Spherical Harmonics Yl / Multipole |
Symmetric Power [Γl(xyz)] |
l |
2l+1 |
Multipole |
Symmetry |
Rank |
[Γl(xyz)] |
s (l=0) |
1 |
Monopole |
Ag |
1 |
Ag |
p (l=1) |
3 |
Dipole |
3Au |
3 |
3Au |
d (l=2) |
5 |
Quadrupole |
5Ag |
6 |
6Ag |
f (l=3) |
7 |
Octupole |
7Au |
10 |
10Au |
g (l=4) |
9 |
Hexadecapole |
9Ag |
15 |
15Ag |
h (l=5) |
11 |
Dotricontapole |
11Au |
21 |
21Au |
i (l=6) |
13 |
Tetrahexacontapole |
13Ag |
28 |
28Ag |
j (l=7) |
15 |
Octacosahectapole |
15Au |
36 |
36Au |
k (l=8) |
17 |
256--pole |
17Ag |
45 |
45Ag |
l (l=9) |
19 |
512--pole |
19Au |
55 |
55Au |
m (l=10) |
21 |
1.024--pole |
21Ag |
66 |
66Ag |
n (l=11) |
23 |
2.048--pole |
23Au |
78 |
78Au |
o (l=12) |
25 |
4.096--pole |
25Ag |
91 |
91Ag |
q (l=13) |
27 |
8.192--pole |
27Au |
105 |
105Au |
r (l=14) |
29 |
16.384--pole |
29Ag |
120 |
120Ag |
t (l=15) |
31 |
32.768--pole |
31Au |
136 |
136Au |
u (l=16) |
33 |
65.536--pole |
33Ag |
153 |
153Ag |
v (l=17) |
35 |
131.072--pole |
35Au |
171 |
171Au |
w (l=18) |
37 |
262.144--pole |
37Ag |
190 |
190Ag |
x (l=19) |
39 |
524.288--pole |
39Au |
210 |
210Au |
y (l=20) |
41 |
1.048.576--pole |
41Ag |
231 |
231Ag |
z (l=21) |
43 |
2.097.152--pole |
43Au |
253 |
253Au |
(l=22) |
45 |
4.194.304--pole |
45Ag |
276 |
276Ag |
(l=23) |
47 |
8.388.608--pole |
47Au |
300 |
300Au |
(l=24) |
49 |
16.777.216--pole |
49Ag |
325 |
325Ag |
(l=25) |
51 |
33.554.432--pole |
51Au |
351 |
351Au |
(l=26) |
53 |
67.108.864--pole |
53Ag |
378 |
378Ag |
(l=27) |
55 |
134.217.728--pole |
55Au |
406 |
406Au |
(l=28) |
57 |
268.435.456--pole |
57Ag |
435 |
435Ag |
(l=29) |
59 |
536.870.912--pole |
59Au |
465 |
465Au |
(l=30) |
61 |
1.073.741.824--pole |
61Ag |
496 |
496Ag |
(l=31) |
63 |
2.147.483.648--pole |
63Au |
528 |
528Au |
(l=32) |
65 |
4.294.967.296--pole |
65Ag |
561 |
561Ag |
(l=33) |
67 |
8.589.934.592--pole |
67Au |
595 |
595Au |
(l=34) |
69 |
17.179.869.184--pole |
69Ag |
630 |
630Ag |
(l=35) |
71 |
34.359.738.368--pole |
71Au |
666 |
666Au |
(l=36) |
73 |
68.719.476.736--pole |
73Ag |
703 |
703Ag |
(l=37) |
75 |
137.438.953.472--pole |
75Au |
741 |
741Au |
(l=38) |
77 |
274.877.906.944--pole |
77Ag |
780 |
780Ag |
(l=39) |
79 |
549.755.813.888--pole |
79Au |
820 |
820Au |
(l=40) |
81 |
1.099.511.627.776--pole |
81Ag |
861 |
861Ag |
(l=41) |
83 |
2.199.023.255.552--pole |
83Au |
903 |
903Au |
(l=42) |
85 |
4.398.046.511.104--pole |
85Ag |
946 |
946Ag |
(l=43) |
87 |
8.796.093.022.208--pole |
87Au |
990 |
990Au |
(l=44) |
89 |
17.592.186.044.416--pole |
89Ag |
1.035 |
1035Ag |
(l=45) |
91 |
35.184.372.088.832--pole |
91Au |
1.081 |
1081Au |
(l=46) |
93 |
70.368.744.177.664--pole |
93Ag |
1.128 |
1128Ag |
(l=47) |
95 |
140.737.488.355.328--pole |
