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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
23.1.b.a 23.b 23.b $1$ $0.011$ \(\Q\) \(\Q(\sqrt{-23}) \) None \(-1\) \(-1\) \(0\) \(0\) \(q-q^{2}-q^{3}+q^{6}+q^{8}-q^{13}-q^{16}+\cdots\)
23.2.a.a 23.a 1.a $2$ $0.184$ \(\Q(\sqrt{5}) \) None None \(-1\) \(0\) \(-2\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+(-1+2\beta )q^{3}+(-1+\beta )q^{4}+\cdots\)
23.2.c.a 23.c 23.c $10$ $0.184$ \(\Q(\zeta_{22})\) None None \(-7\) \(-7\) \(-3\) \(-5\) $\mathrm{SU}(2)[C_{11}]$ \(q+(-\zeta_{22}+\zeta_{22}^{4}-\zeta_{22}^{5}+\zeta_{22}^{6}+\cdots)q^{2}+\cdots\)
23.3.b.a 23.b 23.b $3$ $0.627$ 3.3.621.1 \(\Q(\sqrt{-23}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(\beta _{1}+\beta _{2})q^{2}+(-2\beta _{1}-\beta _{2})q^{3}+(4+\cdots)q^{4}+\cdots\)
23.3.d.a 23.d 23.d $30$ $0.627$ None None \(-11\) \(-11\) \(-11\) \(-11\) $\mathrm{SU}(2)[C_{22}]$
23.4.a.a 23.a 1.a $1$ $1.357$ \(\Q\) None None \(-2\) \(-5\) \(-6\) \(-8\) $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-5q^{3}-4q^{4}-6q^{5}+10q^{6}+\cdots\)
23.4.a.b 23.a 1.a $4$ $1.357$ 4.4.334189.1 None None \(2\) \(7\) \(14\) \(16\) $+$ $\mathrm{SU}(2)$ \(q+(1+\beta _{3})q^{2}+(1+\beta _{1}+\beta _{2})q^{3}+(6+\cdots)q^{4}+\cdots\)
23.4.c.a 23.c 23.c $50$ $1.357$ None None \(-11\) \(-13\) \(-19\) \(-19\) $\mathrm{SU}(2)[C_{11}]$
23.5.b.a 23.b 23.b $3$ $2.378$ 3.3.621.1 \(\Q(\sqrt{-23}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(\beta _{1}-2\beta _{2})q^{2}+(6\beta _{1}-\beta _{2})q^{3}+(2^{4}+\cdots)q^{4}+\cdots\)
23.5.b.b 23.b 23.b $4$ $2.378$ \(\mathbb{Q}[x]/(x^{4} + \cdots)\) None None \(-8\) \(-12\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-2-\beta _{3})q^{2}+(-3+3\beta _{3})q^{3}+(-6+\cdots)q^{4}+\cdots\)
23.5.d.a 23.d 23.d $70$ $2.378$ None None \(-3\) \(1\) \(-11\) \(-11\) $\mathrm{SU}(2)[C_{22}]$
23.6.a.a 23.a 1.a $3$ $3.689$ 3.3.7925.1 None None \(-4\) \(-20\) \(-58\) \(-282\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(-7-2\beta _{1}-\beta _{2})q^{3}+\cdots\)
23.6.a.b 23.a 1.a $6$ $3.689$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None None \(4\) \(16\) \(42\) \(300\) $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(3-\beta _{1}+\beta _{4})q^{3}+(19+\cdots)q^{4}+\cdots\)
23.6.c.a 23.c 23.c $90$ $3.689$ None None \(-11\) \(-7\) \(5\) \(-29\) $\mathrm{SU}(2)[C_{11}]$
23.7.b.a 23.b 23.b $1$ $5.291$ \(\Q\) \(\Q(\sqrt{-23}) \) None \(-7\) \(-38\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-7q^{2}-38q^{3}-15q^{4}+266q^{6}+\cdots\)
23.7.b.b 23.b 23.b $2$ $5.291$ \(\Q(\sqrt{69}) \) \(\Q(\sqrt{-23}) \) None \(7\) \(38\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(2+3\beta )q^{2}+(23-8\beta )q^{3}+(93+21\beta )q^{4}+\cdots\)
23.7.b.c 23.b 23.b $8$ $5.291$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None None \(8\) \(30\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1+\beta _{1})q^{2}+(4+\beta _{3})q^{3}+(21-3\beta _{1}+\cdots)q^{4}+\cdots\)
23.7.d.a 23.d 23.d $110$ $5.291$ None None \(-19\) \(-41\) \(-11\) \(-11\) $\mathrm{SU}(2)[C_{22}]$
23.8.a.a 23.a 1.a $5$ $7.185$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None None \(-16\) \(-68\) \(-56\) \(-1156\) $-$ $\mathrm{SU}(2)$ \(q+(-3+\beta _{1})q^{2}+(-14+\beta _{2})q^{3}+(51+\cdots)q^{4}+\cdots\)
23.8.a.b 23.a 1.a $8$ $7.185$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None None \(0\) \(40\) \(444\) \(1446\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(5-\beta _{1}+\beta _{2})q^{3}+(80+2\beta _{1}+\cdots)q^{4}+\cdots\)
23.8.c.a 23.c 23.c $130$ $7.185$ None None \(5\) \(17\) \(-399\) \(-301\) $\mathrm{SU}(2)[C_{11}]$
23.9.b.a 23.b 23.b $3$ $9.370$ 3.3.621.1 \(\Q(\sqrt{-23}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(-3\beta _{1}-2\beta _{2})q^{2}+(13\beta _{1}-17\beta _{2})q^{3}+\cdots\)
23.9.b.b 23.b 23.b $12$ $9.370$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(-8\) \(-72\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1+\beta _{2})q^{2}+(-6+\beta _{3})q^{3}+(30+\cdots)q^{4}+\cdots\)
23.9.d.a 23.d 23.d $150$ $9.370$ None None \(-3\) \(61\) \(-11\) \(-11\) $\mathrm{SU}(2)[C_{22}]$
23.10.a.a 23.a 1.a $7$ $11.846$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None None \(0\) \(-89\) \(-2388\) \(-9896\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(-13-2\beta _{1}-\beta _{4})q^{3}+(220+\cdots)q^{4}+\cdots\)
23.10.a.b 23.a 1.a $10$ $11.846$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None None \(32\) \(235\) \(112\) \(1280\) $-$ $\mathrm{SU}(2)$ \(q+(3+\beta _{1})q^{2}+(23+\beta _{1}+\beta _{3})q^{3}+(307+\cdots)q^{4}+\cdots\)
23.10.c.a 23.c 23.c $170$ $11.846$ None None \(-43\) \(-157\) \(2265\) \(8605\) $\mathrm{SU}(2)[C_{11}]$
23.11.b.a 23.b 23.b $3$ $14.613$ 3.3.621.1 \(\Q(\sqrt{-23}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(-23\beta _{1}-2\beta _{2})q^{2}+(-66\beta _{1}+119\beta _{2})q^{3}+\cdots\)
23.11.b.b 23.b 23.b $16$ $14.613$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(-24\) \(60\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-2+\beta _{2})q^{2}+(4-\beta _{2}-\beta _{3})q^{3}+\cdots\)
23.11.d.a 23.d 23.d $190$ $14.613$ None None \(13\) \(-71\) \(-11\) \(-11\) $\mathrm{SU}(2)[C_{22}]$
23.12.a.a 23.a 1.a $8$ $17.672$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None None \(-32\) \(-992\) \(-11466\) \(-54118\) $-$ $\mathrm{SU}(2)$ \(q+(-4-\beta _{1})q^{2}+(-124-\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
23.12.a.b 23.a 1.a $11$ $17.672$ \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None None \(32\) \(-20\) \(1034\) \(159584\) $+$ $\mathrm{SU}(2)$ \(q+(3-\beta _{1})q^{2}+(-2+\beta _{1}-\beta _{2})q^{3}+\cdots\)
23.12.c.a 23.c 23.c $210$ $17.672$ None None \(37\) \(497\) \(761\) \(-71989\) $\mathrm{SU}(2)[C_{11}]$
