| Spherical Harmonics Yl / Multipole | Symmetric Power [Γl(xyz)] | ||||
|---|---|---|---|---|---|
| l | 2l+1 | Multipole | Symmetry | Rank | [Γl(xyz)] |
| s (l=0) | 1 | Monopole | A1g | 1 | A1g |
| p (l=1) | 3 | Dipole | E1g | 3 | E1g |
| d (l=2) | 5 | Quadrupole | 6 | ||
| f (l=3) | 7 | Octupole | 10 | ||
| g (l=4) | 9 | Hexadecapole | 15 | ||
| h (l=5) | 11 | Dotricontapole | 21 | ||
| i (l=6) | 13 | Tetrahexacontapole | 28 | ||
| j (l=7) | 15 | Octacosahectapole | 36 | ||
| k (l=8) | 17 | 256--pole | 45 | ||
| l (l=9) | 19 | 512--pole | 55 | ||
| m (l=10) | 21 | 1.024--pole | 66 | ||
| n (l=11) | 23 | 2.048--pole | 78 | ||
| o (l=12) | 25 | 4.096--pole | 91 | ||
| q (l=13) | 27 | 8.192--pole | 105 | ||
| r (l=14) | 29 | 16.384--pole | 120 | ||
| t (l=15) | 31 | 32.768--pole | 136 | ||
| u (l=16) | 33 | 65.536--pole | 153 | ||
| v (l=17) | 35 | 131.072--pole | 171 | ||
| w (l=18) | 37 | 262.144--pole | 190 | ||
| x (l=19) | 39 | 524.288--pole | 210 | ||
| y (l=20) | 41 | 1.048.576--pole | 231 | ||
| z (l=21) | 43 | 2.097.152--pole | 253 | ||
| (l=22) | 45 | 4.194.304--pole | 276 | ||
| (l=23) | 47 | 8.388.608--pole | 300 | ||
| (l=24) | 49 | 16.777.216--pole | 325 | ||
| (l=25) | 51 | 33.554.432--pole | 351 | ||
| (l=26) | 53 | 67.108.864--pole | 378 | ||
| (l=27) | 55 | 134.217.728--pole | 406 | ||
| (l=28) | 57 | 268.435.456--pole | 435 | ||
| (l=29) | 59 | 536.870.912--pole | 465 | ||
| (l=30) | 61 | 1.073.741.824--pole | 496 | ||
| (l=31) | 63 | 2.147.483.648--pole | 528 | ||
| (l=32) | 65 | 4.294.967.296--pole | 561 | ||
| (l=33) | 67 | 8.589.934.592--pole | 595 | ||
| (l=34) | 69 | 17.179.869.184--pole | 630 | ||
| (l=35) | 71 | 34.359.738.368--pole | 666 | ||
| (l=36) | 73 | 68.719.476.736--pole | 703 | ||
| (l=37) | 75 | 137.438.953.472--pole | 741 | ||
| (l=38) | 77 | 274.877.906.944--pole | 780 | ||
| (l=39) | 79 | 549.755.813.888--pole | 820 | ||
| (l=40) | 81 | 1.099.511.627.776--pole | 861 | ||
| (l=41) | 83 | 2.199.023.255.552--pole | 903 | ||
| (l=42) | 85 | 4.398.046.511.104--pole | 946 | ||
| (l=43) | 87 | 8.796.093.022.208--pole | 990 | ||
| (l=44) | 89 | 17.592.186.044.416--pole | 1.035 | ||
| (l=45) | 91 | 35.184.372.088.832--pole | 1.081 | ||
| (l=46) | 93 | 70.368.744.177.664--pole | 1.128 | ||
| (l=47) | 95 | 140.737.488.355.328--pole | 1.176 | ||
| (l=48) | 97 | 281.474.976.710.656--pole | 1.225 | ||
| (l=49) | 99 | 562.949.953.421.312--pole | 1.275 | ||
| (l=50) | 101 | 1.125.899.906.842.624--pole | 1.326 | ||
| (l=51) | 103 | 2.251.799.813.685.248--pole | 1.378 | ||
| (l=52) | 105 | 4.503.599.627.370.496--pole | 1.431 | ||
| (l=53) | 107 | 9.007.199.254.740.992--pole | 1.485 | ||
| (l=54) | 109 | 18.014.398.509.481.984--pole | 1.540 | ||
| (l=55) | 111 | 36.028.797.018.963.968--pole | 1.596 | ||
| (l=56) | 113 | 72.057.594.037.927.936--pole | 1.653 | ||
| (l=57) | 115 | 144.115.188.075.855.872--pole | 1.711 | ||
| (l=58) | 117 | 288.230.376.151.711.744--pole | 1.770 | ||
| (l=59) | 119 | 576.460.752.303.423.488--pole | 1.830 | ||
| (l=60) | 121 | 1.152.921.504.606.846.976--pole | 1.891 | ||
| (l=61) | 123 | 2.305.843.009.213.693.952--pole | 1.953 | ||
| (l=62) | 125 | 4.611.686.018.427.387.904--pole | 2.016 | ||
| (l=63) | 127 | ----- | 2.080 | ||
| (l=64) | 129 | ----- | 2.145 | ||
| (l=65) | 131 | ----- | 2.211 | ||
| (l=66) | 133 | ----- | 2.278 | ||
| (l=67) | 135 | ----- | 2.346 | ||
| (l=68) | 137 | ----- | 2.415 | ||
| (l=69) | 139 | ----- | 2.485 | ||
| (l=70) | 141 | ----- | 2.556 | ||
| (l=71) | 143 | ----- | 2.628 | ||
| (l=72) | 145 | ----- | 2.701 | ||
| (l=73) | 147 | ----- | 2.775 | ||
| (l=74) | 149 | ----- | 2.850 | ||
| (l=75) | 151 | ----- | 2.926 | ||
| (l=76) | 153 | ----- | 3.003 | ||
| (l=77) | 155 | ----- | 3.081 | ||
| (l=78) | 157 | ----- | 3.160 | ||
| (l=79) | 159 | ----- | 3.240 | ||
| (l=80) | 161 | ----- | 3.321 | ||
| (l=81) | 163 | ----- | 3.403 | ||
| (l=82) | 165 | ----- | 3.486 | ||
| (l=83) | 167 | ----- | 3.570 | ||
| (l=84) | 169 | ----- | 3.655 | ||
| (l=85) | 171 | ----- | 3.741 | ||
| (l=86) | 173 | ----- | 3.828 | ||
| (l=87) | 175 | ----- | 3.916 | ||
| (l=88) | 177 | ----- | 4.005 | ||
| (l=89) | 179 | ----- | 4.095 | ||
| (l=90) | 181 | ----- | 4.186 | ||
| (l=91) | 183 | ----- | 4.278 | ||
| (l=92) | 185 | ----- | 4.371 | ||
| (l=93) | 187 | ----- | 4.465 | ||
| (l=94) | 189 | ----- | 4.560 | ||
| (l=95) | 191 | ----- | 4.656 | ||
| (l=96) | 193 | ----- | 4.753 | ||
| (l=97) | 195 | ----- | 4.851 | ||
| (l=98) | 197 | ----- | 4.950 | ||
| (l=99) | 199 | ----- | 5.050 | ||
| (l=100) | 201 | ----- | 5.151 | ||
| (l=101) | 203 | ----- | 5.253 | ||
| (l=102) | 205 | ----- | 5.356 | ||
| (l=103) | 207 | ----- | 5.460 | ||
| (l=104) | 209 | ----- | 5.565 | ||
| (l=105) | 211 | ----- | 5.671 | ||
| (l=106) | 213 | ----- | 5.778 | ||
| (l=107) | 215 | ----- | 5.886 | ||
| (l=108) | 217 | ----- | 5.995 | ||
| (l=109) | 219 | ----- | 6.105 | ||
| (l=110) | 221 | ----- | 6.216 | ||
| (l=111) | 223 | ----- | 6.328 | ||
| (l=112) | 225 | ----- | 6.441 | ||
| (l=113) | 227 | ----- | 6.555 | ||
| (l=114) | 229 | ----- | 6.670 | ||
| (l=115) | 231 | ----- | 6.786 | ||
| (l=116) | 233 | ----- | 6.903 | ||
| (l=117) | 235 | ----- | 7.021 | ||
| (l=118) | 237 | ----- | 7.140 | ||
| (l=119) | 239 | ----- | 7.260 | ||
| (l=120) | 241 | ----- | 7.381 | ||
| (l=121) | 243 | ----- | 7.503 | ||
| (l=122) | 245 | ----- | 7.626 | ||
| (l=123) | 247 | ----- | 7.750 | ||
| (l=124) | 249 | ----- | 7.875 | ||
| (l=125) | 251 | ----- | 8.001 | ||
| (l=126) | 253 | ----- | 8.128 | ||
| (l=127) | 255 | ----- | 8.256 | ||
| (l=128) | 257 | ----- | 8.385 | ||
| (l=129) | 259 | ----- | 8.515 | ||
| (l=130) | 261 | ----- | 8.646 | ||
| (l=131) | 263 | ----- | 8.778 | ||
| (l=132) | 265 | ----- | 8.911 | ||
| (l=133) | 267 | ----- | 9.045 | ||
| (l=134) | 269 | ----- | 9.180 | ||
| (l=135) | 271 | ----- | 9.316 | ||
| (l=136) | 273 | ----- | 9.453 | ||
| (l=137) | 275 | ----- | 9.591 | ||
| (l=138) | 277 | ----- | 9.730 | ||
| (l=139) | 279 | ----- | 9.870 | ||
| (l=140) | 281 | ----- | 10.011 | ||
| (l=141) | 283 | ----- | 10.153 | ||
| (l=142) | 285 | ----- | 10.296 | ||
| (l=143) | 287 | ----- | 10.440 | ||
| (l=144) | 289 | ----- | 10.585 | ||
| (l=145) | 291 | ----- | 10.731 | ||
| (l=146) | 293 | ----- | 10.878 | ||
| (l=147) | 295 | ----- | 11.026 | ||
| (l=148) | 297 | ----- | 11.175 | ||
| (l=149) | 299 | ----- | 11.325 | ||
| (l=150) | 301 | ----- | 11.476 | ||
| (l=151) | 303 | ----- | 11.628 | ||
| (l=152) | 305 | ----- | 11.781 | ||
| (l=153) | 307 | ----- | 11.935 | ||
| (l=154) | 309 | ----- | 12.090 | ||
| (l=155) | 311 | ----- | 12.246 | ||
| (l=156) | 313 | ----- | 12.403 | ||
| (l=157) | 315 | ----- | 12.561 | ||
| (l=158) | 317 | ----- | 12.720 | ||
| (l=159) | 319 | ----- | 12.880 | ||
| (l=160) | 321 | ----- | 13.041 | ||
| (l=161) | 323 | ----- | 13.203 | ||
| (l=162) | 325 | ----- | 13.366 | ||
| (l=163) | 327 | ----- | 13.530 | ||
| (l=164) | 329 | ----- | 13.695 | ||
| (l=165) | 331 | ----- | 13.861 | ||
| (l=166) | 333 | ----- | 14.028 | ||
| (l=167) | 335 | ----- | 14.196 | ||
| (l=168) | 337 | ----- | 14.365 | ||
| (l=169) | 339 | ----- | 14.535 | ||
| (l=170) | 341 | ----- | 14.706 | ||
| (l=171) | 343 | ----- | 14.878 | ||
| (l=172) | 345 | ----- | 15.051 | ||
| (l=173) | 347 | ----- | 15.225 | ||
| (l=174) | 349 | ----- | 15.400 | ||
| (l=175) | 351 | ----- | 15.576 | ||
| (l=176) | 353 | ----- | 15.753 | ||
| (l=177) | 355 | ----- | 15.931 | ||
| (l=178) | 357 | ----- | 16.110 | ||
| (l=179) | 359 | ----- | 16.290 | ||
| (l=180) | 361 | ----- | 16.471 | ||
| (l=181) | 363 | ----- | 16.653 | ||
| (l=182) | 365 | ----- | 16.836 | ||
| (l=183) | 367 | ----- | 17.020 | ||
| (l=184) | 369 | ----- | 17.205 | ||
| (l=185) | 371 | ----- | 17.391 | ||
| (l=186) | 373 | ----- | 17.578 | ||
| (l=187) | 375 | ----- | 17.766 | ||
