Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [78,6,Mod(25,78)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(78, 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("78.25");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 78.b (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 | 25.6 | ||
Root | of defining polynomial | ||
Character | 78.25 | ||
Dual form | 78.6.b.a.25.1 |
-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of on generators for .
Coefficient data
For each we display the coefficients of the -expansion , the Satake parameters , and the Satake angles .
4.00000i | 0.707107i | |||||||||
−9.00000 | −0.577350 | |||||||||
−16.0000 | −0.500000 | |||||||||
37.1158i | 0.663948i | 0.943289 | + | 0.331974i | ||||||
−0.943289 | + | 0.331974i | ||||||||
− | 36.0000i | − | 0.408248i | |||||||
176.407i | 1.36072i | 0.732876 | + | 0.680362i | ||||||
−0.732876 | + | 0.680362i | ||||||||
− | 64.0000i | − | 0.353553i | |||||||
81.0000 | 0.333333 | |||||||||
−148.463 | −0.469482 | |||||||||
− | 179.404i | − | 0.447044i | −0.974699 | − | 0.223522i | ||||
0.974699 | − | 0.223522i | ||||||||
144.000 | 0.288675 | |||||||||
−554.740 | − | 252.104i | −0.910397 | − | 0.413735i | |||||
−705.627 | −0.962177 | |||||||||
− | 334.042i | − | 0.383330i | |||||||
256.000 | 0.250000 | |||||||||
−933.141 | −0.783114 | −0.391557 | − | 0.920154i | ||||||
−0.391557 | + | 0.920154i | ||||||||
324.000i | 0.235702i | |||||||||
− | 2335.97i | − | 1.48451i | −0.670117 | − | 0.742256i | ||||
0.670117 | − | 0.742256i | ||||||||
− | 593.853i | − | 0.331974i | |||||||
− | 1587.66i | − | 0.785614i | |||||||
717.615 | 0.316108 | |||||||||
−2792.36 | −1.10066 | −0.550328 | − | 0.834948i | ||||||
−0.550328 | + | 0.834948i | ||||||||
576.000i | 0.204124i | |||||||||
1747.42 | 0.559174 | |||||||||
1008.42 | − | 2218.96i | 0.292555 | − | 0.643748i | |||||
−729.000 | −0.192450 | |||||||||
− | 2822.51i | − | 0.680362i | |||||||
1503.58 | 0.331996 | 0.165998 | − | 0.986126i | ||||||
0.165998 | + | 0.986126i | ||||||||
1336.17 | 0.271055 | |||||||||
− | 737.236i | − | 0.137785i | −0.997624 | − | 0.0688926i | ||||
0.997624 | − | 0.0688926i | ||||||||
1024.00i | 0.176777i | |||||||||
1614.63i | 0.258101i | |||||||||
− | 3732.56i | − | 0.553745i | |||||||
−6547.48 | −0.903450 | |||||||||
−1296.00 | −0.166667 | |||||||||
− | 3775.41i | − | 0.453377i | −0.973967 | − | 0.226689i | ||||
0.973967 | − | 0.226689i | ||||||||
9343.88 | 1.04971 | |||||||||
4992.66 | + | 2268.94i | 0.525618 | + | 0.238870i | |||||
2375.41 | 0.234741 | |||||||||
368.848i | 0.0342680i | 0.999853 | + | 0.0171340i | ||||||
−0.999853 | + | 0.0171340i | ||||||||
6350.64 | 0.555513 | |||||||||
−20180.6 | −1.66442 | −0.832211 | − | 0.554459i | ||||||
−0.832211 | + | 0.554459i | ||||||||
2870.46i | 0.223522i | |||||||||
3006.38i | 0.221316i | |||||||||
− | 11169.4i | − | 0.778282i | |||||||
20526.5i | 1.35541i | 0.735335 | + | 0.677704i | ||||||
−0.735335 | + | 0.677704i | ||||||||
−2304.00 | −0.144338 | |||||||||
−14312.3 | −0.851570 | |||||||||
6989.67i | 0.395395i | |||||||||
8398.27 | 0.452131 | |||||||||
8875.84 | + | 4033.67i | 0.455199 | + | 0.206867i | |||||
−25081.9 | −1.22651 | −0.613253 | − | 0.789886i | ||||||
−0.613253 | + | 0.789886i | ||||||||
− | 2916.00i | − | 0.136083i | |||||||
6658.72 | 0.296814 | |||||||||
11290.0 | 0.481089 | |||||||||
21023.7i | 0.857083i | |||||||||
6014.33i | 0.234756i | |||||||||
35326.3i | 1.32120i | 0.750738 | + | 0.660600i | ||||||
−0.750738 | + | 0.660600i | ||||||||
5344.68i | 0.191665i | |||||||||
31741.4 | 1.09220 | 0.546099 | − | 0.837721i | ||||||
0.546099 | + | 0.837721i | ||||||||
2948.94 | 0.0974288 | |||||||||
14288.9i | 0.453575i | |||||||||
−4096.00 | −0.125000 | |||||||||
9357.06 | − | 20589.6i | 0.274698 | − | 0.604456i | |||||
−6458.54 | −0.182505 | |||||||||
− | 46661.3i | − | 1.26990i | −0.772552 | − | 0.634951i | ||||
0.772552 | − | 0.634951i | ||||||||
14930.3 | 0.391557 | |||||||||
25131.2 | 0.635465 | |||||||||
− | 26189.9i | − | 0.638835i | |||||||
58973.4i | 1.38839i | 0.719789 | + | 0.694193i | ||||||
−0.719789 | + | 0.694193i | ||||||||
− | 5184.00i | − | 0.117851i | |||||||
3411.20i | 0.0749204i | 0.999298 | + | 0.0374602i | ||||||
−0.999298 | + | 0.0374602i | ||||||||
15101.6 | 0.320586 | |||||||||
−15726.8 | −0.322839 | |||||||||
37375.5i | 0.742256i | |||||||||
31648.1 | 0.608303 | |||||||||
−9075.76 | + | 19970.6i | −0.168907 | + | 0.371668i | |||||
−64977.3 | −1.17137 | −0.585685 | − | 0.810539i | ||||||
−0.585685 | + | 0.810539i | ||||||||
9501.64i | 0.165987i | |||||||||
6561.00 | 0.111111 | |||||||||
−1475.39 | −0.0242311 | |||||||||
12233.4i | 0.194918i | 0.995240 | + | 0.0974591i | ||||||
−0.995240 | + | 0.0974591i | ||||||||
25402.6i | 0.392807i | |||||||||
− | 34634.3i | − | 0.519947i | |||||||
− | 80722.5i | − | 1.17692i | |||||||
−13532.2 | −0.191678 | |||||||||
−11481.8 | −0.158054 | |||||||||
− | 61754.7i | − | 0.826409i | −0.910638 | − | 0.413204i | ||||
0.910638 | − | 0.413204i | ||||||||
−12025.5 | −0.156494 | |||||||||
44472.9 | − | 97859.9i | 0.562979 | − | 1.23880i | |||||
44677.8 | 0.550328 | |||||||||
6635.12i | 0.0795503i | |||||||||
−82106.0 | −0.958418 | |||||||||
86701.4 | 0.985638 | |||||||||
− | 9216.00i | − | 0.102062i | |||||||
− | 28030.7i | − | 0.302485i | −0.988497 | − | 0.151243i | ||||
0.988497 | − | 0.151243i | ||||||||
− | 57249.4i | − | 0.602151i | |||||||
− | 14531.7i | − | 0.149015i | |||||||
−27958.7 | −0.279587 | |||||||||
102600. | 1.00080 | 0.500398 | − | 0.865796i | ||||||
0.500398 | + | 0.865796i | ||||||||
33593.1i | 0.319705i | |||||||||
−203803. | −1.89286 | −0.946430 | − | 0.322909i | ||||||
−0.946430 | + | 0.322909i | ||||||||
−16134.7 | + | 35503.4i | −0.146277 | + | 0.321874i | |||||
58927.3 | 0.521607 | |||||||||
− | 100327.i | − | 0.867271i | |||||||
−147356. | −1.24425 | −0.622125 | − | 0.782918i | ||||||
−0.622125 | + | 0.782918i | ||||||||
11664.0 | 0.0962250 | |||||||||
7846.65i | 0.0632584i | 0.999500 | + | 0.0316292i | ||||||
−0.999500 | + | 0.0316292i | ||||||||
26634.9i | 0.209879i | |||||||||
33978.7i | 0.261758i | |||||||||
45160.1i | 0.340181i | |||||||||
−192673. | −1.41947 | −0.709733 | − | 0.704471i | ||||||
−0.709733 | + | 0.704471i | ||||||||
−84095.0 | −0.606049 | |||||||||
− | 103641.i | − | 0.730778i | |||||||
−24057.3 | −0.165998 | |||||||||
−44933.9 | − | 20420.5i | −0.303466 | − | 0.137912i | |||||
−141305. | −0.934229 | |||||||||
− | 164612.i | − | 1.06560i | |||||||
−21378.7 | −0.135528 | |||||||||
128865. | 0.800152 | |||||||||
126966.i | 0.772301i | |||||||||
− | 3319.64i | − | 0.0197846i | |||||||
11795.8i | 0.0688926i | |||||||||
180844.i | 1.03521i | |||||||||
−57155.8 | −0.320726 | |||||||||
255644. | 1.40646 | 0.703229 | − | 0.710964i | ||||||
0.703229 | + | 0.710964i | ||||||||
− | 16384.0i | − | 0.0883883i | |||||||
181626. | 0.960955 | |||||||||
82358.5 | + | 37428.2i | 0.427415 | + | 0.194241i | |||||
−134257. | −0.683530 | −0.341765 | − | 0.939786i | ||||||
−0.341765 | + | 0.939786i | ||||||||
− | 25834.2i | − | 0.129050i | |||||||
412081. | 2.02001 | |||||||||
186645. | 0.897956 | |||||||||
− | 27057.4i | − | 0.127777i | |||||||
59721.0i | 0.276873i | |||||||||
− | 74373.4i | − | 0.338545i | −0.985569 | − | 0.169272i | ||||
0.985569 | − | 0.169272i | ||||||||
100525.i | 0.449341i | |||||||||
36348.4 | 0.159569 | 0.0797844 | − | 0.996812i | ||||||
0.0797844 | + | 0.996812i | ||||||||
104760. | 0.451725 | |||||||||
− | 184738.i | − | 0.782545i | |||||||
−235893. | −0.981737 | |||||||||
−45228.5 | + | 99522.5i | −0.184958 | + | 0.406988i | |||||
20736.0 | 0.0833333 | |||||||||
55806.7i | 0.220428i | |||||||||
−13644.8 | −0.0529767 | |||||||||
128811. | 0.491654 | |||||||||
60406.6i | 0.226689i | |||||||||
221253.i | 0.816440i | 0.912884 | + | 0.408220i | ||||||
−0.912884 | + | 0.408220i | ||||||||
− | 62907.0i | − | 0.228282i | |||||||
482448.i | 1.72190i | 0.508690 | + | 0.860950i | ||||||
−0.508690 | + | 0.860950i | ||||||||
−149502. | −0.524854 | |||||||||
−75584.4 | −0.261038 | |||||||||
126592.i | 0.430135i | |||||||||
27363.1 | 0.0914821 | |||||||||
−79882.5 | − | 36303.0i | −0.262809 | − | 0.119435i | |||||
−110726. | −0.358508 | −0.179254 | − | 0.983803i | ||||||
−0.179254 | + | 0.983803i | ||||||||
− | 259909.i | − | 0.828283i | |||||||
225737. | 0.708124 | |||||||||
−38006.6 | −0.117370 | |||||||||
− | 492591.i | − | 1.49769i | |||||||
26244.0i | 0.0785674i | |||||||||
161064.i | 0.474819i | 0.971410 | + | 0.237410i | ||||||
−0.971410 | + | 0.237410i | ||||||||
− | 5901.58i | − | 0.0171340i | |||||||
−59928.5 | −0.171365 | |||||||||
−48933.7 | −0.137828 | |||||||||
466578.i | 1.29459i | 0.762238 | + | 0.647296i | ||||||
−0.762238 | + | 0.647296i | ||||||||
−101610. | −0.277757 | |||||||||
244180. | + | 279705.i | 0.657647 | + | 0.753326i | |||||
138537. | 0.367658 | |||||||||
− | 189214.i | − | 0.494837i | |||||||
322890. | 0.832211 | |||||||||
−240767. | −0.611620 | −0.305810 | − | 0.952093i | ||||||
−0.305810 | + | 0.952093i | ||||||||
− | 54129.0i | − | 0.135537i | |||||||
308256.i | 0.760881i | |||||||||
− | 45927.4i | − | 0.111761i | |||||||
− | 317937.i | − | 0.762795i | |||||||
247019. | 0.584359 | |||||||||
−266435. | −0.621526 | −0.310763 | − | 0.950487i | ||||||
−0.310763 | + | 0.950487i | ||||||||
− | 48102.1i | − | 0.110658i | |||||||
64307.2 | 0.145903 | 0.0729513 | − | 0.997336i | ||||||
0.0729513 | + | 0.997336i | ||||||||
391439. | + | 177892.i | 0.875964 | + | 0.398086i | |||||
−285673. | −0.630581 | |||||||||
178711.i | 0.389141i | |||||||||
140127. | 0.301019 | |||||||||
−26540.5 | −0.0562505 | |||||||||
167409.i | 0.350086i | |||||||||
− | 328424.i | − | 0.677704i | |||||||
− | 128601.i | − | 0.261871i | |||||||
346806.i | 0.696951i | |||||||||
−925387. | −1.83544 | −0.917720 | − | 0.397228i | ||||||
−0.917720 | + | 0.397228i | ||||||||
36864.0 | 0.0721688 | |||||||||
− | 632306.i | − | 1.22190i | −0.791671 | − | 0.610948i | ||||
0.791671 | − | 0.610948i | ||||||||
112123. | 0.213889 | |||||||||
−84213.5 | + | 185307.i | −0.158597 | + | 0.348983i | |||||
228997. | 0.425785 | |||||||||
100048.i | 0.183671i | 0.995774 | + | 0.0918357i | ||||||
−0.995774 | + | 0.0918357i | ||||||||
58126.8 | 0.105369 | |||||||||
−723076. | −1.29435 | −0.647174 | − | 0.762342i | ||||||
−0.647174 | + | 0.762342i | ||||||||
− | 111835.i | − | 0.197698i | |||||||
419952.i | 0.733178i | |||||||||
410401.i | 0.707669i | |||||||||
265242.i | 0.451754i | |||||||||
−134372. | −0.226066 | |||||||||
−13690.1 | −0.0227521 | |||||||||
− | 815214.i | − | 1.33845i | |||||||
−226181. | −0.366886 | |||||||||
−142013. | − | 64538.7i | −0.227599 | − | 0.103434i | |||||
−419082. | −0.663641 | |||||||||
235709.i | 0.368832i | |||||||||
259548. | 0.401340 | 0.200670 | − | 0.979659i | ||||||
0.200670 | + | 0.979659i | ||||||||
401310. | 0.613253 | |||||||||
− | 530760.i | − | 0.801585i | |||||||
− | 589423.i | − | 0.879818i | |||||||
− | 749020.i | − | 1.10509i | |||||||
46656.0i | 0.0680414i | |||||||||
130053. | 0.187488 | |||||||||
−31386.6 | −0.0447304 | |||||||||
− | 30700.8i | − | 0.0432553i | |||||||
−106539. | −0.148407 | |||||||||
517651. | + | 235249.i | 0.712945 | + | 0.324002i | |||||
−135915. | −0.185091 | |||||||||
− | 1.07196e6i | − | 1.44349i | −0.692156 | − | 0.721747i | ||||
0.692156 | − | 0.721747i | ||||||||
−180641. | −0.240544 | |||||||||
141541. | 0.186391 | |||||||||
− | 770692.i | − | 1.00371i | |||||||
65210.0i | 0.0839942i | 0.999118 | + | 0.0419971i | ||||||
−0.999118 | + | 0.0419971i | ||||||||
− | 336380.i | − | 0.428541i | |||||||
191854.i | 0.241759i | 0.992667 | + | 0.120879i | ||||||
−0.992667 | + | 0.120879i | ||||||||
414563. | 0.516738 | |||||||||
−284832. | −0.351204 | |||||||||
− | 96229.3i | − | 0.117378i | |||||||
353920. | 0.427087 | 0.213543 | − | 0.976934i | ||||||
0.213543 | + | 0.976934i | ||||||||
81681.8 | − | 179736.i | 0.0975182 | − | 0.214583i | |||||
−761857. | −0.899920 | |||||||||
− | 565221.i | − | 0.660600i | |||||||
584796. | 0.676291 | |||||||||
658450. | 0.753495 | |||||||||
− | 1.15374e6i | − | 1.30651i | −0.757138 | − | 0.653255i | ||||
0.757138 | − | 0.653255i | ||||||||
− | 85514.8i | − | 0.0958326i | |||||||
209753.i | 0.232630i | 0.993212 | + | 0.116315i | ||||||
−0.993212 | + | 0.116315i | ||||||||
515461.i | 0.565793i | |||||||||
−59049.0 | −0.0641500 | |||||||||
−507862. | −0.546099 | |||||||||
− | 531214.i | − | 0.565398i | |||||||
13278.5 | 0.0139898 | |||||||||
−588909. | + | 1.29586e6i | −0.614194 | + | 1.35150i | |||||
−47183.1 | −0.0487144 | |||||||||
− | 110101.i | − | 0.112536i | |||||||
−723375. | −0.732004 | |||||||||
427156. | 0.427959 | 0.213979 | − | 0.976838i | ||||||
0.213979 | + | 0.976838i | ||||||||
− | 228623.i | − | 0.226787i | |||||||
500960.i | 0.492042i | |||||||||
1.02258e6i | 0.994515i | |||||||||
311708.i | 0.300191i | |||||||||
65536.0 | 0.0625000 | |||||||||
207722. | 0.196177 | 0.0980887 | − | 0.995178i | ||||||
0.0980887 | + | 0.995178i | ||||||||
726503.i | 0.679498i | |||||||||
666008. | 0.616922 | |||||||||
−149713. | + | 329434.i | −0.137349 | + | 0.302228i | |||||
121790. | 0.110665 | |||||||||
− | 537026.i | − | 0.483328i | |||||||
−831712. | −0.741453 | −0.370726 | − | 0.928742i | ||||||
−0.370726 | + | 0.928742i | ||||||||
103337. | 0.0912524 | |||||||||
− | 930933.i | − | 0.814336i | |||||||
1.64832e6i | 1.42836i | |||||||||
555792.i | 0.477127i | |||||||||
746581.i | 0.634951i | |||||||||
1.67365e6 | 1.41021 | 0.705104 | − | 0.709104i | ||||||
0.705104 | + | 0.709104i | ||||||||
108230. | 0.0903518 | |||||||||
69792.6i | 0.0577279i | 0.999583 | + | 0.0288640i | ||||||
−0.999583 | + | 0.0288640i | ||||||||
−238884. | −0.195779 | |||||||||
−400256. | + | 880739.i | −0.325036 | + | 0.715221i | |||||
297494. | 0.239387 | |||||||||
− | 313493.i | − | 0.249975i | |||||||
−402100. | −0.317732 | |||||||||
1.61380e6 | 1.26372 | 0.631859 | − | 0.775083i | ||||||
0.631859 | + | 0.775083i | ||||||||
145394.i | 0.112832i | |||||||||
− | 59716.1i | − | 0.0459284i | |||||||
419039.i | 0.319418i | |||||||||
1.05655e6i | 0.798224i | 0.916902 | + | 0.399112i | ||||||
−0.916902 | + | 0.399112i | ||||||||
738954. | 0.553343 | |||||||||
−512741. | −0.380567 | −0.190284 | − | 0.981729i | ||||||
−0.190284 | + | 0.981729i | ||||||||
− | 943574.i | − | 0.694193i | |||||||
−780313. | −0.569058 | |||||||||
−398090. | − | 180914.i | −0.287784 | − | 0.130785i | |||||
−65067.4 | −0.0466293 | |||||||||
82944.0i | 0.0589256i | |||||||||
−549105. | −0.386732 | |||||||||
−223227. | −0.155866 | |||||||||
252276.i | 0.174640i | |||||||||
− | 54579.2i | − | 0.0374602i | |||||||
2.71268e6i | 1.84599i | 0.384809 | + | 0.922996i | ||||||
−0.384809 | + | 0.922996i | ||||||||
515244.i | 0.347652i | |||||||||
−1.31117e6 | −0.877207 | |||||||||
−241626. | −0.160293 | |||||||||
130785.i | 0.0860336i | |||||||||
−885014. | −0.577310 | |||||||||
1.54903e6 | + | 703967.i | 1.00204 | + | 0.455380i | |||||
251628. | 0.161420 | |||||||||
− | 3.56000e6i | − | 2.26482i | |||||||
−1.92979e6 | −1.21757 | |||||||||
−923403. | −0.577810 | |||||||||
− | 598009.i | − | 0.371128i | |||||||
1.17811e6i | 0.725162i | |||||||||
− | 302338.i | − | 0.184582i | |||||||
2.44475e6i | 1.48043i | 0.672371 | + | 0.740215i | ||||||
−0.672371 | + | 0.740215i | ||||||||
−506369. | −0.304152 | |||||||||
1.83423e6 | 1.09284 | |||||||||
109452.i | 0.0646876i | |||||||||
1.99183e6 | 1.16775 | 0.583877 | − | 0.811842i | ||||||
0.583877 | + | 0.811842i | ||||||||
145212. | − | 319530.i | 0.0844533 | − | 0.185834i | |||||
1.66396e6 | 0.960025 | 0.480013 | − | 0.877262i | ||||||
0.480013 | + | 0.877262i | ||||||||
− | 442903.i | − | 0.253504i | |||||||
−530346. | −0.301150 | |||||||||
1.03964e6 | 0.585685 | |||||||||
− | 3.20482e6i | − | 1.79125i | −0.444813 | − | 0.895624i | ||||
0.444813 | − | 0.895624i | ||||||||
902947.i | 0.500719i | |||||||||
− | 269749.i | − | 0.148417i | |||||||
− | 152026.i | − | 0.0829935i | |||||||
1.32620e6 | 0.718369 | |||||||||
1.97037e6 | 1.05903 | |||||||||
2.17979e6i | 1.16254i | |||||||||
−104976. | −0.0555556 | |||||||||
−969362. | − | 440532.i | −0.509070 | − | 0.231350i | |||||
−644254. | −0.335748 | |||||||||
− | 70619.9i | − | 0.0365222i | |||||||
23606.3 | 0.0121156 | |||||||||
−3.62101e6 | −1.84434 | |||||||||
− | 239714.i | − | 0.121174i | |||||||
− | 3.53386e6i | − | 1.77288i | −0.462844 | − | 0.886440i | ||||
0.462844 | − | 0.886440i | ||||||||
− | 195735.i | − | 0.0974591i | |||||||
− | 305808.i | − | 0.151126i | |||||||
−1.86631e6 | −0.915415 | |||||||||
1.73187e6 | 0.843148 | |||||||||
− | 406441.i | − | 0.196404i | |||||||
1.10242e6 | 0.528777 | 0.264389 | − | 0.964416i | ||||||
0.264389 | + | 0.964416i | ||||||||
−1.11882e6 | + | 976719.i | −0.532682 | + | 0.465027i | |||||
1.73406e6 | 0.819529 | |||||||||
554148.i | 0.259973i | |||||||||
−132263. | −0.0615960 | |||||||||
756855. | 0.349903 | |||||||||
440075.i | 0.201972i | |||||||||
1.29156e6i | 0.588462i | |||||||||
932766.i | 0.421915i | |||||||||
− | 963068.i | − | 0.432481i | |||||||
3.16432e6 | 1.41077 | 0.705386 | − | 0.708823i | ||||||
0.705386 | + | 0.708823i | ||||||||
216516. | 0.0958389 | |||||||||
− | 1.97526e6i | − | 0.868080i | −0.900894 | − | 0.434040i | ||||
0.900894 | − | 0.434040i | ||||||||
−1.23302e6 | −0.538024 | |||||||||
404405. | + | 183784.i | 0.175206 | + | 0.0796233i | |||||
183710. | 0.0790269 | |||||||||
− | 2.24015e6i | − | 0.956843i | −0.878130 | − | 0.478422i | ||||
0.878130 | − | 0.478422i | ||||||||
1.27175e6 | 0.539378 | |||||||||
−2.18884e6 | −0.921815 | |||||||||
988075.i | 0.413204i | |||||||||
1.48151e6i | 0.615226i | |||||||||
− | 1.06574e6i | − | 0.439485i | |||||||
2.13770e6i | 0.875407i | 0.899119 | + | 0.437704i | ||||||
−0.899119 | + | 0.437704i | ||||||||
192408. | 0.0782470 | |||||||||
−2.98066e6 | −1.20377 | |||||||||
257229.i | 0.103169i | |||||||||
−1.15979e6 | −0.461968 | |||||||||
−711567. | + | 1.56576e6i | −0.281490 | + | 0.619400i | |||||
−126609. | −0.0497432 | |||||||||
− | 1.14269e6i | − | 0.445888i | |||||||
1.70502e6 | 0.660791 | 0.330395 | − | 0.943843i | ||||||
0.330395 | + | 0.943843i | ||||||||
−714844. | −0.275164 | |||||||||
29876.7i | 0.0114227i | |||||||||
560509.i | 0.212852i | |||||||||
− | 4.42461e6i | − | 1.66894i | |||||||
− | 106162.i | − | 0.0397751i | |||||||
−2.31503e6 | −0.861558 | −0.430779 | − | 0.902458i | ||||||
−0.430779 | + | 0.902458i | ||||||||
−669636. | −0.247548 | |||||||||
− | 1.62759e6i | − | 0.597679i | |||||||
1.31370e6 | 0.479209 | |||||||||
−834097. | − | 379060.i | −0.302248 | − | 0.137358i | |||||
514402. | 0.185171 | |||||||||
− | 4.32354e6i | − | 1.54612i | −0.634336 | − | 0.773058i | ||||
0.634336 | − | 0.773058i | ||||||||
−1.38722e6 | −0.492819 | |||||||||
−2.30080e6 | −0.812018 | |||||||||
− | 3.70155e6i | − | 1.29785i | |||||||
2.00351e6i | 0.697901i | 0.937141 | + | 0.348951i | ||||||
−0.937141 | + | 0.348951i | ||||||||
147456.i | 0.0510310i | |||||||||
1.17464e6i | 0.403882i | |||||||||
2.52922e6 | 0.864011 | |||||||||
−1.63463e6 | −0.554807 | |||||||||
448490.i | 0.151243i | |||||||||
1.70696e6 | 0.571940 | 0.285970 | − | 0.958239i | ||||||
0.285970 | + | 0.958239i | ||||||||
−741226. | − | 336854.i | −0.246768 | − | 0.112145i | |||||
2.60567e6 | 0.861940 | |||||||||
915990.i | 0.301076i | |||||||||
1.20831e6 | 0.394636 | |||||||||
−400191. | −0.129875 | |||||||||
− | 2.41168e6i | − | 0.777728i | |||||||
232507.i | 0.0745073i | |||||||||
1.22427e6i | 0.389853i | 0.980818 | + | 0.194927i | ||||||
−0.980818 | + | 0.194927i | ||||||||
− | 2.89230e6i | − | 0.915243i | |||||||
−3.70873e6 | −1.16625 | |||||||||
447339. | 0.139793 | |||||||||
− | 4.15598e6i | − | 1.29066i | −0.763903 | − | 0.645332i | ||||
0.763903 | − | 0.645332i | ||||||||
−1.67981e6 | −0.518435 | |||||||||
−185860. | + | 408974.i | −0.0570065 | + | 0.125439i | |||||
−1.64161e6 | −0.500398 | |||||||||
243517.i | 0.0737720i | |||||||||
−1.06097e6 | −0.319439 | |||||||||
−677323. | −0.202680 | |||||||||
− | 537489.i | − | 0.159852i | |||||||
6.52428e6i | 1.92852i | 0.264958 | + | 0.964260i | ||||||
−0.264958 | + | 0.964260i | ||||||||
− | 54760.4i | − | 0.0160882i | |||||||
669361.i | 0.195459i | |||||||||
3.26086e6 | 0.946430 | |||||||||
−6.23180e6 | −1.79779 | |||||||||
− | 904725.i | − | 0.259427i | |||||||
−454053. | −0.129416 | |||||||||
258155. | − | 568054.i | 0.0731387 | − | 0.160937i | |||||
−327136. | −0.0921271 | |||||||||
− | 1.67633e6i | − | 0.469265i | |||||||
4.77950e6 | 1.32999 | 0.664994 | − | 0.746849i | ||||||
0.664994 | + | 0.746849i | ||||||||
−942837. | −0.260803 | |||||||||
3.41558e6i | 0.939203i | 0.882878 | + | 0.469602i | ||||||
−0.882878 | + | 0.469602i | ||||||||
1.03819e6i | 0.283790i | |||||||||
1.66265e6i | 0.451803i | |||||||||
1.60524e6i | 0.433636i | |||||||||
−1.63059e6 | −0.437897 | |||||||||
2.12304e6 | 0.566806 | |||||||||
5.59940e6i | 1.48618i | |||||||||
2.35769e6 | 0.622125 | |||||||||
407057. | − | 895702.i | 0.106785 | − | 0.234974i | |||||
2.99608e6 | 0.781416 | |||||||||
− | 6.21413e6i | − | 1.61134i | −0.592365 | − | 0.805670i | ||||
0.592365 | − | 0.805670i | ||||||||
−186624. | −0.0481125 | |||||||||
−5.83362e6 | −1.49526 | −0.747632 | − | 0.664113i | ||||||
−0.747632 | + | 0.664113i | ||||||||
520214.i | 0.132574i | |||||||||
− | 502260.i | − | 0.127264i | |||||||
− | 125546.i | − | 0.0316292i | |||||||
6.52287e6i | 1.63394i | |||||||||
122803. | 0.0305861 | |||||||||
−766922. | −0.189928 | −0.0949642 | − | 0.995481i | ||||||
−0.0949642 | + | 0.995481i | ||||||||
− | 426158.i | − | 0.104939i | |||||||
−1.15930e6 | −0.283857 | |||||||||
−940996. | + | 2.07060e6i | −0.229104 | + | 0.504128i | |||||
1.02042e6 | 0.247042 | 0.123521 | − | 0.992342i | ||||||
0.123521 | + | 0.992342i | ||||||||
− | 543659.i | − | 0.130879i | |||||||
2.29207e6 | 0.548692 | |||||||||
4.28783e6 | 1.02071 | |||||||||
− | 1.99128e6i | − | 0.471372i | |||||||
− | 722562.i | − | 0.170091i | |||||||
4.18123e6i | 0.978787i | 0.872063 | + | 0.489394i | ||||||
−0.872063 | + | 0.489394i | ||||||||
566163.i | 0.131798i | |||||||||
66172.8 | 0.0153193 | |||||||||
3.08277e6 | 0.709733 | |||||||||
− | 4.34203e6i | − | 0.994139i | |||||||
−260840. | −0.0593929 | |||||||||
3.63215e6 | + | 1.65065e6i | 0.822498 | + | 0.373789i | |||||
1.34552e6 | 0.303025 | |||||||||
3.58333e6i | 0.802594i | 0.915948 | + | 0.401297i | ||||||
−0.915948 | + | 0.401297i | ||||||||
−767417. | −0.170949 | |||||||||
680260. | 0.150710 | |||||||||
1.65825e6i | 0.365389i | |||||||||
− | 1.67459e6i | − | 0.366992i | −0.983020 | − | 0.183496i | ||||
0.983020 | − | 0.183496i | ||||||||
− | 1.13933e6i | − | 0.248339i | |||||||
6.62362e6i | 1.43596i | 0.696063 | + | 0.717981i | ||||||
−0.696063 | + | 0.717981i | ||||||||
384917. | 0.0829989 | |||||||||
−246268. | −0.0528172 | |||||||||
1.41568e6i | 0.301996i | |||||||||
3.80744e6 | 0.807868 | 0.403934 | − | 0.914788i | ||||||
0.403934 | + | 0.914788i | ||||||||
718943. | + | 326727.i | 0.151733 | + | 0.0689558i | |||||
8.23138e6 | 1.72799 | |||||||||
− | 3.04743e6i | − | 0.636339i | |||||||
996531. | 0.206985 | |||||||||
2.26089e6 | 0.467115 | |||||||||
3.62048e6i | 0.744070i | |||||||||
2.33918e6i | 0.478210i | |||||||||
− | 4.08192e6i | − | 0.830099i | |||||||
2.63380e6i | 0.532801i | |||||||||
−2.03163e6 | −0.408836 | |||||||||
4.61495e6 | 0.923841 | |||||||||
− | 4.85878e6i | − | 0.967583i | −0.875183 | − | 0.483792i | ||||
0.875183 | − | 0.483792i | ||||||||
342059. | 0.0677639 | |||||||||
−951798. | + | 2.09437e6i | −0.187578 | + | 0.412754i | |||||
−839013. | −0.164494 | |||||||||
4.43332e6i | 0.864692i | |||||||||
−2.06184e6 | −0.400076 | |||||||||
1.04038e6 | 0.200834 | |||||||||
− | 236196.i | − | 0.0453609i | |||||||
− | 71255.1i | − | 0.0136142i | −0.999977 | − | 0.00680712i | ||||
0.999977 | − | 0.00680712i | ||||||||
− | 2.03145e6i | − | 0.386150i | |||||||
− | 1.44957e6i | − | 0.274137i | |||||||
2.12486e6 | 0.399797 | |||||||||
−6.78617e6 | −1.27034 | −0.635172 | − | 0.772371i | ||||||
−0.635172 | + | 0.772371i | ||||||||
53114.2i | 0.00989231i | |||||||||
−1.40305e6 | −0.259990 | |||||||||
−5.18343e6 | − | 2.35563e6i | −0.955651 | − | 0.434301i | |||||
539356. | 0.0989379 | |||||||||
− | 188732.i | − | 0.0344463i | |||||||
−1.04033e7 | −1.88921 | |||||||||
440403. | 0.0795750 | |||||||||
