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Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2
2.8.a.a 2.a 1.a $1$ $0.625$ \(\Q\) None 2.8.a.a \(-8\) \(12\) \(-210\) \(1016\) $+$ $\mathrm{SU}(2)$ \(q-8q^{2}+12q^{3}+2^{6}q^{4}-210q^{5}+\cdots\)
2.10.a.a 2.a 1.a $1$ $1.030$ \(\Q\) None 2.10.a.a \(16\) \(-156\) \(870\) \(-952\) $-$ $\mathrm{SU}(2)$ \(q+2^{4}q^{2}-156q^{3}+2^{8}q^{4}+870q^{5}+\cdots\)
2.14.a.a 2.a 1.a $1$ $2.145$ \(\Q\) None 2.14.a.a \(-64\) \(-1836\) \(3990\) \(-433432\) $+$ $\mathrm{SU}(2)$ \(q-2^{6}q^{2}-1836q^{3}+2^{12}q^{4}+3990q^{5}+\cdots\)
2.14.a.b 2.a 1.a $1$ $2.145$ \(\Q\) None 2.14.a.b \(64\) \(1236\) \(-57450\) \(64232\) $-$ $\mathrm{SU}(2)$ \(q+2^{6}q^{2}+1236q^{3}+2^{12}q^{4}-57450q^{5}+\cdots\)
2.16.a.a 2.a 1.a $1$ $2.854$ \(\Q\) None 2.16.a.a \(-128\) \(6252\) \(90510\) \(56\) $+$ $\mathrm{SU}(2)$ \(q-2^{7}q^{2}+6252q^{3}+2^{14}q^{4}+90510q^{5}+\cdots\)
2.18.a.a 2.a 1.a $1$ $3.664$ \(\Q\) None 2.18.a.a \(256\) \(6084\) \(1255110\) \(-22465912\) $-$ $\mathrm{SU}(2)$ \(q+2^{8}q^{2}+78^{2}q^{3}+2^{16}q^{4}+1255110q^{5}+\cdots\)
2.20.a.a 2.a 1.a $1$ $4.576$ \(\Q\) None 2.20.a.a \(-512\) \(-13092\) \(6546750\) \(96674264\) $+$ $\mathrm{SU}(2)$ \(q-2^{9}q^{2}-13092q^{3}+2^{18}q^{4}+6546750q^{5}+\cdots\)
2.20.a.b 2.a 1.a $1$ $4.576$ \(\Q\) None 2.20.a.b \(512\) \(-53028\) \(-5556930\) \(-44496424\) $-$ $\mathrm{SU}(2)$ \(q+2^{9}q^{2}-53028q^{3}+2^{18}q^{4}-5556930q^{5}+\cdots\)
2.22.a.a 2.a 1.a $1$ $5.590$ \(\Q\) None 2.22.a.a \(-1024\) \(71604\) \(-28693770\) \(-853202392\) $+$ $\mathrm{SU}(2)$ \(q-2^{10}q^{2}+71604q^{3}+2^{20}q^{4}-28693770q^{5}+\cdots\)
2.22.a.b 2.a 1.a $1$ $5.590$ \(\Q\) None 2.22.a.b \(1024\) \(59316\) \(4975350\) \(1427425832\) $-$ $\mathrm{SU}(2)$ \(q+2^{10}q^{2}+59316q^{3}+2^{20}q^{4}+4975350q^{5}+\cdots\)
2.24.a.a 2.a 1.a $1$ $6.704$ \(\Q\) None 2.24.a.a \(-2048\) \(-505908\) \(-90135570\) \(6872255096\) $+$ $\mathrm{SU}(2)$ \(q-2^{11}q^{2}-505908q^{3}+2^{22}q^{4}+\cdots\)
2.26.a.a 2.a 1.a $1$ $7.920$ \(\Q\) None 2.26.a.a \(-4096\) \(97956\) \(341005350\) \(-40882637368\) $+$ $\mathrm{SU}(2)$ \(q-2^{12}q^{2}+97956q^{3}+2^{24}q^{4}+341005350q^{5}+\cdots\)
2.26.a.b 2.a 1.a $2$ $7.920$ \(\Q(\sqrt{106705}) \) None 2.26.a.b \(8192\) \(379848\) \(741953100\) \(-376536944\) $-$ $\mathrm{SU}(2)$ \(q+2^{12}q^{2}+(189924-\beta )q^{3}+2^{24}q^{4}+\cdots\)
2.28.a.a 2.a 1.a $1$ $9.237$ \(\Q\) None 2.28.a.a \(-8192\) \(3984828\) \(-2851889250\) \(368721063704\) $+$ $\mathrm{SU}(2)$ \(q-2^{13}q^{2}+3984828q^{3}+2^{26}q^{4}+\cdots\)