95Au |
1.176 |
1176Au |
(l=48) |
97 |
281.474.976.710.656--pole |
97Ag |
1.225 |
1225Ag |
(l=49) |
99 |
562.949.953.421.312--pole |
99Au |
1.275 |
1275Au |
(l=50) |
101 |
1.125.899.906.842.624--pole |
101Ag |
1.326 |
1326Ag |
(l=51) |
103 |
2.251.799.813.685.248--pole |
103Au |
1.378 |
1378Au |
(l=52) |
105 |
4.503.599.627.370.496--pole |
105Ag |
1.431 |
1431Ag |
(l=53) |
107 |
9.007.199.254.740.992--pole |
107Au |
1.485 |
1485Au |
(l=54) |
109 |
18.014.398.509.481.984--pole |
109Ag |
1.540 |
1540Ag |
(l=55) |
111 |
36.028.797.018.963.968--pole |
111Au |
1.596 |
1596Au |
(l=56) |
113 |
72.057.594.037.927.936--pole |
113Ag |
1.653 |
1653Ag |
(l=57) |
115 |
144.115.188.075.855.872--pole |
115Au |
1.711 |
1711Au |
(l=58) |
117 |
288.230.376.151.711.744--pole |
117Ag |
1.770 |
1770Ag |
(l=59) |
119 |
576.460.752.303.423.488--pole |
119Au |
1.830 |
1830Au |
(l=60) |
121 |
1.152.921.504.606.846.976--pole |
121Ag |
1.891 |
1891Ag |
(l=61) |
123 |
2.305.843.009.213.693.952--pole |
123Au |
1.953 |
1953Au |
(l=62) |
125 |
4.611.686.018.427.387.904--pole |
125Ag |
2.016 |
2016Ag |
(l=63) |
127 |
----- |
127Au |
2.080 |
2080Au |
(l=64) |
129 |
----- |
129Ag |
2.145 |
2145Ag |
(l=65) |
131 |
----- |
131Au |
2.211 |
2211Au |
(l=66) |
133 |
----- |
133Ag |
2.278 |
2278Ag |
(l=67) |
135 |
----- |
135Au |
2.346 |
2346Au |
(l=68) |
137 |
----- |
137Ag |
2.415 |
2415Ag |
(l=69) |
139 |
----- |
139Au |
2.485 |
2485Au |
(l=70) |
141 |
----- |
141Ag |
2.556 |
2556Ag |
(l=71) |
143 |
----- |
143Au |
2.628 |
2628Au |
(l=72) |
145 |
----- |
145Ag |
2.701 |
2701Ag |
(l=73) |
147 |
----- |
147Au |
2.775 |
2775Au |
(l=74) |
149 |
----- |
149Ag |
2.850 |
2850Ag |
(l=75) |
151 |
----- |
151Au |
2.926 |
2926Au |
(l=76) |
153 |
----- |
153Ag |
3.003 |
3003Ag |
(l=77) |
155 |
----- |
155Au |
3.081 |
3081Au |
(l=78) |
157 |
----- |
157Ag |
3.160 |
3160Ag |
(l=79) |
159 |
----- |
159Au |
3.240 |
3240Au |
(l=80) |
161 |
----- |
161Ag |
3.321 |
3321Ag |
(l=81) |
163 |
----- |
163Au |
3.403 |
3403Au |
(l=82) |
165 |
----- |
165Ag |
3.486 |
3486Ag |
(l=83) |
167 |
----- |
167Au |
3.570 |
3570Au |
(l=84) |
169 |
----- |
169Ag |
3.655 |
3655Ag |
(l=85) |
171 |
----- |
171Au |
3.741 |
3741Au |
(l=86) |
173 |
----- |
173Ag |
3.828 |
3828Ag |
(l=87) |
175 |
----- |
175Au |
3.916 |
3916Au |
(l=88) |
177 |
----- |
177Ag |
4.005 |
4005Ag |
(l=89) |
179 |
----- |
179Au |
4.095 |
4095Au |
(l=90) |
181 |
----- |
181Ag |
4.186 |
4186Ag |
(l=91) |
183 |
----- |
183Au |
4.278 |
4278Au |
(l=92) |
185 |
----- |
185Ag |
4.371 |
4371Ag |
(l=93) |
187 |
----- |
187Au |
4.465 |
4465Au |
(l=94) |
189 |
----- |
189Ag |
4.560 |
4560Ag |
(l=95) |
191 |
----- |
191Au |
4.656 |
4656Au |
(l=96) |
193 |
----- |
