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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2600.1.b.a 2600.b 520.b $2$ $1.298$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-26}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-iq^{3}-q^{4}-q^{6}+iq^{7}+iq^{8}+\cdots\)
2600.1.b.b 2600.b 520.b $2$ $1.298$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-26}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-iq^{3}-q^{4}+q^{6}-iq^{7}-iq^{8}+\cdots\)
2600.1.o.a 2600.o 104.h $1$ $1.298$ \(\Q\) \(\Q(\sqrt{-10}) \), \(\Q(\sqrt{-26}) \) \(\Q(\sqrt{65}) \) \(-1\) \(0\) \(0\) \(-2\) \(q-q^{2}+q^{4}-2q^{7}-q^{8}-q^{9}+q^{13}+\cdots\)
2600.1.o.b 2600.o 104.h $1$ $1.298$ \(\Q\) \(\Q(\sqrt{-26}) \) None \(-1\) \(1\) \(0\) \(1\) \(q-q^{2}+q^{3}+q^{4}-q^{6}+q^{7}-q^{8}+\cdots\)
2600.1.o.c 2600.o 104.h $1$ $1.298$ \(\Q\) \(\Q(\sqrt{-10}) \), \(\Q(\sqrt{-26}) \) \(\Q(\sqrt{65}) \) \(1\) \(0\) \(0\) \(2\) \(q+q^{2}+q^{4}+2q^{7}+q^{8}-q^{9}-q^{13}+\cdots\)
2600.1.o.d 2600.o 104.h $1$ $1.298$ \(\Q\) \(\Q(\sqrt{-26}) \) None \(1\) \(1\) \(0\) \(-1\) \(q+q^{2}+q^{3}+q^{4}+q^{6}-q^{7}+q^{8}+\cdots\)
2600.1.o.e 2600.o 104.h $2$ $1.298$ \(\Q(\sqrt{3}) \) \(\Q(\sqrt{-26}) \) None \(-2\) \(0\) \(0\) \(2\) \(q-q^{2}-\beta q^{3}+q^{4}+\beta q^{6}+q^{7}-q^{8}+\cdots\)
2600.1.o.f 2600.o 104.h $2$ $1.298$ \(\Q(\sqrt{3}) \) \(\Q(\sqrt{-26}) \) None \(2\) \(0\) \(0\) \(-2\) \(q+q^{2}-\beta q^{3}+q^{4}-\beta q^{6}-q^{7}+q^{8}+\cdots\)
2600.1.r.a 2600.r 104.j $4$ $1.298$ \(\Q(\zeta_{8})\) None \(\Q(\sqrt{10}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}^{3}q^{2}+(-\zeta_{8}-\zeta_{8}^{3})q^{3}-\zeta_{8}^{2}q^{4}+\cdots\)
2600.1.u.a 2600.u 65.g $2$ $1.298$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(-2\) \(q+iq^{3}+(-1+i)q^{7}+(-1-i)q^{11}+\cdots\)
2600.1.u.b 2600.u 65.g $2$ $1.298$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(2\) \(q-iq^{3}+(1-i)q^{7}+(-1-i)q^{11}+\cdots\)
2600.1.x.a 2600.x 520.x $2$ $1.298$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-10}) \) None \(-2\) \(0\) \(0\) \(0\) \(q-q^{2}+q^{4}-q^{8}+iq^{9}+(-1+i+\cdots)q^{11}+\cdots\)
2600.1.x.b 2600.x 520.x $2$ $1.298$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-10}) \) None \(2\) \(0\) \(0\) \(0\) \(q+q^{2}+q^{4}+q^{8}+iq^{9}+(-1+i+\cdots)q^{11}+\cdots\)
2600.1.bg.a 2600.bg 520.ag $4$ $1.298$ \(\Q(\zeta_{8})\) None \(\Q(\sqrt{26}) \) \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+\zeta_{8}q^{8}+\zeta_{8}^{2}q^{9}+\cdots\)
2600.1.bk.a 2600.bk 520.ak $2$ $1.298$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-10}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-q^{4}+iq^{8}-iq^{9}+(-1+i+\cdots)q^{11}+\cdots\)
2600.1.bk.b 2600.bk 520.ak $2$ $1.298$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-10}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-q^{4}-iq^{8}-iq^{9}+(-1+i+\cdots)q^{11}+\cdots\)
2600.1.bl.a 2600.bl 13.d $2$ $1.298$ \(\Q(\sqrt{-1}) \) None None \(0\) \(-2\) \(0\) \(2\) \(q-q^{3}+(1+i)q^{7}+(-1-i)q^{11}+q^{13}+\cdots\)
