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Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 11 19
4598.2.a.a 4598.a 1.a $1$ $36.715$ \(\Q\) None \(-1\) \(-1\) \(-4\) \(-3\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-4q^{5}+q^{6}-3q^{7}+\cdots\)
4598.2.a.b 4598.a 1.a $1$ $36.715$ \(\Q\) None \(-1\) \(-1\) \(-2\) \(3\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}+3q^{7}+\cdots\)
4598.2.a.c 4598.a 1.a $1$ $36.715$ \(\Q\) None \(-1\) \(-1\) \(2\) \(3\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}+3q^{7}+\cdots\)
4598.2.a.d 4598.a 1.a $1$ $36.715$ \(\Q\) None \(-1\) \(0\) \(-1\) \(4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{5}+4q^{7}-q^{8}-3q^{9}+\cdots\)
4598.2.a.e 4598.a 1.a $1$ $36.715$ \(\Q\) None \(-1\) \(0\) \(0\) \(-3\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-3q^{7}-q^{8}-3q^{9}-q^{13}+\cdots\)
4598.2.a.f 4598.a 1.a $1$ $36.715$ \(\Q\) None \(-1\) \(0\) \(2\) \(-2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+2q^{5}-2q^{7}-q^{8}-3q^{9}+\cdots\)
4598.2.a.g 4598.a 1.a $1$ $36.715$ \(\Q\) None \(-1\) \(0\) \(4\) \(-1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+4q^{5}-q^{7}-q^{8}-3q^{9}+\cdots\)
4598.2.a.h 4598.a 1.a $1$ $36.715$ \(\Q\) None \(-1\) \(1\) \(0\) \(-1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots\)
4598.2.a.i 4598.a 1.a $1$ $36.715$ \(\Q\) None \(-1\) \(2\) \(-2\) \(-4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+2q^{3}+q^{4}-2q^{5}-2q^{6}-4q^{7}+\cdots\)
4598.2.a.j 4598.a 1.a $1$ $36.715$ \(\Q\) None \(-1\) \(3\) \(-2\) \(-1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+3q^{3}+q^{4}-2q^{5}-3q^{6}-q^{7}+\cdots\)
4598.2.a.k 4598.a 1.a $1$ $36.715$ \(\Q\) None \(-1\) \(3\) \(0\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+3q^{3}+q^{4}-3q^{6}-q^{8}+6q^{9}+\cdots\)
4598.2.a.l 4598.a 1.a $1$ $36.715$ \(\Q\) None \(1\) \(-1\) \(2\) \(-3\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}-3q^{7}+\cdots\)
4598.2.a.m 4598.a 1.a $1$ $36.715$ \(\Q\) None \(1\) \(0\) \(-1\) \(-4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{5}-4q^{7}+q^{8}-3q^{9}+\cdots\)
4598.2.a.n 4598.a 1.a $1$ $36.715$ \(\Q\) None \(1\) \(0\) \(0\) \(3\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+3q^{7}+q^{8}-3q^{9}+q^{13}+\cdots\)
4598.2.a.o 4598.a 1.a $1$ $36.715$ \(\Q\) None \(1\) \(0\) \(4\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+4q^{5}+q^{7}+q^{8}-3q^{9}+\cdots\)
4598.2.a.p 4598.a 1.a $1$ $36.715$ \(\Q\) None \(1\) \(1\) \(0\) \(1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{7}+q^{8}+\cdots\)
4598.2.a.q 4598.a 1.a $1$ $36.715$ \(\Q\) None \(1\) \(1\) \(0\) \(1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{7}+q^{8}+\cdots\)
4598.2.a.r 4598.a 1.a $1$ $36.715$ \(\Q\) None \(1\) \(2\) \(-2\) \(4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+2q^{3}+q^{4}-2q^{5}+2q^{6}+4q^{7}+\cdots\)
4598.2.a.s 4598.a 1.a $1$ $36.715$ \(\Q\) None \(1\) \(3\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+3q^{3}+q^{4}+3q^{6}+q^{8}+6q^{9}+\cdots\)
