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\begin{document}
Let $n$ be a natural number larger than one,
$r_1$, $r_2$ nonnnegative integer with $r_1+2r_2=n$, and
$G$ a transitive permutation group on $n$ letters.
We denote by $N_{(r_1,r_2)}(G,X)$
the number of the isomorphism classes of number fields of signature $(r_1,r_2)$
and discriminant not exceeding $X$ in absolute value
whose normal closure has Galois group isomorphic to $G$.
We tabulate known values of $N_{(r_1,r_2)}(G,X)$ for small $n$ and $X$.

\begin{center}
\begin{tabular}{|r|r|r|}
\hline
$X$ & $N_{(2,0)}(C_2,X)$ & $N_{(0,1)}(C_2,X)$ \cr
\hline
$10^1$ & $2$ & $4$ \cr
$10^2$ & $30$ & $31$ \cr
$10^3$ & $302$ & $305$ \cr
$10^4$ & $3043$ & $3043$ \cr
$10^5$ & $30394$ & $30392$ \cr
$10^6$ & $303957$ & $303968$ \cr
$10^7$ & $3039653$ & $3039632$ \cr
$10^8$ & $30396324$ & $30396385$ \cr
$10^9$ & $303963559$ & $303963510$ \cr
$10^{10}$ & $3039635379$ & $3039635443$ \cr
$10^{11}$ & $30396355148$ & $30396355052$ \cr
$10^{12}$ & $303963551039$ & $303963550712$ \cr
$10^{13}$ & $3039635509103$ & $3039635509360$ \cr
$10^{14}$ & $30396355093462$ & $30396355092880$ \cr
$10^{15}$ & $303963550926173$ & $303963550926479$ \cr
$10^{16}$ & $3039635509271389$ & $3039635509273025$ \cr
$10^{17}$ & $30396355092697223$ & $30396355092696593$ \cr
$10^{18}$ & $303963550927008744$ & $303963550927017751$ \cr
$10^{19}$ & $3039635509270131961$ & $3039635509270110507$ \cr
$10^{20}$ & $30396355092701313737$ & $30396355092701291066$ \cr
$10^{21}$ & $303963550927013401272$ & $303963550927013312649$ \cr
$10^{22}$ & $3039635509270133130535$ & $3039635509270133092175$ \cr
$10^{23}$ & $30396355092701331456323$ & $30396355092701331531457$ \cr
$10^{24}$ & $303963550927013314010676$ & $303963550927013314554179$ \cr
$10^{25}$ & $3039635509270133143448215$ & $3039635509270133143069580$ \cr
\hline
\end{tabular}
\end{center}

\begin{center}
\begin{tabular}{|r|r||r|r||r|r|}
\hline
$X$ & $N_{(3,0)}(C_3,X)$ & $X$ & $N_{(3,0)}(C_3,X)$ & $X$ & $N_{(3,0)}(C_3,X)$ \cr
\hline
$10^1$ & $0$ & $10^{14}$ & $1585249$ & $10^{27}$ & $5013103697105$ \cr
$10^2$ & $2$ & $10^{15}$ & $5013206$ & $10^{28}$ & $15852825840369$ \cr
$10^3$ & $5$ & $10^{16}$ & $15852618$ & $10^{29}$ & $50131036986701$ \cr
$10^4$ & $16$ & $10^{17}$ & $50131008$ & $10^{30}$ & $158528258396671$ \cr
$10^5$ & $51$ & $10^{18}$ & $158528150$ & $10^{31}$ & $501310370020343$ \cr
$10^6$ & $159$ & $10^{19}$ & $501309943$ & $10^{32}$ & $1585282583932681$ \cr
$10^7$ & $501$ & $10^{20}$ & $1585282684$ & $10^{33}$ & $5013103700345884$ \cr
$10^8$ & $1592$ & $10^{21}$ & $5013103291$ & $10^{34}$ & $15852825839615504$ \cr
$10^9$ & $5008$ & $10^{22}$ & $15852826251$ & $10^{35}$ & $50131037003076114$ \cr
$10^{10}$ & $15851$ & $10^{23}$ & $50131036382$ & $10^{36}$ & $158528258396205064$ \cr
$10^{11}$ & $50152$ & $10^{24}$ & $158528255967$ & $10^{37}$ & $501310370031289126$ \cr
$10^{12}$ & $158542$ & $10^{25}$ & $501310368157$ &  &  \cr
$10^{13}$ & $501306$ & $10^{26}$ & $1585282578080$ &  &  \cr
\hline
\end{tabular}
\end{center}

\begin{center}
\begin{tabular}{|r|r|r|}
\hline
$X$ & $N_{(3,0)}(S_3,X)$ & $N_{(1,1)}(S_3,X)$ \cr
\hline
$10^1$ & $0$ & $0$ \cr
$10^2$ & $0$ & $7$ \cr
$10^3$ & $22$ & $127$ \cr
$10^4$ & $366$ & $1520$ \cr
$10^5$ & $4753$ & $17041$ \cr
$10^6$ & $54441$ & $182417$ \cr
$10^7$ & $592421$ & $1905514$ \cr
$10^8$ & $6246698$ & $19609185$ \cr
$10^9$ & $64654353$ & $199884780$ \cr
$10^{10}$ & $661432230$ & $2024660098$ \cr
$10^{11}$ & $6715773873$ & $20422230540$ \cr
\hline
\end{tabular}
\end{center}

\begin{center}
\begin{tabular}{|r|r|r|}
\hline
$X$ & $N_{(4,0)}(C_4,X)$ & $N_{(0,2)}(C_4,X)$ \cr
\hline
$10^1$ & $0$ & $0$ \cr
$10^2$ & $0$ & $0$ \cr
$10^3$ & $0$ & $1$ \cr
$10^4$ & $6$ & $4$ \cr
$10^5$ & $15$ & $17$ \cr
$10^6$ & $59$ & $54$ \cr
$10^7$ & $182$ & $181$ \cr
$10^8$ & $586$ & $582$ \cr
$10^9$ & $1867$ & $1865$ \cr
$10^{10}$ & $5966$ & $5964$ \cr
$10^{11}$ & $19017$ & $19028$ \cr
$10^{12}$ & $60456$ & $60469$ \cr
$10^{13}$ & $191736$ & $191764$ \cr
$10^{14}$ & $607589$ & $607609$ \cr
$10^{15}$ & $1924160$ & $1924059$ \cr
$10^{16}$ & $6090130$ & $6090110$ \cr
$10^{17}$ & $19271385$ & $19271321$ \cr
$10^{18}$ & $60968525$ & $60968399$ \cr
$10^{19}$ & $192857593$ & $192857870$ \cr
$10^{20}$ & $609994937$ & $609994964$ \cr
$10^{21}$ & $1929244391$ & $1929243674$ \cr
$10^{22}$ & $6101387381$ & $6101387860$ \cr
$10^{23}$ & $19295537531$ & $19295537010$ \cr
$10^{24}$ & $61020552533$ & $61020552938$ \cr
$10^{25}$ & $192969762398$ & $192969758223$ \cr
$10^{26}$ & $610236520653$ & $610236519548$ \cr
$10^{27}$ & $1929764373961$ & $1929764373161$ \cr
$10^{28}$ & $6102509058257$ & $6102509054460$ \cr
$10^{29}$ & $19297953643936$ & $19297953644691$ \cr
$10^{30}$ & $61025758244048$ & $61025758248309$ \cr
$10^{31}$ & $192980974911603$ & $192980974923193$ \cr
$10^{32}$ & $610260681684841$ & $610260681669563$ \cr
\hline
\end{tabular}
\end{center}

\begin{center}
\begin{tabular}{|r|r|r|}
\hline
$X$ & $N_{(4,0)}(V_4,X)$ & $N_{(0,2)}(V_4,X)$ \cr
\hline
$10^1$ & $0$ & $0$ \cr
$10^2$ & $0$ & $0$ \cr
$10^3$ & $0$ & $8$ \cr
$10^4$ & $6$ & $41$ \cr
$10^5$ & $42$ & $201$ \cr
$10^6$ & $196$ & $818$ \cr
$10^7$ & $876$ & $3331$ \cr
$10^8$ & $3603$ & $13076$ \cr
$10^9$ & $14249$ & $50067$ \cr
$10^{10}$ & $54940$ & $187770$ \cr
$10^{11}$ & $207295$ & $694262$ \cr
$10^{12}$ & $769284$ & $2536801$ \cr
$10^{13}$ & $2814497$ & $9167570$ \cr
$10^{14}$ & $10181802$ & $32835581$ \cr
$10^{15}$ & $36478693$ & $116677591$ \cr
$10^{16}$ & $129620531$ & $411762457$ \cr
$10^{17}$ & $457321963$ & $1444383361$ \cr
$10^{18}$ & $1603453447$ & $5039360330$ \cr
$10^{19}$ & $5590953378$ & $17497040934$ \cr
$10^{20}$ & $19398735478$ & $60486267277$ \cr
$10^{21}$ & $67009600870$ & $208270612830$ \cr
$10^{22}$ & $230548142363$ & $714545063480$ \cr
$10^{23}$ & $790326082314$ & $2443396436299$ \cr
$10^{24}$ & $2700275901104$ & $8329834172525$ \cr
$10^{25}$ & $9197857451663$ & $28317754338743$ \cr
$10^{26}$ & $31242564815515$ & $96017758881843$ \cr
$10^{27}$ & $105847491463943$ & $324784293743259$ \cr
$10^{28}$ & $357742322840950$ & $1096127612328756$ \cr
$10^{29}$ & $1206393568766650$ & $3691598900680670$ \cr
$10^{30}$ & $4059776186016270$ & $12408334995379417$ \cr
$10^{31}$ & $13635417115241023$ & $41630433288940969$ \cr
$10^{32}$ & $45713153519958996$ & $139429524939542248$ \cr
$10^{33}$ & $152991934395591362$ & $466217622608203817$ \cr
$10^{34}$ & $511204072681788782$ & $1556512861826445892$ \cr
$10^{35}$ & $1705526466144745140$ & $5188997592667511054$ \cr
$10^{36}$ & $5681952310883424255$ & $17274863370464181629$ \cr
\hline
\end{tabular}
\end{center}

\begin{center}
\begin{tabular}{|r|r|r|r|}
\hline
$X$ & $N_{(4,0)}(D_4,X)$ & $N_{(2,1)}(D_4,X)$ & $N_{(0,2)}(D_4,X)$ \cr
\hline
$10^1$ & $0$ & $0$ & $0$ \cr
$10^2$ & $0$ & $0$ & $0$ \cr
$10^3$ & $1$ & $68$ & $17$ \cr
$10^4$ & $25$ & $93$ & $295$ \cr
$10^5$ & $379$ & $968$ & $3417$ \cr
$10^6$ & $4468$ & $9772$ & $36238$ \cr
$10^7$ & $47562$ & $98413$ & $370424$ \cr
$10^8$ & $486314$ & $984708$ & $3734826$ \cr
$10^9$ & $4903607$ & $9852244$ & $37469573$ \cr
$10^{10}$ & $49188349$ & $98546786$ & $375154025$ \cr
$10^{11}$ & $492454432$ & $985536549$ & $3753258277$ \cr
$10^{12}$ & $4926654580$ & $9855572218$ & $37538880690$ \cr
$10^{13}$ & $49274156836$ & $98556488881$ & $375411901218$ \cr
$10^{14}$ & $492769145545$ & $985567509497$ & $375411901218$ \cr
$10^{15}$ & $4927790007755$ & $9855683662056$ & $37542317217650$ \cr
$10^{16}$ & $49278249627160$ & $98556864596086$ & $375424223055946$ \cr
$10^{17}$ & $492783730187748$ & $985568739794773$ & $3754245940051259$ \cr
\hline
\end{tabular}
\end{center}

\begin{center}
\begin{tabular}{|r|r|r|}
\hline
$X$ & $N_{(4,0)}(A_4,X)$ & $N_{(0,2)}(A_4,X)$ \cr
\hline
$10^1$ & $0$ & $0$ \cr
$10^2$ & $0$ & $0$ \cr
$10^3$ & $0$ & $0$ \cr
$10^4$ & $0$ & $4$ \cr
$10^5$ & $4$ & $23$ \cr
$10^6$ & $31$ & $90$ \cr
$10^7$ & $129$ & $385$ \cr
$10^8$ & $527$ & $1483$ \cr
$10^9$ & $2037$ & $5662$ \cr
$10^{10}$ & $7662$ & $21097$ \cr
$10^{11}$ & $28182$ & $76584$ \cr
$10^{12}$ & $100576$ & $273894$ \cr
$10^{13}$ & $354302$ & $965304$ \cr
\hline
\end{tabular}
\end{center}

\begin{center}
\begin{tabular}{|r|r|r|r|}
\hline
$X$ & $N_{(4,0)}(S_4,X)$ & $N_{(2,1)}(S_4,X)$ & $N_{(0,2)}(S_4,X)$ \cr
\hline
$10^1$ & $0$ & $0$ & $0$ \cr
$10^2$ & $0$ & $0$ & $0$ \cr
$10^3$ & $0$ & $10$ & $8$ \cr
$10^4$ & $13$ & $351$ & $206$ \cr
$10^5$ & $449$ & $5916$ & $3374$ \cr
$10^6$ & $8301$ & $80899$ & $44122$ \cr
$10^7$ & $120622$ & $989587$ & $525099$ \cr
\hline
\end{tabular}
\end{center}

\end{document}

