − | 0.295413i | −0.989031 | − | 0.147707i | ||||
0.989031 | − | 0.147707i | ||||||||
232604.i | 0.156946i | |||||||||
1.19106e6 | 0.796856 | |||||||||
212065. | 0.140682 | |||||||||
1.58716e6i | 1.04407i | |||||||||
−555189. | −0.362160 | |||||||||
435287. | + | 354528.i | 0.281578 | + | 0.229336i | |||||
216968. | 0.139185 | |||||||||
15133.6i | 0.00962781i | |||||||||
323942. | 0.204386 | |||||||||
1.64638e6 | 1.03021 | |||||||||
2.66136e6i | 1.65165i | |||||||||
− | 645218.i | − | 0.397152i | |||||||
214295.i | 0.130830i | |||||||||
− | 1.33224e6i | − | 0.806748i | −0.915035 | − | 0.403374i | ||||
0.915035 | − | 0.403374i | ||||||||
73305.6 | 0.0440312 | |||||||||
73641.3 | 0.0438758 | |||||||||
53337.2i | 0.0315229i | |||||||||
−1.22090e6 | −0.715781 | −0.357891 | − | 0.933764i | ||||||
−0.357891 | + | 0.933764i | ||||||||
−333670. | + | 409677.i | −0.194057 | + | 0.238262i | |||||
−3.36877e6 | −1.94362 | −0.971808 | − | 0.235772i | ||||||
−0.971808 | + | 0.235772i | ||||||||
− | 195480.i | − | 0.111887i | |||||||
−17433.2 | −0.00989922 | |||||||||
2.67407e6 | 1.50645 | |||||||||
− | 181109.i | − | 0.101226i | −0.998718 | − | 0.0506131i | ||||
0.998718 | − | 0.0506131i | ||||||||
− | 379831.i | − | 0.210631i | |||||||
− | 2.05349e6i | − | 1.12984i | |||||||
599633.i | 0.327349i | |||||||||
−1.02366e6 | −0.554491 | |||||||||
−6897.28 | −0.00370713 | |||||||||
4.66204e6i | 2.48639i | |||||||||
−566180. | −0.299635 | |||||||||
−295288. | − | 240503.i | −0.155073 | − | 0.126302i | |||||
508449. | 0.264974 | |||||||||
− | 420246.i | − | 0.217337i | |||||||
556516. | 0.285623 | |||||||||
−139050. | −0.0708241 | |||||||||
− | 135675.i | − | 0.0685827i | |||||||
− | 1.72873e6i | − | 0.867277i | −0.901087 | − | 0.433639i | ||||
0.901087 | − | 0.433639i | ||||||||
2.51631e6i | 1.25291i | |||||||||
− | 315984.i | − | 0.156154i | |||||||
103548. | 0.0507898 | |||||||||
−905175. | −0.440677 | |||||||||
61719.4i | 0.0298245i | |||||||||
2.31320e6 | 1.10953 | 0.554764 | − | 0.832008i | ||||||
0.554764 | + | 0.832008i | ||||||||
443317. | − | 91616.8i | 0.211068 | − | 0.0436198i | |||||
−315183. | −0.148958 | |||||||||
1.18063e6i | 0.553883i | |||||||||
−684649. | −0.318847 | |||||||||
−417082. | −0.192822 | |||||||||
− | 206168.i | − | 0.0946205i | |||||||
187849.i | 0.0855880i | |||||||||
− | 262044.i | − | 0.118530i | |||||||
148897.i | 0.0668646i | |||||||||
1.45965e6 | 0.650766 | 0.325383 | − | 0.945582i | ||||||
0.325383 | + | 0.945582i | ||||||||
1.82201e6 | 0.806498 | |||||||||
441041.i | 0.193828i | 0.995293 | + | 0.0969138i | ||||||
−0.995293 | + | 0.0969138i | ||||||||
4678.93 | 0.00204163 | |||||||||
1.91659e6 | + | 1.56100e6i | 0.830350 | + | 0.676295i | |||||
1.37569e6 | 0.591787 | |||||||||
− | 1.75552e6i | − | 0.749843i | −0.927057 | − | 0.374921i | ||||
0.927057 | − | 0.374921i | ||||||||
660842. | 0.280278 | |||||||||
−631631. | −0.266006 | |||||||||
795257.i | 0.332569i | |||||||||
108117.i | 0.0448977i | |||||||||
− | 560121.i | − | 0.230980i | |||||||
− | 2.60457e6i | − | 1.06659i | −0.845928 | − | 0.533297i | ||||
0.845928 | − | 0.533297i | ||||||||
−216393. | −0.0880008 | |||||||||
−6.59763e6 | −2.66453 | |||||||||
− | 407761.i | − | 0.163544i | |||||||
−90705.5 | −0.0361299 | |||||||||
72097.5 | − | 88520.8i | 0.0285211 | − | 0.0350181i | |||||
1.51461e6 | 0.595070 | |||||||||
− | 357989.i | − | 0.139690i | |||||||
−1.40036e6 | −0.542717 | −0.271359 | − | 0.962478i | ||||||
−0.271359 | + | 0.962478i | ||||||||
813994. | 0.313330 | |||||||||
− | 829229.i | − | 0.317036i | |||||||
84807.5i | 0.0322055i | |||||||||
168142.i | 0.0634221i | |||||||||
− | 607473.i | − | 0.227599i | |||||||
−698420. | −0.259923 | −0.129961 | − | 0.991519i | ||||||
−0.129961 | + | 0.991519i | ||||||||
738276. | 0.272923 | |||||||||
177764.i | 0.0652778i | |||||||||
−1.72598e6 | −0.629603 | |||||||||
−2.47971e6 | − | 2.01965e6i | −0.898560 | − | 0.731850i | |||||
−30369.0 | −0.0109320 | |||||||||
860183.i | 0.307605i | 0.988102 | + | 0.153802i | ||||||
−0.988102 | + | 0.153802i | ||||||||
−2.29787e6 | −0.816331 | |||||||||
−2.25910e6 | −0.797302 | |||||||||
62969.2i | 0.0220785i | |||||||||
− | 3.53928e6i | − | 1.23287i | −0.787406 | − | 0.616435i | ||||
