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 | 25.5 | ||
Root | of defining polynomial | ||
Character | 78.25 | ||
Dual form | 78.6.b.a.25.2 |
-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of on generators for .
Coefficient data
For each we display the coefficients of the -expansion , the Satake parameters , and the Satake angles .
4.00000i | 0.707107i | |||||||||
−9.00000 | −0.577350 | |||||||||
−16.0000 | −0.500000 | |||||||||
9.73803i | 0.174199i | 0.996200 | + | 0.0870996i | ||||||
−0.996200 | + | 0.0870996i | ||||||||
− | 36.0000i | − | 0.408248i | |||||||
− | 105.184i | − | 0.811344i | −0.914019 | − | 0.405672i | ||||
0.914019 | − | 0.405672i | ||||||||
− | 64.0000i | − | 0.353553i | |||||||
81.0000 | 0.333333 | |||||||||
−38.9521 | −0.123177 | |||||||||
− | 269.350i | − | 0.671175i | −0.942009 | − | 0.335588i | ||||
0.942009 | − | 0.335588i | ||||||||
144.000 | 0.288675 | |||||||||
227.464 | + | 565.290i | 0.373297 | + | 0.927712i | |||||
420.736 | 0.573707 | |||||||||
− | 87.6423i | − | 0.100574i | |||||||
256.000 | 0.250000 | |||||||||
1663.75 | 1.39625 | 0.698127 | − | 0.715974i | ||||||
0.698127 | + | 0.715974i | ||||||||
324.000i | 0.235702i | |||||||||
2.82742i | 0.00179683i | 1.00000 | 0.000898415i | |||||||
−1.00000 | 0.000898415i | |||||||||
− | 155.809i | − | 0.0870996i | |||||||
946.657i | 0.468430i | |||||||||
1077.40 | 0.474592 | |||||||||
2151.14 | 0.847908 | 0.423954 | − | 0.905684i | ||||||
0.423954 | + | 0.905684i | ||||||||
576.000i | 0.204124i | |||||||||
3030.17 | 0.969655 | |||||||||
−2261.16 | + | 909.856i | −0.655991 | + | 0.263961i | |||||
−729.000 | −0.192450 | |||||||||
1682.95i | 0.405672i | |||||||||
220.829 | 0.0487598 | 0.0243799 | − | 0.999703i | ||||||
0.0243799 | + | 0.999703i | ||||||||
350.569 | 0.0711165 | |||||||||
788.106i | 0.147292i | 0.997284 | + | 0.0736462i | ||||||
−0.997284 | + | 0.0736462i | ||||||||
1024.00i | 0.176777i | |||||||||
2424.15i | 0.387503i | |||||||||
6654.98i | 0.987301i | |||||||||
1024.29 | 0.141335 | |||||||||
−1296.00 | −0.166667 | |||||||||
980.445i | 0.117739i | 0.998266 | + | 0.0588693i | ||||||
−0.998266 | + | 0.0588693i | ||||||||
−11.3097 | −0.00127055 | |||||||||
−2047.18 | − | 5087.61i | −0.215523 | − | 0.535615i | |||||
623.234 | 0.0615887 | |||||||||
− | 14809.7i | − | 1.37590i | −0.725759 | − | 0.687949i | ||||
0.725759 | − | 0.687949i | ||||||||
−3786.63 | −0.331230 | |||||||||
14142.2 | 1.16640 | 0.583198 | − | 0.812330i | ||||||
0.583198 | + | 0.812330i | ||||||||
4309.61i | 0.335588i | |||||||||
788.781i | 0.0580664i | |||||||||
8604.55i | 0.599561i | |||||||||
− | 25181.2i | − | 1.66277i | −0.555699 | − | 0.831383i | ||||
0.555699 | − | 0.831383i | ||||||||
−2304.00 | −0.144338 | |||||||||
5743.31 | 0.341721 | |||||||||
12120.7i | 0.685649i | |||||||||
−14973.7 | −0.806128 | |||||||||
−3639.42 | − | 9044.65i | −0.186648 | − | 0.463856i | |||||
−30900.9 | −1.51106 | −0.755530 | − | 0.655114i | ||||||
−0.755530 | + | 0.655114i | ||||||||
− | 2916.00i | − | 0.136083i | |||||||
2622.94 | 0.116918 | |||||||||
−6731.78 | −0.286853 | |||||||||
− | 25.4468i | − | 0.00103740i | |||||||
883.317i | 0.0344784i | |||||||||
− | 25094.7i | − | 0.938538i | −0.883055 | − | 0.469269i | ||||
0.883055 | − | 0.469269i | ||||||||
1402.28i | 0.0502870i | |||||||||
12060.8 | 0.415003 | 0.207501 | − | 0.978235i | ||||||
0.207501 | + | 0.978235i | ||||||||
−3152.42 | −0.104151 | |||||||||
− | 8519.91i | − | 0.270448i | |||||||
−4096.00 | −0.125000 | |||||||||
−5504.81 | + | 2215.05i | −0.161607 | + | 0.0650280i | |||||
−9696.61 | −0.274006 | |||||||||
− | 14450.5i | − | 0.393276i | −0.980476 | − | 0.196638i | ||||
0.980476 | − | 0.196638i | ||||||||
−26619.9 | −0.698127 | |||||||||
−19360.2 | −0.489540 | |||||||||
4097.14i | 0.0999393i | |||||||||
33547.5i | 0.789795i | 0.918725 | + | 0.394897i | ||||||
−0.918725 | + | 0.394897i | ||||||||
− | 5184.00i | − | 0.117851i | |||||||
25805.7i | 0.566772i | 0.959006 | + | 0.283386i | ||||||
−0.959006 | + | 0.283386i | ||||||||
−3921.78 | −0.0832538 | |||||||||
−27271.5 | −0.559830 | |||||||||
− | 45.2388i | − | 0.000898415i | |||||||
−28331.4 | −0.544554 | |||||||||
20350.5 | − | 8188.70i | 0.378737 | − | 0.152398i | |||||
15620.3 | 0.281593 | 0.140797 | − | 0.990039i | ||||||
0.140797 | + | 0.990039i | ||||||||
2492.94i | 0.0435498i | |||||||||
6561.00 | 0.111111 | |||||||||
59238.7 | 0.972906 | |||||||||
− | 2819.78i | − | 0.0449284i | −0.999748 | − | 0.0224642i | ||||
0.999748 | − | 0.0224642i | ||||||||
− | 15146.5i | − | 0.234215i | |||||||
16201.6i | 0.243226i | |||||||||
56568.8i | 0.824766i | |||||||||
−1987.46 | −0.0281515 | |||||||||
−17238.4 | −0.237296 | |||||||||
16227.2i | 0.217154i | 0.994088 | + | 0.108577i | ||||||
−0.994088 | + | 0.108577i | ||||||||
−3155.12 | −0.0410591 | |||||||||
59459.6 | − | 23925.6i | 0.752693 | − | 0.302872i | |||||
−34418.2 | −0.423954 | |||||||||
− | 7092.95i | − | 0.0850393i | |||||||
100725. | 1.17575 | |||||||||
−27.5335 | −0.000313006 | |||||||||
− | 9216.00i | − | 0.102062i | |||||||
126289.i | 1.36281i | 0.731906 | + | 0.681406i | ||||||
−0.731906 | + | 0.681406i | ||||||||
22973.2i | 0.241633i | |||||||||
− | 21817.4i | − | 0.223725i | |||||||
−48482.7 | −0.484827 | |||||||||
92398.8 | 0.901287 | 0.450643 | − | 0.892704i | ||||||
0.450643 | + | 0.892704i | ||||||||
− | 59894.8i | − | 0.570018i | |||||||
148091. | 1.37542 | 0.687711 | − | 0.725985i | ||||||
0.687711 | + | 0.725985i | ||||||||
36178.6 | − | 14557.7i | 0.327996 | − | 0.131980i | |||||
−9218.57 | −0.0816001 | |||||||||
− | 123604.i | − | 1.06848i | |||||||
88180.1 | 0.744580 | 0.372290 | − | 0.928117i | ||||||
0.372290 | + | 0.928117i | ||||||||
11664.0 | 0.0962250 | |||||||||
61467.2i | 0.495538i | 0.968819 | + | 0.247769i | ||||||
−0.968819 | + | 0.247769i | ||||||||
10491.8i | 0.0826736i | |||||||||
− | 8824.01i | − | 0.0679764i | |||||||
− | 26927.1i | − | 0.202836i | |||||||
−82256.1 | −0.605999 | −0.303000 | − | 0.952991i | ||||||
−0.303000 | + | 0.952991i | ||||||||
101.787 | 0.000733553 | |||||||||
