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Residue characteristic $p$ Rel. degree $n$ Rel. ram. index $e$ Rel. res. field degree $f$ Rel. disc. exponent $c$
Base Base degree $n_0$ Base ram. index $e_0$ Base res. field degree $f_0$ Base disc. exponent $c_0$
Herbrand invariant Abs. degree $n_{\mathrm{abs}}$ Abs. ram. index $e_{\mathrm{abs}}$ Abs. res. field degree $f_{\mathrm{abs}}$ Abs. disc. exponent $c_{\mathrm{abs}}$
Mass Absolute mass Ambiguity Field count Wild segments
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Label $p$ $n$ $f$ $e$ $c$ Base Abs. Artin slopes Swan slopes Means Rams Generic poly Ambiguity Field count Mass
3.2.2.2a1.2-2.1.0a $3$ $2$ $2$ $1$ $0$ 3.2.2.2a1.2 $[\ ]$ $[ ]$ $\langle \rangle$ $( )$ $x$ $2$ $1$ $1$
3.2.2.2a1.2-1.2.1a $3$ $2$ $1$ $2$ $1$ 3.2.2.2a1.2 $[\ ]$ $[ ]$ $\langle \rangle$ $( )$ $x^2 + d_{0} \pi$ $2$ $2$ $1$
3.2.2.2a1.2-3.1.0a $3$ $3$ $3$ $1$ $0$ 3.2.2.2a1.2 $[\ ]$ $[ ]$ $\langle \rangle$ $( )$ $x$ $3$ $1$ $1$
3.2.2.2a1.2-1.3.3a $3$ $3$ $1$ $3$ $3$ 3.2.2.2a1.2 $[\frac{5}{4}]$ $[\frac{1}{2}]$ $\langle\frac{1}{3}\rangle$ $(\frac{1}{2})$ $x^3 + a_{1} \pi x + \pi$ $1$ $3$ $8$
3.2.2.2a1.2-1.3.4a $3$ $3$ $1$ $3$ $4$ 3.2.2.2a1.2 $[\frac{3}{2}]$ $[1]$ $\langle\frac{2}{3}\rangle$ $(1)$ $x^3 + a_{2} \pi x^2 + c_{3} \pi^2 + \pi$ $3$ $8$ $8$
3.2.2.2a1.2-1.3.6a $3$ $3$ $1$ $3$ $6$ 3.2.2.2a1.2 $[2]$ $[2]$ $\langle\frac{4}{3}\rangle$ $(2)$ $x^3 + b_{5} \pi^2 x^2 + a_{4} \pi^2 x + c_{6} \pi^3 + \pi$ $3$ $46$ $72$
3.2.2.2a1.2-1.3.7a $3$ $3$ $1$ $3$ $7$ 3.2.2.2a1.2 $[\frac{9}{4}]$ $[\frac{5}{2}]$ $\langle\frac{5}{3}\rangle$ $(\frac{5}{2})$ $x^3 + a_{5} \pi^2 x^2 + b_{7} \pi^3 x + \pi$ $1$ $21$ $72$
3.2.2.2a1.2-1.3.8a $3$ $3$ $1$ $3$ $8$ 3.2.2.2a1.2 $[\frac{5}{2}]$ $[3]$ $\langle2\rangle$ $(3)$ $x^3 + b_{8} \pi^3 x^2 + b_{7} \pi^3 x + c_{9} \pi^4 + \pi$ $3$ $72$ $81$