167487.i | 0.0301114i | 0.999887 | + | 0.0150557i | ||||||
−0.999887 | + | 0.0150557i | ||||||||
− | 2.89350e6i | − | 0.517605i | |||||||
− | 4.19920e6i | − | 0.747433i | |||||||
1.70862e6i | 0.302613i | |||||||||
1.00972e7 | 1.77942 | 0.889712 | − | 0.456522i | ||||||
0.889712 | + | 0.456522i | ||||||||
914493. | 0.160363 | |||||||||
3.80809e6i | 0.664476i | |||||||||
−2.00384e6 | −0.347926 | |||||||||
−2.19762e6 | − | 2.51734e6i | −0.379693 | − | 0.434933i | |||||
−4.09031e6 | −0.703229 | |||||||||
9.79146e6i | 1.67515i | 0.546324 | + | 0.837574i | ||||||
−0.546324 | + | 0.837574i | ||||||||
−1.24683e6 | −0.212267 | |||||||||
−601758. | −0.101946 | |||||||||
262144.i | 0.0441942i | |||||||||
1.70292e6i | 0.285694i | |||||||||
830887.i | 0.138718i | |||||||||
− | 7.56433e6i | − | 1.25676i | |||||||
−2.90601e6 | −0.480477 | |||||||||
3.68253e6 | 0.605927 | |||||||||
2.66403e6i | 0.436229i | |||||||||
2.16690e6 | 0.353119 | |||||||||
−1.31774e6 | − | 598852.i | −0.213708 | − | 0.0971205i | |||||
−9.42352e6 | −1.52096 | −0.760481 | − | 0.649360i | ||||||
−0.760481 | + | 0.649360i | ||||||||
487161.i | 0.0782521i | |||||||||
5.16320e6 | 0.825400 | 0.412700 | − | 0.910867i | ||||||
0.412700 | + | 0.910867i | ||||||||
2.14811e6 | 0.341765 | |||||||||
− | 2.77431e6i | − | 0.439295i | |||||||
− | 3.32685e6i | − | 0.524286i | |||||||
687945.i | 0.107901i | |||||||||
413346.i | 0.0645252i | |||||||||
1.36094e6 | 0.211445 | |||||||||
3.72373e6 | 0.575823 | |||||||||
2.86143e6i | 0.440400i | |||||||||
−6.59330e6 | −1.01001 | |||||||||
92988.3 | − | 204615.i | 0.0141779 | − | 0.0311975i | |||||
−2.22317e6 | −0.337380 | |||||||||
− | 5.46923e6i | − | 0.826117i | |||||||
−2.98633e6 | −0.448978 | |||||||||
2.39792e6 | 0.358838 | |||||||||
6.69458e6i | 0.997167i | |||||||||
2.56769e6i | 0.380689i | |||||||||
432919.i | 0.0638884i | |||||||||
− | 1.03918e7i | − | 1.52650i | −0.646104 | − | 0.763250i | ||||
0.646104 | − | 0.763250i | ||||||||
−279170. | −0.0408198 | |||||||||
−578765. | −0.0842369 | |||||||||
− | 955536.i | − | 0.138436i | |||||||
−291235. | −0.0420002 | |||||||||
−3.52295e6 | − | 1.60103e6i | −0.505738 | − | 0.229835i | |||||
−7.33920e6 | −1.04877 | −0.524385 | − | 0.851481i | ||||||
−0.524385 | + | 0.851481i | ||||||||
1.18997e6i | 0.169272i | |||||||||
2.57105e6 | 0.364066 | |||||||||
1.25397e6 | 0.176759 | |||||||||
− | 3.51233e6i | − | 0.492851i | |||||||
− | 1.60840e6i | − | 0.224671i | |||||||
− | 1.14624e7i | − | 1.59391i | |||||||
6.45520e6i | 0.893584i | |||||||||
−1.26115e6 | −0.173793 | |||||||||
−581574. | −0.0797844 | |||||||||
− | 7.97266e6i | − | 1.08884i | −0.838812 | − | 0.544421i | ||||
0.838812 | − | 0.544421i | ||||||||
238864. | 0.0324763 | |||||||||
1.11950e7 | + | 5.08763e6i | 1.51529 | + | 0.688630i | |||||
−1.67615e6 | −0.225862 | |||||||||
− | 1.50668e6i | − | 0.202122i | |||||||
−4.22621e6 | −0.564430 | |||||||||
5.23721e6 | 0.696352 | 0.348176 | − | 0.937429i | ||||||
0.348176 | + | 0.937429i | ||||||||
2.95581e6i | 0.391273i | |||||||||
− | 7.15122e6i | − | 0.942451i | |||||||
− | 2.05096e6i | − | 0.269102i | |||||||
1.15740e6i | 0.151192i | |||||||||
3.77430e6 | 0.490868 | |||||||||
−8.15975e6 | −1.05657 | −0.528283 | − | 0.849069i | ||||||
−0.528283 | + | 0.849069i | ||||||||
− | 3.12125e6i | − | 0.402385i | |||||||
−6.61371e6 | −0.848897 | −0.424448 | − | 0.905452i | ||||||
−0.424448 | + | 0.905452i | ||||||||
723656. | − | 1.59236e6i | 0.0924788 | − | 0.203494i | |||||
8.32849e6 | 1.05969 | |||||||||
− | 260269.i | − | 0.0329719i | |||||||
−4.87942e6 | −0.615458 | |||||||||
−331776. | −0.0416667 | |||||||||
4.82867e6i | 0.603793i | 0.953341 | + | 0.301896i | ||||||
−0.953341 | + | 0.301896i | ||||||||
− | 2.19642e6i | − | 0.273461i | |||||||
5.69075e6i | 0.705462i | |||||||||
− | 892907.i | − | 0.110214i | |||||||
−2.15806e6 | −0.265230 | |||||||||
−1.00910e6 | −0.123489 | |||||||||
4.49978e6i | 0.548302i | |||||||||
218317. | 0.0264883 | |||||||||
757922. | − | 1.66776e6i | 0.0915661 | − | 0.201485i | |||||
−1.08507e7 | −1.30531 | |||||||||
7.52814e6i | 0.901763i | 0.892584 | + | 0.450881i | ||||||
−0.892584 | + | 0.450881i | ||||||||
−2.06098e6 | −0.245827 | |||||||||
−1.72216e6 | −0.204544 | |||||||||
− | 5.24466e6i | − | 0.620279i | |||||||
− | 900430.i | − | 0.106043i | |||||||
− | 966505.i | − | 0.113344i | |||||||
− | 8.22445e6i | − | 0.960439i | −0.877148 | − | 0.480220i | ||||
0.877148 | − | 0.480220i | ||||||||
−523142. | −0.0608350 | |||||||||
6.10972e6 | 0.707504 | |||||||||
− | 3.54006e6i | − | 0.408220i | |||||||
6.50769e6 | 0.747293 | |||||||||
−2.81587e6 | + | 6.19614e6i | −0.322002 | + | 0.708546i | |||||
−1.25959e6 | −0.143437 | −0.0717185 | − | 0.997425i | ||||||
−0.0717185 | + | 0.997425i | ||||||||
1.00651e6i | 0.114141i | |||||||||
6.56541e6 | 0.741439 | 0.370720 | − | 0.928745i | ||||||
0.370720 | + | 0.928745i | ||||||||
1.42400e7 | 1.60147 | |||||||||
− | 3.77957e6i | − | 0.423301i | |||||||
− | 7.71916e6i | − | 0.860950i | |||||||
4.78294e6i | 0.531259i | |||||||||
− | 3.69361e6i | − | 0.408573i | |||||||
−7.92228e6 | −0.872727 | −0.436364 | − | 0.899770i | ||||||
−0.436364 | + | 0.899770i | ||||||||
2.39203e6 | 0.262427 | |||||||||
− | 2.38718e6i | − | 0.260821i | |||||||
−4.71243e6 | −0.512767 | |||||||||
5.17482e6 | − | 1.13869e7i | 0.560780 | − | 1.23396i | |||||
1.20935e6 | 0.130519 | |||||||||
− | 9.74465e6i | − | 1.04741i | −0.851901 | − | 0.523703i | ||||
0.851901 | − | 0.523703i | ||||||||
−9.77898e6 | −1.04682 | |||||||||
123211. | 0.0131360 | |||||||||
− | 2.02548e6i | − | 0.215068i | |||||||
1.14334e7i | 1.20910i | 0.796569 | + | 0.604548i | ||||||
−0.796569 | + | 0.604548i | ||||||||
7.33693e6i | 0.772757i | |||||||||
− | 1.07067e7i | − | 1.12313i | −0.827432 | − | 0.561566i | ||||
0.827432 | − | 0.561566i | ||||||||
−437810. | −0.0457411 | |||||||||
2.03563e6 | 0.211822 | |||||||||
7.96732e6i | 0.825726i | |||||||||
1.08939e7 | 1.12451 | |||||||||
1.27812e6 | + | 580849.i | 0.131405 | + | 0.0597175i | |||||
−1.25148e6 | −0.128151 | |||||||||
6.65585e6i | 0.678840i | |||||||||
