Point Group C2

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 A⊕2B 3 A⊕2B
d (l=2) 5 Quadrupole 3A⊕2B 6 4A⊕2B
f (l=3) 7 Octupole 3A⊕4B 10 4A⊕6B
g (l=4) 9 Hexadecapole 5A⊕4B 15 9A⊕6B
h (l=5) 11 Dotricontapole 5A⊕6B 21 9A⊕12B
i (l=6) 13 Tetrahexacontapole 7A⊕6B 28 16A⊕12B
j (l=7) 15 Octacosahectapole 7A⊕8B 36 16A⊕20B
k (l=8) 17 256--pole 9A⊕8B 45 25A⊕20B
l (l=9) 19 512--pole 9A⊕10B 55 25A⊕30B
m (l=10) 21 1.024--pole 11A⊕10B 66 36A⊕30B
n (l=11) 23 2.048--pole 11A⊕12B 78 36A⊕42B
o (l=12) 25 4.096--pole 13A⊕12B 91 49A⊕42B
q (l=13) 27 8.192--pole 13A⊕14B 105 49A⊕56B
r (l=14) 29 16.384--pole 15A⊕14B 120 64A⊕56B
t (l=15) 31 32.768--pole 15A⊕16B 136 64A⊕72B
u (l=16) 33 65.536--pole 17A⊕16B 153 81A⊕72B
v (l=17) 35 131.072--pole 17A⊕18B 171 81A⊕90B
w (l=18) 37 262.144--pole 19A⊕18B 190 100A⊕90B
x (l=19) 39 524.288--pole 19A⊕20B 210 100A⊕110B
y (l=20) 41 1.048.576--pole 21A⊕20B 231 121A⊕110B
z (l=21) 43 2.097.152--pole 21A⊕22B 253 121A⊕132B
(l=22) 45 4.194.304--pole 23A⊕22B 276 144A⊕132B
(l=23) 47 8.388.608--pole 23A⊕24B 300 144A⊕156B
(l=24) 49 16.777.216--pole 25A⊕24B 325 169A⊕156B
(l=25) 51 33.554.432--pole 25A⊕26B 351 169A⊕182B
(l=26) 53 67.108.864--pole 27A⊕26B 378 196A⊕182B
(l=27) 55 134.217.728--pole 27A⊕28B 406 196A⊕210B
(l=28) 57 268.435.456--pole 29A⊕28B 435 225A⊕210B
(l=29) 59 536.870.912--pole 29A⊕30B 465 225A⊕240B
(l=30) 61 1.073.741.824--pole 31A⊕30B 496 256A⊕240B
(l=31) 63 2.147.483.648--pole 31A⊕32B 528 256A⊕272B
(l=32) 65 4.294.967.296--pole 33A⊕32B 561 289A⊕272B
(l=33) 67 8.589.934.592--pole 33A⊕34B 595 289A⊕306B
(l=34) 69 17.179.869.184--pole 35A⊕34B 630 324A⊕306B
(l=35) 71 34.359.738.368--pole 35A⊕36B 666 324A⊕342B
(l=36) 73 68.719.476.736--pole 37A⊕36B 703 361A⊕342B
(l=37) 75 137.438.953.472--pole 37A⊕38B 741 361A⊕380B
(l=38) 77 274.877.906.944--pole 39A⊕38B 780 400A⊕380B
(l=39) 79 549.755.813.888--pole 39A⊕40B 820 400A⊕420B
(l=40) 81 1.099.511.627.776--pole 41A⊕40B 861 441A⊕420B
(l=41) 83 2.199.023.255.552--pole 41A⊕42B 903 441A⊕462B
(l=42) 85 4.398.046.511.104--pole 43A⊕42B 946 484A⊕462B
(l=43) 87 8.796.093.022.208--pole 43A⊕44B 990 484A⊕506B
(l=44) 89 17.592.186.044.416--pole 45A⊕44B 1.035 529A⊕506B
(l=45) 91 35.184.372.088.832--pole 45A⊕46B 1.081 529A⊕552B
(l=46) 93 70.368.744.177.664--pole 47A⊕46B 1.128 576A⊕552B
(l=47) 95 140.737.488.355.328--pole 47A⊕48B 1.176 576A⊕600B
(l=48) 97 281.474.976.710.656--pole 49A⊕48B 1.225 625A⊕600B
(l=49) 99 562.949.953.421.312--pole 49A⊕50B 1.275 625A⊕650B
(l=50) 101 1.125.899.906.842.624--pole 51A⊕50B 1.326 676A⊕650B
(l=51) 103 2.251.799.813.685.248--pole 51A⊕52B 1.378 676A⊕702B
(l=52) 105 4.503.599.627.370.496--pole 53A⊕52B 1.431 729A⊕702B
(l=53) 107 9.007.199.254.740.992--pole 53A⊕54B 1.485 729A⊕756B
(l=54) 109 18.014.398.509.481.984--pole 55A⊕54B 1.540 784A⊕756B
(l=55) 111 36.028.797.018.963.968--pole 55A⊕56B 1.596 784A⊕812B
(l=56) 113 72.057.594.037.927.936--pole 57A⊕56B 1.653 841A⊕812B
(l=57) 115 144.115.188.075.855.872--pole 57A⊕58B 1.711 841A⊕870B
(l=58) 117 288.230.376.151.711.744--pole 59A⊕58B 1.770 900A⊕870B
(l=59) 119 576.460.752.303.423.488--pole 59A⊕60B 1.830 900A⊕930B
(l=60) 121 1.152.921.504.606.846.976--pole 61A⊕60B 1.891 961A⊕930B
(l=61) 123 2.305.843.009.213.693.952--pole 61A⊕62B 1.953 961A⊕992B
(l=62) 125 4.611.686.018.427.387.904--pole 63A⊕62B 2.016 1024A⊕992B
(l=63) 127 ----- 63A⊕64B 2.080 1024A⊕1056B
(l=64) 129 ----- 65A⊕64B 2.145 1089A⊕1056B
(l=65) 131 ----- 65A⊕66B 2.211 1089A⊕1122B
(l=66) 133 ----- 67A⊕66B 2.278 1156A⊕1122B
(l=67) 135 ----- 67A⊕68B 2.346 1156A⊕1190B
(l=68) 137 ----- 69A⊕68B 2.415 1225A⊕1190B
(l=69) 139 ----- 69A⊕70B 2.485 1225A⊕1260B
(l=70) 141 ----- 71A⊕70B 2.556 1296A⊕1260B
(l=71) 143 ----- 71A⊕72B 2.628 1296A⊕1332B
(l=72) 145 ----- 73A⊕72B 2.701 1369A⊕1332B
(l=73) 147 ----- 73A⊕74B 2.775 1369A⊕1406B
(l=74) 149 ----- 75A⊕74B 2.850 1444A⊕1406B
(l=75) 151 ----- 75A⊕76B 2.926 1444A⊕1482B
(l=76) 153 ----- 77A⊕76B 3.003 1521A⊕1482B
(l=77) 155 ----- 77A⊕78B 3.081 1521A⊕1560B
(l=78) 157 ----- 79A⊕78B 3.160 1600A⊕1560B
(l=79) 159 ----- 79A⊕80B 3.240 1600A⊕1640B
(l=80) 161 ----- 81A⊕80B 3.321 1681A⊕1640B
(l=81) 163 ----- 81A⊕82B 3.403 1681A⊕1722B
(l=82) 165 ----- 83A⊕82B 3.486 1764A⊕1722B
(l=83) 167 ----- 83A⊕84B 3.570 1764A⊕1806B
(l=84) 169 ----- 85A⊕84B 3.655 1849A⊕1806B
(l=85) 171 ----- 85A⊕86B 3.741 1849A⊕1892B
(l=86) 173 ----- 87A⊕86B 3.828 1936A⊕1892B
(l=87) 175 ----- 87A⊕88B 3.916 1936A⊕1980B
(l=88) 177 ----- 89A⊕88B 4.005 2025A⊕1980B
(l=89) 179 ----- 89A⊕90B 4.095 2025A⊕2070B
(l=90) 181 ----- 91A⊕90B 4.186 2116A⊕2070B
(l=91) 183 ----- 91A⊕92B 4.278 2116A⊕2162B
(l=92) 185 ----- 93A⊕92B 4.371 2209A⊕2162B
(l=93) 187 ----- 93A⊕94B 4.465 2209A⊕2256B
(l=94) 189 ----- 95A⊕94B 4.560 2304A⊕2256B
(l=95) 191 ----- 95A⊕96B 4.656 2304A⊕2352B
(l=96) 193 ----- 97A⊕96B 4.753 2401A⊕2352B
(l=97) 195 ----- 97A⊕98B 4.851 2401A⊕2450B
(l=98) 197 ----- 99A⊕98B 4.950 2500A⊕2450B
(l=99) 199 ----- 99A⊕100B 5.050 2500A⊕2550B
(l=100) 201 ----- 101A⊕100B 5.151 2601A⊕2550B
(l=101) 203 ----- 101A⊕102B 5.253 2601A⊕2652B
(l=102) 205 ----- 103A⊕102B 5.356 2704A⊕2652B
(l=103) 207 ----- 103A⊕104B 5.460 2704A⊕2756B
(l=104) 209 ----- 105A⊕104B 5.565 2809A⊕2756B
(l=105) 211 ----- 105A⊕106B 5.671 2809A⊕2862B
(l=106) 213 ----- 107A⊕106B 5.778 2916A⊕2862B
(l=107) 215 ----- 107A⊕108B 5.886 2916A⊕2970B
(l=108) 217 ----- 109A⊕108B 5.995 3025A⊕2970B
(l=109) 219 ----- 109A⊕110B 6.105 3025A⊕3080B
(l=110) 221 ----- 111A⊕110B 6.216 3136A⊕3080B
(l=111) 223 ----- 111A⊕112B 6.328 3136A⊕3192B
(l=112) 225 ----- 113A⊕112B 6.441 3249A⊕3192B
(l=113) 227 ----- 113A⊕114B 6.555 3249A⊕3306B
(l=114) 229 ----- 115A⊕114B 6.670 3364A⊕3306B
(l=115) 231 ----- 115A⊕116B 6.786 3364A⊕3422B
(l=116) 233 ----- 117A⊕116B 6.903 3481A⊕3422B
(l=117) 235 ----- 117A⊕118B 7.021 3481A⊕3540B
(l=118) 237 ----- 119A⊕118B 7.140 3600A⊕3540B
(l=119) 239 ----- 119A⊕120B 7.260 3600A⊕3660B
(l=120) 241 ----- 121A⊕120B 7.381 3721A⊕3660B
(l=121) 243 ----- 121A⊕122B 7.503 3721A⊕3782B
(l=122) 245 ----- 123A⊕122B 7.626 3844A⊕3782B
(l=123) 247 ----- 123A⊕124B 7.750 3844A⊕3906B
(l=124) 249 ----- 125A⊕124B 7.875 3969A⊕3906B
(l=125) 251 ----- 125A⊕126B 8.001 3969A⊕4032B
(l=126) 253 ----- 127A⊕126B 8.128 4096A⊕4032B
(l=127) 255 ----- 127A⊕128B 8.256 4096A⊕4160B
(l=128) 257 ----- 129A⊕128B 8.385 4225A⊕4160B
(l=129) 259 ----- 129A⊕130B 8.515 4225A⊕4290B
(l=130) 261 ----- 131A⊕130B 8.646 4356A⊕4290B
(l=131) 263 ----- 131A⊕132B 8.778 4356A⊕4422B
(l=132) 265 ----- 133A⊕132B 8.911 4489A⊕4422B
(l=133) 267 ----- 133A⊕134B 9.045 4489A⊕4556B
(l=134) 269 ----- 135A⊕134B 9.180 4624A⊕4556B
(l=135) 271 ----- 135A⊕136B 9.316 4624A⊕4692B
(l=136) 273 ----- 137A⊕136B 9.453 4761A⊕4692B
(l=137) 275 ----- 137A⊕138B 9.591 4761A⊕4830B
(l=138) 277 ----- 139A⊕138B 9.730 4900A⊕4830B
(l=139) 279 ----- 139A⊕140B 9.870 4900A⊕4970B
(l=140) 281 ----- 141A⊕140B 10.011 5041A⊕4970B
(l=141) 283 ----- 141A⊕142B 10.153 5041A⊕5112B
(l=142) 285 ----- 143A⊕142B 10.296 5184A⊕5112B
(l=143) 287 ----- 143A⊕144B 10.440 5184A⊕5256B
(l=144) 289 ----- 145A⊕144B 10.585 5329A⊕5256B
(l=145) 291 ----- 145A⊕146B 10.731 5329A⊕5402B
(l=146) 293 ----- 147A⊕146B 10.878 5476A⊕5402B
(l=147) 295 ----- 147A⊕148B 11.026 5476A⊕5550B
(l=148) 297 ----- 149A⊕148B 11.175 5625A⊕5550B
(l=149) 299 ----- 149A⊕150B 11.325 5625A⊕5700B
(l=150) 301 ----- 151A⊕150B 11.476 5776A⊕5700B
(l=151) 303 ----- 151A⊕152B 11.628 5776A⊕5852B
(l=152) 305 ----- 153A⊕152B 11.781 5929A⊕5852B
(l=153) 307 ----- 153A⊕154B 11.935 5929A⊕6006B
(l=154) 309 ----- 155A⊕154B 12.090 6084A⊕6006B