4598.2.a.t 4598.a 1.a $2$ $36.715$ \(\Q(\sqrt{5}) \) None \(-2\) \(-4\) \(1\) \(3\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-2q^{3}+q^{4}+(1-\beta )q^{5}+2q^{6}+\cdots\)
4598.2.a.u 4598.a 1.a $2$ $36.715$ \(\Q(\sqrt{5}) \) None \(-2\) \(-2\) \(-3\) \(-1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+(-1-\beta )q^{5}+q^{6}+\cdots\)
4598.2.a.v 4598.a 1.a $2$ $36.715$ \(\Q(\sqrt{5}) \) None \(-2\) \(-2\) \(1\) \(1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-2\beta q^{3}+q^{4}+(-1+3\beta )q^{5}+\cdots\)
4598.2.a.w 4598.a 1.a $2$ $36.715$ \(\Q(\sqrt{3}) \) None \(-2\) \(-2\) \(2\) \(4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+(1+\beta )q^{5}+q^{6}+\cdots\)
4598.2.a.x 4598.a 1.a $2$ $36.715$ \(\Q(\sqrt{5}) \) None \(-2\) \(-1\) \(-1\) \(-1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta q^{3}+q^{4}-\beta q^{5}+\beta q^{6}+(1+\cdots)q^{7}+\cdots\)
4598.2.a.y 4598.a 1.a $2$ $36.715$ \(\Q(\sqrt{21}) \) None \(-2\) \(-1\) \(3\) \(5\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta q^{3}+q^{4}+(2-\beta )q^{5}+\beta q^{6}+\cdots\)
4598.2.a.z 4598.a 1.a $2$ $36.715$ \(\Q(\sqrt{5}) \) None \(-2\) \(0\) \(-1\) \(1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+(1-3\beta )q^{5}+(1-\beta )q^{7}+\cdots\)
4598.2.a.ba 4598.a 1.a $2$ $36.715$ \(\Q(\sqrt{5}) \) None \(-2\) \(0\) \(-1\) \(1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+(1-2\beta )q^{3}+q^{4}+(-1+\beta )q^{5}+\cdots\)
4598.2.a.bb 4598.a 1.a $2$ $36.715$ \(\Q(\sqrt{5}) \) None \(2\) \(-4\) \(1\) \(-3\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-2q^{3}+q^{4}+\beta q^{5}-2q^{6}-3\beta q^{7}+\cdots\)
4598.2.a.bc 4598.a 1.a $2$ $36.715$ \(\Q(\sqrt{13}) \) None \(2\) \(-3\) \(-1\) \(1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1-\beta )q^{3}+q^{4}+(-1+\beta )q^{5}+\cdots\)
4598.2.a.bd 4598.a 1.a $2$ $36.715$ \(\Q(\sqrt{5}) \) None \(2\) \(-2\) \(-3\) \(1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+(-1-\beta )q^{5}-q^{6}+\cdots\)
4598.2.a.be 4598.a 1.a $2$ $36.715$ \(\Q(\sqrt{5}) \) None \(2\) \(-2\) \(1\) \(-1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-2\beta q^{3}+q^{4}+(-1+3\beta )q^{5}+\cdots\)
4598.2.a.bf 4598.a 1.a $2$ $36.715$ \(\Q(\sqrt{3}) \) None \(2\) \(-2\) \(2\) \(-4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+(1+\beta )q^{5}-q^{6}+\cdots\)
4598.2.a.bg 4598.a 1.a $2$ $36.715$ \(\Q(\sqrt{5}) \) None \(2\) \(-1\) \(-1\) \(1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta q^{3}+q^{4}-\beta q^{5}-\beta q^{6}+(-1+\cdots)q^{7}+\cdots\)
4598.2.a.bh 4598.a 1.a $2$ $36.715$ \(\Q(\sqrt{5}) \) None \(2\) \(0\) \(-1\) \(-1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+(1-3\beta )q^{5}+(-1+\beta )q^{7}+\cdots\)
4598.2.a.bi 4598.a 1.a $2$ $36.715$ \(\Q(\sqrt{5}) \) None \(2\) \(0\) \(-1\) \(-1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(1-2\beta )q^{3}+q^{4}+(-1+\beta )q^{5}+\cdots\)