3.77174e6 | 0.383154 | |||||||||
1.77161e6 | 0.179254 | |||||||||
3.52299e6i | 0.355046i | |||||||||
− | 2.12138e6i | − | 0.212945i | |||||||
− | 475976.i | − | 0.0475895i | −0.999717 | − | 0.0237948i | ||||
0.999717 | − | 0.0237948i | ||||||||
4.15855e6i | 0.414142i | |||||||||
−2.33593e6 | −0.231714 | |||||||||
1.28193e7 | 1.26660 | |||||||||
9.48844e6i | 0.933814i | |||||||||
−3.61179e6 | −0.354062 | |||||||||
7.93963e6 | + | 3.60820e6i | 0.775267 | + | 0.352324i | |||||
1.07899e6 | 0.104946 | |||||||||
4.77684e6i | 0.462795i | |||||||||
608105. | 0.0586852 | |||||||||
−1.90742e7 | −1.83358 | −0.916791 | − | 0.399368i | ||||||
−0.916791 | + | 0.399368i | ||||||||
5.30481e6i | 0.507963i | |||||||||
− | 1.16474e7i | − | 1.11097i | −0.831528 | − | 0.555483i | ||||
0.831528 | − | 0.555483i | ||||||||
7.88146e6i | 0.748845i | |||||||||
6.74118e6i | 0.638024i | |||||||||
−8.71916e6 | −0.822041 | |||||||||
1.83045e6 | 0.171908 | 0.0859540 | − | 0.996299i | ||||||
0.0859540 | + | 0.996299i | ||||||||
− | 419904.i | − | 0.0392837i | |||||||
6.33768e6 | 0.590634 | |||||||||
1.76213e6 | − | 3.87745e6i | 0.163589 | − | 0.359967i | |||||
−1.17048e6 | −0.108246 | |||||||||
− | 2.57702e6i | − | 0.237410i | |||||||
1.75829e7 | 1.61365 | 0.806824 | − | 0.590792i | ||||||
0.806824 | + | 0.590792i | ||||||||
282479. | 0.0258251 | |||||||||
− | 4.98304e6i | − | 0.453828i | |||||||
94425.2i | 0.00856699i | |||||||||
276307.i | 0.0249735i | |||||||||
− | 1.44840e7i | − | 1.30414i | |||||||
−1.84370e7 | −1.65378 | −0.826888 | − | 0.562367i | ||||||
−0.826888 | + | 0.562367i | ||||||||
958855. | 0.0856827 | |||||||||
1.08046e7i | 0.961845i | 0.876763 | + | 0.480922i | ||||||
−0.876763 | + | 0.480922i | ||||||||
1.41354e7 | 1.25362 | |||||||||
−4.65886e6 | − | 2.11724e6i | −0.411619 | − | 0.187062i | |||||
782939. | 0.0689140 | |||||||||
1.52947e7i | 1.34118i | |||||||||
1.22323e6 | 0.106862 | |||||||||
−4.19855e6 | −0.365413 | |||||||||
− | 7.46525e6i | − | 0.647296i | |||||||
9.64761e6i | 0.833402i | |||||||||
6.92749e6i | 0.596196i | |||||||||
− | 5.69453e6i | − | 0.488260i | |||||||
1.62576e6 | 0.138878 | |||||||||
−1.57676e7 | −1.34193 | −0.670964 | − | 0.741490i | ||||||
−0.670964 | + | 0.741490i | ||||||||
4.40968e6i | 0.373902i | |||||||||
−1.27387e6 | −0.107613 | |||||||||
−3.90688e6 | − | 4.47528e6i | −0.328823 | − | 0.376663i | |||||
2.86244e6 | 0.240029 | 0.120015 | − | 0.992772i | ||||||
0.120015 | + | 0.992772i | ||||||||
6.93623e6i | 0.579495i | |||||||||
4.94480e6 | 0.411599 | |||||||||
−2.21659e6 | −0.183829 | |||||||||
− | 586890.i | − | 0.0484941i | |||||||
− | 529052.i | − | 0.0435549i | |||||||
4.91047e6i | 0.402783i | 0.979511 | + | 0.201391i | ||||||
−0.979511 | + | 0.201391i | ||||||||
3.02742e6i | 0.247419i | |||||||||
2.76043e6 | 0.224776 | |||||||||
−1.76030e6 | −0.142816 | |||||||||
− | 1.72669e6i | − | 0.139580i | |||||||
−5.16624e6 | −0.416106 | |||||||||
1.39139e7 | + | 6.32325e6i | 1.11661 | + | 0.507449i | |||||
−3.73107e6 | −0.298339 | |||||||||
1.79749e7i | 1.43209i | 0.698052 | + | 0.716047i | ||||||
−0.698052 | + | 0.716047i | ||||||||
3.85227e6 | 0.305810 | |||||||||
2.56349e6 | 0.202768 | |||||||||
1.26573e7i | 0.997566i | |||||||||
1.34910e6i | 0.105945i | |||||||||
866064.i | 0.0677683i | |||||||||
− | 344188.i | − | 0.0268357i | |||||||
7.90102e6 | 0.613825 | |||||||||
−3.18528e6 | −0.246579 | |||||||||
− | 4.93210e6i | − | 0.380440i | |||||||
−8.74640e6 | −0.672255 | −0.336128 | − | 0.941816i | ||||||
−0.336128 | + | 0.941816i | ||||||||
−735137. | + | 1.61762e6i | −0.0563022 | + | 0.123889i | |||||
−8.81925e6 | −0.673044 | |||||||||
734838.i | 0.0558805i | |||||||||
6.85671e6 | 0.519569 | |||||||||
8.96061e6 | 0.676590 | |||||||||
1.80994e7i | 1.36181i | |||||||||
5.08699e6i | 0.381398i | |||||||||
− | 2.43397e6i | − | 0.181844i | −0.995858 | − | 0.0909221i | ||||
0.995858 | − | 0.0909221i | ||||||||
− | 8.75538e6i | − | 0.651822i | |||||||
−5.26316e6 | −0.390457 | |||||||||
−3.95230e6 | −0.292180 | |||||||||
2.05863e6i | 0.151654i | |||||||||
−5.92605e6 | −0.435030 | |||||||||
−3.69386e6 | − | 1.67869e6i | −0.270218 | − | 0.122802i | |||||
4.26297e6 | 0.310763 | |||||||||
1.03836e7i | 0.754313i | |||||||||
−8.55079e6 | −0.619006 | |||||||||
6.81620e6 | 0.491723 | 0.245861 | − | 0.969305i | ||||||
0.245861 | + | 0.969305i | ||||||||
769633.i | 0.0553290i | |||||||||
− | 3.59523e7i | − | 2.57566i | |||||||
− | 1.19226e7i | − | 0.851196i | |||||||
− | 1.88778e6i | − | 0.134309i | |||||||
−1.02892e6 | −0.0729513 | |||||||||
2.62739e6 | 0.185643 | |||||||||
− | 4.63915e6i | − | 0.326661i | |||||||
−4.33605e6 | −0.304269 | −0.152135 | − | 0.988360i | ||||||
−0.152135 | + | 0.988360i | ||||||||
−6.26303e6 | − | 2.84627e6i | −0.437982 | − | 0.199043i | |||||
531441. | 0.0370370 | |||||||||
− | 506437.i | − | 0.0351737i | |||||||
1.88314e7 | 1.30343 | |||||||||
4.57076e6 | 0.315290 | |||||||||
2.01689e7i | 1.38651i | 0.720693 | + | 0.693254i | ||||||
−0.720693 | + | 0.693254i | ||||||||
6.82008e6i | 0.467250i | |||||||||
4.78093e6i | 0.326433i | |||||||||
− | 2.85938e6i | − | 0.194570i | |||||||
−8.37122e6 | −0.567702 | |||||||||
−119507. | −0.00807704 | |||||||||
2.05423e7i | 1.38369i | 0.722048 | + | 0.691843i | ||||||
−0.722048 | + | 0.691843i | ||||||||
−2.24204e6 | −0.150509 | |||||||||
5.30018e6 | − | 1.16627e7i | 0.354605 | − | 0.780286i | |||||
1.76984e7 | 1.18012 | |||||||||
1.48776e7i | 0.988689i | 0.869266 | + | 0.494345i | ||||||
−0.869266 | + | 0.494345i | ||||||||
424648. | 0.0281253 | |||||||||
−8.21200e6 | −0.542074 | |||||||||
− | 9.26012e6i | − | 0.609213i | |||||||
990907.i | 0.0649728i | |||||||||
− | 2.67855e6i | − | 0.175043i | |||||||
− | 2.59946e7i | − | 1.69308i | |||||||
6.51037e6 | 0.422623 | |||||||||
−2.94950e7 | −1.90831 | −0.954154 | − | 0.299315i | ||||||
−0.954154 | + | 0.299315i | ||||||||
5.25478e6i | 0.338852i | |||||||||
−3.84440e6 | −0.247082 | |||||||||
1.51624e6 | − | 3.33639e6i | 0.0971269 | − | 0.213722i | |||||
−1.79064e7 | −1.14325 | |||||||||
2.05761e6i | 0.130936i | |||||||||
