\begingroup\footnotesize\setlength{\tabcolsep}{4pt}\setlength{\abovetopsep}{4pt}
\begin{longtable}{@{}r r r r >{\raggedright\arraybackslash}p{0.38\textwidth} >{\raggedright\arraybackslash}p{0.30\textwidth}@{}}
\caption{The primes $\qQ_1,\dots,\qQ_m$ of $\Lt$ above the auxiliary primes $q$, in the order used for $\Mq$ and $\Iq$.  The prime $\qq_k=\qQ_k\cap\Lo$ is $(q,h_k(a))$, and $k(\qq_k)=\Fq q[x]/(h_k)$ with $a\mapsto x$.  The last column gives the residue of $b$: either $b\equiv r(a)\pmod{\qQ_k}$ with $r\in\Fq q[x]$ (then $f(\qQ_k)=\deg h_k$); or ``cubic'', when $\psi$ is irreducible over $k(\qq_k)$ and $\qQ_k=\qq_k\mathcal O_{\Lt}$; or ``quadratic'', when $\psi$ has one root in $k(\qq_k)$ and $\qQ_k$ is the prime above $\qq_k$ at which $b$ reduces to a root of the quadratic factor.  The column $\zeta_q$ gives the fifth root of unity of \eqref{eq:symbol}.}\label{tab:primesq}\\
\toprule $q$ & $\zeta_q$ & $k$ & $f(\qQ_k)$ & $h_k$ & residue of $b$\\\midrule\endfirsthead
\toprule $q$ & $\zeta_q$ & $k$ & $f(\qQ_k)$ & $h_k$ & residue of $b$\\\midrule\endhead
\bottomrule\endfoot
$11$ & $4$ & $1$ & $3$ & $x+7$ & cubic\\
 &  & $2$ & $3$ & $x+6$ & cubic\\
 &  & $3$ & $6$ & $x^{2}+3x+9$ & cubic\\
 &  & $4$ & $12$ & $x^{4}+10x^{3}+8x^{2}+2x+7$ & cubic\\
\addlinespace[3pt]
$101$ & $95$ & $1$ & $2$ & $x^{2}+46x+64$ & $b\equiv 70a+3$\\
 &  & $2$ & $2$ & $x^{2}+46x+64$ & $b\equiv 62$\\
 &  & $3$ & $2$ & $x^{2}+46x+64$ & $b\equiv 31a+15$\\
 &  & $4$ & $3$ & $x^{3}+54x^{2}+85x+97$ & $b\equiv 62$\\
 &  & $5$ & $3$ & $x^{3}+5x^{2}+71x+81$ & $b\equiv 62$\\
 &  & $6$ & $6$ & $x^{3}+5x^{2}+71x+81$ & quadratic\\
 &  & $7$ & $6$ & $x^{3}+54x^{2}+85x+97$ & quadratic\\
\addlinespace[3pt]
$131$ & $53$ & $1$ & $2$ & $x^{2}+23x+77$ & $b\equiv 56a+62$\\
 &  & $2$ & $2$ & $x^{2}+41x+41$ & $b\equiv 126a+36$\\
 &  & $3$ & $2$ & $x^{2}+23x+77$ & $b\equiv 75a+84$\\
 &  & $4$ & $2$ & $x^{2}+41x+41$ & $b\equiv 5a+110$\\
 &  & $5$ & $2$ & $x^{2}+23x+77$ & $b\equiv 89$\\
 &  & $6$ & $2$ & $x^{2}+41x+41$ & $b\equiv 89$\\
 &  & $7$ & $4$ & $x^{4}+71x^{3}+49x+99$ & $b\equiv 89$\\
 &  & $8$ & $4$ & $x^{4}+71x^{3}+49x+99$ & $b\equiv 31a^{3}+41a^{2}+96a+27$\\
 &  & $9$ & $4$ & $x^{4}+71x^{3}+49x+99$ & $b\equiv 100a^{3}+90a^{2}+35a+119$\\
\addlinespace[3pt]
$181$ & $59$ & $1$ & $1$ & $x+95$ & $b\equiv 141$\\
 &  & $2$ & $1$ & $x+69$ & $b\equiv 141$\\
 &  & $3$ & $1$ & $x+66$ & $b\equiv 141$\\
 &  & $4$ & $2$ & $x+95$ & quadratic\\
 &  & $5$ & $2$ & $x^{2}+177x+168$ & $b\equiv 142a+170$\\
 &  & $6$ & $2$ & $x^{2}+177x+168$ & $b\equiv 141$\\
 &  & $7$ & $2$ & $x+69$ & quadratic\\
 &  & $8$ & $2$ & $x+66$ & quadratic\\
 &  & $9$ & $2$ & $x^{2}+177x+168$ & $b\equiv 39a+14$\\
 &  & $10$ & $3$ & $x^{3}+140x^{2}+32x+148$ & $b\equiv 141$\\
 &  & $11$ & $6$ & $x^{3}+140x^{2}+32x+148$ & quadratic\\
\addlinespace[3pt]
$211$ & $107$ & $1$ & $6$ & $x^{6}+175x^{5}+47x^{4}+39x^{3}+188x^{2}+151x+31$ & $b\equiv 52a^{5}+158a^{4}+69a^{3}+54a^{2}+187a+135$\\
 &  & $2$ & $6$ & $x^{2}+40x+99$ & cubic\\
 &  & $3$ & $6$ & $x^{6}+175x^{5}+47x^{4}+39x^{3}+188x^{2}+151x+31$ & $b\equiv 125a^{5}+174a^{4}+149a^{3}+76a^{2}+90a+94$\\
 &  & $4$ & $6$ & $x^{6}+175x^{5}+47x^{4}+39x^{3}+188x^{2}+151x+31$ & $b\equiv 34a^{5}+90a^{4}+204a^{3}+81a^{2}+145a+150$\\
\addlinespace[3pt]
$251$ & $219$ & $1$ & $2$ & $x^{2}+121x+50$ & $b\equiv 196a+171$\\
 &  & $2$ & $2$ & $x^{2}+121x+50$ & $b\equiv 231$\\
 &  & $3$ & $2$ & $x^{2}+144x+228$ & $b\equiv 76a+60$\\
 &  & $4$ & $2$ & $x^{2}+121x+50$ & $b\equiv 55a+49$\\
 &  & $5$ & $2$ & $x^{2}+144x+228$ & $b\equiv 175a+160$\\
 &  & $6$ & $2$ & $x^{2}+144x+228$ & $b\equiv 231$\\
 &  & $7$ & $4$ & $x^{4}+241x^{3}+231x^{2}+27x+3$ & $b\equiv 28a^{3}+6a^{2}+242a+208$\\
 &  & $8$ & $4$ & $x^{4}+241x^{3}+231x^{2}+27x+3$ & $b\equiv 231$\\
 &  & $9$ & $4$ & $x^{4}+241x^{3}+231x^{2}+27x+3$ & $b\equiv 223a^{3}+245a^{2}+9a+12$\\
\addlinespace[3pt]
$271$ & $10$ & $1$ & $8$ & $x^{8}+4x^{7}+243x^{6}+103x^{5}+131x^{4}+18x^{3}+27x^{2}+62x+144$ & $b\equiv 46a^{7}+135a^{6}+61a^{5}+203a^{4}+261a^{3}+251a^{2}+166a+196$\\
 &  & $2$ & $8$ & $x^{8}+4x^{7}+243x^{6}+103x^{5}+131x^{4}+18x^{3}+27x^{2}+62x+144$ & $b\equiv 57$\\
 &  & $3$ & $8$ & $x^{8}+4x^{7}+243x^{6}+103x^{5}+131x^{4}+18x^{3}+27x^{2}+62x+144$ & $b\equiv 225a^{7}+136a^{6}+210a^{5}+68a^{4}+10a^{3}+20a^{2}+105a+234$\\
\addlinespace[3pt]
$311$ & $36$ & $1$ & $1$ & $x+301$ & $b\equiv 160$\\
 &  & $2$ & $1$ & $x+122$ & $b\equiv 160$\\
 &  & $3$ & $1$ & $x+249$ & $b\equiv 160$\\
 &  & $4$ & $1$ & $x+44$ & $b\equiv 160$\\
 &  & $5$ & $2$ & $x+249$ & quadratic\\
 &  & $6$ & $2$ & $x+122$ & quadratic\\
 &  & $7$ & $2$ & $x+44$ & quadratic\\
 &  & $8$ & $2$ & $x+301$ & quadratic\\
 &  & $9$ & $4$ & $x^{4}+221x^{3}+90x^{2}+50x+25$ & $b\equiv 206a^{3}+232a^{2}+166a+73$\\
 &  & $10$ & $4$ & $x^{4}+221x^{3}+90x^{2}+50x+25$ & $b\equiv 105a^{3}+79a^{2}+145a+15$\\
 &  & $11$ & $4$ & $x^{4}+221x^{3}+90x^{2}+50x+25$ & $b\equiv 160$\\
\addlinespace[3pt]
$331$ & $64$ & $1$ & $4$ & $x^{4}+253x^{3}+279x^{2}+96x+39$ & $b\equiv 258$\\
 &  & $2$ & $4$ & $x^{4}+253x^{3}+279x^{2}+96x+39$ & $b\equiv 25$\\
 &  & $3$ & $4$ & $x^{4}+82x^{3}+131x^{2}+316x+239$ & $b\equiv 312$\\
 &  & $4$ & $4$ & $x^{4}+82x^{3}+131x^{2}+316x+239$ & $b\equiv 25$\\
 &  & $5$ & $4$ & $x^{4}+82x^{3}+131x^{2}+316x+239$ & $b\equiv 258$\\
 &  & $6$ & $4$ & $x^{4}+253x^{3}+279x^{2}+96x+39$ & $b\equiv 312$\\
\addlinespace[3pt]
$401$ & $72$ & $1$ & $3$ & $x+276$ & cubic\\
 &  & $2$ & $21$ & $x^{7}+129x^{6}+57x^{5}+140x^{4}+117x^{3}+348x^{2}+230x+200$ & cubic\\
\addlinespace[3pt]
$431$ & $95$ & $1$ & $3$ & $x+154$ & cubic\\
 &  & $2$ & $21$ & $x^{7}+281x^{6}+229x^{5}+339x^{4}+236x^{3}+420x^{2}+379x+201$ & cubic\\
\addlinespace[3pt]
$461$ & $88$ & $1$ & $1$ & $x+122$ & $b\equiv 367$\\
 &  & $2$ & $2$ & $x+122$ & quadratic\\
 &  & $3$ & $3$ & $x^{3}+354x^{2}+309x+22$ & $b\equiv 367$\\
 &  & $4$ & $4$ & $x^{4}+450x^{3}+435x^{2}+253x+405$ & $b\equiv 97a^{3}+253a^{2}+241a+279$\\
 &  & $5$ & $4$ & $x^{4}+450x^{3}+435x^{2}+253x+405$ & $b\equiv 367$\\
 &  & $6$ & $4$ & $x^{4}+450x^{3}+435x^{2}+253x+405$ & $b\equiv 364a^{3}+208a^{2}+220a+183$\\
 &  & $7$ & $6$ & $x^{3}+354x^{2}+309x+22$ & quadratic\\
\addlinespace[3pt]
$541$ & $48$ & $1$ & $3$ & $x+52$ & cubic\\
 &  & $2$ & $21$ & $x^{7}+493x^{6}+304x^{5}+254x^{4}+177x^{3}+12x^{2}+216x+190$ & cubic\\
\addlinespace[3pt]
$601$ & $423$ & $1$ & $1$ & $x+350$ & $b\equiv 127$\\
 &  & $2$ & $1$ & $x+545$ & $b\equiv 127$\\
 &  & $3$ & $2$ & $x+545$ & quadratic\\
 &  & $4$ & $2$ & $x+350$ & quadratic\\
 &  & $5$ & $6$ & $x^{6}+311x^{5}+258x^{4}+565x^{3}+213x^{2}+416x+192$ & $b\equiv 127$\\
 &  & $6$ & $6$ & $x^{6}+311x^{5}+258x^{4}+565x^{3}+213x^{2}+416x+192$ & $b\equiv 85a^{5}+502a^{4}+469a^{3}+269a^{2}+185a+169$\\
 &  & $7$ & $6$ & $x^{6}+311x^{5}+258x^{4}+565x^{3}+213x^{2}+416x+192$ & $b\equiv 516a^{5}+99a^{4}+132a^{3}+332a^{2}+416a+184$\\
\addlinespace[3pt]
$631$ & $242$ & $1$ & $3$ & $x^{3}+152x^{2}+58x+174$ & $b\equiv 124a^{2}+330a+387$\\
 &  & $2$ & $3$ & $x^{3}+152x^{2}+58x+174$ & $b\equiv 47a^{2}+442a+423$\\
 &  & $3$ & $3$ & $x^{3}+152x^{2}+58x+174$ & $b\equiv 460a^{2}+490a+325$\\
 &  & $4$ & $3$ & $x+494$ & cubic\\
 &  & $5$ & $6$ & $x^{2}+325x+318$ & cubic\\
 &  & $6$ & $6$ & $x^{2}+295x+430$ & cubic\\
\addlinespace[3pt]
$661$ & $247$ & $1$ & $2$ & $x^{2}+300x+466$ & $b\equiv 657$\\
 &  & $2$ & $2$ & $x^{2}+300x+466$ & $b\equiv 129a+447$\\
 &  & $3$ & $2$ & $x^{2}+300x+466$ & $b\equiv 532a+85$\\
 &  & $4$ & $3$ & $x^{3}+493x^{2}+437x+378$ & $b\equiv 657$\\
 &  & $5$ & $3$ & $x^{3}+533x^{2}+265x+305$ & $b\equiv 657$\\
 &  & $6$ & $6$ & $x^{3}+533x^{2}+265x+305$ & quadratic\\
 &  & $7$ & $6$ & $x^{3}+493x^{2}+437x+378$ & quadratic\\
\addlinespace[3pt]
\end{longtable}\endgroup