Point Group C1

Spherical harmonics and Multipoles
Symmetric Powers of Γxyz


First nonvanshing multipole: Dipole


Spherical Harmonics Yl / Multipole Symmetric Power [Γl(xyz)]
l 2l+1 Multipole Symmetry Rank l(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



Last update August, 27th 2019 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement