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## Results (1-50 of 364 matches)

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Label Dim $A$ Field CM Traces Fricke sign $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
9.3.d.a $2$ $0.245$ $$\Q(\sqrt{-3})$$ None $$-3$$ $$-3$$ $$6$$ $$-2$$ $$q+(-1-\zeta_{6})q^{2}+(-3+3\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
9.4.a.a $1$ $0.531$ $$\Q$$ $$\Q(\sqrt{-3})$$ $$0$$ $$0$$ $$0$$ $$20$$ $+$ $$q-8q^{4}+20q^{7}-70q^{13}+2^{6}q^{16}+\cdots$$
9.4.c.a $4$ $0.531$ $$\Q(\sqrt{-3}, \sqrt{-11})$$ None $$-3$$ $$-3$$ $$-15$$ $$-7$$ $$q+(-\beta _{1}-\beta _{3})q^{2}+(-1+\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots$$
9.5.b.a $2$ $0.930$ $$\Q(\sqrt{-2})$$ None $$0$$ $$0$$ $$0$$ $$-56$$ $$q+\beta q^{2}-2q^{4}-7\beta q^{5}-28q^{7}+14\beta q^{8}+\cdots$$
9.5.d.a $6$ $0.930$ 6.0.39400128.1 None $$-3$$ $$-3$$ $$-12$$ $$12$$ $$q+\beta _{2}q^{2}+(-3+\beta _{1}-3\beta _{3}+\beta _{4})q^{3}+\cdots$$
9.6.a.a $1$ $1.443$ $$\Q$$ None $$6$$ $$0$$ $$-6$$ $$-40$$ $-$ $$q+6q^{2}+4q^{4}-6q^{5}-40q^{7}-168q^{8}+\cdots$$
9.6.c.a $8$ $1.443$ $$\mathbb{Q}[x]/(x^{8} + \cdots)$$ None $$3$$ $$-12$$ $$78$$ $$28$$ $$q+(1-\beta _{1}+\beta _{4}+\beta _{5})q^{2}+(-3+3\beta _{1}+\cdots)q^{3}+\cdots$$
9.7.b.a $2$ $2.070$ $$\Q(\sqrt{-2})$$ None $$0$$ $$0$$ $$0$$ $$1048$$ $$q+\beta q^{2}-98q^{4}+5\beta q^{5}+524q^{7}+\cdots$$
9.7.d.a $10$ $2.070$ $$\mathbb{Q}[x]/(x^{10} - \cdots)$$ None $$-3$$ $$24$$ $$-219$$ $$-121$$ $$q-\beta _{1}q^{2}+(2+\beta _{1}-\beta _{2}+\beta _{3}+\beta _{6}+\cdots)q^{3}+\cdots$$
9.8.a.a $1$ $2.811$ $$\Q$$ None $$-6$$ $$0$$ $$-390$$ $$-64$$ $-$ $$q-6q^{2}-92q^{4}-390q^{5}-2^{6}q^{7}+\cdots$$
9.8.a.b $2$ $2.811$ $$\Q(\sqrt{10})$$ None $$0$$ $$0$$ $$0$$ $$520$$ $+$ $$q+\beta q^{2}+232q^{4}-2^{4}\beta q^{5}+260q^{7}+\cdots$$
9.8.c.a $12$ $2.811$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$-9$$ $$24$$ $$-180$$ $$-84$$ $$q+(-\beta _{2}-\beta _{3})q^{2}+(1-\beta _{1}-\beta _{4}+\beta _{6}+\cdots)q^{3}+\cdots$$
9.9.b.a $2$ $3.666$ $$\Q(\sqrt{-2})$$ None $$0$$ $$0$$ $$0$$ $$3304$$ $$q+\beta q^{2}+238q^{4}+233\beta q^{5}+1652q^{7}+\cdots$$
9.9.d.a $14$ $3.666$ $$\mathbb{Q}[x]/(x^{14} - \cdots)$$ None $$-3$$ $$-93$$ $$438$$ $$922$$ $$q-\beta _{1}q^{2}+(-5-3\beta _{3}+\beta _{4}+\beta _{6})q^{3}+\cdots$$
9.10.a.a $1$ $4.635$ $$\Q$$ None $$-18$$ $$0$$ $$1530$$ $$9128$$ $-$ $$q-18q^{2}-188q^{4}+1530q^{5}+9128q^{7}+\cdots$$
9.10.a.b $1$ $4.635$ $$\Q$$ $$\Q(\sqrt{-3})$$ $$0$$ $$0$$ $$0$$ $$-12580$$ $+$ $$q-2^{9}q^{4}-12580q^{7}+118370q^{13}+\cdots$$
9.10.a.c $1$ $4.635$ $$\Q$$ None $$36$$ $$0$$ $$1314$$ $$-4480$$ $-$ $$q+6^{2}q^{2}+28^{2}q^{4}+1314q^{5}-4480q^{7}+\cdots$$
9.10.c.a $16$ $4.635$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$15$$ $$-3$$ $$453$$ $$-343$$ $$q+(2+\beta _{2}-2\beta _{3})q^{2}+(9-18\beta _{3}+\beta _{5}+\cdots)q^{3}+\cdots$$
9.11.b.a $4$ $5.718$ $$\Q(\sqrt{-2}, \sqrt{385})$$ None $$0$$ $$0$$ $$0$$ $$-44464$$ $$q-\beta _{1}q^{2}+(-1073-\beta _{2})q^{4}+(-35\beta _{1}+\cdots)q^{5}+\cdots$$
9.11.d.a $18$ $5.718$ $$\mathbb{Q}[x]/(x^{18} - \cdots)$$ None $$-3$$ $$51$$ $$4956$$ $$-6120$$ $$q-\beta _{3}q^{2}+(3-\beta _{1}+\beta _{3}+\beta _{4}-\beta _{6}+\cdots)q^{3}+\cdots$$
9.12.a.a $1$ $6.915$ $$\Q$$ None $$-78$$ $$0$$ $$5370$$ $$-27760$$ $-$ $$q-78q^{2}+4036q^{4}+5370q^{5}-27760q^{7}+\cdots$$
9.12.a.b $1$ $6.915$ $$\Q$$ None $$24$$ $$0$$ $$-4830$$ $$-16744$$ $-$ $$q+24q^{2}-1472q^{4}-4830q^{5}-16744q^{7}+\cdots$$
9.12.a.c $2$ $6.915$ $$\Q(\sqrt{70})$$ None $$0$$ $$0$$ $$0$$ $$116200$$ $+$ $$q+\beta q^{2}+472q^{4}+224\beta q^{5}+58100q^{7}+\cdots$$
9.12.c.a $20$ $6.915$ $$\mathbb{Q}[x]/(x^{20} + \cdots)$$ None $$-33$$ $$-12$$ $$-7230$$ $$8512$$ $$q+(\beta _{1}-3\beta _{3})q^{2}+(24-51\beta _{3}+\beta _{4}+\cdots)q^{3}+\cdots$$
9.13.b.a $2$ $8.226$ $$\Q(\sqrt{-2})$$ None $$0$$ $$0$$ $$0$$ $$-223736$$ $$q+8\beta q^{2}-6272q^{4}-2291\beta q^{5}-111868q^{7}+\cdots$$
9.13.b.b $2$ $8.226$ $$\Q(\sqrt{-2})$$ None $$0$$ $$0$$ $$0$$ $$232456$$ $$q+\beta q^{2}+2638q^{4}-175\beta q^{5}+116228q^{7}+\cdots$$
9.13.d.a $22$ $8.226$ None $$-3$$ $$618$$ $$-15987$$ $$34319$$
9.14.a.a $1$ $9.651$ $$\Q$$ None $$12$$ $$0$$ $$30210$$ $$235088$$ $-$ $$q+12q^{2}-8048q^{4}+30210q^{5}+235088q^{7}+\cdots$$
9.14.a.b $2$ $9.651$ $$\Q(\sqrt{55})$$ None $$0$$ $$0$$ $$0$$ $$-266600$$ $+$ $$q+\beta q^{2}-272q^{4}-520\beta q^{5}-133300q^{7}+\cdots$$
9.14.a.c $2$ $9.651$ $$\Q(\sqrt{1969})$$ None $$54$$ $$0$$ $$-40716$$ $$-21008$$ $-$ $$q+(3^{3}-\beta )q^{2}+(10258-54\beta )q^{4}+(-20358+\cdots)q^{5}+\cdots$$
9.14.c.a $24$ $9.651$ None $$63$$ $$-732$$ $$52128$$ $$-93912$$
