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We prove that for any generic polynomial $f$ in two variables of degree$(d_1,d_2)$ over the rationals, for $p$ large enough the Newton slopes of thecharacter power series $C_f^*(\chi_m,s)$ of $f$ at $p$ is independent of thechoice of the character $\chi_m$ (of conductor $p^m$); and the Newton slopes ofthe $L$-function $L_f^*(\chi_m,s)$ of $f$ at $p$ is in weighted arithmeticprogression.

Generic Newton Slopes for Artin-Schreier-Witt Tower in two variables