Point Group Ci

Spherical harmonics and Multipoles
Symmetric Powers of Γxyz


First nonvanshing multipole: Quadrupole


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


Last update November, 13th 2023 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement