#
ZZ Polynomials for Isomers of (5,6)-Fullerenes C_{n} with n = 20–50

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. ZZ Polynomials

## 3. List of ZZ Polynomials for Fullerene Isomers

- Kekulé count K is equal to the coefficient of ${x}^{0}$, so here we have $K=2541$. Note that one can alternatively evaluate the ZZ polynomial at $x=0$ to obtain the same value.
- Clar number $Cl$ is equal to the degree of the ZZ polynomial, so here we have $Cl=5$.
- The total number C of Clar covers is equal to the sum of all the coefficients in the ZZ polynomial. C is most conveniently computed by evaluating the ZZ polynomial at $x=1$. For C${}_{50}:22$, we have $\mathrm{C}=\mathrm{ZZ}({\mathrm{C}}_{50}:22,1)=12293$.
- The number of Clar formulas, i.e., the number of Clar covers with the maximal number $Cl$ of aromatic sextets, is equal to the coefficient of ${x}^{Cl}$, which for C${}_{50}:22$ is equal to 16.
- The first Herndon number is equal to the coefficient of ${x}^{1}$, which for C${}_{50}:22$ is equal to 4820.

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**35 Clar covers can be constructed in total for benze[e]pyrene: 11 of order 0 (orange), 16 of order 1 (purple), 7 of order 2, and 1 of order 3 (blue). These numbers can be conveniently represented in the form of a combinatorial polynomial usually referred to as a ZZ polynomial, $\mathrm{ZZ}(\mathrm{benzo}\left[\mathrm{e}\right]\mathrm{pyrene},x)$.

**Figure 2.**A comparison between the optimized DFTB energy per carbon atom (in atomic units, vertical axes) and the Kekulé count K (horizontal axes) represented in a form of scattered plot. Each blue circle represents a single isomer. Similarly to C${}_{60}$ [1,48], the isomers with high values of K are usually corresponding to the most unstable forms of a given fullerene. The most stable isomer is usually characterized by an intermediate value of K.

**Figure 3.**A comparison between the optimized DFTB energy per carbon atom (in atomic units, vertical axes) and the Clar count C (horizontal axes) represented in a form of scattered plot. Each green circle represents a single isomer. The most stable isomer is usually characterized by an intermediate value of C.

**Figure 4.**Energy per atom (negative, in atomic units) for all the isomers of C${}_{36}$ and C${}_{50}$ plotted as a function of Clar number $Cl$ and Kekulé number K. The three most stable isomers of each fullerene are denoted with encircled symbols 1, 2, and 3. For a detailed discussion, see text.

**Table 1.**Compilation of ZZ polynomials for all the isomers of small (5,6)-fullerenes C${}_{n}$ with $n=20\u201350$. The columns specify: the fullerene type, the isomer number (following the convention introduced in [3]), point group symmetry, Schlegel diagram, The Kekulé count K, the ZZ polynomial, and the total number C of Clar covers of a given isomer.

Fullerene | Isomer | Symmetry | Schlegel Diagram | ZZ Polynomial |
---|---|---|---|---|