23.13.b.a 23.b 23.b $1$ $21.022$ \(\Q\) \(\Q(\sqrt{-23}) \) None \(-79\) \(-14\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-79q^{2}-14q^{3}+2145q^{4}+1106q^{6}+\cdots\)
23.13.b.b 23.b 23.b $2$ $21.022$ \(\Q(\sqrt{69}) \) \(\Q(\sqrt{-23}) \) None \(79\) \(14\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(29+21\beta )q^{2}+(159-304\beta )q^{3}+\cdots\)
23.13.b.c 23.b 23.b $20$ $21.022$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(88\) \(318\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(4+\beta _{1})q^{2}+(15+2\beta _{1}-\beta _{3})q^{3}+\cdots\)
23.13.d.a 23.d 23.d $230$ $21.022$ None None \(-99\) \(-329\) \(-11\) \(-11\) $\mathrm{SU}(2)[C_{22}]$
23.14.a.a 23.a 1.a $11$ $24.663$ \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None None \(-64\) \(-860\) \(-10318\) \(-430944\) $+$ $\mathrm{SU}(2)$ \(q+(-6+\beta _{1})q^{2}+(-78-\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)
23.14.a.b 23.a 1.a $14$ $24.663$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None None \(64\) \(2056\) \(52182\) \(190602\) $-$ $\mathrm{SU}(2)$ \(q+(5-\beta _{1})q^{2}+(148-2\beta _{1}+\beta _{2})q^{3}+\cdots\)
23.14.c.a 23.c 23.c $250$ $24.663$ None None \(-11\) \(-1207\) \(-41875\) \(240331\) $\mathrm{SU}(2)[C_{11}]$
23.15.b.a 23.b 23.b $3$ $28.596$ 3.3.621.1 \(\Q(\sqrt{-23}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(13\beta _{1}-71\beta _{2})q^{2}+(622\beta _{1}-1057\beta _{2})q^{3}+\cdots\)
23.15.b.b 23.b 23.b $24$ $28.596$ None None \(-184\) \(-2160\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
23.15.d.a 23.d 23.d $270$ $28.596$ None None \(173\) \(2149\) \(-11\) \(-11\) $\mathrm{SU}(2)[C_{22}]$
23.16.a.a 23.a 1.a $12$ $32.820$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(-256\) \(-1745\) \(-204476\) \(-5717328\) $-$ $\mathrm{SU}(2)$ \(q+(-21+\beta _{1})q^{2}+(-145+\beta _{2})q^{3}+\cdots\)
23.16.a.b 23.a 1.a $15$ $32.820$ \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None None \(0\) \(7003\) \(108024\) \(-135224\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(467-\beta _{1}-\beta _{2})q^{3}+(17476+\cdots)q^{4}+\cdots\)
23.16.c.a 23.c 23.c $290$ $32.820$ None None \(-187\) \(1427\) \(-7779\) \(207629\) $\mathrm{SU}(2)[C_{11}]$
23.17.b.a 23.b 23.b $3$ $37.335$ 3.3.621.1 \(\Q(\sqrt{-23}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(48\beta _{1}-47\beta _{2})q^{2}+(-1075\beta _{1}+1359\beta _{2})q^{3}+\cdots\)
23.17.b.b 23.b 23.b $28$ $37.335$ None None \(184\) \(7908\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
23.17.d.a 23.d 23.d $310$ $37.335$ None None \(-195\) \(-7919\) \(-11\) \(-11\) $\mathrm{SU}(2)[C_{22}]$
23.18.a.a 23.a 1.a $14$ $42.141$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None None \(0\) \(-10640\) \(-363048\) \(-39649066\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(-760+\beta _{1}+\beta _{2})q^{3}+(56174+\cdots)q^{4}+\cdots\)
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