3.2.2.2a1.2-4.1.0a $3$ $4$ $4$ $1$ $0$ 3.2.2.2a1.2 $[\ ]$ $[ ]$ $\langle \rangle$ $( )$ $x$ $4$ $1$ $1$
3.2.2.2a1.2-2.2.2a $3$ $4$ $2$ $2$ $2$ 3.2.2.2a1.2 $[\ ]$ $[ ]$ $\langle \rangle$ $( )$ $x^2 + d_{0} \pi$ $4$ $2$ $1$
3.2.2.2a1.2-1.4.3a $3$ $4$ $1$ $4$ $3$ 3.2.2.2a1.2 $[\ ]$ $[ ]$ $\langle \rangle$ $( )$ $x^4 + d_{0} \pi$ $4$ $3$ $1$
3.2.2.2a1.2-5.1.0a $3$ $5$ $5$ $1$ $0$ 3.2.2.2a1.2 $[\ ]$ $[ ]$ $\langle \rangle$ $( )$ $x$ $5$ $1$ $1$
3.2.2.2a1.2-1.5.4a $3$ $5$ $1$ $5$ $4$ 3.2.2.2a1.2 $[\ ]$ $[ ]$ $\langle \rangle$ $( )$ $x^5 + \pi$ $1$ $1$ $1$
3.2.2.2a1.2-6.1.0a $3$ $6$ $6$ $1$ $0$ 3.2.2.2a1.2 $[\ ]$ $[ ]$ $\langle \rangle$ $( )$ $x$ $6$ $0$ $1$
3.2.2.2a1.2-3.2.3a $3$ $6$ $3$ $2$ $3$ 3.2.2.2a1.2 $[\ ]$ $[ ]$ $\langle \rangle$ $( )$ $x^2 + d_{0} \pi$ $6$ $0$ $1$
3.2.2.2a1.2-2.3.6a $3$ $6$ $2$ $3$ $6$ 3.2.2.2a1.2 $[\frac{5}{4}]$ $[\frac{1}{2}]$ $\langle\frac{1}{3}\rangle$ $(\frac{1}{2})$ $x^3 + a_{1} \pi x + \pi$ $2$ $0$ $80$
3.2.2.2a1.2-2.3.8a $3$ $6$ $2$ $3$ $8$ 3.2.2.2a1.2 $[\frac{3}{2}]$ $[1]$ $\langle\frac{2}{3}\rangle$ $(1)$ $x^3 + a_{2} \pi x^2 + c_{3} \pi^2 + \pi$ $6$ $0$ $80$
3.2.2.2a1.2-2.3.12a $3$ $6$ $2$ $3$ $12$ 3.2.2.2a1.2 $[2]$ $[2]$ $\langle\frac{4}{3}\rangle$ $(2)$ $x^3 + b_{5} \pi^2 x^2 + a_{4} \pi^2 x + c_{6} \pi^3 + \pi$ $6$ $0$ $6480$
3.2.2.2a1.2-2.3.14a $3$ $6$ $2$ $3$ $14$ 3.2.2.2a1.2 $[\frac{9}{4}]$ $[\frac{5}{2}]$ $\langle\frac{5}{3}\rangle$ $(\frac{5}{2})$ $x^3 + a_{5} \pi^2 x^2 + b_{7} \pi^3 x + \pi$ $2$ $0$ $6480$
3.2.2.2a1.2-2.3.16a $3$ $6$ $2$ $3$ $16$ 3.2.2.2a1.2 $[\frac{5}{2}]$ $[3]$ $\langle2\rangle$ $(3)$ $x^3 + b_{8} \pi^3 x^2 + b_{7} \pi^3 x + c_{9} \pi^4 + \pi$ $6$ $0$ $6561$
3.2.2.2a1.2-1.6.6a $3$ $6$ $1$ $6$ $6$ 3.2.2.2a1.2 $[\frac{9}{8}]$ $[\frac{1}{4}]$ $\langle\frac{1}{6}\rangle$ $(\frac{1}{2})$ $x^6 + a_{1} \pi x + d_{0} \pi$ $2$ $0$ $8$