0.787406 | − | 0.616435i | ||||||||
1.61278e6i | 0.558146i | |||||||||
60059.9i | 0.0206506i | |||||||||
806964. | 0.275668 | |||||||||
279902. | 0.0950010 | |||||||||
− | 4.14041e6i | − | 1.39625i | |||||||
854347. | 0.286260 | 0.143130 | − | 0.989704i | ||||||
0.143130 | + | 0.989704i | ||||||||
−163835. | − | 133439.i | −0.0545439 | − | 0.0444244i | |||||
1.42592e6 | 0.471685 | |||||||||
− | 1.27811e6i | − | 0.420100i | |||||||
1.16163e6 | 0.379390 | |||||||||
−509671. | −0.165405 | |||||||||
2.19089e6i | 0.706526i | |||||||||
− | 1.35581e6i | − | 0.434471i | |||||||
− | 4.61900e6i | − | 1.47086i | −0.677601 | − | 0.735430i | ||||
0.677601 | − | 0.735430i | ||||||||
− | 1.03155e6i | − | 0.326425i | |||||||
−210428. | −0.0661717 | |||||||||
−552192. | −0.172560 | |||||||||
147425.i | 0.0457835i | 0.999738 | + | 0.0228917i | ||||||
−0.999738 | + | 0.0228917i | ||||||||
−502221. | −0.154999 | |||||||||
−673366. | + | 826754.i | −0.206533 | + | 0.253579i | |||||
−4.41570e6 | −1.34600 | |||||||||
− | 463876.i | − | 0.140529i | |||||||
39291.8 | 0.0118301 | |||||||||
−1.08861e6 | −0.325751 | |||||||||
1.34202e6i | 0.399125i | |||||||||
− | 5.88390e6i | − | 1.73923i | −0.493731 | − | 0.869615i | ||||
0.493731 | − | 0.869615i | ||||||||
222558.i | 0.0653859i | |||||||||
4.42275e6i | 1.29148i | |||||||||
−197511. | −0.0573254 | |||||||||
−292538. | −0.0843932 | |||||||||
127567.i | 0.0365796i | |||||||||
−2.06164e6 | −0.587613 | |||||||||
1.35302e6 | − | 1.66123e6i | 0.383329 | − | 0.470649i | |||||
2.79025e6 | 0.785782 | |||||||||
1.43691e6i | 0.402243i | |||||||||
875261. | 0.243558 | 0.121779 | − | 0.992557i | ||||||
0.121779 | + | 0.992557i | ||||||||
−53289.8 | −0.0147408 | |||||||||
− | 268396.i | − | 0.0738025i | −0.999319 | − | 0.0369012i | ||||
0.999319 | − | 0.0369012i | ||||||||
− | 572475.i | − | 0.156486i | |||||||
2.57177e6i | 0.698847i | |||||||||
2.08709e6i | 0.563802i | |||||||||
−967304. | −0.259771 | |||||||||
−350450. | −0.0935625 | |||||||||
158473.i | 0.0420615i | |||||||||
2.74553e6 | 0.724463 | |||||||||
1.71285e6 | − | 2.10303e6i | 0.449342 | − | 0.551699i | |||||
−75123.3 | −0.0195931 | |||||||||
5.07495e6i | 1.31595i | 0.753041 | + | 0.657974i | ||||||
−0.753041 | + | 0.657974i | ||||||||
3.58405e6 | 0.923985 | |||||||||
192569. | 0.0493590 | 0.0246795 | − | 0.999695i | ||||||
0.0246795 | + | 0.999695i | ||||||||
− | 13100.2i | − | 0.00333852i | |||||||
1.49279e6i | 0.378247i | |||||||||
1.12713e6i | 0.283959i | |||||||||
2.77526e6i | 0.695185i | |||||||||
840356. | 0.209304 | |||||||||
7.75585e6 | 1.92074 | 0.960368 | − | 0.278734i | ||||||
0.960368 | + | 0.278734i | ||||||||
745504.i | 0.183577i | |||||||||
−1.90443e6 | −0.466303 | |||||||||
726109. | − | 891512.i | 0.176785 | − | 0.217056i | |||||
−1.65318e6 | −0.400230 | −0.200115 | − | 0.979772i | ||||||
−0.200115 | + | 0.979772i | ||||||||
− | 965898.i | − | 0.232527i | |||||||
−651561. | −0.155975 | |||||||||
−902205. | −0.214767 | |||||||||
5.18066e6i | 1.22636i | |||||||||
− | 147277.i | − | 0.0346688i | |||||||
4.12655e6i | 0.965988i | 0.875624 | + | 0.482994i | ||||||
−0.875624 | + | 0.482994i | ||||||||
− | 86538.4i | − | 0.0201455i | |||||||
−2.85681e6 | −0.661363 | |||||||||
845341. | 0.194619 | |||||||||
− | 3.02282e6i | − | 0.692096i | |||||||
−125094. | −0.0284836 | |||||||||
72525.9 | + | 59070.1i | 0.0164235 | + | 0.0133764i | |||||
−2.61198e6 | −0.588244 | |||||||||
− | 2.76471e6i | − | 0.619239i | −0.950861 | − | 0.309620i | ||||
0.950861 | − | 0.309620i | ||||||||
100748. | 0.0224425 | |||||||||
6.27837e6 | 1.39096 | |||||||||
702819.i | 0.154863i | |||||||||
4.25293e6i | 0.932043i | 0.884773 | + | 0.466022i | ||||||
−0.884773 | + | 0.466022i | ||||||||
33323.2i | 0.00726344i | |||||||||
2.81006e6i | 0.609204i | 0.952480 | + | 0.304602i | ||||||
−0.952480 | + | 0.304602i | ||||||||
−4.63709e6 | −0.999887 | |||||||||
497708. | 0.106744 | |||||||||
176981.i | 0.0377539i | |||||||||
8.91425e6 | 1.89144 | 0.945720 | − | 0.324982i | ||||||
0.945720 | + | 0.324982i | ||||||||
−1.63722e6 | − | 1.33347e6i | −0.345535 | − | 0.281428i | |||||
222321. | 0.0466711 | |||||||||
− | 690243.i | − | 0.144131i | |||||||