20947.8i | 0.147705i | |||||||||
−3533.27 | −0.0243799 | |||||||||
18424.6 | + | 45788.5i | 0.124432 | + | 0.309237i | |||||
100379. | 0.663647 | |||||||||
− | 175000.i | − | 1.13284i | |||||||
−5609.11 | −0.0355583 | |||||||||
88501.4 | 0.549524 | |||||||||
48243.1i | 0.293451i | |||||||||
133287.i | 0.794375i | |||||||||
− | 12609.7i | − | 0.0736462i | |||||||
59939.2i | 0.343112i | |||||||||
34079.6 | 0.191236 | |||||||||
−143150. | −0.787556 | −0.393778 | − | 0.919206i | ||||||
−0.393778 | + | 0.919206i | ||||||||
− | 16384.0i | − | 0.0883883i | |||||||
−127280. | −0.673419 | |||||||||
−8860.20 | − | 22019.3i | −0.0459817 | − | 0.114273i | |||||
−141329. | −0.719539 | −0.359769 | − | 0.933041i | ||||||
−0.359769 | + | 0.933041i | ||||||||
− | 38786.4i | − | 0.193752i | |||||||
297.400 | 0.00145785 | |||||||||
57802.2 | 0.278088 | |||||||||
− | 7099.02i | − | 0.0335247i | |||||||
− | 106480.i | − | 0.493650i | |||||||
− | 3958.33i | − | 0.0180182i | −0.999959 | − | 0.00900909i | ||||
0.999959 | − | 0.00900909i | ||||||||
− | 77440.9i | − | 0.346157i | |||||||
−445579. | −1.95608 | −0.978042 | − | 0.208408i | ||||||
−0.978042 | + | 0.208408i | ||||||||
−16388.6 | −0.0706677 | |||||||||
226631.i | 0.959999i | |||||||||
−134190. | −0.558469 | |||||||||
152261. | − | 61267.5i | 0.622657 | − | 0.250547i | |||||
20736.0 | 0.0833333 | |||||||||
2150.44i | 0.00849391i | |||||||||
−103223. | −0.400769 | |||||||||
−51689.7 | −0.197293 | |||||||||
− | 15687.1i | − | 0.0588693i | |||||||
49619.3i | 0.183098i | 0.995801 | + | 0.0915492i | ||||||
−0.995801 | + | 0.0915492i | ||||||||
− | 109086.i | − | 0.395860i | |||||||
402323.i | 1.43593i | 0.696081 | + | 0.717964i | ||||||
−0.696081 | + | 0.717964i | ||||||||
180.955 | 0.000635275 | |||||||||
134763. | 0.465418 | |||||||||
− | 113325.i | − | 0.385058i | |||||||
−7674.60 | −0.0256582 | |||||||||
32754.8 | + | 81401.8i | 0.107761 | + | 0.267807i | |||||
−562429. | −1.82104 | −0.910519 | − | 0.413468i | ||||||
−0.910519 | + | 0.413468i | ||||||||
62481.3i | 0.199116i | |||||||||
278108. | 0.872411 | |||||||||
−9971.74 | −0.0307944 | |||||||||
− | 226265.i | − | 0.687945i | |||||||
26244.0i | 0.0785674i | |||||||||
− | 313878.i | − | 0.925319i | −0.886536 | − | 0.462659i | ||||
0.886536 | − | 0.462659i | ||||||||
236955.i | 0.687949i | |||||||||
−23606.5 | −0.0675027 | |||||||||
11279.1 | 0.0317691 | |||||||||
− | 602228.i | − | 1.67097i | −0.549510 | − | 0.835487i | ||||
0.549510 | − | 0.835487i | ||||||||
60586.0 | 0.165615 | |||||||||
−267813. | + | 257166.i | −0.721299 | + | 0.692624i | |||||
−64806.4 | −0.171987 | |||||||||
229.021i | 0.000598943i | |||||||||
−226275. | −0.583198 | |||||||||
304021. | 0.772304 | 0.386152 | − | 0.922435i | ||||||
0.386152 | + | 0.922435i | ||||||||
− | 7949.85i | − | 0.0199061i | |||||||
− | 318726.i | − | 0.786723i | |||||||
− | 68953.7i | − | 0.167794i | |||||||
225852.i | 0.541865i | |||||||||
−64908.7 | −0.153551 | |||||||||
406190. | 0.947539 | 0.473769 | − | 0.880649i | ||||||
0.473769 | + | 0.880649i | ||||||||
− | 12620.5i | − | 0.0290332i | |||||||
−240967. | −0.546714 | −0.273357 | − | 0.961913i | ||||||
−0.273357 | + | 0.961913i | ||||||||
95702.4 | + | 237838.i | 0.214163 | + | 0.532235i | |||||
−108547. | −0.239602 | |||||||||
− | 137673.i | − | 0.299781i | |||||||
−9547.60 | −0.0205100 | |||||||||
28371.8 | 0.0601319 | |||||||||
− | 448130.i | − | 0.937131i | |||||||
402899.i | 0.831383i | |||||||||
76679.2i | 0.156143i | |||||||||
− | 110.134i | − | 0.000221329i | |||||||
226140. | 0.448532 | 0.224266 | − | 0.974528i | ||||||
0.224266 | + | 0.974528i | ||||||||
36864.0 | 0.0721688 | |||||||||
− | 406075.i | − | 0.784717i | −0.919812 | − | 0.392359i | ||||
0.919812 | − | 0.392359i | ||||||||
−505156. | −0.963653 | |||||||||
49543.3 | − | 19935.5i | 0.0933037 | − | 0.0375439i | |||||
−91892.9 | −0.170861 | |||||||||
− | 407390.i | − | 0.747902i | −0.927449 | − | 0.373951i | ||||
0.927449 | − | 0.373951i | ||||||||
87269.5 | 0.158197 | |||||||||
202865. | 0.363140 | 0.181570 | − | 0.983378i | ||||||
0.181570 | + | 0.983378i | ||||||||
− | 193931.i | − | 0.342825i | |||||||
130055.i | 0.227058i | |||||||||
369595.i | 0.637306i | |||||||||
− | 23227.7i | − | 0.0395609i | |||||||
239579. | 0.403064 | |||||||||
144217. | 0.239680 | |||||||||
592364.i | 0.972570i | |||||||||
174242. | 0.282636 | |||||||||
58230.8 | + | 144714.i | 0.0933242 | + | 0.231928i | |||||
761.568 | 0.00120599 | |||||||||
− | 36874.3i | − | 0.0577000i | |||||||
657970. | 1.01742 | 0.508710 | − | 0.860938i | ||||||
0.508710 | + | 0.860938i | ||||||||
494415. | 0.755530 | |||||||||
− | 301927.i | − | 0.455988i | |||||||
352720.i | 0.526497i | |||||||||
137717.i | 0.203185i | |||||||||
46656.0i | 0.0680414i | |||||||||
82896.2 | 0.119505 | |||||||||
−245869. | −0.350398 | |||||||||
− | 232251.i | − | 0.327226i | |||||||
−41967.1 | −0.0584591 | |||||||||
378442. | + | 940499.i | 0.521217 | + | 1.29532i | |||||
35296.0 | 0.0480666 | |||||||||
− | 978060.i | − | 1.31705i | −0.752558 | − | 0.658527i | ||||
0.752558 | − | 0.658527i | ||||||||
107709. | 0.143427 | |||||||||
245444. | 0.323218 | |||||||||
− | 329024.i | − | 0.428506i | |||||||
812137.i | 1.04608i | 0.852308 | + | 0.523040i | ||||||
−0.852308 | + | 0.523040i | ||||||||
407.149i | 0.000518700i | |||||||||
1.36329e6i | 1.71790i | 0.512058 | + | 0.858951i | ||||||
−0.512058 | + | 0.858951i | ||||||||
−83791.4 | −0.104443 | |||||||||
254982. | 0.314398 | |||||||||
− | 14133.1i | − | 0.0172392i | |||||||
931926. | 1.12458 | 0.562292 | − | 0.826939i | ||||||
0.562292 | + | 0.826939i | ||||||||
−183154. | + | 73698.3i | −0.218664 | + | 0.0879869i | |||||
245215. | 0.289653 | |||||||||
401515.i | 0.469269i | |||||||||
−140583. | −0.162578 | |||||||||
699998. | 0.801041 | |||||||||
− | 885874.i | − | 1.00318i | −0.865107 | − | 0.501588i | ||||
0.865107 | − | 0.501588i | ||||||||
− | 22436.4i | − | 0.0251435i | |||||||
1.32690e6i | 1.47161i | 0.677191 | + | 0.735807i | ||||||
−0.677191 | + | 0.735807i | ||||||||