${C}_{20}$ | 1 | ${I}_{h}$ | 36 | |

${C}_{24}$ | 1 | ${D}_{6d}$ | $54+8x+2{x}^{2}$ | |

${C}_{26}$ | 1 | ${D}_{3h}$ | $63+12x$ | |

${C}_{28}$ | 1 | ${D}_{2}$ | $90+36x+6{x}^{2}$ | |

${C}_{28}$ | 2 | ${T}_{d}$ | $75+24x$ | |

${C}_{30}$ | 1 | ${D}_{5h}$ | $151+90x$ | |

${C}_{30}$ | 2 | ${C}_{2v}$ | $117+58x+8{x}^{2}$ | |

${C}_{30}$ | 3 | ${C}_{2v}$ | $107+52x+6{x}^{2}$ | |

${C}_{32}$ | 1 | ${C}_{2}$ | $168+110x+19{x}^{2}$ | |

${C}_{32}$ | 2 | ${D}_{2}$ | $184+132x+28{x}^{2}$ | |

${C}_{32}$ | 3 | ${D}_{3d}$ | $180+132x+30{x}^{2}$ | |

${C}_{32}$ | 4 | ${C}_{2}$ | $151+98x+19{x}^{2}$ | |

${C}_{32}$ | 5 | ${D}_{3h}$ | $150+108x+30{x}^{2}$ | |

${C}_{32}$ | 6 | ${D}_{3}$ | $144+84x+15{x}^{2}$ | |

${C}_{34}$ | 1 | ${C}_{2}$ | $212+154x+28{x}^{2}+{x}^{3}$ | |

${C}_{34}$ | 2 | ${C}_{s}$ | $219+160x+24{x}^{2}$ | |

${C}_{34}$ | 3 | ${C}_{s}$ | $196+142x+31{x}^{2}$ | |

${C}_{34}$ | 4 | ${C}_{2}$ | $229+188x+48{x}^{2}+4{x}^{3}$ | |

${C}_{34}$ | 5 | ${C}_{2}$ | $204+146x+28{x}^{2}$ | |

${C}_{34}$ | 6 | ${C}_{3v}$ | $195+141x+27{x}^{2}$ | |

${C}_{36}$ | 1 | ${C}_{2}$ | $275+228x+52{x}^{2}+4{x}^{3}$ | |

${C}_{36}$ | 2 | ${D}_{2}$ | $319+300x+76{x}^{2}$ | |

${C}_{36}$ | 3 | ${C}_{1}$ | $290+262x+68{x}^{2}+3{x}^{3}$ | |

${C}_{36}$ | 4 | ${C}_{s}$ | $299+279x+70{x}^{2}$ | |

${C}_{36}$ | 5 | ${D}_{2}$ | $270+248x+88{x}^{2}+12{x}^{3}+{x}^{4}$ | |

${C}_{36}$ | 6 | ${D}_{2d}$ | $283+280x+120{x}^{2}+24{x}^{3}+2{x}^{4}$ | |

${C}_{36}$ | 7 | ${C}_{1}$ | $283+251x+70{x}^{2}+6{x}^{3}$ | |

${C}_{36}$ | 8 | ${C}_{s}$ | $299+271x+73{x}^{2}+4{x}^{3}$ | |

${C}_{36}$ | 9 | ${C}_{2v}$ | $312+276x+78{x}^{2}+8{x}^{3}$ | |

${C}_{36}$ | 10 | ${C}_{2}$ | $266+220x+48{x}^{2}$ | |

${C}_{36}$ | 11 | ${C}_{2}$ | $269+218x+48{x}^{2}$ | |

${C}_{36}$ | 12 | ${C}_{2}$ | $289+238x+52{x}^{2}$ | |

${C}_{36}$ | 13 | ${D}_{3h}$ | $364+364x+104{x}^{2}+8{x}^{3}$ | |

${C}_{36}$ | 14 | ${D}_{2d}$ | $288+232x+56{x}^{2}$ | |

${C}_{36}$ | 15 | ${D}_{6h}$ | $272+184x+22{x}^{2}$ | |

${C}_{38}$ | 1 | ${C}_{2}$ | $355+321x+72{x}^{2}+5{x}^{3}$ | |

${C}_{38}$ | 2 | ${D}_{3h}$ | $456+522x+168{x}^{2}+9{x}^{3}$ | |

${C}_{38}$ | 3 | ${C}_{1}$ | $353+336x+92{x}^{2}+3{x}^{3}$ | |

${C}_{38}$ | 4 | ${C}_{1}$ | $402+427x+139{x}^{2}+15{x}^{3}$ | |

${C}_{38}$ | 5 | ${C}_{1}$ | $375+382x+129{x}^{2}+14{x}^{3}$ | |

${C}_{38}$ | 6 | ${C}_{2}$ | $385+406x+143{x}^{2}+16{x}^{3}$ | |

${C}_{38}$ | 7 | ${C}_{1}$ | $367+360x+107{x}^{2}+7{x}^{3}$ | |

${C}_{38}$ | 8 | ${C}_{1}$ | $409+407x+118{x}^{2}+9{x}^{3}$ | |

${C}_{38}$ | 9 | ${D}_{3}$ | $468+522x+168{x}^{2}+15{x}^{3}$ | |

${C}_{38}$ | 10 | ${C}_{2}$ | $355+342x+109{x}^{2}+12{x}^{3}$ | |

${C}_{38}$ | 11 | ${C}_{1}$ | $360+332x+82{x}^{2}+2{x}^{3}$ | |

${C}_{38}$ | 12 | ${C}_{2v}$ | $360+350x+102{x}^{2}+6{x}^{3}$ | |

${C}_{38}$ | 13 | ${C}_{2}$ | $386+380x+124{x}^{2}+14{x}^{3}$ | |

${C}_{38}$ | 14 | ${C}_{1}$ | $377+346x+95{x}^{2}+6{x}^{3}$ | |

${C}_{38}$ | 15 | ${C}_{2v}$ | $365+316x+60{x}^{2}$ | |

${C}_{38}$ | 16 | ${C}_{3v}$ | $378+324x+72{x}^{2}$ | |

${C}_{38}$ | 17 | ${C}_{2}$ | $382+357x+119{x}^{2}+16{x}^{3}$ | |

${C}_{40}$ | 1 | ${D}_{5d}$ | $701+860x+250{x}^{2}$ | |

${C}_{40}$ | 2 | ${C}_{2}$ | $493+546x+206{x}^{2}+42{x}^{3}+3{x}^{4}$ | |

${C}_{40}$ | 3 | ${D}_{2}$ | $596+708x+231{x}^{2}+12{x}^{3}+{x}^{4}$ | |

${C}_{40}$ | 4 | ${C}_{1}$ | $508+614x+273{x}^{2}+49{x}^{3}+3{x}^{4}$ | |

${C}_{40}$ | 5 | ${C}_{s}$ | $536+713x+389{x}^{2}+96{x}^{3}+8{x}^{4}$ | |

${C}_{40}$ | 6 | ${C}_{1}$ | $498+550x+175{x}^{2}+16{x}^{3}$ | |

${C}_{40}$ | 7 | ${C}_{s}$ | $528+621x+222{x}^{2}+20{x}^{3}$ | |

${C}_{40}$ | 8 | ${C}_{2v}$ | $565+654x+186{x}^{2}$ | |

${C}_{40}$ | 9 | ${C}_{2}$ | $535+672x+316{x}^{2}+62{x}^{3}+4{x}^{4}$ | |

${C}_{40}$ | 10 | ${C}_{1}$ | $476+526x+185{x}^{2}+17{x}^{3}$ | |

${C}_{40}$ | 11 | ${C}_{2}$ | $533+656x+286{x}^{2}+48{x}^{3}+3{x}^{4}$ | |

${C}_{40}$ | 12 | ${C}_{1}$ | $512+598x+238{x}^{2}+36{x}^{3}+2{x}^{4}$ | |

${C}_{40}$ | 13 | ${C}_{s}$ | $489+543x+184{x}^{2}+16{x}^{3}$ | |

${C}_{40}$ | 14 | ${C}_{s}$ | $507+553x+187{x}^{2}+18{x}^{3}$ | |

${C}_{40}$ | 15 | ${C}_{2}$ | $542+598x+196{x}^{2}+14{x}^{3}$ | |

${C}_{40}$ | 16 | ${C}_{2}$ | $582+700x+281{x}^{2}+42{x}^{3}+{x}^{4}$ | |

${C}_{40}$ | 17 | ${C}_{1}$ | $540+601x+200{x}^{2}+19{x}^{3}$ | |

${C}_{40}$ | 18 | ${C}_{2}$ | $560+642x+222{x}^{2}+24{x}^{3}+{x}^{4}$ | |

${C}_{40}$ | 19 | ${C}_{2}$ | $524+568x+180{x}^{2}+12{x}^{3}$ | |

${C}_{40}$ | 20 | ${C}_{3v}$ | $432+396x+81{x}^{2}$ | |

${C}_{40}$ | 21 | ${C}_{2}$ | $454+478x+154{x}^{2}+12{x}^{3}$ | |

${C}_{40}$ | 22 | ${C}_{1}$ | $474+506x+166{x}^{2}+15{x}^{3}$ | |

${C}_{40}$ | 23 | ${C}_{2}$ | $487+536x+194{x}^{2}+22{x}^{3}+1{x}^{4}$ | |

${C}_{40}$ | 24 | ${C}_{s}$ | $480+505x+175{x}^{2}+20{x}^{3}$ | |

${C}_{40}$ | 25 | ${C}_{2}$ | $500+544x+188{x}^{2}+18{x}^{3}$ | |

${C}_{40}$ | 26 | ${C}_{1}$ | $497+523x+183{x}^{2}+22{x}^{3}$ | |

${C}_{40}$ | 27 | ${C}_{2}$ | $496+534x+182{x}^{2}+20{x}^{3}$ | |

${C}_{40}$ | 28 | ${C}_{s}$ | $541+630x+270{x}^{2}+54{x}^{3}+5{x}^{4}$ | |

${C}_{40}$ | 29 | ${C}_{2}$ | $494+510x+169{x}^{2}+18{x}^{3}+{x}^{4}$ | |

${C}_{40}$ | 30 | ${C}_{3}$ | $483+486x+135{x}^{2}+6{x}^{3}$ | |

${C}_{40}$ | 31 | ${C}_{s}$ | $520+566x+226{x}^{2}+45{x}^{3}+5{x}^{4}$ | |

${C}_{40}$ | 32 | ${D}_{2}$ | $502+552x+164{x}^{2}+4{x}^{3}$ | |

${C}_{40}$ | 33 | ${D}_{2h}$ | $541+608x+210{x}^{2}+24{x}^{3}+{x}^{4}$ | |

${C}_{40}$ | 34 | ${C}_{1}$ | $494+510x+163{x}^{2}+15{x}^{3}$ | |

${C}_{40}$ | 35 | ${C}_{2}$ | $493+500x+157{x}^{2}+12{x}^{3}$ | |

${C}_{40}$ | 36 | ${C}_{2}$ | $473+454x+135{x}^{2}+12{x}^{3}$ | |

${C}_{40}$ | 37 | ${C}_{2v}$ | $513+564x+252{x}^{2}+62{x}^{3}+7{x}^{4}$ | |

${C}_{40}$ | 38 | ${D}_{2}$ | $518+600x+314{x}^{2}+96{x}^{3}+14{x}^{4}$ | |

${C}_{40}$ | 39 | ${D}_{5d}$ | $562+710x+425{x}^{2}+150{x}^{3}+25{x}^{4}$ | |

${C}_{40}$ | 40 | ${T}_{d}$ | $576+636x+234{x}^{2}+36{x}^{3}+3{x}^{4}$ | |

${C}_{42}$ | 1 | ${C}_{2}$ | $659+786x+283{x}^{2}+37{x}^{3}$ | |

${C}_{42}$ | 2 | ${C}_{1}$ | $696+902x+388{x}^{2}+61{x}^{3}+2{x}^{4}$ | |

${C}_{42}$ | 3 | ${C}_{1}$ | $724+955x+416{x}^{2}+72{x}^{3}+5{x}^{4}$ | |

${C}_{42}$ | 4 | ${C}_{1}$ | $675+841x+317{x}^{2}+35{x}^{3}$ | |

${C}_{42}$ | 5 | ${C}_{2}$ | $786+1075x+466{x}^{2}+70{x}^{3}+{x}^{4}$ | |

${C}_{42}$ | 6 | ${C}_{2v}$ | $641+788x+332{x}^{2}+60{x}^{3}+4{x}^{4}$ | |

${C}_{42}$ | 7 | ${C}_{2}$ | $685+887x+387{x}^{2}+56{x}^{3}$ | |

${C}_{42}$ | 8 | ${C}_{1}$ | $655+810x+324{x}^{2}+41{x}^{3}+{x}^{4}$ | |

${C}_{42}$ | 9 | ${C}_{1}$ | $707+945x+446{x}^{2}+81{x}^{3}+3{x}^{4}$ | |

${C}_{42}$ | 10 | ${C}_{1}$ | $668+853x+374{x}^{2}+64{x}^{3}+5{x}^{4}$ | |

${C}_{42}$ | 11 | ${C}_{s}$ | $749+1015x+482{x}^{2}+96{x}^{3}+8{x}^{4}$ | |

${C}_{42}$ | 12 | ${C}_{s}$ | $682+885x+419{x}^{2}+88{x}^{3}+8{x}^{4}$ | |

${C}_{42}$ | 13 | ${C}_{2v}$ | $744+1072x+602{x}^{2}+170{x}^{3}+21{x}^{4}$ | |

${C}_{42}$ | 14 | ${C}_{1}$ | $721+907x+386{x}^{2}+58{x}^{3}$ | |

${C}_{42}$ | 15 | ${C}_{1}$ | $711+879x+339{x}^{2}+39{x}^{3}$ | |

${C}_{42}$ | 16 | ${C}_{2v}$ | $812+1094x+504{x}^{2}+104{x}^{3}+9{x}^{4}$ | |

${C}_{42}$ | 17 | ${C}_{1}$ | $700+847x+304{x}^{2}+30{x}^{3}$ | |

${C}_{42}$ | 18 | ${C}_{1}$ | $696+834x+287{x}^{2}+25{x}^{3}$ | |

${C}_{42}$ | 19 | ${C}_{s}$ | $698+859x+353{x}^{2}+46{x}^{3}$ | |

${C}_{42}$ | 20 | ${C}_{1}$ | $692+828x+306{x}^{2}+32{x}^{3}$ | |

${C}_{42}$ | 21 | ${C}_{2v}$ | $660+782x+318{x}^{2}+48{x}^{3}$ | |

${C}_{42}$ | 22 | ${C}_{s}$ | $622+718x+238{x}^{2}+16{x}^{3}$ | |

${C}_{42}$ | 23 | ${C}_{2}$ | $629+736x+266{x}^{2}+25{x}^{3}$ | |

${C}_{42}$ | 24 | ${C}_{1}$ | $657+806x+336{x}^{2}+49{x}^{3}$ | |

${C}_{42}$ | 25 | ${C}_{1}$ | $621+716x+266{x}^{2}+32{x}^{3}$ | |

${C}_{42}$ | 26 | ${C}_{1}$ | $631+754x+280{x}^{2}+30{x}^{3}$ | |

${C}_{42}$ | 27 | ${C}_{2}$ | $598+702x+256{x}^{2}+27{x}^{3}$ | |

${C}_{42}$ | 28 | ${C}_{2}$ | $678+834x+327{x}^{2}+39{x}^{3}$ | |

${C}_{42}$ | 29 | ${C}_{1}$ | $639+725x+242{x}^{2}+18{x}^{3}$ | |

${C}_{42}$ | 30 | ${C}_{1}$ | $657+764x+269{x}^{2}+25{x}^{3}$ | |

${C}_{42}$ | 31 | ${C}_{2}$ | $672+827x+340{x}^{2}+49{x}^{3}$ | |

${C}_{42}$ | 32 | ${C}_{1}$ | $644+749x+293{x}^{2}+39{x}^{3}$ | |

${C}_{42}$ | 33 | ${C}_{1}$ | $642+766x+340{x}^{2}+66{x}^{3}+4{x}^{4}$ | |

${C}_{42}$ | 34 | ${C}_{1}$ | $658+763x+280{x}^{2}+31{x}^{3}$ | |

${C}_{42}$ | 35 | ${C}_{s}$ | $655+770x+320{x}^{2}+48{x}^{3}$ | |

${C}_{42}$ | 36 | ${C}_{1}$ | $632+717x+273{x}^{2}+39{x}^{3}+2{x}^{4}$ | |

${C}_{42}$ | 37 | ${C}_{1}$ | $681+814x+324{x}^{2}+46{x}^{3}+2{x}^{4}$ | |

${C}_{42}$ | 38 | ${C}_{2}$ | $697+838x+332{x}^{2}+50{x}^{3}+3{x}^{4}$ | |

${C}_{42}$ | 39 | ${C}_{1}$ | $672+800x+335{x}^{2}+53{x}^{3}+{x}^{4}$ | |

${C}_{42}$ | 40 | ${C}_{2}$ | $668+775x+298{x}^{2}+39{x}^{3}+{x}^{4}$ | |

${C}_{42}$ | 41 | ${C}_{2}$ | $662+776x+301{x}^{2}+37{x}^{3}$ | |

${C}_{42}$ | 42 | ${C}_{s}$ | $681+832x+400{x}^{2}+96{x}^{3}+10{x}^{4}$ | |

${C}_{42}$ | 43 | ${C}_{2}$ | $671+835x+429{x}^{2}+120{x}^{3}+18{x}^{4}+{x}^{5}$ | |

${C}_{42}$ | 44 | ${C}_{1}$ | $642+747x+322{x}^{2}+63{x}^{3}+5{x}^{4}$ | |

${C}_{42}$ | 45 | ${D}_{3}$ | $680+893x+522{x}^{2}+164{x}^{3}+24{x}^{4}+{x}^{5}$ | |