−1.82409e6 | −0.378873 | |||||||||
−3.63118e6 | −0.750228 | |||||||||
− | 964301.i | − | 0.198180i | |||||||
1.21558e6i | 0.248507i | |||||||||
− | 1.88266e6i | − | 0.382859i | |||||||
− | 289977.i | − | 0.0586605i | |||||||
3.10984e6 | 0.625809 | |||||||||
372508. | 0.0745703 | |||||||||
1.04773e6i | 0.208647i | 0.994543 | + | 0.104323i | ||||||
−0.994543 | + | 0.104323i | ||||||||
−1.00007e6 | −0.198119 | |||||||||
−1.07067e6 | + | 1.31456e6i | −0.211005 | + | 0.259070i | |||||
−1.64938e6 | −0.323373 | |||||||||
64360.9i | 0.0125532i | |||||||||
243278. | 0.0472051 | |||||||||
3.39227e6 | 0.654842 | |||||||||
944473.i | 0.181384i | |||||||||
2.64473e6i | 0.505311i | 0.967556 | + | 0.252656i | ||||||
−0.967556 | + | 0.252656i | ||||||||
1.96707e6i | 0.373913i | |||||||||
− | 4.74451e6i | − | 0.897262i | |||||||
511133. | 0.0961709 | |||||||||
−2.58589e6 | −0.484069 | −0.242034 | − | 0.970268i | ||||||
−0.242034 | + | 0.970268i | ||||||||
− | 2.53478e6i | − | 0.472093i | |||||||
−8.12304e6 | −1.50522 | |||||||||
1.73515e6 | + | 1.41323e6i | 0.319904 | + | 0.260552i | |||||
1.11083e6 | 0.203767 | |||||||||
1.54604e6i | 0.282174i | |||||||||
155135. | 0.0281722 | |||||||||
−1.14386e6 | −0.206681 | |||||||||
− | 8.62141e6i | − | 1.54998i | −0.631972 | − | 0.774992i | ||||
0.631972 | − | 0.774992i | ||||||||
− | 476774.i | − | 0.0852879i | |||||||
− | 966245.i | − | 0.171986i | |||||||
− | 336059.i | − | 0.0595191i | |||||||
4.82702e6 | 0.850665 | 0.425333 | − | 0.905037i | ||||||
0.425333 | + | 0.905037i | ||||||||
53148.5 | 0.00931997 | |||||||||
− | 3.61782e6i | − | 0.631275i | |||||||
439488. | 0.0763081 | |||||||||
−854909. | − | 4.13674e6i | −0.147707 | − | 0.714725i | |||||
6.05905e6 | 1.04171 | |||||||||
7.34279e6i | 1.25622i | 0.778124 | + | 0.628111i | ||||||
−0.778124 | + | 0.628111i | ||||||||
−536693. | −0.0913693 | |||||||||
−372005. | −0.0630225 | |||||||||
− | 5.26136e6i | − | 0.887000i | |||||||
1.22196e7i | 2.05005i | |||||||||
− | 745936.i | − | 0.124536i | |||||||
− | 161822.i | − | 0.0268856i | |||||||
855602. | 0.141464 | |||||||||
8.86012e6 | 1.45785 | |||||||||
− | 20829.7i | − | 0.00341081i | |||||||
1.38941e6 | 0.226419 | |||||||||
900240. | + | 733218.i | 0.145999 | + | 0.118912i | |||||
1.06181e7 | 1.71377 | 0.856885 | − | 0.515508i | ||||||
0.856885 | + | 0.515508i | ||||||||
− | 726715.i | − | 0.116731i | |||||||
−7.02911e6 | −1.12369 | −0.561844 | − | 0.827243i | ||||||
−0.561844 | + | 0.827243i | ||||||||
−3.11556e6 | −0.495687 | |||||||||
− | 43660.8i | − | 0.00691342i | |||||||
615880.i | 0.0970581i | |||||||||
2.70828e6i | 0.424784i | |||||||||
− | 3.93270e6i | − | 0.613912i | |||||||
−5.58751e6 | −0.868119 | |||||||||
−834655. | −0.129068 | |||||||||
5.41059e6i | 0.832738i | |||||||||
564382. | 0.0864558 | |||||||||
−2.80973e6 | + | 3.44977e6i | −0.428397 | + | 0.525983i | |||||
−361508. | −0.0548611 | |||||||||
2.24943e6i | 0.339773i | |||||||||
2.75960e6 | 0.414891 | |||||||||
−5.22668e6 | −0.782150 | |||||||||
− | 396760.i | − | 0.0590979i | |||||||
6.56102e6i | 0.972746i | |||||||||
3.09454e6i | 0.456680i | |||||||||
1.98960e6i | 0.292263i | 0.989265 | + | 0.146131i | ||||||
−0.989265 | + | 0.146131i | ||||||||
383668. | 0.0560993 | |||||||||
−3.80496e6 | −0.553796 | |||||||||
− | 5.44187e6i | − | 0.788408i | |||||||
−923464. | −0.133177 | |||||||||
40239.8 | + | 32774.1i | 0.00577663 | + | 0.00470488i | |||||
−7.00138e6 | −1.00050 | −0.500248 | − | 0.865882i | ||||||
−0.500248 | + | 0.865882i | ||||||||
− | 1.18621e7i | − | 1.68737i | |||||||
2.93100e6 | 0.415036 | |||||||||
−298137. | −0.0420251 | |||||||||
− | 1.58099e7i | − | 2.21845i | |||||||
798891.i | 0.111594i | |||||||||
− | 538107.i | − | 0.0748266i | |||||||
2.07410e6i | 0.287115i | |||||||||
791369. | 0.109055 | |||||||||
−7.48361e6 | −1.02665 | |||||||||
− | 2.38525e6i | − | 0.325759i | −0.986646 | − | 0.162879i | ||||
0.986646 | − | 0.162879i | ||||||||
−242292. | −0.0329423 | |||||||||
−1.16445e6 | − | 948409.i | −0.157613 | − | 0.128371i | |||||
135625. | 0.0182755 | |||||||||
− | 6.88911e6i | − | 0.924179i | |||||||
−1.18649e6 | −0.158461 | |||||||||
1.10441e7 | 1.46845 | 0.734226 | − | 0.678905i | ||||||
0.734226 | + | 0.678905i | ||||||||
7.86138e6i | 1.04064i | |||||||||
692595.i | 0.0912764i | |||||||||
− | 1.04304e6i | − | 0.136855i | |||||||
113933.i | 0.0148831i | |||||||||
1.92564e6 | 0.250441 | |||||||||
−1.05466e7 | −1.36563 | −0.682815 | − | 0.730591i | ||||||
−0.682815 | + | 0.730591i | ||||||||
− | 1.04457e6i | − | 0.134663i | |||||||
−2.56217e6 | −0.328865 | −0.164433 | − | 0.986388i | ||||||
−0.164433 | + | 0.986388i | ||||||||
−4.59398e6 | + | 5.64046e6i | −0.587082 | + | 0.720816i | |||||
587588. | 0.0747629 | |||||||||
− | 54662.8i | − | 0.00692487i | |||||||
−575826. | −0.0726309 | |||||||||
−2.72393e6 | −0.342089 | |||||||||
− | 1.48196e7i | − | 1.85309i | −0.376183 | − | 0.926545i | ||||
0.376183 | − | 0.926545i | ||||||||
− | 1.18931e6i | − | 0.148073i | |||||||
− | 7.53006e6i | − | 0.933474i | |||||||
− | 4.00376e6i | − | 0.494194i | |||||||
506360. | 0.0622328 | |||||||||
1.88215e6 | 0.230328 | |||||||||
− | 1.07138e7i | − | 1.30549i | |||||||
−4.61757e6 | −0.560249 | |||||||||
1.09252e6 | − | 1.34139e6i | 0.131990 | − | 0.162056i | |||||
−529271. | −0.0636699 | |||||||||
1.20402e7i | 1.44224i | 0.692809 | + | 0.721121i | ||||||
−0.692809 | + | 0.721121i | ||||||||
−5.82145e6 | −0.694364 | |||||||||
−5.27113e6 | −0.626060 | |||||||||
− | 1.45216e6i | − | 0.171745i | |||||||
4.75592e6i | 0.560100i | |||||||||
2.45825e6i | 0.288285i | |||||||||
2.36654e6i | 0.276361i | 0.990407 | + | 0.138180i | ||||||
−0.990407 | + | 0.138180i | ||||||||
1.93508e6 | 0.225026 | |||||||||
237581. | 0.0275118 | |||||||||
− | 1.38949e7i | − | 1.60228i | |||||||
−9.62578e6 | −1.10535 | |||||||||
432245. | − | 530708.i | 0.0494284 | − | 0.0606879i | |||||
−292768. | −0.0333392 | −0.0166696 | − | 0.999861i | ||||||
−0.0166696 | + | 0.999861i | ||||||||
− | 541947.i | − | 0.0614580i | |||||||
1.20438e7 | 1.36011 | 0.680057 | − | 0.733159i | ||||||
0.680057 | + | 0.733159i | ||||||||
18451.1 | 0.00207506 | |||||||||
− | 4.11190e6i | − | 0.460520i | |||||||
8.10738e6i | 0.904250i | |||||||||
199320.i | 0.0221392i | |||||||||
− | 2.00729e6i | − | 0.222039i | |||||||
−1.05634e7 | −1.16367 | −0.581836 | − | 0.813306i | ||||||
−0.581836 | + | 0.813306i | ||||||||
1.05915e7 | 1.16198 | |||||||||
− | 366646.i | − | 0.0400593i | |||||||
−786657. | −0.0855975 | |||||||||
8.71411e6 | − | 1.06991e7i | 0.944322 | − | 1.15943i | |||||
−5.36321e6 | −0.578824 | |||||||||
1.72742e7i | 1.85673i | 0.371675 | + | 0.928363i | ||||||
−0.371675 | + | 0.928363i | ||||||||
−1.62429e6 | −0.173877 | |||||||||
2.07677e6 | 0.221412 | |||||||||
− | 183104.i | − | 0.0194422i | |||||||
1.23381e7i | 1.30477i | 0.757886 | + | 0.652387i | ||||||
−0.757886 | + | 0.652387i | ||||||||
− | 89784.4i | − | 0.00945648i | |||||||
3.76541e6i | 0.394990i | 0.980304 | + | 0.197495i | ||||||
−0.980304 | + | 0.197495i | ||||||||
−1.33488e6 | −0.139465 | |||||||||
3.73745e6 | 0.388907 | |||||||||
1.48854e6i | 0.154271i | |||||||||
160031. | 0.0165190 | |||||||||
−4.74897e6 | − | 3.86789e6i | −0.488245 | − | 0.397660i | |||||
390625. | 0.0400000 | |||||||||
4.10724e6i | 0.418904i | |||||||||
1.34083e7 | 1.36209 | |||||||||
4.89232e6 | 0.495012 | |||||||||
4.30624e6i | 0.433982i | |||||||||
21254.8i | 0.00213356i | |||||||||
4.25951e6i | 0.425879i | 0.977065 | + | 0.212940i | ||||||
−0.977065 | + | 0.212940i | ||||||||
− | 6.67935e6i | − | 0.665183i | |||||||
−5.34197e6 | −0.529898 | |||||||||
−220811. | −0.0218171 | |||||||||
4.96423e6i | 0.488560i | |||||||||
9.50613e6 | 0.931882 | |||||||||
7.92283e6 | + | 6.45290e6i | 0.773627 | + | 0.630095i | |||||
−2.50364e6 | −0.243511 | |||||||||
− | 2.86928e6i | − | 0.277985i | |||||||
3.54399e6 | 0.342013 | |||||||||
2.97347e6 | 0.285837 | 0.142918 | − | 0.989734i | ||||||
0.142918 | + | 0.989734i | ||||||||
1.24806e6i | 0.119508i | |||||||||
9.08699e6i | 0.866748i | 0.901214 | + | 0.433374i | ||||||
−0.901214 | + | 0.433374i | ||||||||
− | 172620.i | − | 0.0164012i | |||||||
701002.i | 0.0663468i | |||||||||
5.68401e6 | 0.535888 | |||||||||
−1.70405e7 | −1.60037 | −0.800185 | − | 0.599753i | ||||||
−0.800185 | + | 0.599753i | ||||||||
1.41421e6i | 0.132306i | |||||||||
1.86402e7 | 1.73716 | |||||||||
−293224. | + | 360018.i | −0.0272217 | + | 0.0334227i | |||||
−122243. | −0.0113050 | |||||||||
1.27251e7i | 1.17231i | |||||||||
33156.7 | 0.00304291 | 0.00152145 | − | 0.999999i | ||||||
0.00152145 | + | 0.999999i | ||||||||
−512369. | −0.0468423 | |||||||||
− | 2.55260e6i | − | 0.232477i | |||||||
6.45112e6i | 0.585296i | |||||||||
6.88034e6i | 0.621866i | |||||||||
169531.i | 0.0152646i | |||||||||
1.21273e7 | 1.08780 | 0.543902 | − | 0.839149i | ||||||
0.543902 | + | 0.839149i | ||||||||
3.39557e6 | 0.303426 | |||||||||
− | 7.42160e6i | − | 0.660684i | −0.943861 | − | 0.330342i | ||||
0.943861 | − | 0.330342i | ||||||||
−2.10769e6 | −0.186923 | |||||||||
−8.31901e6 | − | 6.77558e6i | −0.735001 | − | 0.598636i | |||||
6.28528e6 | 0.553229 | |||||||||
462403.i | 0.0405477i | |||||||||
−385251. | −0.0336557 | |||||||||
−4.83555e6 | −0.420854 | |||||||||
2.59153e6i | 0.224706i | |||||||||
8.41879e6i | 0.727251i | |||||||||
1.10360e6i | 0.0949783i | |||||||||
− | 1.00977e7i | − | 0.865799i | |||||||
245627. | 0.0209823 | |||||||||
1.24325e7 | 1.05809 | 0.529043 | − | 0.848595i | ||||||
0.529043 | + | 0.848595i | ||||||||
− | 2.82028e6i | − | 0.239135i | |||||||
−2.53539e6 | −0.214183 | |||||||||
2.29292e6 | + | 1.10950e7i | 0.192984 | + | 0.933815i | |||||
−8.45003e6 | −0.708576 | −0.354288 | − | 0.935136i | ||||||
−0.354288 | + | 0.935136i | ||||||||
384275.i | 0.0321047i | |||||||||
−833179. | −0.0693528 | |||||||||
2.94901e6 | 0.244570 | |||||||||
1.16729e6i | 0.0964520i | |||||||||
834732.i | 0.0687205i | |||||||||
− | 9.91289e6i | − | 0.813108i | −0.913627 | − | 0.406554i | ||||
0.913627 | − | 0.406554i | ||||||||
− | 1.04384e7i | − | 0.853090i | |||||||
9.71871e6 | 0.791375 | |||||||||
−251362. | −0.0203934 | |||||||||
− | 940113.i | − | 0.0759956i | |||||||
−2.17754e6 | −0.175386 | |||||||||
−1.29376e7 | − | 1.05373e7i | −1.03826 | − | 0.845629i | |||||
−319487. | −0.0255465 | |||||||||
− | 3.01942e6i | − | 0.240563i | −0.992740 | − | 0.120281i | ||||
0.992740 | − | 0.120281i | ||||||||
−3.72649e6 | −0.295825 | |||||||||
−272831. | −0.0215805 | |||||||||
− | 1.77962e6i | − | 0.140258i | |||||||
− | 6.13139e6i | − | 0.481501i | |||||||
− | 4.55105e6i | − | 0.356114i | |||||||
1.13008e7i | 0.881101i | |||||||||
537722. | 0.0417753 | |||||||||
1.65147e6 | 0.127843 | |||||||||
117101.i | 0.00903265i | |||||||||
7.55729e6 | 0.580859 | 0.290430 | − | 0.956896i | ||||||
0.290430 | + | 0.956896i | ||||||||
1.90319e6 | − | 2.33673e6i | 0.145761 | − | 0.178964i | |||||
−8.38124e6 | −0.639617 | |||||||||
9.38431e6i | 0.713626i | |||||||||
−6.44090e6 | −0.488061 | |||||||||
−2.14036e6 | −0.161612 | |||||||||
888577.i | 0.0668570i | |||||||||
1.65391e7i | 1.24002i | |||||||||
8.22641e6i | 0.614603i | 0.951612 | + | 0.307302i | ||||||
−0.951612 | + | 0.307302i | ||||||||
770091.i | 0.0573319i | |||||||||
−9.95247e6 | −0.738341 | |||||||||
1.98641e6 | 0.146848 | |||||||||
1.61221e6i | 0.118768i | |||||||||
131818. | 0.00967672 | |||||||||
−4.62128e6 | − | 3.76389e6i | −0.338062 | − | 0.275341i | |||||
1.40183e7 | 1.02191 | |||||||||
− | 3.47600e6i | − | 0.252512i | |||||||
−3.17552e6 | −0.229881 | |||||||||
−2.42533e7 | −1.74964 | −0.874821 | − | 0.484446i | ||||||
−0.874821 | + | 0.484446i | ||||||||
− | 2.50842e6i | − | 0.180330i | |||||||
39745.3i | 0.00284740i | |||||||||
8.04391e6i | 0.574280i | |||||||||
1.53910e7i | 1.09501i | |||||||||
1.02051e7 | 0.723556 | |||||||||
3.28031e6 | 0.231777 | |||||||||
110589.i | 0.00778702i | |||||||||
−4.40741e6 | −0.309277 | −0.154638 | − | 0.987971i | ||||||
−0.154638 | + | 0.987971i | ||||||||
−221109. | − | 180086.i | −0.0154624 | − | 0.0125937i | |||||
1.33221e7 | 0.928439 | |||||||||
− | 1.84663e6i | − | 0.128254i | |||||||
−3.81451e6 | −0.264025 | |||||||||
8.95947e6 | 0.618023 | |||||||||
− | 1.70711e7i | − | 1.17355i | −0.809751 | − | 0.586774i | ||||
0.809751 | − | 0.586774i | ||||||||
1.70733e6i | 0.116971i | |||||||||
− | 4.76956e6i | − | 0.325657i | |||||||
− | 3.23949e6i | − | 0.220436i | |||||||
−1.41661e7 | −0.960684 | |||||||||
−1.01101e6 | −0.0683302 | |||||||||
− | 6.86306e6i | − | 0.462281i | −0.972920 | − | 0.231141i | ||||
0.972920 | − | 0.231141i | ||||||||
−2.12250e6 | −0.142485 | |||||||||
1.31873e7 | − | 1.61913e7i | 0.882289 | − | 1.08327i | |||||
205000. | 0.0136693 | |||||||||
− | 7.82433e6i | − | 0.519966i | −0.965613 | − | 0.259983i | ||||
0.965613 | − | 0.259983i | ||||||||
−1.51736e6 | −0.100498 | |||||||||
1.13842e7 | 0.751469 | |||||||||
851521.i | 0.0560207i | |||||||||
− | 9.36530e6i | − | 0.614073i | |||||||
1.84770e7i | 1.20747i | |||||||||
− | 552486.i | − | 0.0359846i | |||||||
216732. | 0.0140692 | |||||||||
−1.55733e7 | −1.00758 | −0.503790 | − | 0.863826i | ||||||
−0.503790 | + | 0.863826i | ||||||||
− | 2.00075e7i | − | 1.29018i | |||||||
−3.13588e6 | −0.201545 | |||||||||
−2.46238e6 | + | 3.02329e6i | −0.157734 | + | 0.193665i | |||||
−6.64245e6 | −0.424093 | |||||||||
− | 760053.i | − | 0.0483659i | |||||||
4.30381e6 | 0.272969 | 0.136485 | − | 0.990642i | ||||||
0.136485 | + | 0.990642i | ||||||||
1.04874e6 | 0.0662974 | |||||||||
− | 4.10101e6i | − | 0.258397i | |||||||
5.73966e6i | 0.360456i | |||||||||
2.17549e7i | 1.36174i | 0.732403 | + | 0.680871i | ||||||
−0.732403 | + | 0.680871i | ||||||||
2.75432e6i | 0.171841i | |||||||||
226813. | 0.0141045 | |||||||||
−1.57595e6 | −0.0976805 | |||||||||
− | 4.39413e6i | − | 0.271468i | |||||||
−4.31513e6 | −0.265718 | |||||||||
1.83331e7 | − | 2.25092e7i | 1.12524 | − | 1.38157i | |||||
−6.76579e6 | −0.413919 | |||||||||
2.85348e7i | 1.74004i | 0.493017 | + | 0.870020i | ||||||
−0.493017 | + | 0.870020i | ||||||||
73225.7 | 0.00445079 | |||||||||
−6.96059e6 | −0.421706 | |||||||||
2.01961e7i | 1.21962i | |||||||||
− | 2.79269e7i | − | 1.68102i | −0.541795 | − | 0.840511i | ||||
0.541795 | − | 0.840511i | ||||||||
− | 341259.i | − | 0.0204754i | |||||||
− | 1.09368e6i | − | 0.0654089i | |||||||
−1.03420e7 | −0.616523 | |||||||||
−194369. | −0.0115498 | |||||||||
− | 1.04163e6i | − | 0.0616971i | |||||||
−2.19947e7 | −1.29860 | |||||||||
3.33961e6 | − | 4.10035e6i | 0.196544 | − | 0.241315i | |||||
−9.88507e6 | −0.579899 | |||||||||
− | 1.73849e6i | − | 0.101661i | |||||||
−2.12912e7 | −1.24107 | |||||||||
1.48158e7 | 0.860865 | |||||||||
4.00832e6i | 0.232161i | |||||||||
− | 1.41627e6i | − | 0.0817692i | |||||||
− | 2.09367e7i | − | 1.20496i | −0.798136 | − | 0.602478i | ||||
0.798136 | − | 0.602478i | ||||||||
− | 1.27557e7i | − | 0.731792i | |||||||
5.74700e6 | 0.328661 | |||||||||
2.67116e6 | 0.152276 | |||||||||
− | 170109.i | − | 0.00966688i | |||||||
−3.38657e6 | −0.191843 | |||||||||
−1.21936e7 | − | 9.93131e6i | −0.688571 | − | 0.560820i | |||||
−5.63153e6 | −0.317012 | |||||||||
7.78846e6i | 0.437052i | |||||||||
2.58169e7 | 1.44418 | |||||||||
1.45712e7 | 0.812549 | 0.406274 | − | 0.913751i | ||||||
0.406274 | + | 0.913751i | ||||||||
256557.i | 0.0142619i | |||||||||
− | 3.50482e7i | − | 1.94222i | |||||||
2.19758e6i | 0.121400i | |||||||||
− | 2.95982e6i | − | 0.162998i | |||||||
179742. | 0.00986763 | |||||||||
2.37037e7 | 1.29726 | |||||||||
− | 1.25692e7i | − | 0.685754i | |||||||
141429. | 0.00769217 | |||||||||
1.00799e6 | + | 820975.i | 0.0546535 | + | 0.0445136i | |||||
−3.70231e6 | −0.200119 | |||||||||
1.10296e7i | 0.594336i | |||||||||
−2.59047e7 | −1.39158 | −0.695789 | − | 0.718246i | ||||||
−0.695789 | + | 0.718246i | ||||||||
−565564. | −0.0302879 | |||||||||
9.38778e6i | 0.501200i | 0.968091 | + | 0.250600i | ||||||
−0.968091 | + | 0.250600i | ||||||||
983367.i | 0.0523390i | |||||||||
− | 3.58014e6i | − | 0.189965i | |||||||
1.32725e6i | 0.0702086i | |||||||||
−1.04258e7 | −0.549812 | |||||||||
−1.55567e7 | −0.817884 | |||||||||
− | 7.42418e6i | − | 0.389129i | |||||||
−7.17372e6 | −0.374853 | |||||||||
−268335. | + | 329460.i | −0.0139787 | + | 0.0171630i | |||||
−5.57002e6 | −0.289283 | |||||||||
7.37712e6i | 0.381970i | 0.981593 | + | 0.190985i | ||||||
−0.981593 | + | 0.190985i | ||||||||
5.39227e6 | 0.278350 | |||||||||
2.13960e7 | 1.10111 | 0.550557 | − | 0.834798i | ||||||
0.550557 | + | 0.834798i | ||||||||
493345.i | 0.0253124i | |||||||||
2.78202e6i | 0.142307i | |||||||||
356666.i | 0.0181891i | |||||||||
− | 6.14027e6i | − | 0.312194i | −0.987742 | − | 0.156097i | ||||
0.987742 | − | 0.156097i | ||||||||
−3.19266e6 | −0.161837 | |||||||||
−1.46790e7 | −0.741838 | −0.370919 | − | 0.928665i | ||||||
−0.370919 | + | 0.928665i | ||||||||
2.51357e6i | 0.126647i | |||||||||
1.93542e7 | 0.972237 | |||||||||
1.13321e7 | + | 9.22966e6i | 0.567548 | + | 0.462251i | |||||
2.59536e7 | 1.29594 | |||||||||
− | 3.40190e6i | − | 0.169358i | |||||||
−2.12326e6 | −0.105387 | |||||||||
−3.59618e7 | −1.77962 | |||||||||
7.09864e6i | 0.350237i | |||||||||
− | 1.06713e6i | − | 0.0524937i | |||||||
2.35783e7i | 1.15640i | 0.815896 | + | 0.578198i | ||||||
−0.815896 | + | 0.578198i | ||||||||
133108.i | 0.00650888i | |||||||||
7.03561e6 | 0.343014 | |||||||||
−327232. | −0.0159065 | |||||||||
1.10715e7i | 0.536586i | |||||||||
1.43275e7 | 0.692331 | |||||||||
−9.09024e6 | + | 1.87861e6i | −0.437959 | + | 0.0905096i | |||||
3.13554e6 | 0.150621 | |||||||||
− | 48955.1i | − | 0.00234471i | |||||||
−2.41935e7 | −1.15534 | |||||||||
−9.73298e6 | −0.463422 | |||||||||
1.17935e6i | 0.0559880i | |||||||||
2.56346e6i | 0.121340i | |||||||||
− | 8.77080e6i | − | 0.413943i | |||||||
1.60837e7i | 0.756856i | 0.925631 | + | 0.378428i | ||||||
−0.925631 | + | 0.378428i | ||||||||
193212. | 0.00906544 | |||||||||
8.55229e6 | 0.400099 | |||||||||
− | 6.85782e6i | − | 0.319891i | |||||||
2.45455e7 | 1.14162 | 0.570809 | − | 0.821083i | ||||||
0.570809 | + | 0.821083i | ||||||||
−2.56404e6 | − | 2.08833e6i | −0.118907 | − | 0.0968459i | |||||
2.36147e7 | 1.09194 | 0.545971 | − | 0.837804i | ||||||
0.545971 | + | 0.837804i | ||||||||
− | 1.88013e6i | − | 0.0866846i | |||||||
−510077. | −0.0234492 | |||||||||
6.18744e6 | 0.283624 | |||||||||
− | 2.10316e7i | − | 0.961271i | −0.876920 | − | 0.480635i | ||||
0.876920 | − | 0.480635i | ||||||||
− | 1.42636e7i | − | 0.650047i | |||||||
− | 3.05314e6i | − | 0.138742i | |||||||
− | 234782.i | − | 0.0106383i | |||||||
−1.10979e7 | −0.501410 | |||||||||
327862. | 0.0147704 | |||||||||
3.42876e7i | 1.54024i | |||||||||
1.82003e6 | 0.0815229 | |||||||||
−1.39326e7 | + | 1.71064e7i | −0.622282 | + | 0.764033i | |||||
2.81535e6 | 0.125384 | |||||||||
1.54099e7i | 0.684329i | |||||||||
3.38363e6 | 0.149832 | |||||||||
−95941.8 | −0.00423631 | |||||||||
2.10318e7i | 0.926011i | |||||||||
2.16451e7i | 0.950298i | 0.879905 | + | 0.475149i | ||||||
−0.879905 | + | 0.475149i | ||||||||
− | 9.45602e6i | − | 0.413973i | |||||||
4.93881e6i | 0.215601i | |||||||||
−8.64186e6 | −0.376184 | |||||||||
1.25222e7 | 0.543552 | 0.271776 | − | 0.962360i | ||||||
0.271776 | + | 0.962360i | ||||||||
2.32190e6i | 0.100501i | |||||||||
4.38601e6 | 0.189307 | 0.0946537 | − | 0.995510i | ||||||
0.0946537 | + | 0.995510i | ||||||||
2.23121e7 | + | 1.81725e7i | 0.960307 | + | 0.782140i | |||||
−1.35506e7 | −0.581568 | |||||||||
2.01557e6i | 0.0862609i | |||||||||
3.48074e7 | 1.48547 | 0.742733 | − | 0.669587i | ||||||
0.742733 | + | 0.669587i | ||||||||
−2.41264e6 | −0.102674 | |||||||||
− | 1.21927e6i | − | 0.0517423i | |||||||
794391.i | 0.0336170i | |||||||||
− | 7.25971e6i | − | 0.306355i | |||||||
− | 2.25797e7i | − | 0.950181i | |||||||
6.82144e7 | 2.86251 | |||||||||
6.31632e6 | 0.264314 | |||||||||
1.14853e7i | 0.479275i | |||||||||
−870442. | −0.0362218 | |||||||||
−4.95222e6 | − | 4.03343e6i | −0.205503 | − | 0.167376i | |||||
5.03114e6 | 0.208198 | |||||||||
− | 9.18431e6i | − | 0.379007i | |||||||
2.16582e6 | 0.0891283 | |||||||||
−4.23810e7 | −1.73924 | |||||||||
3.48306e6i | 0.142542i | |||||||||
− | 172174.i | − | 0.00702664i | |||||||
− | 2.11151e6i | − | 0.0859353i | |||||||
8.36115e6i | 0.339347i | |||||||||
−3.68546e6 | −0.149166 | |||||||||
−8.74330e6 | −0.352904 | −0.176452 | − | 0.984309i | ||||||
−0.176452 | + | 0.984309i | ||||||||
− | 3.13075e6i | − | 0.126018i | |||||||
1.64345e7 | 0.659701 | |||||||||
72019.0 | − | 88424.4i | 0.00288299 | − | 0.00353972i | |||||
−2.23703e7 | −0.893048 | −0.446524 | − | 0.894772i | ||||||
−0.446524 | + | 0.894772i | ||||||||
− | 3.02780e7i | − | 1.20542i | |||||||
−3.22648e7 | −1.28101 | |||||||||
−3.37076e6 | −0.133463 | |||||||||
7.34058e6i | 0.289853i | |||||||||
2.52144e6i | 0.0992911i | |||||||||
626947.i | 0.0246211i | |||||||||
− | 7.65466e6i | − | 0.299792i | |||||||
−3.29243e6 | −0.128596 | −0.0642981 | − | 0.997931i | ||||||