2.01715e7 | 1.27938 | 0.639690 | − | 0.768633i | ||||||
0.639690 | + | 0.768633i | ||||||||
1.72942e7 | 1.09327 | |||||||||
− | 4.50864e6i | − | 0.284080i | |||||||
− | 5.54889e6i | − | 0.348476i | |||||||
2.06956e7i | 1.29544i | 0.761880 | + | 0.647719i | ||||||
−0.761880 | + | 0.647719i | ||||||||
− | 9.20319e6i | − | 0.574184i | |||||||
−1.38420e6 | −0.0860772 | |||||||||
1.48062e7 | 0.917720 | |||||||||
− | 2.80538e6i | − | 0.173316i | |||||||
−8.01403e6 | −0.493491 | |||||||||
8.90592e6 | − | 1.95969e7i | 0.546626 | − | 1.20282i | |||||
−589824. | −0.0360844 | |||||||||
− | 1.69130e7i | − | 1.03135i | −0.856785 | − | 0.515674i | ||||
0.856785 | − | 0.515674i | ||||||||
−4.69857e6 | −0.285587 | |||||||||
−1.86950e6 | −0.113263 | |||||||||
1.01169e7i | 0.610948i | |||||||||
− | 3.10969e7i | − | 1.87184i | −0.352212 | − | 0.935920i | ||||
0.352212 | − | 0.935920i | ||||||||
− | 6.53852e6i | − | 0.392308i | |||||||
− | 1.28826e6i | − | 0.0770458i | |||||||
−1.79396e6 | −0.106945 | |||||||||
−5.99407e6 | −0.356180 | |||||||||
6.82786e6i | 0.404423i | |||||||||
861619. | 0.0508712 | |||||||||
1.34742e6 | − | 2.96490e6i | 0.0792986 | − | 0.174491i | |||||
1.05800e7 | 0.620669 | |||||||||
1.04227e7i | 0.609483i | |||||||||
−1.09611e6 | −0.0638926 | |||||||||
−3.66396e6 | −0.212893 | |||||||||
− | 4.10967e6i | − | 0.238031i | |||||||
4.83324e6i | 0.279050i | |||||||||
− | 628913.i | − | 0.0361954i | −0.999836 | − | 0.0180977i | ||||
0.999836 | − | 0.0180977i | ||||||||
− | 1.60076e6i | − | 0.0918357i | |||||||
7.48541e6 | 0.428078 | |||||||||
9.64674e6 | 0.549937 | |||||||||
− | 3.39888e7i | − | 1.93150i | |||||||
−930030. | −0.0526846 | |||||||||
−1.76082e7 | − | 8.00215e6i | −0.994335 | − | 0.451881i | |||||
−4.89708e6 | −0.275668 | |||||||||
8.37840e6i | 0.470157i | |||||||||
1.15692e7 | 0.647174 | |||||||||
−2.43866e7 | −1.35990 | −0.679948 | − | 0.733260i | ||||||
−0.679948 | + | 0.733260i | ||||||||
− | 1.48349e7i | − | 0.824666i | |||||||
− | 1.91541e7i | − | 1.06144i | |||||||
1.78936e6i | 0.0988489i | |||||||||
− | 5.00213e6i | − | 0.275470i | |||||||
1.66239e7 | 0.912637 | |||||||||
611982. | 0.0334927 | |||||||||
− | 6.71923e6i | − | 0.366589i | |||||||
1.82829e7 | 0.994388 | |||||||||
−1.63590e6 | − | 743442.i | −0.0886989 | − | 0.0403097i | |||||
−1.50628e7 | −0.814183 | |||||||||
− | 6.56642e6i | − | 0.353835i | |||||||
−2.86033e7 | −1.53654 | −0.768272 | − | 0.640123i | ||||||
−0.768272 | + | 0.640123i | ||||||||
−974067. | −0.0521647 | |||||||||
5.97923e6i | 0.319222i | 0.987180 | + | 0.159611i | ||||||
−0.987180 | + | 0.159611i | ||||||||
− | 4.24387e6i | − | 0.225877i | |||||||
− | 628133.i | − | 0.0333292i | |||||||
− | 2.70929e6i | − | 0.143316i | |||||||
−5.97800e6 | −0.315255 | |||||||||
2.14996e6 | 0.113033 | |||||||||
4.71414e7i | 2.47085i | |||||||||
−2.60971e7 | −1.36367 | |||||||||
3.60231e6 | − | 7.92665e6i | 0.187660 | − | 0.412933i | |||||
219042. | 0.0113761 | |||||||||
− | 1.46642e7i | − | 0.759279i | −0.925134 | − | 0.379640i | ||||
0.925134 | − | 0.379640i | ||||||||
−2.67744e6 | −0.138210 | |||||||||
1.80149e7 | 0.927113 | 0.463557 | − | 0.886067i | ||||||
0.463557 | + | 0.886067i | ||||||||
1.30434e7i | 0.669227i | |||||||||
2.82144e6i | 0.144323i | |||||||||
− | 2.49272e7i | − | 1.27123i | |||||||
9.93027e6i | 0.504891i | 0.967611 | + | 0.252445i | ||||||
−0.967611 | + | 0.252445i | ||||||||
3.61890e6 | 0.183443 | |||||||||
2.97991e7 | 1.50597 | 0.752986 | − | 0.658037i | ||||||
0.752986 | + | 0.658037i | ||||||||
− | 1.81621e6i | − | 0.0915106i | |||||||
−1.45242e7 | −0.729608 | |||||||||
2.27221e6 | + | 1.03262e6i | 0.113800 | + | 0.0517169i | |||||
1.33554e7 | 0.666877 | |||||||||
− | 1.30854e6i | − | 0.0651437i | |||||||
−1.73174e7 | −0.859542 | |||||||||
6.70532e6 | 0.331821 | |||||||||
537445.i | 0.0265168i | |||||||||
1.91180e7i | 0.940443i | |||||||||
− | 1.35283e7i | − | 0.663496i | −0.943368 | − | 0.331748i | ||||
0.943368 | − | 0.331748i | ||||||||
− | 3.77135e6i | − | 0.184416i | |||||||
−1.82504e7 | −0.889779 | |||||||||
−1.36623e7 | −0.664117 | |||||||||
− | 9.50897e6i | − | 0.460855i | |||||||
−4.15277e6 | −0.200670 | |||||||||
−1.03815e7 | + | 9.06293e6i | −0.500169 | + | 0.436643i | |||||
−6.65058e6 | −0.319473 | |||||||||
2.27327e7i | 1.08879i | |||||||||
−6.42096e6 | −0.306627 | |||||||||
4.61467e6 | 0.219721 | |||||||||
− | 6.52235e6i | − | 0.309640i | |||||||
1.05423e7i | 0.499013i | |||||||||
8.49217e6i | 0.400792i | |||||||||
− | 9.03698e6i | − | 0.425257i | −0.977133 | − | 0.212628i | ||||
0.977133 | − | 0.212628i | ||||||||
−2.23976e7 | −1.05089 | |||||||||
7.02282e6 | 0.328546 | |||||||||
9.43078e6i | 0.439909i | |||||||||
−9.55364e6 | −0.444341 | −0.222171 | − | 0.975008i | ||||||
−0.222171 | + | 0.975008i | ||||||||
3.58281e6 | + | 1.62823e6i | 0.166152 | + | 0.0755086i | |||||
3.73649e6 | 0.172775 | 0.0863874 | − | 0.996262i | ||||||
0.0863874 | + | 0.996262i | ||||||||
1.19843e7i | 0.552545i | |||||||||
585606. | 0.0269214 | |||||||||
2.48565e7 | 1.13939 | |||||||||
3.44318e7i | 1.57374i | 0.617120 | + | 0.786869i | ||||||
−0.617120 | + | 0.786869i | ||||||||
− | 746496.i | − | 0.0340207i | |||||||
− | 8.93626e6i | − | 0.406084i | |||||||
− | 2.33345e7i | − | 1.05731i | |||||||
4.94194e6 | 0.223280 | |||||||||
−2.08085e6 | −0.0937438 | |||||||||
1.16572e7i | 0.523653i | |||||||||
2.00904e6 | 0.0899892 | |||||||||
−1.17635e7 | + | 2.58849e7i | −0.525403 | + | 1.15612i | |||||
502186. | 0.0223652 | |||||||||
− | 2.27048e6i | − | 0.100828i | |||||||
−2.60915e7 | −1.15537 | |||||||||
−3.19020e7 | −1.40863 | |||||||||
491213.i | 0.0216276i | |||||||||
− | 2.12195e7i | − | 0.931613i | −0.884887 | − | 0.465807i | ||||
0.884887 | − | 0.465807i | ||||||||
− | 3.06769e6i | − | 0.134300i | |||||||
− | 2.44141e7i | − | 1.06578i | |||||||
1.70463e6 | 0.0742034 | |||||||||
3.83954e7 | 1.66663 | 0.833315 | − | 0.552798i | ||||||
0.833315 | + | 0.552798i | ||||||||
− | 4.63720e6i | − | 0.200717i | |||||||
3.58049e7 | 1.54540 | 0.772699 | − | 0.634773i | ||||||
0.772699 | + | 0.634773i | ||||||||