${C}_{44}$ | 1 | ${C}_{2}$ | $892+1206x+563{x}^{2}+124{x}^{3}+9{x}^{4}$ | |

${C}_{44}$ | 2 | ${D}_{2}$ | $1091+1552x+694{x}^{2}+116{x}^{3}+12{x}^{4}$ | |

${C}_{44}$ | 3 | ${D}_{3d}$ | $1170+1758x+831{x}^{2}+132{x}^{3}+9{x}^{4}$ | |

${C}_{44}$ | 4 | ${C}_{2}$ | $1080+1714x+977{x}^{2}+212{x}^{3}+13{x}^{4}$ | |

${C}_{44}$ | 5 | ${C}_{2}$ | $1108+1846x+1177{x}^{2}+316{x}^{3}+27{x}^{4}$ | |

${C}_{44}$ | 6 | ${C}_{2}$ | $1073+1698x+975{x}^{2}+220{x}^{3}+14{x}^{4}$ | |

${C}_{44}$ | 7 | ${C}_{1}$ | $1036+1587x+854{x}^{2}+180{x}^{3}+12{x}^{4}$ | |

${C}_{44}$ | 8 | ${C}_{1}$ | $920+1262x+535{x}^{2}+63{x}^{3}$ | |

${C}_{44}$ | 9 | ${C}_{1}$ | $959+1373x+657{x}^{2}+123{x}^{3}+8{x}^{4}$ | |

${C}_{44}$ | 10 | ${C}_{1}$ | $1007+1493x+761{x}^{2}+157{x}^{3}+11{x}^{4}$ | |

${C}_{44}$ | 11 | ${C}_{s}$ | $924+1286x+601{x}^{2}+111{x}^{3}+6{x}^{4}$ | |

${C}_{44}$ | 12 | ${C}_{2}$ | $911+1340x+731{x}^{2}+174{x}^{3}+16{x}^{4}$ | |

${C}_{44}$ | 13 | ${C}_{2v}$ | $928+1352x+686{x}^{2}+136{x}^{3}+10{x}^{4}$ | |

${C}_{44}$ | 14 | ${C}_{2}$ | $940+1354x+693{x}^{2}+148{x}^{3}+14{x}^{4}$ | |

${C}_{44}$ | 15 | ${C}_{1}$ | $932+1358x+726{x}^{2}+167{x}^{3}+14{x}^{4}$ | |

${C}_{44}$ | 16 | ${C}_{1}$ | $962+1423x+774{x}^{2}+176{x}^{3}+14{x}^{4}$ | |

${C}_{44}$ | 17 | ${C}_{1}$ | $1052+1578x+815{x}^{2}+163{x}^{3}+10{x}^{4}$ | |

${C}_{44}$ | 18 | ${C}_{1}$ | $930+1315x+665{x}^{2}+138{x}^{3}+9{x}^{4}$ | |

${C}_{44}$ | 19 | ${C}_{1}$ | $950+1397x+746{x}^{2}+172{x}^{3}+14{x}^{4}$ | |

${C}_{44}$ | 20 | ${C}_{2}$ | $965+1420x+738{x}^{2}+154{x}^{3}+11{x}^{4}$ | |

${C}_{44}$ | 21 | ${C}_{1}$ | $869+1194x+556{x}^{2}+96{x}^{3}+4{x}^{4}$ | |

${C}_{44}$ | 22 | ${C}_{1}$ | $984+1364x+647{x}^{2}+130{x}^{3}+10{x}^{4}$ | |

${C}_{44}$ | 23 | ${C}_{1}$ | $962+1340x+627{x}^{2}+111{x}^{3}+5{x}^{4}$ | |

${C}_{44}$ | 24 | ${D}_{2}$ | $1156+1732x+884{x}^{2}+184{x}^{3}+17{x}^{4}$ | |

${C}_{44}$ | 25 | ${C}_{1}$ | $1000+1420x+712{x}^{2}+144{x}^{3}+8{x}^{4}$ | |

${C}_{44}$ | 26 | ${C}_{1}$ | $940+1279x+569{x}^{2}+86{x}^{3}+2{x}^{4}$ | |

${C}_{44}$ | 27 | ${C}_{1}$ | $939+1265x+556{x}^{2}+83{x}^{3}+2{x}^{4}$ | |

${C}_{44}$ | 28 | ${C}_{s}$ | $907+1185x+510{x}^{2}+76{x}^{3}$ | |

${C}_{44}$ | 29 | ${C}_{1}$ | $938+1282x+624{x}^{2}+130{x}^{3}+10{x}^{4}$ | |

${C}_{44}$ | 30 | ${C}_{1}$ | $968+1419x+821{x}^{2}+231{x}^{3}+26{x}^{4}$ | |

${C}_{44}$ | 31 | ${C}_{1}$ | $994+1436x+748{x}^{2}+165{x}^{3}+13{x}^{4}$ | |

${C}_{44}$ | 32 | ${C}_{2}$ | $994+1506x+938{x}^{2}+292{x}^{3}+39{x}^{4}$ | |

${C}_{44}$ | 33 | ${C}_{s}$ | $893+1152x+472{x}^{2}+64{x}^{3}$ | |

${C}_{44}$ | 34 | ${C}_{2}$ | $961+1344x+639{x}^{2}+114{x}^{3}+7{x}^{4}$ | |

${C}_{44}$ | 35 | ${D}_{3}$ | $1125+1746x+939{x}^{2}+186{x}^{3}+9{x}^{4}$ | |

${C}_{44}$ | 36 | ${C}_{2}$ | $872+1072x+384{x}^{2}+36{x}^{3}$ | |

${C}_{44}$ | 37 | ${D}_{3h}$ | $780+978x+417{x}^{2}+66{x}^{3}+3{x}^{4}$ | |

${C}_{44}$ | 38 | ${D}_{3d}$ | $765+888x+267{x}^{2}+{x}^{3}$ | |

${C}_{44}$ | 39 | ${C}_{2v}$ | $872+1210x+625{x}^{2}+138{x}^{3}+11{x}^{4}$ | |

${C}_{44}$ | 40 | ${C}_{1}$ | $877+1174x+547{x}^{2}+106{x}^{3}+8{x}^{4}$ | |

${C}_{44}$ | 41 | ${C}_{1}$ | $860+1109x+454{x}^{2}+58{x}^{3}+{x}^{4}$ | |

${C}_{44}$ | 42 | ${C}_{1}$ | $847+1058x+406{x}^{2}+41{x}^{3}$ | |

${C}_{44}$ | 43 | ${C}_{1}$ | $869+1150x+481{x}^{2}+63{x}^{3}+{x}^{4}$ | |

${C}_{44}$ | 44 | ${C}_{2}$ | $826+1054x+405{x}^{2}+42{x}^{3}+{x}^{4}$ | |

${C}_{44}$ | 45 | ${C}_{2}$ | $814+1036x+395{x}^{2}+42{x}^{3}+{x}^{4}$ | |

${C}_{44}$ | 46 | ${C}_{2}$ | $929+1270x+560{x}^{2}+76{x}^{3}+{x}^{4}$ | |

${C}_{44}$ | 47 | ${C}_{1}$ | $892+1180x+521{x}^{2}+79{x}^{3}$ | |

${C}_{44}$ | 48 | ${C}_{1}$ | $917+1259x+592{x}^{2}+110{x}^{3}+7{x}^{4}$ | |

${C}_{44}$ | 49 | ${C}_{2}$ | $900+1212x+560{x}^{2}+104{x}^{3}+7{x}^{4}$ | |

${C}_{44}$ | 50 | ${C}_{1}$ | $880+1124x+464{x}^{2}+65{x}^{3}+3{x}^{4}$ | |

${C}_{44}$ | 51 | ${C}_{1}$ | $898+1242x+671{x}^{2}+171{x}^{3}+17{x}^{4}$ | |

${C}_{44}$ | 52 | ${C}_{1}$ | $914+1330x+814{x}^{2}+259{x}^{3}+36{x}^{4}$ | |

${C}_{44}$ | 53 | ${C}_{1}$ | $936+1254x+566{x}^{2}+103{x}^{3}+7{x}^{4}$ | |

${C}_{44}$ | 54 | ${C}_{s}$ | $929+1369x+849{x}^{2}+274{x}^{3}+38{x}^{4}$ | |

${C}_{44}$ | 55 | ${C}_{2v}$ | $920+1308x+750{x}^{2}+212{x}^{3}+27{x}^{4}$ | |

${C}_{44}$ | 56 | ${C}_{1}$ | $882+1195x+604{x}^{2}+137{x}^{3}+12{x}^{4}$ | |

${C}_{44}$ | 57 | ${C}_{1}$ | $881+1175x+580{x}^{2}+122{x}^{3}+8{x}^{4}$ | |

${C}_{44}$ | 58 | ${C}_{1}$ | $861+1084x+401{x}^{2}+37{x}^{3}$ | |

${C}_{44}$ | 59 | ${C}_{1}$ | $858+1165x+605{x}^{2}+152{x}^{3}+16{x}^{4}$ | |