2600.1.bl.b 2600.bl 13.d $2$ $1.298$ \(\Q(\sqrt{-1}) \) None None \(0\) \(2\) \(0\) \(-2\) \(q+q^{3}+(-1-i)q^{7}+(-1-i)q^{11}+\cdots\)
2600.1.br.a 2600.br 104.p $2$ $1.298$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-10}) \) None \(-1\) \(0\) \(0\) \(1\) \(q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+\zeta_{6}q^{7}+q^{8}+\zeta_{6}q^{9}+\cdots\)
2600.1.br.b 2600.br 104.p $2$ $1.298$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-10}) \) None \(1\) \(0\) \(0\) \(-1\) \(q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}-\zeta_{6}q^{7}-q^{8}+\zeta_{6}q^{9}+\cdots\)
2600.1.bt.a 2600.bt 104.n $4$ $1.298$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-10}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{5}q^{7}-\zeta_{12}^{3}q^{8}+\cdots\)
2600.1.ck.a 2600.ck 2600.bk $4$ $1.298$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-26}) \) None \(-1\) \(-2\) \(4\) \(-2\) \(q-\zeta_{10}^{3}q^{2}-\zeta_{10}q^{3}-\zeta_{10}q^{4}+q^{5}+\cdots\)
2600.1.ck.b 2600.ck 2600.bk $4$ $1.298$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-26}) \) None \(1\) \(-2\) \(-4\) \(2\) \(q+\zeta_{10}^{3}q^{2}-\zeta_{10}q^{3}-\zeta_{10}q^{4}-q^{5}+\cdots\)
2600.1.ck.c 2600.ck 2600.bk $8$ $1.298$ \(\Q(\zeta_{15})\) \(\Q(\sqrt{-26}) \) None \(-2\) \(2\) \(-4\) \(2\) \(q-\zeta_{30}^{9}q^{2}+\zeta_{30}^{3}q^{3}-\zeta_{30}^{3}q^{4}+\cdots\)
2600.1.ck.d 2600.ck 2600.bk $8$ $1.298$ \(\Q(\zeta_{15})\) \(\Q(\sqrt{-26}) \) None \(2\) \(2\) \(4\) \(-2\) \(q+\zeta_{30}^{9}q^{2}+\zeta_{30}^{3}q^{3}-\zeta_{30}^{3}q^{4}+\cdots\)
2600.1.cp.a 2600.cp 2600.bp $8$ $1.298$ \(\Q(\zeta_{20})\) \(\Q(\sqrt{-26}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{20}^{7}q^{2}-\zeta_{20}^{4}q^{4}-\zeta_{20}^{5}q^{5}+\cdots\)
2600.1.cp.b 2600.cp 2600.bp $16$ $1.298$ \(\Q(\zeta_{60})\) \(\Q(\sqrt{-26}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{60}^{27}q^{2}+(-\zeta_{60}^{4}-\zeta_{60}^{14})q^{3}+\cdots\)
2600.1.cy.a 2600.cy 520.bi $4$ $1.298$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-10}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(\zeta_{12}+\zeta_{12}^{3}+\cdots)q^{7}+\cdots\)
2600.1.cy.b 2600.cy 520.bi $4$ $1.298$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-10}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(-\zeta_{12}-\zeta_{12}^{3}+\cdots)q^{7}+\cdots\)
2600.1.dl.a 2600.dl 520.bv $4$ $1.298$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-10}) \) None \(-2\) \(0\) \(0\) \(6\) \(q+\zeta_{12}^{4}q^{2}-\zeta_{12}^{2}q^{4}+(1-\zeta_{12}^{4}+\cdots)q^{7}+\cdots\)
2600.1.dl.b 2600.dl 520.bv $4$ $1.298$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-10}) \) None \(2\) \(0\) \(0\) \(-6\) \(q-\zeta_{12}^{4}q^{2}-\zeta_{12}^{2}q^{4}+(-1+\zeta_{12}^{4}+\cdots)q^{7}+\cdots\)
2600.2.a.a 2600.a 1.a $1$ $20.761$ \(\Q\) None None \(0\) \(-3\) \(0\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-3q^{3}-2q^{7}+6q^{9}-2q^{11}+q^{13}+\cdots\)