−0.0642981 | + | 0.997931i | ||||||||
1.75551e6 | 0.0683808 | |||||||||
1.51568e7i | 0.588787i | |||||||||
5.18522e6 | 0.200882 | |||||||||
−9.72217e6 | + | 1.19368e7i | −0.375629 | + | 0.461194i | |||||
−833989. | −0.0321352 | |||||||||
− | 1.73898e6i | − | 0.0668253i | |||||||
3.42606e6 | 0.131301 | |||||||||
735102. | 0.0280963 | |||||||||
1.84544e7i | 0.703446i | |||||||||
2.50376e7i | 0.951817i | 0.879495 | + | 0.475908i | ||||||
−0.879495 | + | 0.475908i | ||||||||
− | 606812.i | − | 0.0230063i | |||||||
5.05135e7i | 1.91000i | |||||||||
−4.42935e6 | −0.167032 | |||||||||
1.38901e7 | 0.522397 | |||||||||
− | 1.08684e7i | − | 0.407659i | |||||||
−1.51384e7 | −0.566305 | |||||||||
−3.33075e6 | + | 4.08948e6i | −0.124266 | + | 0.152573i | |||||
−4.64120e6 | −0.172696 | −0.0863478 | − | 0.996265i | ||||||
−0.0863478 | + | 0.996265i | ||||||||
− | 271056.i | − | 0.0100589i | |||||||
3.83261e7 | 1.41851 | |||||||||
1.72749e7 | 0.637670 | |||||||||
− | 1.62911e7i | − | 0.599760i | −0.953977 | − | 0.299880i | ||||
0.953977 | − | 0.299880i | ||||||||
2.22395e6i | 0.0816579i | |||||||||
6.72722e6i | 0.246352i | |||||||||
− | 4.20926e7i | − | 1.53736i | |||||||
622719. | 0.0226836 | |||||||||
−1.17569e6 | −0.0427134 | |||||||||
2.98948e7i | 1.08323i | 0.840627 | + | 0.541614i | ||||||
−0.840627 | + | 0.541614i | ||||||||
−3.04226e7 | −1.09945 | |||||||||
2.33131e7 | − | 2.86237e7i | 0.840301 | − | 1.03172i | |||||
−2.29537e6 | −0.0825169 | |||||||||
2.06046e6i | 0.0738777i | |||||||||
−724309. | −0.0259019 | |||||||||
4.34693e7 | 1.55043 | 0.775213 | − | 0.631700i | ||||||
0.775213 | + | 0.631700i | ||||||||
− | 3.79155e6i | − | 0.134879i | |||||||
− | 1.29119e6i | − | 0.0458122i | |||||||
9.32286e6i | 0.329917i | |||||||||
2.33623e7i | 0.824586i | |||||||||
1.27741e6 | 0.0449692 | |||||||||
−2.38702e6 | −0.0838127 | |||||||||
− | 6.82196e6i | − | 0.238908i | |||||||
2.55670e7 | 0.893042 | |||||||||
1.60273e6 | + | 1.30537e6i | 0.0558370 | + | 0.0454775i | |||||
−1.02184e7 | −0.355073 | |||||||||
− | 4.12795e7i | − | 1.43068i | |||||||
−1.65468e7 | −0.572001 | |||||||||
78469.6 | 0.00270557 | |||||||||
− | 2.94293e7i | − | 1.01208i | −0.862510 | − | 0.506039i | ||||
0.862510 | − | 0.506039i | ||||||||
− | 607664.i | − | 0.0208437i | |||||||
− | 5.30395e7i | − | 1.81464i | |||||||
− | 4.13590e6i | − | 0.141137i | |||||||
−3.14967e7 | −1.07205 | −0.536027 | − | 0.844201i | ||||||
−0.536027 | + | 0.844201i | ||||||||
−2.36376e7 | −0.802486 | |||||||||
1.50594e6i | 0.0509947i | |||||||||
3.22448e6 | 0.108909 | |||||||||
3.35946e6 | + | 2.73617e6i | 0.113177 | + | 0.0921790i | |||||
−2.28022e7 | −0.766218 | |||||||||
− | 5.67335e6i | − | 0.190153i | −0.995470 | − | 0.0950764i | ||||
0.995470 | − | 0.0950764i | ||||||||
−5.78457e6 | −0.193385 | |||||||||
−1.01970e7 | −0.340028 | |||||||||
1.27923e7i | 0.425483i | |||||||||
− | 4.19498e6i | − | 0.139174i | |||||||
3.15275e6i | 0.104330i | |||||||||
− | 1.96686e7i | − | 0.649217i | −0.945848 | − | 0.324609i | ||||
0.945848 | − | 0.324609i | ||||||||
−6.33142e6 | −0.208456 | |||||||||
1.04508e7 | 0.343210 | |||||||||
9.90370e6i | 0.324418i | |||||||||
1.58196e6 | 0.0516894 | |||||||||
−3.53692e7 | + | 4.34261e7i | −1.15274 | + | 1.41533i | |||||
−2.27074e6 | −0.0738203 | |||||||||
− | 1.35433e6i | − | 0.0439175i | |||||||
3.75674e7 | 1.21514 | 0.607571 | − | 0.794266i | ||||||
0.607571 | + | 0.794266i | ||||||||
6.15285e6 | 0.198517 | |||||||||
1.96676e7i | 0.632963i | |||||||||
− | 189143.i | − | 0.00607189i | |||||||
2.11520e7i | 0.677321i | |||||||||
− | 2.86278e7i | − | 0.914407i | |||||||
−6.54052e6 | −0.208389 | −0.104194 | − | 0.994557i | ||||||
−0.104194 | + | 0.994557i | ||||||||
−1.05113e7 | −0.334065 | |||||||||
1.12870e7i | 0.357821i |
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 65.6.c.b.51.7 | ✓ | 14 | |
13.5 | odd | 4 | 845.6.a.i.1.5 | 7 | |||
13.8 | odd | 4 | 845.6.a.j.1.3 | 7 | |||
13.12 | even | 2 | inner | 65.6.c.b.51.8 | yes | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
65.6.c.b.51.7 | ✓ | 14 | 1.1 | even | 1 | trivial | |
65.6.c.b.51.8 | yes | 14 | 13.12 | even | 2 | inner | |
845.6.a.i.1.5 | 7 | 13.5 | odd | 4 | |||
845.6.a.j.1.3 | 7 | 13.8 | odd | 4 |