| (l=188) | 377 | ----- | 17.955 | ||
| (l=189) | 379 | ----- | 18.145 | ||
| (l=190) | 381 | ----- | 18.336 | ||
| (l=191) | 383 | ----- | 18.528 | ||
| (l=192) | 385 | ----- | 18.721 | ||
| (l=193) | 387 | ----- | 18.915 | ||
| (l=194) | 389 | ----- | 19.110 | ||
| (l=195) | 391 | ----- | 19.306 | ||
| (l=196) | 393 | ----- | 19.503 | ||
| (l=197) | 395 | ----- | 19.701 | ||
| (l=198) | 397 | ----- | 19.900 | ||
| (l=199) | 399 | ----- | 20.100 | ||
| (l=200) | 401 | ----- | 20.301 | ||
| (l=201) | 403 | ----- | 20.503 | ||
| (l=202) | 405 | ----- | 20.706 | ||
| (l=203) | 407 | ----- | 20.910 | ||
| (l=204) | 409 | ----- | 21.115 | ||
| (l=205) | 411 | ----- | 21.321 | ||
| (l=206) | 413 | ----- | 21.528 | ||
| (l=207) | 415 | ----- | 21.736 | ||
| (l=208) | 417 | ----- | 21.945 | ||
| (l=209) | 419 | ----- | 22.155 | ||
| (l=210) | 421 | ----- | 22.366 | ||
| (l=211) | 423 | ----- | 22.578 | ||
| (l=212) | 425 | ----- | 22.791 | ||
| (l=213) | 427 | ----- | 23.005 | ||
| (l=214) | 429 | ----- | 23.220 | ||
| (l=215) | 431 | ----- | 23.436 | ||
| (l=216) | 433 | ----- | 23.653 | ||
| (l=217) | 435 | ----- | 23.871 | ||
| (l=218) | 437 | ----- | 24.090 | ||
| (l=219) | 439 | ----- | 24.310 | ||
| (l=220) | 441 | ----- | 24.531 | ||
| (l=221) | 443 | ----- | 24.753 | ||
| (l=222) | 445 | ----- | 24.976 | ||
| (l=223) | 447 | ----- | 25.200 | ||
| (l=224) | 449 | ----- | 25.425 | ||
| (l=225) | 451 | ----- | 25.651 | ||
| (l=226) | 453 | ----- | 25.878 | ||
| (l=227) | 455 | ----- | 26.106 | ||
| (l=228) | 457 | ----- | 26.335 | ||
| (l=229) | 459 | ----- | 26.565 | ||
| (l=230) | 461 | ----- | 26.796 | ||
| (l=231) | 463 | ----- | 27.028 | ||
| (l=232) | 465 | ----- | 27.261 | ||
| (l=233) | 467 | ----- | 27.495 | ||
| (l=234) | 469 | ----- | 27.730 | ||
| (l=235) | 471 | ----- | 27.966 | ||
| (l=236) | 473 | ----- | 28.203 | ||
| (l=237) | 475 | ----- | 28.441 | ||
| (l=238) | 477 | ----- | 28.680 | ||
| (l=239) | 479 | ----- | 28.920 | ||
| (l=240) | 481 | ----- | 29.161 | ||
| (l=241) | 483 | ----- | 29.403 | ||
| (l=242) | 485 | ----- | 29.646 | ||
| (l=243) | 487 | ----- | 29.890 | ||
| (l=244) | 489 | ----- | 30.135 | ||
| (l=245) | 491 | ----- | 30.381 | ||
| (l=246) | 493 | ----- | 30.628 | ||
| (l=247) | 495 | ----- | 30.876 | ||
| (l=248) | 497 | ----- | 31.125 | ||
| (l=249) | 499 | ----- | 31.375 | ||
| (l=250) | 501 | ----- | 31.626 | ||
| (l=251) | 503 | ----- | 31.878 | ||
| (l=252) | 505 | ----- | 32.131 | ||
| (l=253) | 507 | ----- | 32.385 | ||
| (l=254) | 509 | ----- | 32.640 | ||
| (l=255) | 511 | ----- | 32.896 | ||
| (l=256) | 513 | ----- | 33.153 | ||