3.2.2.2a1.2-1.6.7a $3$ $6$ $1$ $6$ $7$ 3.2.2.2a1.2 $[\frac{5}{4}]$ $[\frac{1}{2}]$ $\langle\frac{1}{3}\rangle$ $(1)$ $x^6 + c_{3} \pi x^3 + a_{2} \pi x^2 + d_{0} \pi$ $6$ $0$ $8$
3.2.2.2a1.2-1.6.9a $3$ $6$ $1$ $6$ $9$ 3.2.2.2a1.2 $[\frac{3}{2}]$ $[1]$ $\langle\frac{2}{3}\rangle$ $(2)$ $x^6 + b_{5} \pi x^5 + a_{4} \pi x^4 + c_{6} \pi^2 + d_{0} \pi$ $6$ $0$ $72$
3.2.2.2a1.2-1.6.10a $3$ $6$ $1$ $6$ $10$ 3.2.2.2a1.2 $[\frac{13}{8}]$ $[\frac{5}{4}]$ $\langle\frac{5}{6}\rangle$ $(\frac{5}{2})$ $x^6 + a_{5} \pi x^5 + b_{7} \pi^2 x + d_{0} \pi$ $2$ $0$ $72$
3.2.2.2a1.2-1.6.12a $3$ $6$ $1$ $6$ $12$ 3.2.2.2a1.2 $[\frac{15}{8}]$ $[\frac{7}{4}]$ $\langle\frac{7}{6}\rangle$ $(\frac{7}{2})$ $x^6 + b_{10} \pi^2 x^4 + b_{8} \pi^2 x^2 + a_{7} \pi^2 x + d_{0} \pi$ $2$ $0$ $648$
3.2.2.2a1.2-1.6.13a $3$ $6$ $1$ $6$ $13$ 3.2.2.2a1.2 $[2]$ $[2]$ $\langle\frac{4}{3}\rangle$ $(4)$ $x^6 + b_{11} \pi^2 x^5 + b_{10} \pi^2 x^4 + a_{8} \pi^2 x^2 + c_{12} \pi^3 + d_{0} \pi$ $6$ $0$ $648$
3.2.2.2a1.2-1.6.15a $3$ $6$ $1$ $6$ $15$ 3.2.2.2a1.2 $[\frac{9}{4}]$ $[\frac{5}{2}]$ $\langle\frac{5}{3}\rangle$ $(5)$ $x^6 + b_{11} \pi^2 x^5 + a_{10} \pi^2 x^4 + c_{15} \pi^3 x^3 + b_{14} \pi^3 x^2 + b_{13} \pi^3 x + d_{0} \pi$ $6$ $0$ $5832$
3.2.2.2a1.2-1.6.16a $3$ $6$ $1$ $6$ $16$ 3.2.2.2a1.2 $[\frac{19}{8}]$ $[\frac{11}{4}]$ $\langle\frac{11}{6}\rangle$ $(\frac{11}{2})$ $x^6 + a_{11} \pi^2 x^5 + b_{16} \pi^3 x^4 + b_{14} \pi^3 x^2 + b_{13} \pi^3 x + d_{0} \pi$ $2$ $0$ $5832$
3.2.2.2a1.2-1.6.17a $3$ $6$ $1$ $6$ $17$ 3.2.2.2a1.2 $[\frac{5}{2}]$ $[3]$ $\langle2\rangle$ $(6)$ $x^6 + b_{17} \pi^3 x^5 + b_{16} \pi^3 x^4 + b_{14} \pi^3 x^2 + b_{13} \pi^3 x + c_{18} \pi^4 + d_{0} \pi$ $6$ $0$ $6561$
3.2.2.2a1.2-7.1.0a $3$ $7$ $7$ $1$ $0$ 3.2.2.2a1.2 $[\ ]$ $[ ]$ $\langle \rangle$ $( )$ $x$ $7$ $0$ $1$
3.2.2.2a1.2-1.7.6a $3$ $7$ $1$ $7$ $6$ 3.2.2.2a1.2 $[\ ]$ $[ ]$ $\langle \rangle$ $( )$ $x^7 + \pi$ $1$ $0$ $1$