${C}_{44}$ | 60 | ${C}_{1}$ | $912+1229x+582{x}^{2}+114{x}^{3}+8{x}^{4}$ | |

${C}_{44}$ | 61 | ${C}_{2}$ | $862+1118x+496{x}^{2}+84{x}^{3}+5{x}^{4}$ | |

${C}_{44}$ | 62 | ${C}_{1}$ | $839+1061x+413{x}^{2}+47{x}^{3}$ | |

${C}_{44}$ | 63 | ${C}_{1}$ | $881+1155x+501{x}^{2}+81{x}^{3}+4{x}^{4}$ | |

${C}_{44}$ | 64 | ${C}_{1}$ | $873+1105x+432{x}^{2}+48{x}^{3}$ | |

${C}_{44}$ | 65 | ${C}_{1}$ | $885+1153x+487{x}^{2}+67{x}^{3}+2{x}^{4}$ | |

${C}_{44}$ | 66 | ${C}_{2}$ | $894+1182x+514{x}^{2}+78{x}^{3}+4{x}^{4}$ | |

${C}_{44}$ | 67 | ${C}_{1}$ | $830+1037x+427{x}^{2}+57{x}^{3}$ | |

${C}_{44}$ | 68 | ${C}_{2}$ | $874+1160x+552{x}^{2}+112{x}^{3}+8{x}^{4}$ | |

${C}_{44}$ | 69 | ${C}_{1}$ | $896+1240x+679{x}^{2}+180{x}^{3}+20{x}^{4}$ | |

${C}_{44}$ | 70 | ${C}_{s}$ | $846+1061x+426{x}^{2}+52{x}^{3}$ | |

${C}_{44}$ | 71 | ${C}_{s}$ | $898+1198x+592{x}^{2}+127{x}^{3}+10{x}^{4}$ | |

${C}_{44}$ | 72 | ${D}_{3h}$ | $960+1362x+774{x}^{2}+216{x}^{3}+27{x}^{4}$ | |

${C}_{44}$ | 73 | T | $864+1104x+432{x}^{2}+48{x}^{3}$ | |

${C}_{44}$ | 74 | ${C}_{2}$ | $882+1158x+514{x}^{2}+86{x}^{3}+4{x}^{4}$ | |

${C}_{44}$ | 75 | ${D}_{2}$ | $924+1376x+896{x}^{2}+304{x}^{3}+44{x}^{4}$ | |

${C}_{44}$ | 76 | ${C}_{2}$ | $891+1214x+660{x}^{2}+174{x}^{3}+20{x}^{4}$ | |

${C}_{44}$ | 77 | ${C}_{1}$ | $840+1090x+519{x}^{2}+101{x}^{3}+5{x}^{4}$ | |

${C}_{44}$ | 78 | ${C}_{1}$ | $856+1101x+487{x}^{2}+74{x}^{3}$ | |

${C}_{44}$ | 79 | ${C}_{2}$ | $850+1110x+532{x}^{2}+108{x}^{3}+8{x}^{4}$ | |

${C}_{44}$ | 80 | ${D}_{3}$ | $846+1092x+510{x}^{2}+90{x}^{3}+3{x}^{4}$ | |

${C}_{44}$ | 81 | ${C}_{2}$ | $870+1132x+542{x}^{2}+110{x}^{3}+8{x}^{4}$ | |

${C}_{44}$ | 82 | ${S}_{4}$ | $804+960x+354{x}^{2}+36{x}^{3}+{x}^{4}$ | |

${C}_{44}$ | 83 | ${D}_{2}$ | $824+984x+373{x}^{2}+36{x}^{3}+{x}^{4}$ | |

${C}_{44}$ | 84 | ${C}_{s}$ | $854+1057x+432{x}^{2}+56{x}^{3}$ | |

${C}_{44}$ | 85 | ${D}_{2}$ | $925+1252x+650{x}^{2}+156{x}^{3}+16{x}^{4}$ | |

${C}_{44}$ | 86 | ${D}_{3d}$ | $900+1152x+534{x}^{2}+108{x}^{3}+9{x}^{4}$ | |

${C}_{44}$ | 87 | ${C}_{2}$ | $864+1102x+462{x}^{2}+60{x}^{3}$ | |

${C}_{44}$ | 88 | ${C}_{1}$ | $828+1042x+444{x}^{2}+64{x}^{3}$ | |

${C}_{44}$ | 89 | ${D}_{2}$ | $868+1236x+752{x}^{2}+236{x}^{3}+32{x}^{4}$ | |

${C}_{46}$ | 1 | ${C}_{2}$ | $1172+1693x+836{x}^{2}+196{x}^{3}+21{x}^{4}+{x}^{5}$ | |

${C}_{46}$ | 2 | ${C}_{s}$ | $1385+2173x+1157{x}^{2}+236{x}^{3}+14{x}^{4}$ | |

${C}_{46}$ | 3 | ${C}_{1}$ | $1291+1992x+1025{x}^{2}+185{x}^{3}+5{x}^{4}$ | |

${C}_{46}$ | 4 | ${C}_{1}$ | $1246+1873x+925{x}^{2}+164{x}^{3}+7{x}^{4}$ | |

${C}_{46}$ | 5 | ${C}_{1}$ | $1380+2213x+1225{x}^{2}+269{x}^{3}+18{x}^{4}$ | |

${C}_{46}$ | 6 | ${C}_{1}$ | $1274+1984x+1068{x}^{2}+230{x}^{3}+18{x}^{4}$ | |

${C}_{46}$ | 7 | ${C}_{s}$ | $1494+2459x+1375{x}^{2}+302{x}^{3}+24{x}^{4}$ | |

${C}_{46}$ | 8 | ${C}_{s}$ | $1373+2185x+1210{x}^{2}+278{x}^{3}+24{x}^{4}$ | |

${C}_{46}$ | 9 | ${C}_{2}$ | $1322+2045x+1085{x}^{2}+263{x}^{3}+32{x}^{4}+{x}^{5}$ | |

${C}_{46}$ | 10 | ${C}_{s}$ | $1434+2483x+1684{x}^{2}+582{x}^{3}+93{x}^{4}+4{x}^{5}$ | |

${C}_{46}$ | 11 | ${C}_{s}$ | $1119+1664x+894{x}^{2}+198{x}^{3}+16{x}^{4}$ | |

${C}_{46}$ | 12 | ${C}_{2}$ | $1393+2377x+1559{x}^{2}+484{x}^{3}+70{x}^{4}+4{x}^{5}$ | |

${C}_{46}$ | 13 | ${C}_{s}$ | $1266+1995x+1141{x}^{2}+260{x}^{3}+16{x}^{4}$ | |

${C}_{46}$ | 14 | ${C}_{1}$ | $1305+2020x+1078{x}^{2}+217{x}^{3}+11{x}^{4}$ | |

${C}_{46}$ | 15 | ${C}_{1}$ | $1231+1861x+975{x}^{2}+201{x}^{3}+14{x}^{4}$ | |

${C}_{46}$ | 16 | ${C}_{1}$ | $1375+2184x+1222{x}^{2}+293{x}^{3}+31{x}^{4}+{x}^{5}$ | |

${C}_{46}$ | 17 | ${C}_{1}$ | $1254+1889x+995{x}^{2}+212{x}^{3}+16{x}^{4}$ | |

${C}_{46}$ | 18 | ${C}_{1}$ | $1322+2106x+1198{x}^{2}+295{x}^{3}+29{x}^{4}$ | |

${C}_{46}$ | 19 | ${C}_{1}$ | $1212+1856x+1003{x}^{2}+221{x}^{3}+16{x}^{4}$ | |

${C}_{46}$ | 20 | ${C}_{2}$ | $1232+1928x+1078{x}^{2}+262{x}^{3}+30{x}^{4}+2{x}^{5}$ | |

${C}_{46}$ | 21 | ${C}_{1}$ | $1164+1709x+837{x}^{2}+153{x}^{3}+10{x}^{4}$ | |

${C}_{46}$ | 22 | ${C}_{2}$ | $1489+2381x+1292{x}^{2}+258{x}^{3}+12{x}^{4}$ | |

${C}_{46}$ | 23 | ${C}_{1}$ | $1333+1991x+983{x}^{2}+189{x}^{3}+15{x}^{4}$ | |

${C}_{46}$ | 24 | ${C}_{1}$ | $1265+1890x+960{x}^{2}+185{x}^{3}+8{x}^{4}$ | |

${C}_{46}$ | 25 | ${C}_{1}$ | $1387+2152x+1179{x}^{2}+275{x}^{3}+25{x}^{4}$ | |

${C}_{46}$ | 26 | ${C}_{1}$ | $1356+2078x+1108{x}^{2}+245{x}^{3}+20{x}^{4}$ | |

${C}_{46}$ | 27 | ${C}_{1}$ | $1242+1852x+1001{x}^{2}+227{x}^{3}+18{x}^{4}$ | |

${C}_{46}$ | 28 | ${C}_{s}$ | $1329+2108x+1277{x}^{2}+362{x}^{3}+46{x}^{4}+2{x}^{5}$ | |

${C}_{46}$ | 29 | ${C}_{1}$ | $1272+1926x+1059{x}^{2}+242{x}^{3}+18{x}^{4}$ | |

${C}_{46}$ | 30 | ${C}_{1}$ | $1291+1983x+1143{x}^{2}+303{x}^{3}+34{x}^{4}+{x}^{5}$ | |

${C}_{46}$ | 31 | ${C}_{1}$ | $1322+1991x+1003{x}^{2}+174{x}^{3}+5{x}^{4}$ | |

${C}_{46}$ | 32 | ${C}_{2}$ | $1338+2182x+1395{x}^{2}+426{x}^{3}+57{x}^{4}+2{x}^{5}$ | |

${C}_{46}$ | 33 | ${C}_{s}$ | $1377+2168x+1171{x}^{2}+258{x}^{3}+19{x}^{4}$ | |

${C}_{46}$ | 34 | ${C}_{1}$ | $1270+1941x+1044{x}^{2}+227{x}^{3}+14{x}^{4}$ | |

${C}_{46}$ | 35 | ${C}_{1}$ | $1261+1877x+964{x}^{2}+189{x}^{3}+9{x}^{4}$ | |

${C}_{46}$ | 36 | ${C}_{1}$ | $1281+1990x+1181{x}^{2}+348{x}^{3}+52{x}^{4}+3{x}^{5}$ | |

${C}_{46}$ | 37 | ${C}_{1}$ | $1218+1741x+810{x}^{2}+131{x}^{3}+5{x}^{4}$ | |

${C}_{46}$ | 38 | ${C}_{s}$ | $1216+1798x+880{x}^{2}+154{x}^{3}+5{x}^{4}$ | |

${C}_{46}$ | 39 | ${C}_{2v}$ | $1346+2068x+1103{x}^{2}+252{x}^{3}+25{x}^{4}$ | |

${C}_{46}$ | 40 | ${C}_{s}$ | $1249+1856x+1012{x}^{2}+273{x}^{3}+35{x}^{4}$ | |

${C}_{46}$ | 41 | ${C}_{s}$ | $1273+1968x+1179{x}^{2}+370{x}^{3}+60{x}^{4}+3{x}^{5}$ | |

${C}_{46}$ | 42 | ${C}_{2v}$ | $1260+1902x+1033{x}^{2}+276{x}^{3}+39{x}^{4}+2{x}^{5}$ | |

${C}_{46}$ | 43 | ${C}_{2}$ | $1137+1594x+718{x}^{2}+101{x}^{3}$ | |

${C}_{46}$ | 44 | ${C}_{1}$ | $1191+1699x+779{x}^{2}+113{x}^{3}$ | |

${C}_{46}$ | 45 | ${C}_{1}$ | $1176+1712x+867{x}^{2}+185{x}^{3}+19{x}^{4}+{x}^{5}$ | |

${C}_{46}$ | 46 | ${C}_{1}$ | $1181+1709x+861{x}^{2}+171{x}^{3}+9{x}^{4}$ | |

${C}_{46}$ | 47 | ${C}_{2}$ | $1143+1644x+775{x}^{2}+128{x}^{3}+5{x}^{4}$ | |

${C}_{46}$ | 48 | ${C}_{1}$ | $1199+1774x+892{x}^{2}+174{x}^{3}+11{x}^{4}$ | |

${C}_{46}$ | 49 | ${C}_{2}$ | $1105+1546x+679{x}^{2}+98{x}^{3}+5{x}^{4}$ | |

${C}_{46}$ | 50 | ${C}_{1}$ | $1171+1675x+814{x}^{2}+165{x}^{3}+17{x}^{4}+{x}^{5}$ | |

${C}_{46}$ | 51 | ${C}_{1}$ | $1107+1502x+626{x}^{2}+77{x}^{3}+{x}^{4}$ | |

${C}_{46}$ | 52 | ${C}_{1}$ | $1164+1640x+721{x}^{2}+95{x}^{3}$ | |

${C}_{46}$ | 53 | ${C}_{2}$ | $1304+1998x+1030{x}^{2}+192{x}^{3}+7{x}^{4}$ | |

${C}_{46}$ | 54 | ${C}_{2}$ | $1239+1832x+915{x}^{2}+162{x}^{3}+{x}^{4}$ | |

${C}_{46}$ | 55 | ${C}_{1}$ | $1225+1794x+911{x}^{2}+186{x}^{3}+12{x}^{4}$ | |

${C}_{46}$ | 56 | ${C}_{1}$ | $1194+1734x+857{x}^{2}+164{x}^{3}+10{x}^{4}$ | |

${C}_{46}$ | 57 | ${C}_{s}$ | $1204+1752x+927{x}^{2}+206{x}^{3}+16{x}^{4}$ | |

${C}_{46}$ | 58 | ${C}_{1}$ | $1229+1827x+1005{x}^{2}+236{x}^{3}+20{x}^{4}$ | |

${C}_{46}$ | 59 | ${C}_{1}$ | $1224+1880x+1150{x}^{2}+353{x}^{3}+55{x}^{4}+3{x}^{5}$ | |

${C}_{46}$ | 60 | ${C}_{1}$ | $1192+1809x+1071{x}^{2}+295{x}^{3}+32{x}^{4}$ | |

${C}_{46}$ | 61 | ${C}_{1}$ | $1151+1641x+839{x}^{2}+177{x}^{3}+13{x}^{4}$ | |

${C}_{46}$ | 62 | ${C}_{1}$ | $1179+1658x+778{x}^{2}+123{x}^{3}+3{x}^{4}$ | |

${C}_{46}$ | 63 | ${C}_{1}$ | $1158+1655x+842{x}^{2}+171{x}^{3}+11{x}^{4}$ | |

${C}_{46}$ | 64 | ${C}_{1}$ | $1190+1705x+833{x}^{2}+146{x}^{3}+5{x}^{4}$ | |

${C}_{46}$ | 65 | ${C}_{s}$ | $1175+1738x+913{x}^{2}+182{x}^{3}+6{x}^{4}$ | |

${C}_{46}$ | 66 | ${C}_{2}$ | $1179+1762x+971{x}^{2}+234{x}^{3}+22{x}^{4}+{x}^{5}$ | |

${C}_{46}$ | 67 | ${C}_{1}$ | $1193+1872x+1198{x}^{2}+396{x}^{3}+65{x}^{4}+4{x}^{5}$ | |

${C}_{46}$ | 68 | ${C}_{1}$ | $1171+1712x+894{x}^{2}+189{x}^{3}+11{x}^{4}$ | |

${C}_{46}$ | 69 | ${C}_{1}$ | $1193+1757x+945{x}^{2}+206{x}^{3}+11{x}^{4}$ | |

${C}_{46}$ | 70 | ${C}_{1}$ | $1131+1602x+805{x}^{2}+167{x}^{3}+13{x}^{4}$ | |

${C}_{46}$ | 71 | ${C}_{1}$ | $1133+1528x+644{x}^{2}+81{x}^{3}$ | |

${C}_{46}$ | 72 | ${C}_{1}$ | $1162+1622x+742{x}^{2}+112{x}^{3}$ | |

${C}_{46}$ | 73 | ${C}_{1}$ | $1166+1611x+711{x}^{2}+102{x}^{3}$ | |

${C}_{46}$ | 74 | ${C}_{1}$ | $1159+1671x+883{x}^{2}+226{x}^{3}+31{x}^{4}+2{x}^{5}$ | |

${C}_{46}$ | 75 | ${C}_{1}$ | $1159+1645x+822{x}^{2}+181{x}^{3}+18{x}^{4}$ | |

${C}_{46}$ | 76 | ${C}_{1}$ | $1213+1768x+885{x}^{2}+173{x}^{3}+10{x}^{4}$ | |

${C}_{46}$ | 77 | ${C}_{2}$ | $1240+1848x+916{x}^{2}+158{x}^{3}+5{x}^{4}$ | |

${C}_{46}$ | 78 | ${C}_{1}$ | $1197+1695x+806{x}^{2}+134{x}^{3}+2{x}^{4}$ | |

${C}_{46}$ | 79 | ${C}_{1}$ | $1140+1579x+732{x}^{2}+128{x}^{3}+7{x}^{4}$ | |

${C}_{46}$ | 80 | ${C}_{1}$ | $1168+1618x+708{x}^{2}+97{x}^{3}$ | |

${C}_{46}$ | 81 | ${C}_{1}$ | $1140+1596x+758{x}^{2}+128{x}^{3}+3{x}^{4}$ | |

${C}_{46}$ | 82 | ${C}_{1}$ | $1132+1604x+768{x}^{2}+139{x}^{3}+8{x}^{4}$ | |

${C}_{46}$ | 83 | ${C}_{s}$ | $1204+1738x+858{x}^{2}+161{x}^{3}+8{x}^{4}$ | |

${C}_{46}$ | 84 | ${C}_{2}$ | $1211+1713x+789{x}^{2}+125{x}^{3}+4{x}^{4}$ | |

${C}_{46}$ | 85 | ${C}_{1}$ | $1164+1701x+920{x}^{2}+212{x}^{3}+15{x}^{4}$ | |

${C}_{46}$ | 86 | ${C}_{1}$ | $1195+1825x+1090{x}^{2}+311{x}^{3}+40{x}^{4}+2{x}^{5}$ | |

${C}_{46}$ | 87 | ${C}_{1}$ | $1177+1750x+987{x}^{2}+265{x}^{3}+35{x}^{4}+2{x}^{5}$ | |

${C}_{46}$ | 88 | ${C}_{1}$ | $1192+1769x+993{x}^{2}+250{x}^{3}+24{x}^{4}$ | |

${C}_{46}$ | 89 | ${C}_{s}$ | $1239+1797x+880{x}^{2}+155{x}^{3}+6{x}^{4}$ | |

${C}_{46}$ | 90 | ${C}_{1}$ | $1133+1604x+804{x}^{2}+159{x}^{3}+8{x}^{4}$ | |

${C}_{46}$ | 91 | ${C}_{2v}$ | $1281+1908x+1012{x}^{2}+242{x}^{3}+28{x}^{4}+2{x}^{5}$ | |

${C}_{46}$ | 92 | ${C}_{2v}$ | $1245+1920x+1138{x}^{2}+318{x}^{3}+40{x}^{4}+2{x}^{5}$ | |

${C}_{46}$ | 93 | ${C}_{1}$ | $1146+1633x+790{x}^{2}+136{x}^{3}+2{x}^{4}$ | |

${C}_{46}$ | 94 | ${C}_{3}$ | $1140+1683x+903{x}^{2}+201{x}^{3}+12{x}^{4}$ | |

${C}_{46}$ | 95 | ${C}_{2}$ | $1172+1664x+748{x}^{2}+104{x}^{3}$ | |

${C}_{46}$ | 96 | ${C}_{2}$ | $1162+1609x+692{x}^{2}+87{x}^{3}$ | |

${C}_{46}$ | 97 | ${C}_{2}$ | $1224+1773x+889{x}^{2}+179{x}^{3}+12{x}^{4}$ | |

${C}_{46}$ | 98 | ${C}_{1}$ | $1152+1639x+834{x}^{2}+166{x}^{3}+8{x}^{4}$ | |

${C}_{46}$ | 99 | ${C}_{s}$ | $1183+1782x+1046{x}^{2}+285{x}^{3}+30{x}^{4}$ | |

${C}_{46}$ | 100 | ${C}_{1}$ | $1182+1763x+1001{x}^{2}+255{x}^{3}+24{x}^{4}$ | |

${C}_{46}$ | 101 | ${C}_{1}$ | $1168+1710x+931{x}^{2}+217{x}^{3}+17{x}^{4}$ | |

${C}_{46}$ | 102 | ${C}_{1}$ | $1208+1869x+1195{x}^{2}+404{x}^{3}+73{x}^{4}+5{x}^{5}$ | |

${C}_{46}$ | 103 | ${C}_{1}$ | $1154+1728x+1021{x}^{2}+284{x}^{3}+32{x}^{4}$ | |

${C}_{46}$ | 104 | ${C}_{2}$ | $1112+1537x+726{x}^{2}+115{x}^{3}$ | |

${C}_{46}$ | 105 | ${C}_{1}$ | $1130+1602x+826{x}^{2}+182{x}^{3}+16{x}^{4}$ | |

${C}_{46}$ | 106 | ${C}_{s}$ | $1168+1696x+895{x}^{2}+198{x}^{3}+12{x}^{4}$ | |

${C}_{46}$ | 107 | ${C}_{s}$ | $1225+2011x+1448{x}^{2}+571{x}^{3}+118{x}^{4}+10{x}^{5}$ | |

${C}_{46}$ | 108 | ${C}_{s}$ | $1218+2011x+1460{x}^{2}+582{x}^{3}+122{x}^{4}+10{x}^{5}$ | |

${C}_{46}$ | 109 | ${C}_{2}$ | $1222+1992x+1394{x}^{2}+526{x}^{3}+104{x}^{4}+8{x}^{5}$ | |

${C}_{46}$ | 110 | ${C}_{1}$ | $1113+1597x+840{x}^{2}+191{x}^{3}+16{x}^{4}$ | |

${C}_{46}$ | 111 | ${C}_{1}$ | $1137+1623x+861{x}^{2}+202{x}^{3}+20{x}^{4}$ | |

${C}_{46}$ | 112 | ${C}_{2}$ | $1070+1398x+590{x}^{2}+74{x}^{3}$ | |

${C}_{46}$ | 113 | ${C}_{2}$ | $1158+1690x+969{x}^{2}+279{x}^{3}+44{x}^{4}+3{x}^{5}$ | |

${C}_{46}$ | 114 | ${C}_{1}$ | $1106+1595x+856{x}^{2}+205{x}^{3}+19{x}^{4}$ | |

${C}_{46}$ | 115 | ${C}_{3}$ | $1032+1356x+567{x}^{2}+75{x}^{3}$ | |

${C}_{46}$ | 116 | ${C}_{2}$ | $1106+1591x+832{x}^{2}+173{x}^{3}+8{x}^{4}$ | |

${C}_{48}$ | 1 | ${C}_{2}$ | $1532+2348x+1228{x}^{2}+286{x}^{3}+24{x}^{4}$ | |

${C}_{48}$ | 2 | ${D}_{2}$ | $2024+3428x+1974{x}^{2}+484{x}^{3}+57{x}^{4}$ | |

${C}_{48}$ | 3 | ${C}_{1}$ | $1937+3482x+2246{x}^{2}+590{x}^{3}+51{x}^{4}$ | |

${C}_{48}$ | 4 | ${C}_{s}$ | $1935+3482x+2236{x}^{2}+580{x}^{3}+48{x}^{4}$ | |

${C}_{48}$ | 5 | ${C}_{2}$ | $1912+3426x+2177{x}^{2}+558{x}^{3}+47{x}^{4}$ | |

${C}_{48}$ | 6 | ${C}_{1}$ | $1736+2927x+1731{x}^{2}+428{x}^{3}+43{x}^{4}$ | |

${C}_{48}$ | 7 | ${C}_{1}$ | $1763+3033x+1883{x}^{2}+506{x}^{3}+53{x}^{4}+{x}^{5}$ | |

${C}_{48}$ | 8 | ${C}_{1}$ | $1835+3116x+1813{x}^{2}+402{x}^{3}+27{x}^{4}$ | |

${C}_{48}$ | 9 | ${C}_{1}$ | $2083+3711x+2258{x}^{2}+527{x}^{3}+36{x}^{4}$ | |

${C}_{48}$ | 10 | ${C}_{1}$ | $1818+3032x+1750{x}^{2}+405{x}^{3}+30{x}^{4}$ | |

${C}_{48}$ | 11 | ${C}_{1}$ | $1826+3171x+2003{x}^{2}+554{x}^{3}+57{x}^{4}+{x}^{5}$ | |

${C}_{48}$ | 12 | ${C}_{1}$ | $1832+3227x+2087{x}^{2}+611{x}^{3}+83{x}^{4}+5{x}^{5}$ | |

${C}_{48}$ | 13 | ${C}_{1}$ | $1616+2613x+1461{x}^{2}+326{x}^{3}+21{x}^{4}$ | |

${C}_{48}$ | 14 | ${C}_{2}$ | $1678+2670x+1401{x}^{2}+300{x}^{3}+28{x}^{4}$ | |

${C}_{48}$ | 15 | ${D}_{2h}$ | $1709+3276x+2670{x}^{2}+1156{x}^{3}+280{x}^{4}+36{x}^{5}+2{x}^{6}$ | |

${C}_{48}$ | 16 | ${D}_{2}$ | $1610+2820x+1967{x}^{2}+692{x}^{3}+140{x}^{4}+16{x}^{5}+{x}^{6}$ | |

${C}_{48}$ | 17 | ${C}_{2v}$ | $1807+3342x+2428{x}^{2}+828{x}^{3}+130{x}^{4}+8{x}^{5}$ | |

${C}_{48}$ | 18 | ${C}_{1}$ | $1645+2708x+1584{x}^{2}+374{x}^{3}+29{x}^{4}$ | |

${C}_{48}$ | 19 | ${C}_{1}$ | $1722+2862x+1701{x}^{2}+423{x}^{3}+37{x}^{4}$ | |

${C}_{48}$ | 20 | ${C}_{1}$ | $1744+2927x+1757{x}^{2}+438{x}^{3}+38{x}^{4}$ | |

${C}_{48}$ | 21 | ${C}_{1}$ | $1904+3412x+2323{x}^{2}+753{x}^{3}+119{x}^{4}+8{x}^{5}$ | |

${C}_{48}$ | 22 | ${C}_{1}$ | $1750+2904x+1725{x}^{2}+430{x}^{3}+39{x}^{4}$ | |

${C}_{48}$ | 23 | ${C}_{1}$ | $1655+2748x+1636{x}^{2}+436{x}^{3}+55{x}^{4}+3{x}^{5}$ | |

${C}_{48}$ | 24 | ${C}_{2}$ | $1882+3570x+2754{x}^{2}+1104{x}^{3}+236{x}^{4}+22{x}^{5}$ | |

${C}_{48}$ | 25 | ${C}_{1}$ | $1831+3184x+2026{x}^{2}+568{x}^{3}+66{x}^{4}+2{x}^{5}$ | |

${C}_{48}$ | 26 | ${C}_{1}$ | $1562+2470x+1312{x}^{2}+265{x}^{3}+17{x}^{4}$ | |

${C}_{48}$ | 27 | ${C}_{2}$ | $1754+3060x+2028{x}^{2}+644{x}^{3}+102{x}^{4}+6{x}^{5}$ | |

${C}_{48}$ | 28 | ${C}_{1}$ | $1758+2894x+1653{x}^{2}+375{x}^{3}+27{x}^{4}$ | |

${C}_{48}$ | 29 | ${C}_{1}$ | $1636+2622x+1445{x}^{2}+311{x}^{3}+21{x}^{4}$ | |

${C}_{48}$ | 30 | ${C}_{1}$ | $1695+2805x+1619{x}^{2}+377{x}^{3}+30{x}^{4}$ | |

${C}_{48}$ | 31 | ${C}_{s}$ | $1776+3096x+2008{x}^{2}+612{x}^{3}+91{x}^{4}+6{x}^{5}$ | |

${C}_{48}$ | 32 | ${C}_{2}$ | $2074+3596x+2186{x}^{2}+554{x}^{3}+48{x}^{4}$ | |

${C}_{48}$ | 33 | ${C}_{1}$ | $1867+3072x+1748{x}^{2}+402{x}^{3}+30{x}^{4}$ | |

${C}_{48}$ | 34 | ${C}_{1}$ | $1863+3090x+1764{x}^{2}+398{x}^{3}+28{x}^{4}$ | |

${C}_{48}$ | 35 | ${C}_{1}$ | $1784+2899x+1607{x}^{2}+347{x}^{3}+26{x}^{4}$ | |

${C}_{48}$ | 36 | ${C}_{1}$ | $1755+2839x+1587{x}^{2}+369{x}^{3}+34{x}^{4}$ | |

${C}_{48}$ | 37 | ${C}_{2}$ | $1853+3132x+1897{x}^{2}+476{x}^{3}+38{x}^{4}$ | |

${C}_{48}$ | 38 | ${C}_{1}$ | $1794+3101x+2039{x}^{2}+594{x}^{3}+64{x}^{4}$ | |

${C}_{48}$ | 39 | ${C}_{s}$ | $1808+2974x+1725{x}^{2}+384{x}^{3}+20{x}^{4}$ | |

${C}_{48}$ | 40 | ${C}_{2}$ | $1952+3374x+2124{x}^{2}+570{x}^{3}+52{x}^{4}$ | |

${C}_{48}$ | 41 | ${D}_{2h}$ | $1865+3368x+2394{x}^{2}+772{x}^{3}+94{x}^{4}$ | |

${C}_{48}$ | 42 | ${C}_{1}$ | $1810+3156x+2129{x}^{2}+664{x}^{3}+80{x}^{4}$ | |

${C}_{48}$ | 43 | ${C}_{2}$ | $1922+3434x+2331{x}^{2}+710{x}^{3}+82{x}^{4}$ | |

${C}_{48}$ | 44 | ${C}_{1}$ | $1796+3032x+1910{x}^{2}+533{x}^{3}+53{x}^{4}$ | |

${C}_{48}$ | 45 | ${C}_{2}$ | $1861+3260x+2194{x}^{2}+678{x}^{3}+85{x}^{4}$ | |

${C}_{48}$ | 46 | ${C}_{2}$ | $1720+2852x+1746{x}^{2}+462{x}^{3}+46{x}^{4}$ | |

${C}_{48}$ | 47 | ${C}_{1}$ | $1830+3107x+1945{x}^{2}+530{x}^{3}+55{x}^{4}+{x}^{5}$ | |

${C}_{48}$ | 48 | ${C}_{1}$ | $1661+2636x+1457{x}^{2}+308{x}^{3}+17{x}^{4}$ | |

${C}_{48}$ | 49 | ${C}_{1}$ | $1723+2784x+1531{x}^{2}+325{x}^{3}+21{x}^{4}$ | |

${C}_{48}$ | 50 | ${C}_{1}$ | $1730+2783x+1554{x}^{2}+338{x}^{3}+19{x}^{4}$ | |

${C}_{48}$ | 51 | ${C}_{1}$ | $1776+3044x+2035{x}^{2}+689{x}^{3}+120{x}^{4}+8{x}^{5}$ | |

${C}_{48}$ | 52 | ${C}_{1}$ | $1719+2786x+1585{x}^{2}+363{x}^{3}+25{x}^{4}$ | |

${C}_{48}$ | 53 | ${C}_{1}$ | $1638+2578x+1435{x}^{2}+331{x}^{3}+27{x}^{4}$ | |

${C}_{48}$ |