4598.2.a.bj 4598.a 1.a $2$ $36.715$ \(\Q(\sqrt{17}) \) None \(2\) \(1\) \(4\) \(-3\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta q^{3}+q^{4}+2q^{5}+\beta q^{6}+(-2+\cdots)q^{7}+\cdots\)
4598.2.a.bk 4598.a 1.a $3$ $36.715$ 3.3.568.1 None \(-3\) \(-2\) \(-1\) \(2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(-1+\beta _{1})q^{3}+q^{4}-\beta _{1}q^{5}+\cdots\)
4598.2.a.bl 4598.a 1.a $3$ $36.715$ 3.3.404.1 None \(-3\) \(1\) \(4\) \(3\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta _{2}q^{3}+q^{4}+(1+2\beta _{1}-\beta _{2})q^{5}+\cdots\)
4598.2.a.bm 4598.a 1.a $3$ $36.715$ 3.3.469.1 None \(-3\) \(1\) \(5\) \(-1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta _{1}q^{3}+q^{4}+(2-\beta _{1})q^{5}-\beta _{1}q^{6}+\cdots\)
4598.2.a.bn 4598.a 1.a $3$ $36.715$ 3.3.568.1 None \(3\) \(-2\) \(-1\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1+\beta _{1})q^{3}+q^{4}-\beta _{1}q^{5}+\cdots\)
4598.2.a.bo 4598.a 1.a $3$ $36.715$ 3.3.621.1 None \(3\) \(0\) \(-3\) \(6\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta _{1}q^{3}+q^{4}+(-1-\beta _{1}-\beta _{2})q^{5}+\cdots\)
4598.2.a.bp 4598.a 1.a $3$ $36.715$ 3.3.404.1 None \(3\) \(1\) \(4\) \(-3\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta _{2}q^{3}+q^{4}+(1+2\beta _{1}-\beta _{2})q^{5}+\cdots\)
4598.2.a.bq 4598.a 1.a $4$ $36.715$ 4.4.7488.1 None \(-4\) \(-2\) \(-2\) \(4\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+(-1-\beta _{3})q^{3}+q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)
4598.2.a.br 4598.a 1.a $4$ $36.715$ 4.4.33452.1 None \(-4\) \(1\) \(3\) \(1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta _{1}q^{3}+q^{4}+(1+\beta _{2}+\beta _{3})q^{5}+\cdots\)
4598.2.a.bs 4598.a 1.a $4$ $36.715$ 4.4.258228.1 None \(-4\) \(2\) \(-2\) \(-3\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+(1-\beta _{1})q^{3}+q^{4}-\beta _{1}q^{5}+(-1+\cdots)q^{6}+\cdots\)
4598.2.a.bt 4598.a 1.a $4$ $36.715$ 4.4.7488.1 None \(4\) \(-2\) \(-2\) \(-4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1-\beta _{3})q^{3}+q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)
4598.2.a.bu 4598.a 1.a $4$ $36.715$ 4.4.33452.1 None \(4\) \(1\) \(3\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta _{1}q^{3}+q^{4}+(1+\beta _{2}+\beta _{3})q^{5}+\cdots\)
4598.2.a.bv 4598.a 1.a $4$ $36.715$ 4.4.258228.1 None \(4\) \(2\) \(-2\) \(3\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(1-\beta _{1})q^{3}+q^{4}-\beta _{1}q^{5}+(1+\cdots)q^{6}+\cdots\)
4598.2.a.bw 4598.a 1.a $8$ $36.715$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-8\) \(-2\) \(-2\) \(14\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta _{1}q^{3}+q^{4}+(-\beta _{1}-\beta _{3}-\beta _{6}+\cdots)q^{5}+\cdots\)
4598.2.a.bx 4598.a 1.a $8$ $36.715$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-8\) \(0\) \(2\) \(-8\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(\beta _{2}+\beta _{4}-\beta _{6})q^{3}+q^{4}-\beta _{3}q^{5}+\cdots\)
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