3.2.2.2a1.2-8.1.0a $3$ $8$ $8$ $1$ $0$ 3.2.2.2a1.2 $[\ ]$ $[ ]$ $\langle \rangle$ $( )$ $x$ $8$ $0$ $1$
3.2.2.2a1.2-4.2.4a $3$ $8$ $4$ $2$ $4$ 3.2.2.2a1.2 $[\ ]$ $[ ]$ $\langle \rangle$ $( )$ $x^2 + d_{0} \pi$ $8$ $0$ $1$
3.2.2.2a1.2-2.4.6a $3$ $8$ $2$ $4$ $6$ 3.2.2.2a1.2 $[\ ]$ $[ ]$ $\langle \rangle$ $( )$ $x^4 + d_{0} \pi$ $8$ $0$ $1$
3.2.2.2a1.2-1.8.7a $3$ $8$ $1$ $8$ $7$ 3.2.2.2a1.2 $[\ ]$ $[ ]$ $\langle \rangle$ $( )$ $x^8 + d_{0} \pi$ $8$ $0$ $1$
3.2.2.2a1.2-9.1.0a $3$ $9$ $9$ $1$ $0$ 3.2.2.2a1.2 $[\ ]$ $[ ]$ $\langle \rangle$ $( )$ $x$ $9$ $0$ $1$
3.2.2.2a1.2-3.3.9a $3$ $9$ $3$ $3$ $9$ 3.2.2.2a1.2 $[\frac{5}{4}]$ $[\frac{1}{2}]$ $\langle\frac{1}{3}\rangle$ $(\frac{1}{2})$ $x^3 + a_{1} \pi x + \pi$ $3$ $0$ $728$
3.2.2.2a1.2-3.3.12a $3$ $9$ $3$ $3$ $12$ 3.2.2.2a1.2 $[\frac{3}{2}]$ $[1]$ $\langle\frac{2}{3}\rangle$ $(1)$ $x^3 + a_{2} \pi x^2 + c_{3} \pi^2 + \pi$ $9$ $0$ $728$
3.2.2.2a1.2-3.3.18a $3$ $9$ $3$ $3$ $18$ 3.2.2.2a1.2 $[2]$ $[2]$ $\langle\frac{4}{3}\rangle$ $(2)$ $x^3 + b_{5} \pi^2 x^2 + a_{4} \pi^2 x + c_{6} \pi^3 + \pi$ $9$ $0$ $530712$
3.2.2.2a1.2-3.3.21a $3$ $9$ $3$ $3$ $21$ 3.2.2.2a1.2 $[\frac{9}{4}]$ $[\frac{5}{2}]$ $\langle\frac{5}{3}\rangle$ $(\frac{5}{2})$ $x^3 + a_{5} \pi^2 x^2 + b_{7} \pi^3 x + \pi$ $3$ $0$ $530712$
3.2.2.2a1.2-3.3.24a $3$ $9$ $3$ $3$ $24$ 3.2.2.2a1.2 $[\frac{5}{2}]$ $[3]$ $\langle2\rangle$ $(3)$ $x^3 + b_{8} \pi^3 x^2 + b_{7} \pi^3 x + c_{9} \pi^4 + \pi$ $9$ $0$ $531441$
3.2.2.2a1.2-1.9.9a $3$ $9$ $1$ $9$ $9$ 3.2.2.2a1.2 $[\frac{17}{16}, \frac{17}{16}]$ $[\frac{1}{8}, \frac{1}{8}]$ $\langle\frac{1}{12}, \frac{1}{9}\rangle$ $(\frac{1}{8}, \frac{1}{8})$ $x^9 + a_{1} \pi x + \pi$ $1$ $0$ $8$
3.2.2.2a1.2-1.9.10a $3$ $9$ $1$ $9$ $10$ 3.2.2.2a1.2 $[\frac{9}{8}, \frac{9}{8}]$ $[\frac{1}{4}, \frac{1}{4}]$ $\langle\frac{1}{6}, \frac{2}{9}\rangle$ $(\frac{1}{4}, \frac{1}{4})$ $x^9 + a_{2} \pi x^2 + \pi$ $1$ $0$ $8$