2.28.a.b 2.a 1.a $1$ $9.237$ \(\Q\) None 2.28.a.b \(8192\) \(-1016388\) \(-3341197410\) \(-51021361384\) $-$ $\mathrm{SU}(2)$ \(q+2^{13}q^{2}-1016388q^{3}+2^{26}q^{4}+\cdots\)
2.30.a.a 2.a 1.a $1$ $10.656$ \(\Q\) None 2.30.a.a \(-16384\) \(-2792556\) \(6651856470\) \(14\!\cdots\!48\) $+$ $\mathrm{SU}(2)$ \(q-2^{14}q^{2}-2792556q^{3}+2^{28}q^{4}+\cdots\)
2.30.a.b 2.a 1.a $1$ $10.656$ \(\Q\) None 2.30.a.b \(16384\) \(4782996\) \(6065841750\) \(904018883432\) $-$ $\mathrm{SU}(2)$ \(q+2^{14}q^{2}+4782996q^{3}+2^{28}q^{4}+\cdots\)
2.32.a.a 2.a 1.a $1$ $12.175$ \(\Q\) None 2.32.a.a \(32768\) \(-19984212\) \(42951708750\) \(-16\!\cdots\!76\) $-$ $\mathrm{SU}(2)$ \(q+2^{15}q^{2}-19984212q^{3}+2^{30}q^{4}+\cdots\)
2.32.a.b 2.a 1.a $2$ $12.175$ \(\mathbb{Q}[x]/(x^{2} - \cdots)\) None 2.32.a.b \(-65536\) \(16716504\) \(-26763065700\) \(-23\!\cdots\!08\) $+$ $\mathrm{SU}(2)$ \(q-2^{15}q^{2}+(8358252-\beta )q^{3}+2^{30}q^{4}+\cdots\)
2.34.a.a 2.a 1.a $1$ $13.797$ \(\Q\) None 2.34.a.a \(-65536\) \(-133005564\) \(538799132550\) \(-33\!\cdots\!68\) $+$ $\mathrm{SU}(2)$ \(q-2^{16}q^{2}-133005564q^{3}+2^{32}q^{4}+\cdots\)
2.34.a.b 2.a 1.a $2$ $13.797$ \(\mathbb{Q}[x]/(x^{2} - \cdots)\) None 2.34.a.b \(131072\) \(8356488\) \(-5332476660\) \(13\!\cdots\!56\) $-$ $\mathrm{SU}(2)$ \(q+2^{16}q^{2}+(4178244-\beta )q^{3}+2^{32}q^{4}+\cdots\)
2.36.a.a 2.a 1.a $1$ $15.519$ \(\Q\) None 2.36.a.a \(-131072\) \(36494748\) \(389070858750\) \(-12\!\cdots\!56\) $+$ $\mathrm{SU}(2)$ \(q-2^{17}q^{2}+36494748q^{3}+2^{34}q^{4}+\cdots\)
2.36.a.b 2.a 1.a $1$ $15.519$ \(\Q\) None 2.36.a.b \(131072\) \(159933852\) \(-28\!\cdots\!90\) \(-78\!\cdots\!44\) $-$ $\mathrm{SU}(2)$ \(q+2^{17}q^{2}+159933852q^{3}+2^{34}q^{4}+\cdots\)
2.38.a.a 2.a 1.a $2$ $17.343$ \(\mathbb{Q}[x]/(x^{2} - \cdots)\) None 2.38.a.a \(-524288\) \(423071208\) \(-13\!\cdots\!40\) \(31\!\cdots\!56\) $+$ $\mathrm{SU}(2)$ \(q-2^{18}q^{2}+(211535604-\beta )q^{3}+2^{36}q^{4}+\cdots\)
2.38.a.b 2.a 1.a $2$ $17.343$ \(\mathbb{Q}[x]/(x^{2} - \cdots)\) None 2.38.a.b \(524288\) \(-501686808\) \(41\!\cdots\!00\) \(-35\!\cdots\!56\) $-$ $\mathrm{SU}(2)$ \(q+2^{18}q^{2}+(-250843404-\beta )q^{3}+\cdots\)
2.40.a.a 2.a 1.a $1$ $19.268$ \(\Q\) None 2.40.a.a \(524288\) \(-735458292\) \(-16\!\cdots\!50\) \(16\!\cdots\!64\) $-$ $\mathrm{SU}(2)$ \(q+2^{19}q^{2}-735458292q^{3}+2^{38}q^{4}+\cdots\)
2.40.a.b 2.a 1.a $2$ $19.268$ \(\mathbb{Q}[x]/(x^{2} - \cdots)\) None 2.40.a.b \(-1048576\) \(287418264\) \(53\!\cdots\!20\) \(74\!\cdots\!12\) $+$ $\mathrm{SU}(2)$ \(q-2^{19}q^{2}+(143709132-\beta )q^{3}+2^{38}q^{4}+\cdots\)
2.42.a.a 2.a 1.a $1$ $21.294$ \(\Q\) None 2.42.a.a \(-1048576\) \(5043516516\) \(-48\!\cdots\!50\) \(-11\!\cdots\!68\) $+$ $\mathrm{SU}(2)$ \(q-2^{20}q^{2}+5043516516q^{3}+2^{40}q^{4}+\cdots\)
2.42.a.b 2.a 1.a $2$ $21.294$ \(\mathbb{Q}[x]/(x^{2} - \cdots)\) None 2.42.a.b \(2097152\) \(8863347528\) \(97\!\cdots\!80\) \(21\!\cdots\!56\) $-$ $\mathrm{SU}(2)$ \(q+2^{20}q^{2}+(4431673764-\beta )q^{3}+\cdots\)
2.44.a.a 2.a 1.a $2$ $23.422$ \(\mathbb{Q}[x]/(x^{2} - \cdots)\) None 2.44.a.a \(-4194304\) \(-12981630984\) \(-39\!\cdots\!00\) \(11\!\cdots\!08\) $+$ $\mathrm{SU}(2)$ \(q-2^{21}q^{2}+(-6490815492-\beta )q^{3}+\cdots\)
2.44.a.b 2.a 1.a $2$ $23.422$ \(\mathbb{Q}[x]/(x^{2} - \cdots)\) None 2.44.a.b \(4194304\) \(-22341634056\) \(-47\!\cdots\!20\) \(-22\!\cdots\!28\) $-$ $\mathrm{SU}(2)$ \(q+2^{21}q^{2}+(-11170817028-\beta )q^{3}+\cdots\)
2.46.a.a 2.a 1.a $2$ $25.651$ \(\mathbb{Q}[x]/(x^{2} - \cdots)\) None 2.46.a.a \(-8388608\) \(-69766206552\) \(-45\!\cdots\!00\) \(-95\!\cdots\!44\) $+$ $\mathrm{SU}(2)$ \(q-2^{22}q^{2}+(-34883103276-\beta )q^{3}+\cdots\)
2.46.a.b 2.a 1.a $2$ $25.651$ \(\mathbb{Q}[x]/(x^{2} - \cdots)\) None 2.46.a.b \(8388608\) \(59861217192\) \(43\!\cdots\!00\) \(79\!\cdots\!24\) $-$ $\mathrm{SU}(2)$ \(q+2^{22}q^{2}+(29930608596-\beta )q^{3}+\cdots\)
2.48.a.a 2.a 1.a $1$ $27.982$ \(\Q\) None 2.48.a.a \(8388608\) \(-196634580372\) \(20\!\cdots\!50\) \(-51\!\cdots\!96\) $-$ $\mathrm{SU}(2)$ \(q+2^{23}q^{2}-196634580372q^{3}+2^{46}q^{4}+\cdots\)
2.48.a.b 2.a 1.a $2$ $27.982$ \(\mathbb{Q}[x]/(x^{2} - \cdots)\) None 2.48.a.b \(-16777216\) \(122289844824\) \(18\!\cdots\!40\) \(16\!\cdots\!32\) $+$ $\mathrm{SU}(2)$ \(q-2^{23}q^{2}+(61144922412-5\beta )q^{3}+\cdots\)
2.50.a.a 2.a 1.a $2$ $30.413$ \(\mathbb{Q}[x]/(x^{2} - \cdots)\) None 2.50.a.a \(-33554432\) \(281051075592\) \(83\!\cdots\!00\) \(-43\!\cdots\!36\) $+$ $\mathrm{SU}(2)$ \(q-2^{24}q^{2}+(140525537796-\beta )q^{3}+\cdots\)
2.50.a.b 2.a 1.a $3$ $30.413$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None 2.50.a.b \(50331648\) \(-16203614388\) \(-10\!\cdots\!30\) \(-12\!\cdots\!96\) $-$ $\mathrm{SU}(2)$ \(q+2^{24}q^{2}+(-5401204796-\beta _{1}+\cdots)q^{3}+\cdots\)
2.52.a.a 2.a 1.a $2$ $32.946$ \(\mathbb{Q}[x]/(x^{2} - \cdots)\) None 2.52.a.a \(-67108864\) \(187290382776\) \(-12\!\cdots\!00\) \(-41\!\cdots\!52\) $+$ $\mathrm{SU}(2)$ \(q-2^{25}q^{2}+(93645191388-17\beta )q^{3}+\cdots\)
2.52.a.b 2.a 1.a $2$ $32.946$ \(\mathbb{Q}[x]/(x^{2} - \cdots)\) None 2.52.a.b \(67108864\) \(889619774904\) \(-50\!\cdots\!00\) \(-64\!\cdots\!08\) $-$ $\mathrm{SU}(2)$ \(q+2^{25}q^{2}+(444809887452-\beta )q^{3}+\cdots\)