(l=155) 311 ----- 155A⊕156B 12.246 6084A⊕6162B
(l=156) 313 ----- 157A⊕156B 12.403 6241A⊕6162B
(l=157) 315 ----- 157A⊕158B 12.561 6241A⊕6320B
(l=158) 317 ----- 159A⊕158B 12.720 6400A⊕6320B
(l=159) 319 ----- 159A⊕160B 12.880 6400A⊕6480B
(l=160) 321 ----- 161A⊕160B 13.041 6561A⊕6480B
(l=161) 323 ----- 161A⊕162B 13.203 6561A⊕6642B
(l=162) 325 ----- 163A⊕162B 13.366 6724A⊕6642B
(l=163) 327 ----- 163A⊕164B 13.530 6724A⊕6806B
(l=164) 329 ----- 165A⊕164B 13.695 6889A⊕6806B
(l=165) 331 ----- 165A⊕166B 13.861 6889A⊕6972B
(l=166) 333 ----- 167A⊕166B 14.028 7056A⊕6972B
(l=167) 335 ----- 167A⊕168B 14.196 7056A⊕7140B
(l=168) 337 ----- 169A⊕168B 14.365 7225A⊕7140B
(l=169) 339 ----- 169A⊕170B 14.535 7225A⊕7310B
(l=170) 341 ----- 171A⊕170B 14.706 7396A⊕7310B
(l=171) 343 ----- 171A⊕172B 14.878 7396A⊕7482B
(l=172) 345 ----- 173A⊕172B 15.051 7569A⊕7482B
(l=173) 347 ----- 173A⊕174B 15.225 7569A⊕7656B
(l=174) 349 ----- 175A⊕174B 15.400 7744A⊕7656B
(l=175) 351 ----- 175A⊕176B 15.576 7744A⊕7832B
(l=176) 353 ----- 177A⊕176B 15.753 7921A⊕7832B
(l=177) 355 ----- 177A⊕178B 15.931 7921A⊕8010B
(l=178) 357 ----- 179A⊕178B 16.110 8100A⊕8010B
(l=179) 359 ----- 179A⊕180B 16.290 8100A⊕8190B
(l=180) 361 ----- 181A⊕180B 16.471 8281A⊕8190B
(l=181) 363 ----- 181A⊕182B 16.653 8281A⊕8372B
(l=182) 365 ----- 183A⊕182B 16.836 8464A⊕8372B
(l=183) 367 ----- 183A⊕184B 17.020 8464A⊕8556B
(l=184) 369 ----- 185A⊕184B 17.205 8649A⊕8556B
(l=185) 371 ----- 185A⊕186B 17.391 8649A⊕8742B
(l=186) 373 ----- 187A⊕186B 17.578 8836A⊕8742B
(l=187) 375 ----- 187A⊕188B 17.766 8836A⊕8930B
(l=188) 377 ----- 189A⊕188B 17.955 9025A⊕8930B
(l=189) 379 ----- 189A⊕190B 18.145 9025A⊕9120B
(l=190) 381 ----- 191A⊕190B 18.336 9216A⊕9120B
(l=191) 383 ----- 191A⊕192B 18.528 9216A⊕9312B
(l=192) 385 ----- 193A⊕192B 18.721 9409A⊕9312B
(l=193) 387 ----- 193A⊕194B 18.915 9409A⊕9506B
(l=194) 389 ----- 195A⊕194B 19.110 9604A⊕9506B
(l=195) 391 ----- 195A⊕196B 19.306 9604A⊕9702B
(l=196) 393 ----- 197A⊕196B 19.503 9801A⊕9702B
(l=197) 395 ----- 197A⊕198B 19.701 9801A⊕9900B
(l=198) 397 ----- 199A⊕198B 19.900 10000A⊕9900B
(l=199) 399 ----- 199A⊕200B 20.100 10000A⊕10100B
(l=200) 401 ----- 201A⊕200B 20.301 10201A⊕10100B
(l=201) 403 ----- 201A⊕202B 20.503 10201A⊕10302B
(l=202) 405 ----- 203A⊕202B 20.706 10404A⊕10302B
(l=203) 407 ----- 203A⊕204B 20.910 10404A⊕10506B
(l=204) 409 ----- 205A⊕204B 21.115 10609A⊕10506B
(l=205) 411 ----- 205A⊕206B 21.321 10609A⊕10712B
(l=206) 413 ----- 207A⊕206B 21.528 10816A⊕10712B
(l=207) 415 ----- 207A⊕208B 21.736 10816A⊕10920B
(l=208) 417 ----- 209A⊕208B 21.945 11025A⊕10920B
(l=209) 419 ----- 209A⊕210B 22.155 11025A⊕11130B
(l=210) 421 ----- 211A⊕210B 22.366 11236A⊕11130B
(l=211) 423 ----- 211A⊕212B 22.578 11236A⊕11342B
(l=212) 425 ----- 213A⊕212B 22.791 11449A⊕11342B
(l=213) 427 ----- 213A⊕214B 23.005 11449A⊕11556B
(l=214) 429 ----- 215A⊕214B 23.220 11664A⊕11556B
(l=215) 431 ----- 215A⊕216B 23.436 11664A⊕11772B
(l=216) 433 ----- 217A⊕216B 23.653 11881A⊕11772B
(l=217) 435 ----- 217A⊕218B 23.871 11881A⊕11990B
(l=218) 437 ----- 219A⊕218B 24.090 12100A⊕11990B
(l=219) 439 ----- 219A⊕220B 24.310 12100A⊕12210B
(l=220) 441 ----- 221A⊕220B 24.531 12321A⊕12210B
(l=221) 443 ----- 221A⊕222B 24.753 12321A⊕12432B
(l=222) 445 ----- 223A⊕222B 24.976 12544A⊕12432B
(l=223) 447 ----- 223A⊕224B 25.200 12544A⊕12656B
(l=224) 449 ----- 225A⊕224B 25.425 12769A⊕12656B
(l=225) 451 ----- 225A⊕226B 25.651 12769A⊕12882B
(l=226) 453 ----- 227A⊕226B 25.878 12996A⊕12882B
(l=227) 455 ----- 227A⊕228B 26.106 12996A⊕13110B
(l=228) 457 ----- 229A⊕228B 26.335 13225A⊕13110B
(l=229) 459 ----- 229A⊕230B 26.565 13225A⊕13340B
(l=230) 461 ----- 231A⊕230B 26.796 13456A⊕13340B
(l=231) 463 ----- 231A⊕232B 27.028 13456A⊕13572B
(l=232) 465 ----- 233A⊕232B 27.261 13689A⊕13572B
(l=233) 467 ----- 233A⊕234B 27.495 13689A⊕13806B
(l=234) 469 ----- 235A⊕234B 27.730 13924A⊕13806B
(l=235) 471 ----- 235A⊕236B 27.966 13924A⊕14042B
(l=236) 473 ----- 237A⊕236B 28.203 14161A⊕14042B
(l=237) 475 ----- 237A⊕238B 28.441 14161A⊕14280B
(l=238) 477 ----- 239A⊕238B 28.680 14400A⊕14280B
(l=239) 479 ----- 239A⊕240B 28.920 14400A⊕14520B
(l=240) 481 ----- 241A⊕240B 29.161 14641A⊕14520B
(l=241) 483 ----- 241A⊕242B 29.403 14641A⊕14762B
(l=242) 485 ----- 243A⊕242B 29.646 14884A⊕14762B
(l=243) 487 ----- 243A⊕244B 29.890 14884A⊕15006B
(l=244) 489 ----- 245A⊕244B 30.135 15129A⊕15006B
(l=245) 491 ----- 245A⊕246B 30.381 15129A⊕15252B
(l=246) 493 ----- 247A⊕246B 30.628 15376A⊕15252B
(l=247) 495 ----- 247A⊕248B 30.876 15376A⊕15500B
(l=248) 497 ----- 249A⊕248B 31.125 15625A⊕15500B
(l=249) 499 ----- 249A⊕250B 31.375 15625A⊕15750B
(l=250) 501 ----- 251A⊕250B 31.626 15876A⊕15750B
(l=251) 503 ----- 251A⊕252B 31.878 15876A⊕16002B
(l=252) 505 ----- 253A⊕252B 32.131 16129A⊕16002B
(l=253) 507 ----- 253A⊕254B 32.385 16129A⊕16256B
(l=254) 509 ----- 255A⊕254B 32.640 16384A⊕16256B
(l=255) 511 ----- 255A⊕256B 32.896 16384A⊕16512B
(l=256) 513 ----- 257A⊕256B 33.153 16641A⊕16512B



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