3.2.2.2a1.2-1.9.12a $3$ $9$ $1$ $9$ $12$ 3.2.2.2a1.2 $[\frac{5}{4}, \frac{5}{4}]$ $[\frac{1}{2}, \frac{1}{2}]$ $\langle\frac{1}{3}, \frac{4}{9}\rangle$ $(\frac{1}{2}, \frac{1}{2})$ $x^9 + a_{4} \pi x^4 + b_{3} \pi x^3 + \pi$ $1$ $0$ $72$
3.2.2.2a1.2-1.9.13a $3$ $9$ $1$ $9$ $13$ 3.2.2.2a1.2 $[\frac{21}{16}, \frac{21}{16}]$ $[\frac{5}{8}, \frac{5}{8}]$ $\langle\frac{5}{12}, \frac{5}{9}\rangle$ $(\frac{5}{8}, \frac{5}{8})$ $x^9 + a_{5} \pi x^5 + \pi$ $1$ $0$ $8$
3.2.2.2a1.2-1.9.13b $3$ $9$ $1$ $9$ $13$ 3.2.2.2a1.2 $[\frac{5}{4}, \frac{4}{3}]$ $[\frac{1}{2}, \frac{2}{3}]$ $\langle\frac{1}{3}, \frac{5}{9}\rangle$ $(\frac{1}{2}, 1)$ $x^9 + c_{6} \pi x^6 + a_{5} \pi x^5 + a_{3} \pi x^3 + \pi$ $3$ $0$ $64$
3.2.2.2a1.2-1.9.15a $3$ $9$ $1$ $9$ $15$ 3.2.2.2a1.2 $[\frac{23}{16}, \frac{23}{16}]$ $[\frac{7}{8}, \frac{7}{8}]$ $\langle\frac{7}{12}, \frac{7}{9}\rangle$ $(\frac{7}{8}, \frac{7}{8})$ $x^9 + a_{7} \pi x^7 + b_{6} \pi x^6 + \pi$ $1$ $0$ $72$
3.2.2.2a1.2-1.9.15b $3$ $9$ $1$ $9$ $15$ 3.2.2.2a1.2 $[\frac{5}{4}, \frac{3}{2}]$ $[\frac{1}{2}, 1]$ $\langle\frac{1}{3}, \frac{7}{9}\rangle$ $(\frac{1}{2}, 2)$ $x^9 + b_{8} \pi x^8 + a_{7} \pi x^7 + a_{3} \pi x^3 + c_{9} \pi^2 + \pi$ $3$ $0$ $576$
3.2.2.2a1.2-1.9.16a $3$ $9$ $1$ $9$ $16$ 3.2.2.2a1.2 $[\frac{3}{2}, \frac{3}{2}]$ $[1, 1]$ $\langle\frac{2}{3}, \frac{8}{9}\rangle$ $(1, 1)$ $x^9 + a_{8} \pi x^8 + b_{6} \pi x^6 + c_{9} \pi^2 + \pi$ $9$ $0$ $72$
3.2.2.2a1.2-1.9.16b $3$ $9$ $1$ $9$ $16$ 3.2.2.2a1.2 $[\frac{5}{4}, \frac{19}{12}]$ $[\frac{1}{2}, \frac{7}{6}]$ $\langle\frac{1}{3}, \frac{8}{9}\rangle$ $(\frac{1}{2}, \frac{5}{2})$ $x^9 + a_{8} \pi x^8 + a_{3} \pi x^3 + b_{10} \pi^2 x + \pi$ $1$ $0$ $576$
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