2600.2.a.b 2600.a 1.a $1$ $20.761$ \(\Q\) None None \(0\) \(-2\) \(0\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q-2q^{3}-3q^{7}+q^{9}+3q^{11}-q^{13}+\cdots\)
2600.2.a.c 2600.a 1.a $1$ $20.761$ \(\Q\) None None \(0\) \(-2\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-2q^{3}+q^{9}+2q^{11}-q^{13}-2q^{17}+\cdots\)
2600.2.a.d 2600.a 1.a $1$ $20.761$ \(\Q\) None None \(0\) \(-2\) \(0\) \(3\) $-$ $\mathrm{SU}(2)$ \(q-2q^{3}+3q^{7}+q^{9}+q^{11}-q^{13}+\cdots\)
2600.2.a.e 2600.a 1.a $1$ $20.761$ \(\Q\) None None \(0\) \(-1\) \(0\) \(-5\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}-5q^{7}-2q^{9}-2q^{11}+q^{13}+\cdots\)
2600.2.a.f 2600.a 1.a $1$ $20.761$ \(\Q\) None None \(0\) \(-1\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{9}-2q^{11}+q^{13}-2q^{17}+\cdots\)
2600.2.a.g 2600.a 1.a $1$ $20.761$ \(\Q\) None None \(0\) \(0\) \(0\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q-4q^{7}-3q^{9}-2q^{11}-q^{13}-4q^{17}+\cdots\)
2600.2.a.h 2600.a 1.a $1$ $20.761$ \(\Q\) None None \(0\) \(0\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-3q^{9}-4q^{11}+q^{13}+6q^{17}+4q^{19}+\cdots\)
2600.2.a.i 2600.a 1.a $1$ $20.761$ \(\Q\) None None \(0\) \(0\) \(0\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+4q^{7}-3q^{9}-2q^{11}+q^{13}+4q^{17}+\cdots\)
2600.2.a.j 2600.a 1.a $1$ $20.761$ \(\Q\) None None \(0\) \(1\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{9}-2q^{11}-q^{13}+2q^{17}+\cdots\)
2600.2.a.k 2600.a 1.a $1$ $20.761$ \(\Q\) None None \(0\) \(2\) \(0\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q+2q^{3}-3q^{7}+q^{9}+q^{11}+q^{13}+\cdots\)
2600.2.a.l 2600.a 1.a $1$ $20.761$ \(\Q\) None None \(0\) \(2\) \(0\) \(3\) $-$ $\mathrm{SU}(2)$ \(q+2q^{3}+3q^{7}+q^{9}+3q^{11}+q^{13}+\cdots\)
2600.2.a.m 2600.a 1.a $1$ $20.761$ \(\Q\) None None \(0\) \(3\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+2q^{7}+6q^{9}-2q^{11}-q^{13}+\cdots\)
2600.2.a.n 2600.a 1.a $2$ $20.761$ \(\Q(\sqrt{73}) \) None None \(0\) \(-2\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{9}+(-1+\beta )q^{11}+q^{13}+\cdots\)
2600.2.a.o 2600.a 1.a $2$ $20.761$ \(\Q(\sqrt{5}) \) None None \(0\) \(-2\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{3}+(3+2\beta )q^{9}+(3-\beta )q^{11}+\cdots\)
2600.2.a.p 2600.a 1.a $2$ $20.761$ \(\Q(\sqrt{17}) \) None None \(0\) \(-1\) \(0\) \(1\) $-$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+\beta q^{7}+(1+\beta )q^{9}-2\beta q^{11}+\cdots\)
2600.2.a.q 2600.a 1.a $2$ $20.761$ \(\Q(\sqrt{6}) \) None None \(0\) \(0\) \(0\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}-2q^{7}+3q^{9}+(-2-\beta )q^{11}+\cdots\)
2600.2.a.r 2600.a 1.a $2$ $20.761$ \(\Q(\sqrt{10}) \) None None \(0\) \(0\) \(0\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{7}-3q^{9}+(3+\beta )q^{11}+\cdots\)
2600.2.a.s 2600.a 1.a $2$ $20.761$ \(\Q(\sqrt{10}) \) None None \(0\) \(0\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{7}-3q^{9}+(3+\beta )q^{11}-q^{13}+\cdots\)
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