−8.28241e6 | − | 3.76398e6i | −0.356472 | − | 0.162001i | |||||
1.18005e7 | 0.506456 | |||||||||
4.08168e6i | 0.174685i | |||||||||
2.52692e7 | 1.07841 | 0.539203 | − | 0.842176i | ||||||
0.539203 | + | 0.842176i | ||||||||
2.17464e6 | 0.0925453 | |||||||||
4.50973e7i | 1.91380i | |||||||||
9.16830e6i | 0.387984i | |||||||||
− | 1.17707e6i | − | 0.0496715i | |||||||
1.71513e7i | 0.721747i | |||||||||
4.79493e7 | 2.01212 | |||||||||
7.96512e6 | 0.333310 | |||||||||
− | 9.88896e6i | − | 0.412661i | |||||||
2.89025e6 | 0.120272 | |||||||||
−1.39413e7 | − | 6.33570e6i | −0.578525 | − | 0.262914i | |||||
−1.67249e7 | −0.692107 | |||||||||
− | 1.10850e6i | − | 0.0457441i | |||||||
−2.26465e6 | −0.0931956 | |||||||||
2.34049e7 | 0.960495 | |||||||||
264691.i | 0.0108324i | |||||||||
3.20400e7i | 1.30759i | |||||||||
1.23311e7i | 0.501857i | |||||||||
2.38681e6i | 0.0968717i | |||||||||
1.73681e7 | 0.702962 | |||||||||
−2.49639e7 | −1.00761 | −0.503806 | − | 0.863817i | ||||||
−0.503806 | + | 0.863817i | ||||||||
− | 1.04336e6i | − | 0.0419971i | |||||||
8.31063e6 | 0.333599 | |||||||||
−6.60259e6 | + | 1.45286e7i | −0.264308 | + | 0.581594i | |||||
−807347. | −0.0322303 | −0.0161151 | − | 0.999870i | ||||||
−0.0161151 | + | 0.999870i | ||||||||
5.38208e6i | 0.214271i | |||||||||
2.19472e6 | 0.0871370 | |||||||||
−1.43333e7 | −0.567520 | |||||||||
− | 1.06030e7i | − | 0.418673i | |||||||
− | 3.06967e6i | − | 0.120879i | |||||||
− | 2.36838e7i | − | 0.930095i | |||||||
2.72104e6i | 0.106568i | |||||||||
−2.92665e6 | −0.114309 | −0.0571547 | − | 0.998365i | ||||||
−0.0571547 | + | 0.998365i | ||||||||
−6.63301e6 | −0.258369 | |||||||||
− | 2.20027e7i | − | 0.854726i | |||||||
6.69836e6 | 0.259502 | |||||||||
1.48674e7 | − | 3.27149e7i | 0.574423 | − | 1.26398i | |||||
4.55732e6 | 0.175602 | |||||||||
− | 6.59722e6i | − | 0.253517i | |||||||
−2.64945e7 | −1.01538 | |||||||||
−1.65081e7 | −0.630953 | |||||||||
1.53967e6i | 0.0586891i | |||||||||
2.03515e7i | 0.773672i | 0.922148 | + | 0.386836i | ||||||
−0.922148 | + | 0.386836i | ||||||||
− | 985072.i | − | 0.0373474i | |||||||
3.34332e7i | 1.26417i | |||||||||
−5.66273e6 | −0.213543 | |||||||||
−1.79265e7 | −0.674203 | |||||||||
1.52297e7i | 0.571249i | |||||||||
−6.21352e6 | −0.232439 | |||||||||
−1.30691e6 | + | 2.87577e6i | −0.0487591 | + | 0.107291i | |||||
−659937. | −0.0245558 | −0.0122779 | − | 0.999925i | ||||||
−0.0122779 | + | 0.999925i | ||||||||
3.29255e7i | 1.22187i | |||||||||
−1.49757e7 | −0.554271 | |||||||||
1.21897e7 | 0.449960 | |||||||||
− | 3.40074e7i | − | 1.25199i | −0.779828 | − | 0.625994i | ||||
0.779828 | − | 0.625994i | ||||||||
3.98612e6i | 0.146360i | |||||||||
− | 1.02996e6i | − | 0.0377173i | |||||||
9.04354e6i | 0.330300i | |||||||||
4.77311e6 | 0.173869 | |||||||||
−1.44819e7 | −0.526137 | |||||||||
− | 1.44758e7i | − | 0.524527i | −0.964996 | − | 0.262263i | ||||
0.964996 | − | 0.262263i | ||||||||
−9.35673e6 | −0.338145 | |||||||||
859978. | − | 1.89233e6i | 0.0309972 | − | 0.0682073i | |||||
1.63277e7 | 0.586969 | |||||||||
2.88434e7i | 1.03418i | |||||||||
−1.05352e7 | −0.376747 | |||||||||
1.88172e7 | 0.671156 | 0.335578 | − | 0.942012i | ||||||
0.335578 | + | 0.942012i | ||||||||
− | 8.12652e6i | − | 0.289090i | |||||||
− | 3.43465e7i | − | 1.21864i | |||||||
1.84598e7i | 0.653255i | |||||||||
2.42774e6i | 0.0856883i | |||||||||
1.94351e7 | 0.684185 | |||||||||
1.31200e7 | 0.460666 | |||||||||
1.36824e6i | 0.0479163i | |||||||||
2.80856e7 | 0.981015 | |||||||||
−8.37748e6 | − | 3.80719e6i | −0.291861 | − | 0.132638i | |||||
−1.19358e7 | −0.414750 | |||||||||
− | 3.35605e6i | − | 0.116315i | |||||||
2.34685e7 | 0.811275 | |||||||||
−1.77333e7 | −0.611430 | |||||||||
4.30702e7i | 1.48119i | 0.671952 | + | 0.740595i | ||||||
−0.671952 | + | 0.740595i | ||||||||
− | 8.24738e6i | − | 0.282896i | |||||||
− | 1.96181e7i | − | 0.671194i | |||||||
4.16152e6i | 0.142011i | |||||||||
2.85474e7 | 0.971668 | 0.485834 | − | 0.874051i | ||||||
0.485834 | + | 0.874051i | ||||||||
944784. | 0.0320750 | |||||||||
6.41210e6i | 0.217129i | |||||||||
285020. | 0.00962673 | |||||||||
8.72426e6 | + | 3.96479e6i | 0.293912 | + | 0.133570i | |||||
8.12580e6 | 0.273050 | |||||||||
4.23484e7i | 1.41939i | 0.704510 | + | 0.709694i | ||||||
−0.704510 | + | 0.709694i | ||||||||
5.79829e6 | 0.193844 | |||||||||
−1.10790e7 | −0.369441 | |||||||||
8.49942e6i | 0.282699i | |||||||||
635579.i | 0.0210861i | |||||||||
− | 2.71447e7i | − | 0.898269i | |||||||
− | 1.39064e7i | − | 0.459020i | −0.973306 | − | 0.229510i | ||||
0.973306 | − | 0.229510i | ||||||||
−212457. | −0.00699492 | |||||||||
−3.71335e6 | −0.121948 | |||||||||
− | 5.61222e6i | − | 0.183841i | |||||||
3.25891e7 | 1.06483 | |||||||||
9.42254e6 | − | 2.07337e7i | 0.307097 | − | 0.675748i | |||||
5.63516e7 | 1.83196 | |||||||||
2.15742e6i | 0.0699597i | |||||||||
−3.49486e6 | −0.113043 | −0.0565217 | − | 0.998401i | ||||||
−0.0565217 | + | 0.998401i | ||||||||
754930. | 0.0243572 | |||||||||
3.18047e7i | 1.02357i | |||||||||
− | 4.16132e7i | − | 1.33587i | |||||||
− | 2.68376e7i | − | 0.859380i | |||||||
1.76161e6i | 0.0562681i | |||||||||
77983.9 | 0.00248466 | 0.00124233 | − | 0.999999i | ||||||
0.00124233 | + | 0.999999i | ||||||||
−669949. | −0.0212920 | |||||||||
2.75227e6i | 0.0872525i |
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 78.6.b.a.25.6 | yes | 6 | |
3.2 | odd | 2 | 234.6.b.c.181.1 | 6 | |||
4.3 | odd | 2 | 624.6.c.d.337.5 | 6 | |||
13.5 | odd | 4 | 1014.6.a.q.1.3 | 3 | |||
13.8 | odd | 4 | 1014.6.a.o.1.1 | 3 | |||
13.12 | even | 2 | inner | 78.6.b.a.25.1 | ✓ | 6 | |
39.38 | odd | 2 | 234.6.b.c.181.6 | 6 | |||
52.51 | odd | 2 | 624.6.c.d.337.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
78.6.b.a.25.1 | ✓ | 6 | 13.12 | even | 2 | inner | |
78.6.b.a.25.6 | yes | 6 | 1.1 | even | 1 | trivial | |
234.6.b.c.181.1 | 6 | 3.2 | odd | 2 | |||
234.6.b.c.181.6 | 6 | 39.38 | odd | 2 | |||
624.6.c.d.337.2 | 6 | 52.51 | odd | 2 | |||
624.6.c.d.337.5 | 6 | 4.3 | odd | 2 | |||
1014.6.a.o.1.1 | 3 | 13.8 | odd | 4 | |||
1014.6.a.q.1.3 | 3 | 13.5 | odd | 4 |