354006.i | 0.388572i | |||||||||
−59049.0 | −0.0641500 | |||||||||
−192973. | −0.207501 | |||||||||
55928.5i | 0.0595275i | |||||||||
−533148. | −0.561708 | |||||||||
−1598.32 | + | 643.137i | −0.00166694 | + | 0.000670751i | |||||
50438.8 | 0.0520757 | |||||||||
25378.1i | 0.0259394i | |||||||||
−239757. | −0.242617 | |||||||||
−547596. | −0.548625 | −0.274313 | − | 0.961641i | ||||||
−0.274313 | + | 0.961641i | ||||||||
136319.i | 0.135224i | |||||||||
− | 579409.i | − | 0.569094i | |||||||
− | 572599.i | − | 0.556886i | |||||||
− | 145814.i | − | 0.140427i | |||||||
65536.0 | 0.0625000 | |||||||||
−1.65509e6 | −1.56311 | −0.781554 | − | 0.623837i | ||||||
−0.781554 | + | 0.623837i | ||||||||
− | 509119.i | − | 0.476179i | |||||||
103127. | 0.0955265 | |||||||||
88077.0 | − | 35440.8i | 0.0808033 | − | 0.0325140i | |||||
17887.2 | 0.0162533 | |||||||||
− | 565317.i | − | 0.508791i | |||||||
−668188. | −0.595675 | −0.297838 | − | 0.954617i | ||||||
−0.297838 | + | 0.954617i | ||||||||
155146. | 0.137003 | |||||||||
− | 300914.i | − | 0.263226i | |||||||
1189.60i | 0.00103085i | |||||||||
− | 146045.i | − | 0.125374i | |||||||
231209.i | 0.196638i | |||||||||
−384942. | −0.324350 | −0.162175 | − | 0.986762i | ||||||
−0.162175 | + | 0.986762i | ||||||||
28396.1 | 0.0237055 | |||||||||
− | 1.05344e6i | − | 0.871334i | −0.900108 | − | 0.435667i | ||||
0.900108 | − | 0.435667i | ||||||||
425919. | 0.349064 | |||||||||
−535136. | + | 215330.i | −0.434568 | + | 0.174863i | |||||
15833.3 | 0.0127408 | |||||||||
− | 816177.i | − | 0.650808i | |||||||
309764. | 0.244770 | |||||||||
−1.62051e6 | −1.26897 | −0.634485 | − | 0.772936i | ||||||
−0.634485 | + | 0.772936i | ||||||||
− | 1.78231e6i | − | 1.38316i | |||||||
63836.6i | 0.0490975i | |||||||||
− | 65554.3i | − | 0.0499696i | |||||||
563009.i | 0.425353i | 0.977123 | + | 0.212677i | ||||||
−0.977123 | + | 0.212677i | ||||||||
−906522. | −0.678822 | |||||||||
361892. | 0.268604 | 0.134302 | − | 0.990940i | ||||||
0.134302 | + | 0.990940i | ||||||||
− | 536760.i | − | 0.394897i | |||||||
247.802 | 0.000180714 | |||||||||
245070. | + | 609045.i | 0.177164 | + | 0.440285i | |||||
−1.55774e6 | −1.11633 | |||||||||
82944.0i | 0.0589256i | |||||||||
1.34819e6 | 0.949526 | |||||||||
−8601.77 | −0.00600610 | |||||||||
− | 1.13660e6i | − | 0.786820i | |||||||
− | 412891.i | − | 0.283386i | |||||||
757318.i | 0.515358i | 0.966231 | + | 0.257679i | ||||||
−0.966231 | + | 0.257679i | ||||||||
− | 206759.i | − | 0.139507i | |||||||
244373. | 0.163493 | |||||||||
62748.5 | 0.0416269 | |||||||||
196356.i | 0.129168i | |||||||||
−198477. | −0.129470 | |||||||||
489306. | + | 1.21602e6i | 0.316521 | + | 0.786614i | |||||
436345. | 0.279915 | |||||||||
− | 1.48753e6i | − | 0.946348i | |||||||
−1.60929e6 | −1.01535 | |||||||||
−831589. | −0.520358 | |||||||||
723.821i | 0.000449207i | |||||||||
117448.i | 0.0722932i | |||||||||
539053.i | 0.329100i | |||||||||
1.96280e6i | 1.18858i | 0.804249 | + | 0.594292i | ||||||
−0.804249 | + | 0.594292i | ||||||||
453302. | 0.272277 | |||||||||
−1.33282e6 | −0.794100 | |||||||||
− | 30698.4i | − | 0.0181431i | |||||||
834419. | 0.489197 | 0.244598 | − | 0.969624i | ||||||
0.244598 | + | 0.969624i | ||||||||
−325607. | + | 131019.i | −0.189368 | + | 0.0761989i | |||||
1.61834e6 | 0.933703 | 0.466851 | − | 0.884336i | ||||||
0.466851 | + | 0.884336i | ||||||||
− | 2.24972e6i | − | 1.28767i | |||||||
82967.2 | 0.0471118 | |||||||||
−249925. | −0.140797 | |||||||||
− | 660304.i | − | 0.369059i | −0.982827 | − | 0.184529i | ||||
0.982827 | − | 0.184529i | ||||||||
1.11243e6i | 0.616888i | |||||||||
− | 59480.4i | − | 0.0327263i | |||||||
− | 39887.0i | − | 0.0217749i | |||||||
−793621. | −0.429883 | |||||||||
905062. | 0.486450 | |||||||||
4704.11i | 0.00250883i | |||||||||
−104976. | −0.0555556 | |||||||||
689255. | + | 1.71293e6i | 0.361969 | + | 0.899560i | |||||
1.25551e6 | 0.654299 | |||||||||
− | 553205.i | − | 0.286099i | |||||||
−947819. | −0.486453 | |||||||||
−2.64866e6 | −1.34908 | |||||||||
− | 94425.9i | − | 0.0477316i | |||||||
2.73497e6i | 1.37209i | 0.727558 | + | 0.686046i | ||||||
−0.727558 | + | 0.686046i | ||||||||
45116.5i | 0.0224642i | |||||||||
79416.1i | 0.0392462i | |||||||||
2.40891e6 | 1.18156 | |||||||||
140720. | 0.0685083 | |||||||||
242344.i | 0.117107i | |||||||||
−880707. | −0.422432 | −0.211216 | − | 0.977439i | ||||||
−0.211216 | + | 0.977439i | ||||||||
−1.02867e6 | − | 1.07125e6i | −0.489759 | − | 0.510035i | |||||
740305. | 0.349874 | |||||||||
− | 259226.i | − | 0.121613i | |||||||
212277. | 0.0988590 | |||||||||
−916.085 | −0.000423517 | |||||||||
− | 2.37193e6i | − | 1.08860i | |||||||
− | 905101.i | − | 0.412383i | |||||||
− | 188531.i | − | 0.0852774i | |||||||
1.21608e6i | 0.546102i | |||||||||
−33079.1 | −0.0147479 | −0.00737395 | − | 0.999973i | ||||||
−0.00737395 | + | 0.999973i | ||||||||
31799.4 | 0.0140757 | |||||||||
4.06448e6i | 1.78624i | 0.449814 | + | 0.893122i | ||||||
−0.449814 | + | 0.893122i | ||||||||
1.27490e6 | 0.556297 | |||||||||
−165821. | − | 412097.i | −0.0718410 | − | 0.178538i | |||||
275815. | 0.118648 | |||||||||
− | 3.57770e6i | − | 1.52815i | −0.645125 | − | 0.764077i | ||||
0.645125 | − | 0.764077i | ||||||||
−903409. | −0.383157 | |||||||||
−326686. | −0.137582 | |||||||||
− | 259635.i | − | 0.108577i | |||||||
1.57500e6i | 0.654047i | |||||||||
1.62476e6i | 0.670011i | |||||||||
3.31455e6i | 1.35734i | 0.734444 | + | 0.678669i | ||||||
−0.734444 | + | 0.678669i | ||||||||
50482.0 | 0.0205296 | |||||||||
2.47609e6 | 0.999997 | |||||||||
− | 963867.i | − | 0.386585i | |||||||
−796513. | −0.317268 | |||||||||
−951353. | + | 382809.i | −0.376347 | + | 0.151436i | |||||
−251297. | −0.0987313 | |||||||||
− | 434188.i | − | 0.169424i | |||||||
192406. | 0.0745681 | 0.0372840 | − | 0.999305i | ||||||
0.0372840 | + | 0.999305i | ||||||||
550691. | 0.211977 | |||||||||
− | 1.19958e6i | − | 0.458632i | |||||||
− | 38190.4i | − | 0.0145027i | |||||||
3.25029e6i | 1.22599i | |||||||||