193Ag |
4.753 |
4753Ag |
(l=97) |
195 |
----- |
195Au |
4.851 |
4851Au |
(l=98) |
197 |
----- |
197Ag |
4.950 |
4950Ag |
(l=99) |
199 |
----- |
199Au |
5.050 |
5050Au |
(l=100) |
201 |
----- |
201Ag |
5.151 |
5151Ag |
(l=101) |
203 |
----- |
203Au |
5.253 |
5253Au |
(l=102) |
205 |
----- |
205Ag |
5.356 |
5356Ag |
(l=103) |
207 |
----- |
207Au |
5.460 |
5460Au |
(l=104) |
209 |
----- |
209Ag |
5.565 |
5565Ag |
(l=105) |
211 |
----- |
211Au |
5.671 |
5671Au |
(l=106) |
213 |
----- |
213Ag |
5.778 |
5778Ag |
(l=107) |
215 |
----- |
215Au |
5.886 |
5886Au |
(l=108) |
217 |
----- |
217Ag |
5.995 |
5995Ag |
(l=109) |
219 |
----- |
219Au |
6.105 |
6105Au |
(l=110) |
221 |
----- |
221Ag |
6.216 |
6216Ag |
(l=111) |
223 |
----- |
223Au |
6.328 |
6328Au |
(l=112) |
225 |
----- |
225Ag |
6.441 |
6441Ag |
(l=113) |
227 |
----- |
227Au |
6.555 |
6555Au |
(l=114) |
229 |
----- |
229Ag |
6.670 |
6670Ag |
(l=115) |
231 |
----- |
231Au |
6.786 |
6786Au |
(l=116) |
233 |
----- |
233Ag |
6.903 |
6903Ag |
(l=117) |
235 |
----- |
235Au |
7.021 |
7021Au |
(l=118) |
237 |
----- |
237Ag |
7.140 |
7140Ag |
(l=119) |
239 |
----- |
239Au |
7.260 |
7260Au |
(l=120) |
241 |
----- |
241Ag |
7.381 |
7381Ag |
(l=121) |
243 |
----- |
243Au |
7.503 |
7503Au |
(l=122) |
245 |
----- |
245Ag |
7.626 |
7626Ag |
(l=123) |
247 |
----- |
247Au |
7.750 |
7750Au |
(l=124) |
249 |
----- |
249Ag |
7.875 |
7875Ag |
(l=125) |
251 |
----- |
251Au |
8.001 |
8001Au |
(l=126) |
253 |
----- |
253Ag |
8.128 |
8128Ag |
(l=127) |
255 |
----- |
255Au |
8.256 |
8256Au |
(l=128) |
257 |
----- |
257Ag |
8.385 |
8385Ag |
(l=129) |
259 |
----- |
259Au |
8.515 |
8515Au |
(l=130) |
261 |
----- |
261Ag |
8.646 |
8646Ag |
(l=131) |
263 |
----- |
263Au |
8.778 |
8778Au |
(l=132) |
265 |
----- |
265Ag |
8.911 |
8911Ag |
(l=133) |
267 |
----- |
267Au |
9.045 |
9045Au |
(l=134) |
269 |
----- |
269Ag |
9.180 |
9180Ag |
(l=135) |
271 |
----- |
271Au |
9.316 |
9316Au |
(l=136) |
273 |
----- |
273Ag |
9.453 |
9453Ag |
(l=137) |
275 |
----- |
275Au |
9.591 |
9591Au |
(l=138) |
277 |
----- |
277Ag |
9.730 |
9730Ag |
(l=139) |
279 |
----- |
279Au |
9.870 |
9870Au |
(l=140) |
281 |
----- |
281Ag |
10.011 |
10011Ag |
(l=141) |
283 |
----- |
283Au |
10.153 |
10153Au |
(l=142) |
285 |
----- |
285Ag |
10.296 |
10296Ag |
(l=143) |
287 |
----- |
287Au |
10.440 |
10440Au |
(l=144) |
289 |
----- |
289Ag |
10.585 |
10585Ag |
(l=145) |
291 |
----- |
291Au |
10.731 |
10731Au |
(l=146) |
293 |
----- |
293Ag |
10.878 |
10878Ag |
(l=147) |
295 |
----- |
295Au |
11.026 |
11026Au |
(l=148) |
297 |
----- |
297Ag |
11.175 |
11175Ag |
(l=149) |
299 |
----- |
299Au |
11.325 |
11325Au |
(l=150) |
301 |
----- |
301Ag |
11.476 |
11476Ag |
(l=151) |
303 |
----- |
303Au |
11.628 |
11628Au |
(l=152) |
305 |
----- |
305Ag |
11.781 |
11781Ag |
(l=153) |
307 |
----- |
307Au |
11.935 |
11935Au |
(l=154) |
309 |
----- |
309Ag |
12.090 |
12090Ag |
(l=155) |
311 |
----- |
311Au |
12.246 |
12246Au |
(l=156) |
313 |
----- |
313Ag |
12.403 |
12403Ag |
(l=157) |
315 |
----- |
315Au |
12.561 |
12561Au |
(l=158) |
317 |
----- |
317Ag |
12.720 |
12720Ag |
(l=159) |
319 |
----- |
319Au |
12.880 |
12880Au |
(l=160) |
321 |
----- |
321Ag |
13.041 |
13041Ag |
(l=161) |
323 |
----- |
323Au |
13.203 |
13203Au |
(l=162) |
325 |
----- |
325Ag |
13.366 |
13366Ag |
(l=163) |
327 |
----- |
327Au |
13.530 |
13530Au |
(l=164) |
329 |
----- |
329Ag |
13.695 |
13695Ag |
(l=165) |
331 |
----- |
331Au |
13.861 |
13861Au |
(l=166) |
333 |
----- |
333Ag |
14.028 |
14028Ag |
(l=167) |
335 |
----- |
335Au |
14.196 |
14196Au |
(l=168) |
337 |
----- |
337Ag |
14.365 |
14365Ag |
(l=169) |
339 |
----- |
339Au |
14.535 |
14535Au |
(l=170) |
341 |
----- |
341Ag |
14.706 |
14706Ag |
(l=171) |
343 |
----- |
343Au |
14.878 |
14878Au |
(l=172) |
345 |
----- |
345Ag |
15.051 |
15051Ag |
(l=173) |
347 |
----- |
347Au |
15.225 |
15225Au |
(l=174) |
349 |
----- |
349Ag |
15.400 |
15400Ag |
(l=175) |
351 |
----- |
351Au |
15.576 |
15576Au |
(l=176) |
353 |
----- |
353Ag |
15.753 |
15753Ag |
(l=177) |
355 |
----- |
355Au |
15.931 |
15931Au |
(l=178) |
357 |
----- |
357Ag |
16.110 |
16110Ag |
(l=179) |
359 |
----- |
359Au |
16.290 |
16290Au |
(l=180) |
361 |
----- |
361Ag |
16.471 |
16471Ag |
(l=181) |
363 |
----- |
363Au |
16.653 |
16653Au |
(l=182) |
365 |
----- |
365Ag |
16.836 |
16836Ag |
(l=183) |
367 |
----- |
367Au |
17.020 |
17020Au |
(l=184) |
369 |
----- |
369Ag |
17.205 |
17205Ag |
(l=185) |
371 |
----- |
371Au |
17.391 |
17391Au |
(l=186) |
373 |
----- |
373Ag |
17.578 |
17578Ag |
(l=187) |
375 |
----- |
375Au |
17.766 |
17766Au |
(l=188) |
377 |
----- |
377Ag |
17.955 |
17955Ag |
(l=189) |
379 |
----- |
379Au |
18.145 |
18145Au |
(l=190) |
381 |
----- |
381Ag |
18.336 |
18336Ag |
(l=191) |
383 |
----- |
383Au |
18.528 |
18528Au |
(l=192) |
385 |
----- |
385Ag |
18.721 |
18721Ag |
(l=193) |
387 |
----- |
387Au |
18.915 |
18915Au |
(l=194) |
389 |
----- |
389Ag |
19.110 |
19110Ag |
(l=195) |
391 |
----- |
391Au |
19.306 |
19306Au |
(l=196) |
393 |
----- |
393Ag |
19.503 |
19503Ag |
(l=197) |
395 |
----- |
395Au |
19.701 |
19701Au |
(l=198) |
397 |
----- |
397Ag |
19.900 |
19900Ag |
(l=199) |
399 |
----- |
399Au |
20.100 |
20100Au |
(l=200) |
401 |
----- |
401Ag |
20.301 |
20301Ag |
(l=201) |
403 |
----- |
403Au |
20.503 |
20503Au |
(l=202) |
405 |
----- |
405Ag |
20.706 |
20706Ag |
(l=203) |
407 |
----- |
407Au |
20.910 |
20910Au |
(l=204) |
409 |
----- |
409Ag |
21.115 |
21115Ag |
(l=205) |
411 |
----- |
411Au |
21.321 |
21321Au |
(l=206) |
413 |
----- |
413Ag |
21.528 |
21528Ag |
(l=207) |
415 |
----- |
415Au |
21.736 |
21736Au |
(l=208) |
417 |
----- |
417Ag |
21.945 |
21945Ag |
(l=209) |
419 |
----- |
419Au |
22.155 |
22155Au |
(l=210) |
421 |
----- |
421Ag |
22.366 |
22366Ag |
(l=211) |
423 |
----- |
423Au |
22.578 |
22578Au |
(l=212) |
425 |
----- |
425Ag |
22.791 |
22791Ag |
(l=213) |
427 |
----- |
427Au |
23.005 |
23005Au |
(l=214) |
429 |
----- |
429Ag |
23.220 |
23220Ag |
(l=215) |
431 |
----- |
431Au |
23.436 |
23436Au |
(l=216) |
433 |
----- |
433Ag |
23.653 |
23653Ag |
(l=217) |
435 |
----- |
435Au |
23.871 |
23871Au |
(l=218) |
437 |
----- |
437Ag |
24.090 |
24090Ag |
(l=219) |
439 |
----- |
439Au |
24.310 |
24310Au |
(l=220) |
441 |
----- |
441Ag |
24.531 |
24531Ag |
(l=221) |
443 |
----- |
443Au |
24.753 |
24753Au |
(l=222) |
445 |
----- |
445Ag |
24.976 |
24976Ag |
(l=223) |
447 |
----- |
447Au |
25.200 |
25200Au |
(l=224) |
449 |
----- |
449Ag |
25.425 |
25425Ag |
(l=225) |
451 |
----- |
451Au |
25.651 |
25651Au |
(l=226) |
453 |
----- |
453Ag |
25.878 |
25878Ag |
(l=227) |
455 |
----- |
455Au |
26.106 |
26106Au |
(l=228) |
457 |
----- |
457Ag |
26.335 |
26335Ag |
(l=229) |
459 |
----- |
459Au |
26.565 |
26565Au |
(l=230) |
461 |
----- |
461Ag |
26.796 |
26796Ag |
(l=231) |
463 |
----- |
463Au |
27.028 |
27028Au |
(l=232) |
465 |
----- |
465Ag |
27.261 |
27261Ag |
(l=233) |
467 |
----- |
467Au |
27.495 |
27495Au |
(l=234) |
469 |
----- |
469Ag |
27.730 |
27730Ag |
(l=235) |
471 |
----- |
471Au |
27.966 |
27966Au |
(l=236) |
473 |
----- |
473Ag |
28.203 |
28203Ag |
(l=237) |
475 |
----- |
475Au |
28.441 |
28441Au |
(l=238) |
477 |
----- |
477Ag |
28.680 |
28680Ag |
(l=239) |
479 |
----- |
479Au |
28.920 |
28920Au |
(l=240) |
481 |
----- |
481Ag |
29.161 |
29161Ag |
(l=241) |
483 |
----- |
483Au |
29.403 |
29403Au |
(l=242) |
485 |
----- |
485Ag |
29.646 |
29646Ag |
(l=243) |
487 |
----- |
487Au |
29.890 |
29890Au |
(l=244) |
489 |
----- |
489Ag |
30.135 |
30135Ag |
(l=245) |
491 |
----- |
491Au |
30.381 |
30381Au |
(l=246) |
493 |
----- |
493Ag |
30.628 |
30628Ag |
(l=247) |
495 |
----- |
495Au |
30.876 |
30876Au |
(l=248) |
497 |
----- |
497Ag |
31.125 |
31125Ag |
(l=249) |
499 |
----- |
499Au |
31.375 |
31375Au |
(l=250) |
501 |
----- |
501Ag |
31.626 |
31626Ag |
(l=251) |
503 |
----- |
503Au |
31.878 |
31878Au |
(l=252) |
505 |
----- |
505Ag |
32.131 |
32131Ag |
(l=253) |
507 |
----- |
507Au |
32.385 |
32385Au |
(l=254) |
509 |
----- |
509Ag |
32.640 |
32640Ag |
(l=255) |
511 |
----- |
511Au |
32.896 |
32896Au |
(l=256) |
513 |
----- |
513Ag |
33.153 |
33153Ag |