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