113487.i | 0.0425197i | |||||||||
1.60161e6 | 0.596053 | 0.298027 | − | 0.954558i | ||||||
0.298027 | + | 0.954558i | ||||||||
1.79252e6 | 0.662652 | |||||||||
− | 539453.i | − | 0.198096i | |||||||
−1.61160e6 | −0.587877 | |||||||||
50230.7 | + | 124833.i | 0.0182019 | + | 0.0452350i | |||||
−306717. | −0.110410 | |||||||||
− | 3.76006e6i | − | 1.34461i | −0.740274 | − | 0.672305i | ||||
0.740274 | − | 0.672305i | ||||||||
440.537 | 0.000156503 | |||||||||
1.28835e6 | 0.454695 | |||||||||
904560.i | 0.317160i | |||||||||
4.69693e6i | 1.63613i | 0.575128 | + | 0.818063i | ||||||
−0.575128 | + | 0.818063i | ||||||||
147456.i | 0.0510310i | |||||||||
− | 275892.i | − | 0.0948608i | |||||||
1.62430e6 | 0.554879 | |||||||||
1.14552e6 | 0.388799 | |||||||||
− | 2.02062e6i | − | 0.681406i | |||||||
4.85881e6 | 1.62801 | 0.814003 | − | 0.580860i | ||||||
0.814003 | + | 0.580860i | ||||||||
79741.8 | + | 198173.i | 0.0265476 | + | 0.0659757i | |||||
3.57894e6 | 1.18389 | |||||||||
− | 367572.i | − | 0.120817i | |||||||
1.27196e6 | 0.415426 | |||||||||
1.62956e6 | 0.528846 | |||||||||
152111.i | 0.0490533i | |||||||||
349078.i | 0.111863i | |||||||||
− | 3.91926e6i | − | 1.24804i | −0.781409 | − | 0.624019i | ||||
0.781409 | − | 0.624019i | ||||||||
811460.i | 0.256779i | |||||||||
−2676.60 | −0.000841688 | |||||||||
775724. | 0.242414 | |||||||||
− | 5.01898e6i | − | 1.55867i | −0.626606 | − | 0.779336i | ||||
0.626606 | − | 0.779336i | ||||||||
−520219. | −0.160554 | |||||||||
−445509. | + | 179266.i | −0.136645 | + | 0.0549838i | |||||
−1.47838e6 | −0.450643 | |||||||||
63891.2i | 0.0193555i | |||||||||
92910.9 | 0.0279738 | |||||||||
264083. | 0.0790232 | |||||||||
958317.i | 0.285009i | |||||||||
− | 2.97886e6i | − | 0.880526i | −0.897869 | − | 0.440263i | ||||
0.897869 | − | 0.440263i | ||||||||
576868.i | 0.169480i | |||||||||
35625.0i | 0.0104028i | |||||||||
−2.36946e6 | −0.687711 | |||||||||
−2.63956e6 | −0.761477 | |||||||||
696968.i | 0.199854i | |||||||||
27459.1 | 0.00782648 | |||||||||
−578857. | + | 232923.i | −0.163998 | + | 0.0659902i | |||||
4.01021e6 | 1.12935 | |||||||||
3046.27i | 0.000852762i | |||||||||
−4.76887e6 | −1.32703 | −0.663515 | − | 0.748163i | ||||||
−0.663515 | + | 0.748163i | ||||||||
147497. | 0.0408000 | |||||||||
651294.i | 0.179090i | 0.995983 | + | 0.0895451i | ||||||
−0.995983 | + | 0.0895451i | ||||||||
2.63188e6i | 0.719424i | |||||||||
− | 2.03968e6i | − | 0.554256i | |||||||
1.97766e6i | 0.534241i | |||||||||
5.04143e6 | 1.35388 | |||||||||
1.20771e6 | 0.322432 | |||||||||
− | 1.26860e6i | − | 0.336710i | |||||||
−1.41088e6 | −0.372290 | |||||||||
−1.37035e6 | + | 551407.i | −0.359491 | + | 0.144654i | |||||
−550869. | −0.143674 | |||||||||
5.22621e6i | 1.35517i | 0.735444 | + | 0.677585i | ||||||
−0.735444 | + | 0.677585i | ||||||||
−186624. | −0.0481125 | |||||||||
−6.33506e6 | −1.62379 | −0.811897 | − | 0.583801i | ||||||
−0.811897 | + | 0.583801i | ||||||||
331585.i | 0.0845026i | |||||||||
− | 19354.0i | − | 0.00490396i | |||||||
− | 983475.i | − | 0.247769i | |||||||
6082.18i | 0.00152355i | |||||||||
929005. | 0.231384 | |||||||||
−7.44321e6 | −1.84331 | −0.921657 | − | 0.388006i | ||||||
−0.921657 | + | 0.388006i | ||||||||
− | 167868.i | − | 0.0413368i | |||||||
465208. | 0.113907 | |||||||||
−3.76200e6 | + | 1.51377e6i | −0.915931 | + | 0.368556i | |||||
327031. | 0.0791734 | 0.0395867 | − | 0.999216i | ||||||
0.0395867 | + | 0.999216i | ||||||||
141184.i | 0.0339882i | |||||||||
−158021. | −0.0378281 | |||||||||
3.91224e6 | 0.931297 | |||||||||
− | 446574.i | − | 0.105712i | |||||||
430834.i | 0.101418i | |||||||||
− | 5.82118e6i | − | 1.36268i | −0.731965 | − | 0.681342i | ||||
0.731965 | − | 0.681342i | ||||||||
981775.i | 0.228550i | |||||||||
−3.98899e6 | −0.923468 | |||||||||
1.31610e6 | 0.303000 | |||||||||
− | 3.62091e6i | − | 0.829033i | |||||||
−3.24855e6 | −0.739690 | |||||||||
232988. | + | 579019.i | 0.0527601 | + | 0.131119i | |||||
−1628.60 | −0.000366776 | |||||||||
− | 8.15788e6i | − | 1.82720i | −0.406612 | − | 0.913601i | ||||
0.406612 | − | 0.913601i | ||||||||
−5.45315e6 | −1.21474 | |||||||||
−1.21287e6 | −0.268709 | |||||||||
− | 335165.i | − | 0.0738524i | |||||||
3.15011e6i | 0.690357i | 0.938537 | + | 0.345179i | ||||||
−0.938537 | + | 0.345179i | ||||||||
1.01993e6i | 0.222313i | |||||||||
202622.i | 0.0439273i | 0.999759 | + | 0.0219637i | ||||||
−0.999759 | + | 0.0219637i | ||||||||
56532.3 | 0.0121899 | |||||||||
69071.4 | 0.0148138 | |||||||||
3.72771e6i | 0.795201i | |||||||||
91749.8 | 0.0194676 | 0.00973382 | − | 0.999953i | ||||||
0.00973382 | + | 0.999953i | ||||||||
−294793. | − | 732616.i | −0.0622161 | − | 0.154619i | |||||
−1.51997e6 | −0.319082 | |||||||||
980860.i | 0.204815i | |||||||||
5.06186e6 | 1.05138 | |||||||||
−1.60606e6 | −0.331823 | |||||||||
− | 3.80921e6i | − | 0.782856i | |||||||
− | 562331.i | − | 0.114960i | |||||||
8567.58i | 0.00174230i | |||||||||
2.79999e6i | 0.566421i | |||||||||
−2.50298e6 | −0.503687 | |||||||||
3.54350e6 | 0.709353 | |||||||||
2.82910e6i | 0.563390i | 0.959504 | + | 0.281695i | ||||||
−0.959504 | + | 0.281695i | ||||||||
89745.7 | 0.0177791 | |||||||||
−554236. | + | 223016.i | −0.109228 | + | 0.0439514i | |||||
−5.30758e6 | −1.04059 | |||||||||
2.03639e6i | 0.397185i | |||||||||
−1.41602e6 | −0.274762 | |||||||||
−1.22981e6 | −0.237401 | |||||||||
− | 236196.i | − | 0.0453609i | |||||||
− | 1.30176e6i | − | 0.248719i | −0.992237 | − | 0.124359i | ||||
0.992237 | − | 0.124359i | ||||||||
− | 771890.i | − | 0.146726i | |||||||
2.82490e6i | 0.534233i | |||||||||
−223714. | −0.0420923 | |||||||||
−6.07696e6 | −1.13758 | −0.568791 | − | 0.822482i | ||||||
−0.568791 | + | 0.822482i | ||||||||
− | 2.13259e6i | − | 0.397187i | |||||||
367404. | 0.0680810 | |||||||||
−2572.55 | − | 6393.26i | −0.000474292 | − | 0.00117870i | |||||
212458. | 0.0389727 | |||||||||
201755.i | 0.0368231i | |||||||||
3.52866e6 | 0.640795 | |||||||||
−101512. | −0.0183419 | |||||||||
3.78708e6i | 0.680853i | 0.940271 | + | 0.340426i | ||||||
−0.940271 | + | 0.340426i | ||||||||
− | 959028.i | − | 0.171556i | |||||||
5.42005e6i | 0.964737i | |||||||||
− | 2.19038e6i | − | 0.387937i | |||||||
2.28832e6 | 0.403271 | 0.201636 | − | 0.979461i | ||||||
0.201636 | + | 0.979461i | ||||||||
−545274. | −0.0956178 | |||||||||
899783.i | 0.157003i | |||||||||
2.31764e6 | 0.402410 | |||||||||
2.41032e6 | − | 2.31450e6i | 0.416442 | − | 0.399886i | |||||
2.29040e6 | 0.393778 | |||||||||
− | 3.70029e6i | − | 0.633055i | −0.948583 | − | 0.316528i | ||||
0.948583 | − | 0.316528i | ||||||||
583258. | 0.0992968 | |||||||||
2.71435e6 | 0.459847 | |||||||||
262144.i | 0.0441942i | |||||||||
− | 2061.19i | − | 0.000345800i | |||||||
− | 6.62037e6i | − | 1.10528i | |||||||
1.44212e6i | 0.239597i | |||||||||
2.03648e6 | 0.336709 | |||||||||
−6.78256e6 | −1.11601 | |||||||||
412509.i | 0.0675474i | |||||||||
−2.73619e6 | −0.445890 | |||||||||
141763. | + | 352308.i | 0.0229909 | + | 0.0571366i | |||||
6.13756e6 | 0.990608 | 0.495304 | − | 0.868720i | ||||||
0.495304 | + | 0.868720i | ||||||||
71548.7i | 0.0114928i | |||||||||
4.10572e6 | 0.656349 | 0.328175 | − | 0.944617i | ||||||
0.328175 | + | 0.944617i | ||||||||
2.26127e6 | 0.359769 | |||||||||
2.86853e6i | 0.454215i | |||||||||
− | 2.67275e6i | − | 0.421206i | |||||||
1.31121e6i | 0.205658i | |||||||||
620583.i | 0.0968758i | |||||||||
−1.80895e6 | −0.281053 | |||||||||
1.20366e6 | 0.186129 | |||||||||
− | 2.03267e6i | − | 0.312846i | |||||||
−4758.40 | −0.000728923 | |||||||||
8.37177e6 | − | 3.36867e6i | 1.27644 | − | 0.513618i | |||||
584178. | 0.0886528 | |||||||||
858701.i | 0.129705i | |||||||||
−924834. | −0.139044 | |||||||||
−3.65571e6 | −0.547062 | |||||||||
− | 1.53977e6i | − | 0.229350i | |||||||
− | 1.54696e6i | − | 0.229355i | |||||||
113584.i | 0.0167623i | |||||||||
2.51266e6i | 0.369098i | 0.982823 | + | 0.184549i | ||||||
−0.982823 | + | 0.184549i | ||||||||
4.21374e6 | 0.616126 | |||||||||
2.16870e6 | 0.315646 | |||||||||
1.70368e6i | 0.246825i | |||||||||
−598569. | −0.0863223 | |||||||||
−861321. | − | 2.14054e6i | −0.123647 | − | 0.307286i | |||||
−2.29454e6 | −0.327889 | −0.163945 | − | 0.986470i | ||||||
−0.163945 | + | 0.986470i | ||||||||
63333.4i | 0.00900909i | |||||||||
976924. | 0.138334 | |||||||||
3.26471e6 | 0.460191 | |||||||||
624.378i | 8.76130e-5i | |||||||||
1.23905e6i | 0.173078i | |||||||||
− | 1.64301e6i | − | 0.228469i | |||||||
− | 6.48202e6i | − | 0.897297i | |||||||
85928.4 | 0.0118414 | |||||||||
7.12926e6 | 0.978042 | |||||||||
− | 5.96324e6i | − | 0.814412i | −0.913336 | − | 0.407206i | ||||
0.913336 | − | 0.407206i | ||||||||
−255346. | −0.0347171 | |||||||||
3.21684e6 | + | 7.99445e6i | 0.435412 | + | 1.08208i | |||||
262217. | 0.0353339 | |||||||||
4.03317e6i | 0.541053i | |||||||||
−2.25204e6 | −0.300770 | |||||||||
−7.37754e6 | −0.980935 | −0.490468 | − | 0.871459i | ||||||
−0.490468 | + | 0.871459i | ||||||||
− | 3.62609e6i | − | 0.479999i | |||||||
− | 801012.i | − | 0.105565i | |||||||
1.44757e6i | 0.189932i | |||||||||
− | 690113.i | − | 0.0901493i | |||||||
2.14704e6 | 0.279235 | |||||||||
2.60845e6 | 0.337756 | 0.168878 | − | 0.985637i | ||||||
0.168878 | + | 0.985637i | ||||||||
991.208i | 0.000127784i | |||||||||
1.09867e7 | 1.41019 | 0.705095 | − | 0.709113i | ||||||
0.705095 | + | 0.709113i | ||||||||
−2.43618e6 | + | 980280.i | −0.311329 | + | 0.125274i | |||||
−2.03526e6 | −0.258960 | |||||||||
− | 6.23097e6i | − | 0.789362i | |||||||
6.51831e6 | 0.822177 | |||||||||
−331776. | −0.0416667 | |||||||||
1.10048e7i | 1.37607i | 0.725677 | + | 0.688036i | ||||||
−0.725677 | + | 0.688036i | ||||||||
5.39276e6i | 0.671416i | |||||||||
3.65468e6i | 0.453057i | |||||||||
− | 34407.1i | − | 0.00424696i | |||||||
−296596. | −0.0364523 | |||||||||
4.54640e6 | 0.556365 | |||||||||
8.32318e6i | 1.01419i | |||||||||
1.65157e6 | 0.200384 | |||||||||
−445890. | + | 179419.i | −0.0538689 | + | 0.0216760i | |||||
−3.02927e6 | −0.364413 | |||||||||
1.09851e7i | 1.31586i | 0.753080 | + | 0.657929i | ||||||
−0.753080 | + | 0.657929i | ||||||||
827036. | 0.0986464 | |||||||||
−2228.31 | −0.000264659 | |||||||||
977492.i | 0.115607i | |||||||||
3.66651e6i | 0.431801i | |||||||||
250994.i | 0.0294347i | |||||||||
− | 3.90620e6i | − | 0.456161i | −0.973642 | − | 0.228081i | ||||
0.973642 | − | 0.228081i | ||||||||
−785426. | −0.0913354 | |||||||||
1.70415e6 | 0.197340 | |||||||||
− | 793908.i | − | 0.0915492i | |||||||
−1.82578e6 | −0.209659 | |||||||||
−4.86407e6 | + | 1.95722e6i | −0.556220 | + | 0.223814i | |||||
−1.69973e7 | −1.93559 | −0.967797 | − | 0.251733i | ||||||
−0.967797 | + | 0.251733i | ||||||||
1.74538e6i | 0.197930i | |||||||||
1.07099e7 | 1.20948 | 0.604739 | − | 0.796424i | ||||||
0.604739 | + | 0.796424i | ||||||||
5.95014e6 | 0.669169 | |||||||||
− | 1.17049e6i | − | 0.131092i | |||||||
− | 6.43717e6i | − | 0.717964i | |||||||
861829.i | 0.0957267i | |||||||||
− | 3.32636e6i | − | 0.367949i | |||||||
−1.43102e7 | −1.57642 | −0.788212 | − | 0.615404i | ||||||
−0.788212 | + | 0.615404i | ||||||||
−2895.28 | −0.000317638 | |||||||||
209050.i | 0.0228405i | |||||||||
−469793. | −0.0511190 | |||||||||
1.42347e7 | − | 5.72781e6i | 1.54257 | − | 0.620705i | |||||
−2.15621e6 | −0.232709 | |||||||||
1.67594e7i | 1.80139i | 0.434450 | + | 0.900696i | ||||||
−0.434450 | + | 0.900696i | ||||||||
−7.85120e6 | −0.840456 | |||||||||
−1.29795e6 | −0.138379 | |||||||||
1.81321e6i | 0.192529i | |||||||||
− | 1.26793e7i | − | 1.34085i | −0.741976 | − | 0.670427i | ||||
0.741976 | − | 0.670427i | ||||||||
− | 5.33128e6i | − | 0.561513i | |||||||
− | 5.43928e6i | − | 0.570577i | −0.958442 | − | 0.285289i | ||||
0.958442 | − | 0.285289i | ||||||||
122794. | 0.0128291 | |||||||||
−1.56818e6 | −0.163180 | |||||||||
3.33768e6i | 0.345914i | |||||||||
1.70684e6 | 0.176187 | |||||||||
−524077. | − | 1.30243e6i | −0.0538807 | − | 0.133904i | |||||
8.88559e6 | 0.909885 | |||||||||
6.47335e6i | 0.660227i | |||||||||
−6854.11 | −0.000696277 | |||||||||
8.99887e6 | 0.910519 | |||||||||
1.63121e6i | 0.164393i | |||||||||
331869.i | 0.0333131i | |||||||||
− | 5.28439e6i | − | 0.528350i | −0.964475 | − | 0.264175i | ||||
0.964475 | − | 0.264175i | ||||||||
− | 999700.i | − | 0.0995582i | |||||||
−5.92173e6 | −0.587407 | |||||||||
2.64121e6 | 0.260964 | |||||||||
− | 1.39400e6i | − | 0.137192i | |||||||
−4.44973e6 | −0.436206 | |||||||||
1.30639e6 | + | 3.24664e6i | 0.127563 | + | 0.317019i | |||||
237922. | 0.0231410 | |||||||||
2.71735e6i | 0.263265i | |||||||||
159548. | 0.0153972 | |||||||||
8.01855e6 | 0.770816 | 0.385408 | − | 0.922746i | ||||||
0.385408 | + | 0.922746i | ||||||||
− | 3.17448e6i | − | 0.303973i | |||||||
− | 1.39227e7i | − | 1.32799i | −0.747735 | − | 0.663997i | ||||
0.747735 | − | 0.663997i | ||||||||
3.62025e6i | 0.343972i | |||||||||
− | 1.23945e6i | − | 0.117309i | |||||||
−18816.5 | −0.00177401 | |||||||||
−9.55517e6 | −0.897383 | −0.448692 | − | 0.893687i | ||||||
−0.448692 | + | 0.893687i | ||||||||
− | 419904.i | − | 0.0392837i | |||||||
−6.75926e6 | −0.629923 | |||||||||
−6.85170e6 | + | 2.75702e6i | −0.636085 | + | 0.255951i | |||||
−746066. | −0.0689961 | |||||||||
5.02204e6i | 0.462659i | |||||||||
−1.87340e7 | −1.71928 | −0.859640 | − | 0.510901i | ||||||
−0.859640 | + | 0.510901i | ||||||||
2.21282e6 | 0.202303 | |||||||||
− | 1.37627e6i | − | 0.125343i | |||||||
− | 3.79128e6i | − | 0.343974i | |||||||
2.09026e6i | 0.188924i | |||||||||
− | 1.05946e7i | − | 0.953941i | |||||||
−3.39787e6 | −0.304785 | −0.152392 | − | 0.988320i | ||||||
−0.152392 | + | 0.988320i | ||||||||
377704. | 0.0337514 | |||||||||
1.81823e7i | 1.61862i | 0.587382 | + | 0.809310i | ||||||
−0.587382 | + | 0.809310i | ||||||||
−1.09399e7 | −0.970215 | |||||||||
−3.40598e6 | − | 8.46449e6i | −0.300925 | − | 0.747854i | |||||
−180466. | −0.0158846 | |||||||||
2896.09i | 0.000253956i | |||||||||
−317664. | −0.0277513 | |||||||||
475034. | 0.0413438 | |||||||||
9.63564e6i | 0.835487i | |||||||||
8.80254e6i | 0.760401i | |||||||||
562879.i | 0.0484427i | |||||||||
− | 3.24858e6i | − | 0.278540i | |||||||
−969377. | −0.0828074 | |||||||||
686844. | 0.0584548 | 0.0292274 | − | 0.999573i | ||||||
0.0292274 | + | 0.999573i | ||||||||
− | 3.52283e6i | − | 0.298704i | |||||||
−2.20899e6 | −0.186610 | |||||||||
4.28501e6 | − | 4.11466e6i | 0.360650 | − | 0.346312i | |||||
−6.64858e6 | −0.557516 | −0.278758 | − | 0.960361i | ||||||
−0.278758 | + | 0.960361i | ||||||||
2.96122e6i | 0.247398i | |||||||||
1.32836e7 | 1.10571 | |||||||||
1.03690e6 | 0.0859935 | |||||||||
− | 7.30923e6i | − | 0.603954i | |||||||
849106.i | 0.0699038i | |||||||||
1.66853e7i | 1.36862i | 0.729193 | + | 0.684308i | ||||||
−0.729193 | + | 0.684308i | ||||||||
− | 3664.34i | − | 0.000299472i | |||||||
38546.4 | 0.00313875 | |||||||||
9.48773e6 | 0.769754 | |||||||||
− | 1.22696e7i | − | 0.991831i | |||||||
3.62040e6 | 0.291599 | |||||||||
−7.02885e6 | − | 1.74680e7i | −0.564074 | − | 1.40183i | |||||
754122. | 0.0603002 | |||||||||
− | 1.75290e7i | − | 1.39657i | −0.715822 | − | 0.698283i | ||||
0.715822 | − | 0.698283i | ||||||||
−4.86434e6 | −0.386152 | |||||||||
−2.29484e6 | −0.181518 | |||||||||
− | 132317.i | − | 0.0104283i | |||||||
− | 4.33906e6i | − | 0.340748i | |||||||
127198.i | 0.00995305i | |||||||||
− | 2.46395e7i | − | 1.92110i | |||||||
−1.62579e7 | −1.26307 | |||||||||
−8.38734e6 | −0.649279 | |||||||||
5.09961e6i | 0.393362i | |||||||||
7.06379e6 | 0.542929 | 0.271464 | − | 0.962449i | ||||||
0.271464 | + | 0.962449i | ||||||||
1.64839e6 | − | 663285.i | 0.126246 | − | 0.0507993i | |||||
−2772.13 | −0.000211556 | |||||||||
1.10326e6i | 0.0838969i | |||||||||
−2.20694e6 | −0.167231 | |||||||||
1.43108e7 | 1.08057 | |||||||||
− | 9.71889e6i | − | 0.731253i | |||||||
− | 3.61364e6i | − | 0.270933i | |||||||
9.07731e6i | 0.678175i | 0.940755 | + | 0.339087i | ||||||
−0.940755 | + | 0.339087i | ||||||||
− | 1.30675e6i | − | 0.0972849i | |||||||
1.26525e6 | 0.0938644 | |||||||||
1.03854e6 | 0.0767755 | |||||||||
1.69532e6i | 0.124890i | |||||||||
−6.29998e6 | −0.462481 | |||||||||
596625. | + | 1.48272e6i | 0.0436452 | + | 0.108466i | |||||
−6.49904e6 | −0.473769 | |||||||||
7.97287e6i | 0.579184i | |||||||||
−1.32582e7 | −0.959783 | |||||||||
−1.03755e7 | −0.748492 | −0.374246 | − | 0.927330i | ||||||
−0.374246 | + | 0.927330i | ||||||||
201928.i | 0.0145166i | |||||||||
− | 1.55768e7i | − | 1.11594i | |||||||
9.90436e6i | 0.707104i | |||||||||
− | 1.19421e7i | − | 0.849637i | |||||||
3.85547e6 | 0.273357 | |||||||||
669150. | 0.0472801 | |||||||||
− | 3.18605e6i | − | 0.224342i | |||||||
−2.94915e6 | −0.206948 | −0.103474 | − | 0.994632i | ||||||
−0.103474 | + | 0.994632i | ||||||||
−1.53124e6 | − | 3.80541e6i | −0.107081 | − | 0.266117i | |||||
531441. | 0.0370370 | |||||||||
− | 1.00519e6i | − | 0.0698136i | |||||||
2.35290e7 | 1.62858 | |||||||||
1.73675e6 | 0.119801 | |||||||||
1.71605e7i | 1.17970i | 0.807513 | + | 0.589849i | ||||||
−0.807513 | + | 0.589849i | ||||||||
769623.i | 0.0527276i | |||||||||
− | 503356.i | − | 0.0343682i | |||||||
2.20276e6i | 0.149890i | |||||||||
−3.89226e6 | −0.263957 | |||||||||
4.79834e6 | 0.324302 | |||||||||
2.20849e7i | 1.48760i | 0.668405 | + | 0.743798i | ||||||
−0.668405 | + | 0.743798i | ||||||||
152762. | 0.0102550 | |||||||||
14384.8 | − | 5788.23i | 0.000962409 | − | 0.000387258i | |||||
−1.30011e7 | −0.866906 | |||||||||
2.21459e7i | 1.47171i | 0.677140 | + | 0.735854i | ||||||
−0.677140 | + | 0.735854i | ||||||||
−453949. | −0.0300659 | |||||||||
−483194. | −0.0318956 | |||||||||
6.40644e6i | 0.421473i | |||||||||
− | 228402.i | − | 0.0149761i | |||||||
7.17008e6i | 0.468565i | |||||||||
− | 9.27514e6i | − | 0.604110i | |||||||
2.15781e6 | 0.140075 | |||||||||
6.38710e6 | 0.413242 | 0.206621 | − | 0.978421i | ||||||
0.206621 | + | 0.978421i | ||||||||
− | 6.44638e6i | − | 0.415692i | |||||||
4.92836e6 | 0.316749 | |||||||||
−499331. | + | 200923.i | −0.0319860 | + | 0.0128707i | |||||
−3.91783e6 | −0.250137 | |||||||||
− | 1.22687e6i | − | 0.0780716i | |||||||