9.15.b.a $4$ $11.190$ $$\Q(\sqrt{-2}, \sqrt{3745})$$ None $$0$$ $$0$$ $$0$$ $$-1065904$$ $$q-\beta _{3}q^{2}+(-833-\beta _{2})q^{4}+(-7\beta _{1}+\cdots)q^{5}+\cdots$$
9.15.d.a $26$ $11.190$ None $$-3$$ $$-2199$$ $$-107994$$ $$-146330$$
9.16.a.a $1$ $12.842$ $$\Q$$ None $$-216$$ $$0$$ $$-52110$$ $$2822456$$ $-$ $$q-6^{3}q^{2}+13888q^{4}-52110q^{5}+\cdots$$
9.16.a.b $1$ $12.842$ $$\Q$$ $$\Q(\sqrt{-3})$$ $$0$$ $$0$$ $$0$$ $$1244900$$ $+$ $$q-2^{15}q^{4}+1244900q^{7}+397771850q^{13}+\cdots$$
9.16.a.c $1$ $12.842$ $$\Q$$ None $$72$$ $$0$$ $$221490$$ $$-2149000$$ $-$ $$q+72q^{2}-27584q^{4}+221490q^{5}+\cdots$$
9.16.a.d $1$ $12.842$ $$\Q$$ None $$234$$ $$0$$ $$-280710$$ $$-1373344$$ $-$ $$q+234q^{2}+21988q^{4}-280710q^{5}+\cdots$$
9.16.a.e $2$ $12.842$ $$\Q(\sqrt{370})$$ None $$0$$ $$0$$ $$0$$ $$-5182520$$ $+$ $$q+\beta q^{2}+87112q^{4}+464\beta q^{5}-2591260q^{7}+\cdots$$
9.16.c.a $28$ $12.842$ None $$-129$$ $$3345$$ $$-152655$$ $$803705$$
9.17.b.a $6$ $14.609$ $$\mathbb{Q}[x]/(x^{6} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$5400696$$ $$q-\beta _{1}q^{2}+(-61382-\beta _{4})q^{4}+(-189\beta _{1}+\cdots)q^{5}+\cdots$$
9.17.d.a $30$ $14.609$ None $$-3$$ $$2049$$ $$507588$$ $$220596$$
9.18.a.a $1$ $16.490$ $$\Q$$ None $$-204$$ $$0$$ $$163554$$ $$-20846560$$ $-$ $$q-204q^{2}-89456q^{4}+163554q^{5}+\cdots$$
9.18.a.b $1$ $16.490$ $$\Q$$ None $$528$$ $$0$$ $$1025850$$ $$3225992$$ $-$ $$q+528q^{2}+147712q^{4}+1025850q^{5}+\cdots$$
9.18.a.c $2$ $16.490$ $$\Q(\sqrt{14569})$$ None $$-594$$ $$0$$ $$-382860$$ $$24471568$$ $-$ $$q+(-297-\beta )q^{2}+(88258+594\beta )q^{4}+\cdots$$
9.18.a.d $2$ $16.490$ $$\Q(\sqrt{910})$$ None $$0$$ $$0$$ $$0$$ $$-392840$$ $+$ $$q+\beta q^{2}-2^{5}q^{4}-280\beta q^{5}-196420q^{7}+\cdots$$
9.18.c.a $32$ $16.490$ None $$255$$ $$-2280$$ $$255678$$ $$-5846540$$
9.19.b.a $6$ $18.485$ $$\mathbb{Q}[x]/(x^{6} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$19180488$$ $$q+\beta _{1}q^{2}+(-42038-\beta _{2})q^{4}+(1082\beta _{1}+\cdots)q^{5}+\cdots$$
9.19.d.a $34$ $18.485$ None $$-3$$ $$3804$$ $$2192181$$ $$4302359$$
9.20.a.a $1$ $20.594$ $$\Q$$ None $$-456$$ $$0$$ $$2377410$$ $$-16917544$$ $-$ $$q-456q^{2}-316352q^{4}+2377410q^{5}+\cdots$$
9.20.a.b $1$ $20.594$ $$\Q$$ None $$1104$$ $$0$$ $$-3516270$$ $$-195590584$$ $-$ $$q+1104q^{2}+694528q^{4}-3516270q^{5}+\cdots$$
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