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Results (48 matches)

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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
83.1.b.a 83.b 83.b $1$ $0.041$ \(\Q\) \(\Q(\sqrt{-83}) \) None \(0\) \(-1\) \(0\) \(-1\) \(q-q^{3}+q^{4}-q^{7}-q^{11}-q^{12}+q^{16}+\cdots\)
83.2.a.a 83.a 1.a $1$ $0.663$ \(\Q\) None None \(-1\) \(-1\) \(-2\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}-q^{4}-2q^{5}+q^{6}-3q^{7}+\cdots\)
83.2.a.b 83.a 1.a $6$ $0.663$ 6.6.9059636.1 None None \(1\) \(1\) \(2\) \(3\) $-$ $\mathrm{SU}(2)$ \(q+(-\beta _{1}-\beta _{2})q^{2}-\beta _{3}q^{3}+(1-\beta _{5})q^{4}+\cdots\)
83.2.c.a 83.c 83.c $240$ $0.663$ None None \(-38\) \(-37\) \(-35\) \(-33\) $\mathrm{SU}(2)[C_{41}]$
83.3.b.a 83.b 83.b $3$ $2.262$ 3.3.2241.1 \(\Q(\sqrt{-83}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(\beta _{1}+\beta _{2})q^{3}+4q^{4}+(-3\beta _{1}-2\beta _{2})q^{7}+\cdots\)
83.3.b.b 83.b 83.b $10$ $2.262$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None None \(0\) \(-6\) \(0\) \(12\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-1+\beta _{2})q^{3}+(-3+\beta _{7}+\cdots)q^{4}+\cdots\)
83.3.d.a 83.d 83.d $520$ $2.262$ None None \(-41\) \(-35\) \(-41\) \(-53\) $\mathrm{SU}(2)[C_{82}]$
83.4.a.a 83.a 1.a $7$ $4.897$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None None \(-5\) \(-11\) \(-17\) \(-46\) $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{4})q^{2}+(-1+\beta _{1}+\beta _{4})q^{3}+\cdots\)
83.4.a.b 83.a 1.a $13$ $4.897$ \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None None \(5\) \(7\) \(33\) \(52\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{8})q^{3}+(6+\beta _{2})q^{4}+\cdots\)
83.4.c.a 83.c 83.c $800$ $4.897$ None None \(-41\) \(-37\) \(-57\) \(-47\) $\mathrm{SU}(2)[C_{41}]$
83.5.b.a 83.b 83.b $3$ $8.580$ 3.3.2241.1 \(\Q(\sqrt{-83}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(2\beta _{1}-3\beta _{2})q^{3}+2^{4}q^{4}+(21\beta _{1}-11\beta _{2})q^{7}+\cdots\)
83.5.b.b 83.b 83.b $24$ $8.580$ None None \(0\) \(6\) \(0\) \(-112\) $\mathrm{SU}(2)[C_{2}]$
83.5.d.a 83.d 83.d $1080$ $8.580$ None None \(-41\) \(-47\) \(-41\) \(71\) $\mathrm{SU}(2)[C_{82}]$
83.6.a.a 83.a 1.a $14$ $13.312$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None None \(-13\) \(-17\) \(-162\) \(-247\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(-1+\beta _{7})q^{3}+(10+\cdots)q^{4}+\cdots\)
83.6.a.b 83.a 1.a $20$ $13.312$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(7\) \(37\) \(88\) \(439\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(2+\beta _{5})q^{3}+(19+\beta _{2})q^{4}+\cdots\)
83.6.c.a 83.c 83.c $1360$ $13.312$ None None \(-35\) \(-61\) \(33\) \(-233\) $\mathrm{SU}(2)[C_{41}]$
83.7.b.a 83.b 83.b $1$ $19.094$ \(\Q\) \(\Q(\sqrt{-83}) \) None \(0\) \(-29\) \(0\) \(-61\) $\mathrm{U}(1)[D_{2}]$ \(q-29q^{3}+2^{6}q^{4}-61q^{7}+112q^{9}+\cdots\)
83.7.b.b 83.b 83.b $2$ $19.094$ \(\Q(\sqrt{249}) \) \(\Q(\sqrt{-83}) \) None \(0\) \(29\) \(0\) \(61\) $\mathrm{U}(1)[D_{2}]$ \(q+(15+\beta )q^{3}+2^{6}q^{4}+(23-15\beta )q^{7}+\cdots\)
83.7.b.c 83.b 83.b $38$ $19.094$ None None \(0\) \(18\) \(0\) \(262\) $\mathrm{SU}(2)[C_{2}]$
83.7.d.a 83.d 83.d $1640$ $19.094$ None None \(-41\) \(-59\) \(-41\) \(-303\) $\mathrm{SU}(2)[C_{82}]$