−2.47266e6 | −0.156828 | −0.0784141 | − | 0.996921i | ||||||
−0.0784141 | + | 0.996921i | ||||||||
1.50402e7 | 0.950783 | |||||||||
5.21469e6i | 0.328567i | |||||||||
1762.15i | 0.000110664i | |||||||||
− | 1.59009e7i | − | 0.995315i | −0.867374 | − | 0.497657i | ||||
0.867374 | − | 0.497657i | ||||||||
5.15339e6i | 0.321518i | |||||||||
6.46537e6 | 0.402052 | |||||||||
−3.61824e6 | −0.224266 | |||||||||
1.31233e6i | 0.0810755i | |||||||||
−1.87877e7 | −1.15692 | |||||||||
1.41858e7 | − | 5.70814e6i | 0.870693 | − | 0.350353i | |||||
−589824. | −0.0360844 | |||||||||
4.80537e6i | 0.293029i | 0.989209 | + | 0.146515i | ||||||
−0.989209 | + | 0.146515i | ||||||||
1.10357e6 | 0.0670767 | |||||||||
1.48958e7 | 0.902461 | |||||||||
6.49720e6i | 0.392359i | |||||||||
2.22008e7i | 1.33635i | 0.744004 | + | 0.668175i | ||||||
−0.744004 | + | 0.668175i | ||||||||
4.58207e6i | 0.274922i | |||||||||
2.38810e6i | 0.142823i | |||||||||
8.08249e6 | 0.481827 | |||||||||
−928145. | −0.0551523 | |||||||||
1.94353e7i | 1.15117i | |||||||||
41873.2 | 0.00247225 | |||||||||
−792693. | + | 318967.i | −0.0466518 | + | 0.0187720i | |||||
9.03603e6 | 0.530090 | |||||||||
1.43158e7i | 0.837140i | |||||||||
−160985. | −0.00938382 | |||||||||
1.47029e6 | 0.0854303 | |||||||||
− | 5.47695e6i | − | 0.317223i | |||||||
5.08786e6i | 0.293750i | |||||||||
− | 2.85397e7i | − | 1.64253i | −0.570548 | − | 0.821264i | ||||
0.570548 | − | 0.821264i | ||||||||
6.51824e6i | 0.373951i | |||||||||
6.01370e6 | 0.343913 | |||||||||
−608444. | −0.0346859 | |||||||||
8.65203e6i | 0.491674i | |||||||||
−1.39631e6 | −0.0790987 | |||||||||
2.74339e6 | + | 6.81785e6i | 0.154919 | + | 0.385003i | |||||
1.56770e7 | 0.882496 | |||||||||
2.70823e6i | 0.151973i | |||||||||
−3.24584e6 | −0.181570 | |||||||||
−2.10013e7 | −1.17112 | −0.585558 | − | 0.810630i | ||||||
−0.585558 | + | 0.810630i | ||||||||
− | 10706.4i | − | 0.000595163i | |||||||
− | 4.18951e7i | − | 2.32165i | |||||||
3.10289e6i | 0.171412i | |||||||||
1.31440e6i | 0.0723847i | |||||||||
2.00759e7 | 1.10215 | |||||||||
6.95078e6 | 0.380403 | |||||||||
− | 2.08088e6i | − | 0.113529i | |||||||
2.20338e6 | 0.119839 | |||||||||
−717063. | − | 1.78203e6i | −0.0388794 | − | 0.0966225i | |||||
3.46448e6 | 0.187264 | |||||||||
− | 5.91352e6i | − | 0.318653i | |||||||
3.59907e7 | 1.93339 | 0.966694 | − | 0.255935i | ||||||
0.966694 | + | 0.255935i | ||||||||
−255565. | −0.0136864 | |||||||||
3.20415e7i | 1.71065i | 0.518093 | + | 0.855324i | ||||||
−0.518093 | + | 0.855324i | ||||||||
371644.i | 0.0197805i | |||||||||
9.48092e6i | 0.503065i | |||||||||
1.05633e6i | 0.0558779i | |||||||||
3.05655e6 | 0.161190 | |||||||||
−3.83327e6 | −0.201532 | |||||||||
39986.0i | 0.00209581i | |||||||||
1.19154e7 | 0.622626 | |||||||||
4.81622e6 | − | 1.93797e6i | 0.250898 | − | 0.100957i | |||||
−2.30747e6 | −0.119840 | |||||||||
2.92849e7i | 1.51630i | 0.652079 | + | 0.758151i | ||||||
−0.652079 | + | 0.758151i | ||||||||
−142500. | −0.00735589 | |||||||||
−1.27788e6 | −0.0657646 | −0.0328823 | − | 0.999459i | ||||||
−0.0328823 | + | 0.999459i | ||||||||
− | 9.47783e6i | − | 0.486285i | |||||||
7.34560e6i | 0.375744i | |||||||||
− | 1.05583e7i | − | 0.538446i | |||||||
− | 3.34508e7i | − | 1.70076i | −0.526169 | − | 0.850380i | ||||
0.526169 | − | 0.850380i | ||||||||
−2.78787e6 | −0.141318 | |||||||||
−1.65727e7 | −0.837541 | −0.418770 | − | 0.908092i | ||||||
−0.418770 | + | 0.908092i | ||||||||
109837.i | 0.00553416i | |||||||||
1.45845e7 | 0.732640 | |||||||||
−931692. | − | 2.31543e6i | −0.0466621 | − | 0.115964i | |||||
9.55540e6 | 0.477129 | |||||||||
1.60408e7i | 0.798568i | |||||||||
5.86451e6 | 0.291082 | |||||||||
−12185.1 | −0.000602994 | |||||||||
− | 574529.i | − | 0.0283464i | |||||||
− | 1.90755e7i | − | 0.938352i | |||||||
− | 7.23411e6i | − | 0.354797i | −0.984139 | − | 0.177399i | ||||
0.984139 | − | 0.177399i | ||||||||
589989.i | 0.0288500i | |||||||||
−2.04624e7 | −0.997622 | |||||||||
−2.60518e6 | −0.126636 | |||||||||
− | 5.06708e6i | − | 0.245578i | |||||||
−1.05275e7 | −0.508710 | |||||||||
−2.50429e6 | − | 2.60797e6i | −0.120654 | − | 0.125650i | |||||
8.15870e6 | 0.391918 | |||||||||
− | 9.30894e6i | − | 0.445853i | |||||||
−7.91064e6 | −0.377765 | |||||||||
−3.25703e6 | −0.155079 | |||||||||
2.01657e7i | 0.957341i | |||||||||
2.10907e6i | 0.0998315i | |||||||||
4.83084e6i | 0.227994i | |||||||||
3.08382e6i | 0.145116i | 0.997364 | + | 0.0725582i | ||||||
−0.997364 | + | 0.0725582i | ||||||||
5.07441e6 | 0.238090 | |||||||||
−2230.22 | −0.000104335 | |||||||||
− | 5.64353e6i | − | 0.263249i | |||||||
9.15615e6 | 0.425854 | 0.212927 | − | 0.977068i | ||||||
0.212927 | + | 0.977068i | ||||||||
−2.20563e6 | − | 5.48140e6i | −0.102286 | − | 0.254199i | |||||
−3.40397e7 | −1.57399 | −0.786996 | − | 0.616958i | ||||||
−0.786996 | + | 0.616958i | ||||||||
− | 2.20348e6i | − | 0.101593i | |||||||
1.40197e7 | 0.644511 | |||||||||
−2.09048e7 | −0.958250 | |||||||||
1.92683e7i | 0.880676i | 0.897832 | + | 0.440338i | ||||||
−0.897832 | + | 0.440338i | ||||||||
− | 746496.i | − | 0.0340207i | |||||||
2.96057e6i | 0.134535i | |||||||||
− | 2.53402e7i | − | 1.14820i | |||||||
−1.21337e7 | −0.548209 | |||||||||
−1.32634e6 | −0.0597524 | |||||||||
− | 4.20734e6i | − | 0.188998i | |||||||
77415.9 | 0.00346763 | |||||||||
8.16875e6 | − | 3.28698e6i | 0.364846 | − | 0.146808i | |||||
3.93390e6 | 0.175199 | |||||||||
1.02294e7i | 0.454270i | |||||||||
−24328.7 | −0.00107731 | |||||||||
6.30466e6 | 0.278382 | |||||||||
3.71602e6i | 0.163613i | |||||||||
− | 2.63479e7i | − | 1.15677i | −0.815765 | − | 0.578384i | ||||
0.815765 | − | 0.578384i | ||||||||
− | 2.97729e7i | − | 1.30342i | |||||||
− | 6.81586e6i | − | 0.297542i | |||||||
671473. | 0.0292295 | |||||||||
4.12657e6 | 0.179122 | 0.0895610 | − | 0.995981i | ||||||
0.0895610 | + | 0.995981i | ||||||||
1.86083e6i | 0.0805444i | |||||||||
1.36506e6 | 0.0589182 | 0.0294591 | − | 0.999566i | ||||||
0.0294591 | + | 0.999566i | ||||||||
−6.05507e6 | − | 1.50480e7i | −0.260609 | − | 0.647661i | |||||
−2.19936e6 | −0.0943925 | |||||||||
1.30812e6i | 0.0559841i | |||||||||
−2.77026e7 | −1.18225 | −0.591127 | − | 0.806578i | ||||||
−0.591127 | + | 0.806578i | ||||||||
−564736. | −0.0240333 | |||||||||
1.50571e7i | 0.638978i | |||||||||
− | 632083.i | − | 0.0267485i | |||||||
− | 1.76721e6i | − | 0.0745750i | |||||||
1.56490e7i | 0.658527i | |||||||||
71197.9 | 0.00298771 | |||||||||
1.78629e6 | 0.0747496 | |||||||||
3.95549e6i | 0.165060i | |||||||||
−1.72334e6 | −0.0717133 | |||||||||
−4.40376e6 | − | 1.09442e7i | −0.182744 | − | 0.454152i | |||||
2.32847e7 | 0.963564 | |||||||||
174037.i | 0.00718194i | |||||||||
−3.92710e6 | −0.161609 | |||||||||
−5.14113e7 | −2.10983 | |||||||||
− | 1.59560e7i | − | 0.652990i | |||||||
1.33878e7i | 0.546374i | |||||||||
5.26439e6i | 0.214253i | |||||||||
− | 2.34654e6i | − | 0.0952372i | |||||||
1.44836e7 | 0.586215 | |||||||||
−2.08574e7 | −0.841863 | −0.420931 | − | 0.907093i | ||||||
−0.420931 | + | 0.907093i | ||||||||
− | 1.29942e7i | − | 0.523040i | |||||||
7.48430e6 | 0.300429 | |||||||||
−2.31608e6 | + | 931953.i | −0.0927149 | + | 0.0373070i | |||||
3.95317e6 | 0.157815 | 0.0789077 | − | 0.996882i | ||||||
0.0789077 | + | 0.996882i | ||||||||
− | 6514.38i | − | 0.000259350i | |||||||
−759510. | −0.0301548 | |||||||||
3.26315e7 | 1.29203 | |||||||||
− | 1.05703e6i | − | 0.0417385i | |||||||
− | 2.18126e7i | − | 0.858951i | |||||||
1.48656e7i | 0.583793i | |||||||||
− | 4.85148e6i | − | 0.190006i | |||||||
1.66130e7 | 0.648873 | 0.324436 | − | 0.945907i | ||||||
0.324436 | + | 0.945907i | ||||||||
1.34066e6 | 0.0522215 | |||||||||
− | 1.76652e7i | − | 0.686230i | |||||||
−1.26005e7 | −0.488156 | |||||||||
−1.89641e7 | + | 7.63084e6i | −0.732702 | + | 0.294828i | |||||
−4.07972e6 | −0.157199 | |||||||||
2.97092e6i | 0.114166i | |||||||||
−810490. | −0.0310613 | |||||||||
1.19954e7 | 0.458474 | |||||||||
226129.i | 0.00861959i | |||||||||
4.33406e7i | 1.64762i | 0.566869 | + | 0.823808i | ||||||
−0.566869 | + | 0.823808i | ||||||||
276286.i | 0.0104749i | |||||||||
16238.8i | 0.000614014i | |||||||||
−1.49108e7 | −0.562292 | |||||||||
−7.50978e6 | −0.282438 | |||||||||
366999.i | 0.0137657i | |||||||||
4.36391e6 | 0.163247 | |||||||||
2.93047e6 | − | 1.17917e6i | 0.109332 | − | 0.0439934i | |||||
−5.84680e6 | −0.217555 | −0.108778 | − | 0.994066i | ||||||
−0.108778 | + | 0.994066i | ||||||||
− | 6.07987e6i | − | 0.225625i | |||||||
−1.45650e7 | −0.539073 | |||||||||
−3.92344e6 | −0.144826 | |||||||||
3.23340e7i | 1.19038i | 0.803585 | + | 0.595190i | ||||||
−0.803585 | + | 0.595190i | ||||||||
2.02475e7i | 0.743435i | |||||||||
− | 3.18577e7i | − | 1.16663i | |||||||
− | 6.42424e6i | − | 0.234634i | |||||||
−746705. | −0.0272000 | |||||||||
1.52368e7 | 0.553563 | |||||||||
− | 3.74163e6i | − | 0.135577i | −0.997700 | − | 0.0677884i | ||||
0.997700 | − | 0.0677884i | ||||||||
2.24933e6 | 0.0812889 | |||||||||
−1.45877e7 | + | 5.86987e6i | −0.525801 | + | 0.211574i | |||||
−34270.3 | −0.00123200 | |||||||||
5.94273e6i | 0.213076i | |||||||||
−1.12000e7 | −0.400520 | |||||||||
−5.30640e7 | −1.89264 | −0.946319 | − | 0.323234i | ||||||
−0.946319 | + | 0.323234i | ||||||||
− | 1.00119e7i | − | 0.356160i | |||||||
2.20216e6i | 0.0781340i | |||||||||
1.41740e7i | 0.501588i | |||||||||
535324.i | 0.0188946i | |||||||||
−1.13164e7 | −0.398377 | |||||||||
−416354. | −0.0146189 | |||||||||
358983.i | 0.0125717i | |||||||||
2.80080e7 | 0.978305 | |||||||||
−892064. | − | 2.21694e6i | −0.0310784 | − | 0.0772355i | |||||
7.14259e6 | 0.248193 | |||||||||
− | 2.12303e7i | − | 0.735807i | |||||||
3.95437e6 | 0.136697 | |||||||||
−8.14555e6 | −0.280852 | |||||||||
888502.i | 0.0305557i | 0.999883 | + | 0.0152779i | ||||||
−0.999883 | + | 0.0152779i | ||||||||
− | 5.66409e6i | − | 0.194286i | |||||||
− | 42337.0i | − | 0.00144847i | |||||||
− | 4.91922e6i | − | 0.167868i | |||||||
−1.92989e7 | −0.656878 | −0.328439 | − | 0.944525i | ||||||
−0.328439 | + | 0.944525i | ||||||||
944784. | 0.0320750 | |||||||||
4.68678e7i | 1.58706i | |||||||||
5.20704e6 | 0.175871 | |||||||||
−6.20329e6 | − | 1.54163e7i | −0.208983 | − | 0.519361i | |||||
3.08756e6 | 0.103751 | |||||||||
2.73358e7i | 0.916212i | 0.888898 | + | 0.458106i | ||||||
−0.888898 | + | 0.458106i | ||||||||
−1.12996e7 | −0.377760 | |||||||||
4.37079e6 | 0.145748 | |||||||||
− | 894856.i | − | 0.0297638i | |||||||
4.97884e6i | 0.165179i | |||||||||
− | 2.43078e7i | − | 0.804391i | |||||||
2.36204e7i | 0.779656i | 0.920888 | + | 0.389828i | ||||||
−0.920888 | + | 0.389828i | ||||||||
8.53038e6 | 0.280854 | |||||||||
3.96717e6 | 0.130284 | |||||||||
1.46961e6i | 0.0481406i | |||||||||
2.38379e7 | 0.778889 | |||||||||
25573.0 | − | 10290.2i | 0.000833470 | − | 0.000335375i | |||||
3.04218e7 | 0.988996 | |||||||||
849833.i | 0.0275579i | |||||||||
−3.49750e7 | −1.13129 | −0.565644 | − | 0.824649i | ||||||
−0.565644 | + | 0.824649i | ||||||||
−807020. | −0.0260379 | |||||||||
− | 2.46148e7i | − | 0.792177i | |||||||
1.41146e7i | 0.453110i | |||||||||
1.97550e6i | 0.0632587i | |||||||||
− | 406049.i | − | 0.0129697i | |||||||
1.96013e7 | 0.624521 | 0.312261 | − | 0.949996i | ||||||
0.312261 | + | 0.949996i | ||||||||
−1.51483e7 | −0.481436 | |||||||||
− | 714744.i | − | 0.0226588i |
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 78.6.b.a.25.5 | yes | 6 | |
3.2 | odd | 2 | 234.6.b.c.181.2 | 6 | |||
4.3 | odd | 2 | 624.6.c.d.337.4 | 6 | |||
13.5 | odd | 4 | 1014.6.a.q.1.2 | 3 | |||
13.8 | odd | 4 | 1014.6.a.o.1.2 | 3 | |||
13.12 | even | 2 | inner | 78.6.b.a.25.2 | ✓ | 6 | |
39.38 | odd | 2 | 234.6.b.c.181.5 | 6 | |||
52.51 | odd | 2 | 624.6.c.d.337.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
78.6.b.a.25.2 | ✓ | 6 | 13.12 | even | 2 | inner | |
78.6.b.a.25.5 | yes | 6 | 1.1 | even | 1 | trivial | |
234.6.b.c.181.2 | 6 | 3.2 | odd | 2 | |||
234.6.b.c.181.5 | 6 | 39.38 | odd | 2 | |||
624.6.c.d.337.3 | 6 | 52.51 | odd | 2 | |||
624.6.c.d.337.4 | 6 | 4.3 | odd | 2 | |||
1014.6.a.o.1.2 | 3 | 13.8 | odd | 4 | |||
1014.6.a.q.1.2 | 3 | 13.5 | odd | 4 |