2.54.a.a 2.a 1.a $2$ $35.581$ \(\mathbb{Q}[x]/(x^{2} - \cdots)\) None 2.54.a.a \(-134217728\) \(-14\!\cdots\!12\) \(30\!\cdots\!40\) \(-26\!\cdots\!44\) $+$ $\mathrm{SU}(2)$ \(q-2^{26}q^{2}+(-721907386956-3\beta )q^{3}+\cdots\)
2.54.a.b 2.a 1.a $2$ $35.581$ \(\mathbb{Q}[x]/(x^{2} - \cdots)\) None 2.54.a.b \(134217728\) \(-116235744408\) \(19\!\cdots\!00\) \(71\!\cdots\!04\) $-$ $\mathrm{SU}(2)$ \(q+2^{26}q^{2}+(-58117872204-\beta )q^{3}+\cdots\)
2.56.a.a 2.a 1.a $2$ $38.316$ \(\mathbb{Q}[x]/(x^{2} - \cdots)\) None 2.56.a.a \(268435456\) \(11\!\cdots\!56\) \(-25\!\cdots\!00\) \(-44\!\cdots\!32\) $-$ $\mathrm{SU}(2)$ \(q+2^{27}q^{2}+(5527700889228-\beta )q^{3}+\cdots\)
2.56.a.b 2.a 1.a $3$ $38.316$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None 2.56.a.b \(-402653184\) \(31\!\cdots\!16\) \(20\!\cdots\!10\) \(27\!\cdots\!48\) $+$ $\mathrm{SU}(2)$ \(q-2^{27}q^{2}+(1035669549772-\beta _{1}+\cdots)q^{3}+\cdots\)
2.58.a.a 2.a 1.a $2$ $41.153$ \(\mathbb{Q}[x]/(x^{2} - \cdots)\) None 2.58.a.a \(-536870912\) \(-48\!\cdots\!08\) \(-44\!\cdots\!00\) \(-72\!\cdots\!56\) $+$ $\mathrm{SU}(2)$ \(q-2^{28}q^{2}+(-24128544277404+\cdots)q^{3}+\cdots\)
2.58.a.b 2.a 1.a $3$ $41.153$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None 2.58.a.b \(805306368\) \(-25\!\cdots\!88\) \(11\!\cdots\!10\) \(-13\!\cdots\!16\) $-$ $\mathrm{SU}(2)$ \(q+2^{28}q^{2}+(-8441370341596+\beta _{1}+\cdots)q^{3}+\cdots\)
2.60.a.a 2.a 1.a $2$ $44.092$ \(\mathbb{Q}[x]/(x^{2} - \cdots)\) None 2.60.a.a \(-1073741824\) \(12\!\cdots\!36\) \(-22\!\cdots\!00\) \(26\!\cdots\!88\) $+$ $\mathrm{SU}(2)$ \(q-2^{29}q^{2}+(61050546196668-\beta )q^{3}+\cdots\)
2.60.a.b 2.a 1.a $2$ $44.092$ \(\mathbb{Q}[x]/(x^{2} - \cdots)\) None 2.60.a.b \(1073741824\) \(-20\!\cdots\!36\) \(-42\!\cdots\!80\) \(57\!\cdots\!12\) $-$ $\mathrm{SU}(2)$ \(q+2^{29}q^{2}+(-103021728505668+\cdots)q^{3}+\cdots\)
2.62.a.a 2.a 1.a $3$ $47.131$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None 2.62.a.a \(-3221225472\) \(75\!\cdots\!12\) \(22\!\cdots\!30\) \(36\!\cdots\!24\) $+$ $\mathrm{SU}(2)$ \(q-2^{30}q^{2}+(25004357142804-\beta _{1}+\cdots)q^{3}+\cdots\)
2.62.a.b 2.a 1.a $3$ $47.131$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None 2.62.a.b \(3221225472\) \(61\!\cdots\!88\) \(24\!\cdots\!50\) \(70\!\cdots\!76\) $-$ $\mathrm{SU}(2)$ \(q+2^{30}q^{2}+(205798698834196-\beta _{1}+\cdots)q^{3}+\cdots\)
2.64.a.a 2.a 1.a $2$ $50.272$ \(\mathbb{Q}[x]/(x^{2} - \cdots)\) None 2.64.a.a \(4294967296\) \(-44\!\cdots\!84\) \(-25\!\cdots\!00\) \(-18\!\cdots\!92\) $-$ $\mathrm{SU}(2)$ \(q+2^{31}q^{2}+(-221922059126292+\cdots)q^{3}+\cdots\)
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