83.8.a.a 83.a 1.a $21$ $25.928$ None None \(-17\) \(-95\) \(-502\) \(-3273\) $-$ $\mathrm{SU}(2)$
83.8.a.b 83.a 1.a $27$ $25.928$ None None \(23\) \(67\) \(748\) \(1529\) $+$ $\mathrm{SU}(2)$
83.8.c.a 83.c 83.c $1920$ $25.928$ None None \(-47\) \(-13\) \(-287\) \(1703\) $\mathrm{SU}(2)[C_{41}]$
83.9.b.a 83.b 83.b $3$ $33.812$ 3.3.2241.1 \(\Q(\sqrt{-83}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(-47\beta _{1}-2\beta _{2})q^{3}+2^{8}q^{4}+(-846\beta _{1}+\cdots)q^{7}+\cdots\)
83.9.b.b 83.b 83.b $52$ $33.812$ None None \(0\) \(-114\) \(0\) \(2028\) $\mathrm{SU}(2)[C_{2}]$
83.9.d.a 83.d 83.d $2200$ $33.812$ None None \(-41\) \(73\) \(-41\) \(-2069\) $\mathrm{SU}(2)[C_{82}]$
83.10.a.a 83.a 1.a $28$ $42.748$ None None \(-49\) \(-317\) \(-3467\) \(-13836\) $+$ $\mathrm{SU}(2)$
83.10.a.b 83.a 1.a $34$ $42.748$ None None \(31\) \(169\) \(2783\) \(19778\) $-$ $\mathrm{SU}(2)$
83.10.c.a 83.c 83.c $2480$ $42.748$ None None \(-23\) \(107\) \(643\) \(-5983\) $\mathrm{SU}(2)[C_{41}]$
83.11.b.a 83.b 83.b $3$ $52.735$ 3.3.2241.1 \(\Q(\sqrt{-83}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(-139\beta _{1}+6\beta _{2})q^{3}+2^{10}q^{4}+(5922\beta _{1}+\cdots)q^{7}+\cdots\)
83.11.b.b 83.b 83.b $66$ $52.735$ None None \(0\) \(42\) \(0\) \(-22288\) $\mathrm{SU}(2)[C_{2}]$
83.11.d.a 83.d 83.d $2760$ $52.735$ None None \(-41\) \(-83\) \(-41\) \(22247\) $\mathrm{SU}(2)[C_{82}]$
83.12.a.a 83.a 1.a $34$ $63.772$ None None \(-41\) \(-719\) \(-19862\) \(-97477\) $-$ $\mathrm{SU}(2)$
83.12.a.b 83.a 1.a $40$ $63.772$ None None \(119\) \(739\) \(11388\) \(137821\) $+$ $\mathrm{SU}(2)$
83.12.c.a 83.c 83.c $3040$ $63.772$ None None \(-71\) \(-565\) \(-1227\) \(-6897\) $\mathrm{SU}(2)[C_{41}]$
83.13.b.a 83.b 83.b $1$ $75.861$ \(\Q\) \(\Q(\sqrt{-83}) \) None \(0\) \(-617\) \(0\) \(-231577\) $\mathrm{U}(1)[D_{2}]$ \(q-617q^{3}+2^{12}q^{4}-231577q^{7}+\cdots\)
83.13.b.b 83.b 83.b $2$ $75.861$ \(\Q(\sqrt{249}) \) \(\Q(\sqrt{-83}) \) None \(0\) \(617\) \(0\) \(231577\) $\mathrm{U}(1)[D_{2}]$ \(q+(294-29\beta )q^{3}+2^{12}q^{4}+(116246+\cdots)q^{7}+\cdots\)
83.13.b.c 83.b 83.b $80$ $75.861$ None None \(0\) \(918\) \(0\) \(103918\) $\mathrm{SU}(2)[C_{2}]$
83.14.a.a 83.a 1.a $42$ $89.002$ None None \(-193\) \(-2057\) \(-78072\) \(-907547\) $+$ $\mathrm{SU}(2)$
83.14.a.b 83.a 1.a $48$ $89.002$ None None \(127\) \(2317\) \(78178\) \(739539\) $-$ $\mathrm{SU}(2)$
83.15.b.a 83.b 83.b $3$ $103.193$ 3.3.2241.1 \(\Q(\sqrt{-83}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(-63\beta _{1}+152\beta _{2})q^{3}+2^{14}q^{4}+\cdots\)
83.15.b.b 83.b 83.b $94$ $103.193$ None None \(0\) \(-2238\) \(0\) \(-386388\) $\mathrm{SU}(2)[C_{2}]$
83.16.a.a 83.a 1.a $48$ $118.436$ None None \(-473\) \(-5843\) \(-442447\) \(-7927854\) $-$ $\mathrm{SU}(2)$
83.16.a.b 83.a 1.a $54$ $118.436$ None None \(167\) \(7279\) \(338803\) \(3601748\) $+$ $\mathrm{SU}(2)$
83.18.a.a 83.a 1.a $55$ $152.074$ None None \(-241\) \(-11321\) \(-1009352\) \(-50694303\) $+$ $\mathrm{SU}(2)$
83.18.a.b 83.a 1.a $61$ $152.074$ None None \(1039\) \(28045\) \(2896898\) \(30012911\) $-$ $\mathrm{SU}(2)$
83.20.a.a 83.a 1.a $62$ $189.918$ None None \(-1481\) \(-94199\) \(-6266132\) \(-202919777\) $-$ $\mathrm{SU}(2)$
83.20.a.b 83.a 1.a $68$ $189.918$ None None \(1079\) \(23899\) \(13265118\) \(362030721\) $+$ $\mathrm{SU}(2)$
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