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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
71.1.b.a 71.b 71.b $3$ $0.035$ \(\Q(\zeta_{14})^+\) \(\Q(\sqrt{-71}) \) None \(-1\) \(-1\) \(-1\) \(0\) \(q-\beta _{1}q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
151.1.b.a 151.b 151.b $3$ $0.075$ \(\Q(\zeta_{14})^+\) \(\Q(\sqrt{-151}) \) None \(-1\) \(0\) \(-1\) \(0\) \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1+\beta _{1}-\beta _{2})q^{5}+\cdots\)
199.1.b.b 199.b 199.b $3$ $0.099$ \(\Q(\zeta_{18})^+\) \(\Q(\sqrt{-199}) \) None \(0\) \(0\) \(0\) \(-3\) \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(\beta _{1}-\beta _{2})q^{5}+\cdots\)
215.1.d.a 215.d 215.d $3$ $0.107$ \(\Q(\zeta_{14})^+\) \(\Q(\sqrt{-215}) \) None \(-1\) \(-1\) \(3\) \(-1\) \(q-\beta _{1}q^{2}+\beta _{2}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots\)
215.1.d.b 215.d 215.d $3$ $0.107$ \(\Q(\zeta_{14})^+\) \(\Q(\sqrt{-215}) \) None \(1\) \(1\) \(-3\) \(1\) \(q+\beta _{1}q^{2}-\beta _{2}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots\)
223.1.b.a 223.b 223.b $3$ $0.111$ \(\Q(\zeta_{14})^+\) \(\Q(\sqrt{-223}) \) None \(-1\) \(0\) \(0\) \(-1\) \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1+\beta _{1}-\beta _{2})q^{7}+\cdots\)
236.1.d.a 236.d 59.b $3$ $0.118$ \(\Q(\zeta_{18})^+\) \(\Q(\sqrt{-59}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{3}+(\beta _{1}-\beta _{2})q^{5}+\beta _{2}q^{7}+(1+\cdots)q^{9}+\cdots\)
251.1.b.a 251.b 251.b $3$ $0.125$ \(\Q(\zeta_{14})^+\) \(\Q(\sqrt{-251}) \) None \(0\) \(-1\) \(-1\) \(-1\) \(q-\beta _{1}q^{3}+q^{4}+(-1+\beta _{1}-\beta _{2})q^{5}+\cdots\)
287.1.d.a 287.d 287.d $3$ $0.143$ \(\Q(\zeta_{14})^+\) \(\Q(\sqrt{-287}) \) None \(-1\) \(-1\) \(0\) \(3\) \(q+(-1+\beta _{1}-\beta _{2})q^{2}-\beta _{1}q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots\)
287.1.d.b 287.d 287.d $3$ $0.143$ \(\Q(\zeta_{14})^+\) \(\Q(\sqrt{-287}) \) None \(-1\) \(1\) \(0\) \(-3\) \(q+(-1+\beta _{1}-\beta _{2})q^{2}+\beta _{1}q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots\)
332.1.d.a 332.d 83.b $3$ $0.166$ \(\Q(\zeta_{18})^+\) \(\Q(\sqrt{-83}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{3}+(\beta _{1}-\beta _{2})q^{7}+(1+\beta _{2})q^{9}+\cdots\)
335.1.d.c 335.d 335.d $3$ $0.167$ \(\Q(\zeta_{18})^+\) \(\Q(\sqrt{-335}) \) None \(0\) \(0\) \(-3\) \(0\) \(q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{2})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
335.1.d.d 335.d 335.d $3$ $0.167$ \(\Q(\zeta_{18})^+\) \(\Q(\sqrt{-335}) \) None \(0\) \(0\) \(3\) \(0\) \(q-\beta _{1}q^{2}+(\beta _{1}-\beta _{2})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
343.1.b.a 343.b 7.b $3$ $0.171$ \(\Q(\zeta_{14})^+\) \(\Q(\sqrt{-7}) \) None \(-1\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1-\beta _{2})q^{8}+\cdots\)
367.1.b.b 367.b 367.b $3$ $0.183$ \(\Q(\zeta_{18})^+\) \(\Q(\sqrt{-367}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(\beta _{1}-\beta _{2})q^{7}+\cdots\)
391.1.c.a 391.c 391.c $3$ $0.195$ \(\Q(\zeta_{14})^+\) \(\Q(\sqrt{-391}) \) None \(-1\) \(0\) \(-1\) \(-1\) \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{1}q^{5}+(-1+\cdots)q^{7}+\cdots\)
391.1.c.b 391.c 391.c $3$ $0.195$ \(\Q(\zeta_{14})^+\) \(\Q(\sqrt{-391}) \) None \(-1\) \(0\) \(1\) \(1\) \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{1}q^{5}+(1-\beta _{1}+\cdots)q^{7}+\cdots\)
404.1.d.a 404.d 404.d $3$ $0.202$ \(\Q(\zeta_{14})^+\) \(\Q(\sqrt{-101}) \) None \(-3\) \(1\) \(-1\) \(1\) \(q-q^{2}+\beta _{1}q^{3}+q^{4}+(-1+\beta _{1}-\beta _{2})q^{5}+\cdots\)
404.1.d.b 404.d 404.d $3$ $0.202$ \(\Q(\zeta_{14})^+\) \(\Q(\sqrt{-101}) \) None \(3\) \(-1\) \(-1\) \(-1\) \(q+q^{2}-\beta _{1}q^{3}+q^{4}+(-1+\beta _{1}-\beta _{2})q^{5}+\cdots\)
419.1.b.b 419.b 419.b $3$ $0.209$ \(\Q(\zeta_{18})^+\) \(\Q(\sqrt{-419}) \) None \(0\) \(0\) \(-3\) \(0\) \(q-\beta _{1}q^{3}+q^{4}-q^{5}+(\beta _{1}-\beta _{2})q^{7}+\cdots\)
428.1.d.a 428.d 107.b $3$ $0.214$ \(\Q(\zeta_{18})^+\) \(\Q(\sqrt{-107}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{3}+(1+\beta _{2})q^{9}+(\beta _{1}-\beta _{2})q^{11}+\cdots\)
431.1.b.b 431.b 431.b $3$ $0.215$ \(\Q(\zeta_{14})^+\) \(\Q(\sqrt{-431}) \) None \(-1\) \(-1\) \(-1\) \(0\) \(q+\beta _{2}q^{2}-\beta _{1}q^{3}+(\beta _{1}-\beta _{2})q^{4}+\beta _{2}q^{5}+\cdots\)
447.1.d.a 447.d 447.d $3$ $0.223$ \(\Q(\zeta_{14})^+\) \(\Q(\sqrt{-447}) \) None \(-1\) \(3\) \(0\) \(-1\) \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
447.1.d.b 447.d 447.d $3$ $0.223$ \(\Q(\zeta_{14})^+\) \(\Q(\sqrt{-447}) \) None \(1\) \(-3\) \(0\) \(-1\) \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
463.1.b.a 463.b 463.b $3$ $0.231$ \(\Q(\zeta_{14})^+\) \(\Q(\sqrt{-463}) \) None \(-1\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1-\beta _{2})q^{8}+\cdots\)
467.1.b.a 467.b 467.b $3$ $0.233$ \(\Q(\zeta_{14})^+\) \(\Q(\sqrt{-467}) \) None \(0\) \(-1\) \(0\) \(-1\) \(q-\beta _{1}q^{3}+q^{4}+(-1+\beta _{1}-\beta _{2})q^{7}+\cdots\)
487.1.b.a 487.b 487.b $3$ $0.243$ \(\Q(\zeta_{14})^+\) \(\Q(\sqrt{-487}) \) None \(-1\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1-\beta _{2})q^{8}+\cdots\)
491.1.b.c 491.b 491.b $3$ $0.245$ \(\Q(\zeta_{18})^+\) \(\Q(\sqrt{-491}) \) None \(0\) \(0\) \(-3\) \(0\) \(q-\beta _{1}q^{3}+q^{4}-q^{5}+(1+\beta _{2})q^{9}+(\beta _{1}+\cdots)q^{11}+\cdots\)
503.1.b.b 503.b 503.b $3$ $0.251$ \(\Q(\zeta_{14})^+\) \(\Q(\sqrt{-503}) \) None \(-1\) \(-1\) \(0\) \(-1\) \(q-\beta _{1}q^{2}-\beta _{1}q^{3}+(1+\beta _{2})q^{4}+(2+\beta _{2})q^{6}+\cdots\)
511.1.c.a 511.c 511.c $3$ $0.255$ \(\Q(\zeta_{14})^+\) \(\Q(\sqrt{-511}) \) None \(-1\) \(0\) \(-1\) \(3\) \(q+(-1+\beta _{1}-\beta _{2})q^{2}+(1-\beta _{1})q^{4}+\cdots\)
511.1.c.b 511.c 511.c $3$ $0.255$ \(\Q(\zeta_{14})^+\) \(\Q(\sqrt{-511}) \) None \(-1\) \(0\) \(1\) \(-3\) \(q+(-1+\beta _{1}-\beta _{2})q^{2}+(1-\beta _{1})q^{4}+\cdots\)
519.1.d.c 519.d 519.d $3$ $0.259$ \(\Q(\zeta_{18})^+\) \(\Q(\sqrt{-519}) \) None \(0\) \(-3\) \(0\) \(0\) \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
519.1.d.d 519.d 519.d $3$ $0.259$ \(\Q(\zeta_{18})^+\) \(\Q(\sqrt{-519}) \) None \(0\) \(3\) \(0\) \(0\) \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(\beta _{1}-\beta _{2})q^{5}+\cdots\)
527.1.d.c 527.d 527.d $3$ $0.263$ \(\Q(\zeta_{18})^+\) \(\Q(\sqrt{-527}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{1}-\beta _{2})q^{2}-\beta _{1}q^{3}+(1-\beta _{1})q^{4}+\cdots\)
527.1.d.d 527.d 527.d $3$ $0.263$ \(\Q(\zeta_{18})^+\) \(\Q(\sqrt{-527}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{1}-\beta _{2})q^{2}+\beta _{1}q^{3}+(1-\beta _{1})q^{4}+\cdots\)
535.1.d.a 535.d 535.d $3$ $0.267$ \(\Q(\zeta_{14})^+\) \(\Q(\sqrt{-535}) \) None \(-1\) \(0\) \(3\) \(-1\) \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{5}+\beta _{2}q^{7}+\cdots\)
535.1.d.b 535.d 535.d $3$ $0.267$ \(\Q(\zeta_{14})^+\) \(\Q(\sqrt{-535}) \) None \(1\) \(0\) \(-3\) \(1\) \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}-\beta _{2}q^{7}+\cdots\)
536.1.h.a 536.h 536.h $3$ $0.267$ \(\Q(\zeta_{14})^+\) \(\Q(\sqrt{-134}) \) None \(-3\) \(1\) \(1\) \(0\) \(q-q^{2}+\beta _{1}q^{3}+q^{4}+(1-\beta _{1}+\beta _{2})q^{5}+\cdots\)
536.1.h.b 536.h 536.h $3$ $0.267$ \(\Q(\zeta_{14})^+\) \(\Q(\sqrt{-134}) \) None \(3\) \(-1\) \(-1\) \(0\) \(q+q^{2}-\beta _{1}q^{3}+q^{4}+(-1+\beta _{1}-\beta _{2})q^{5}+\cdots\)
556.1.c.a 556.c 139.b $3$ $0.277$ \(\Q(\zeta_{18})^+\) \(\Q(\sqrt{-139}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{5}+\beta _{2}q^{7}+q^{9}+(\beta _{1}-\beta _{2})q^{11}+\cdots\)
563.1.b.c 563.b 563.b $3$ $0.281$ \(\Q(\zeta_{18})^+\) \(\Q(\sqrt{-563}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{3}+q^{4}+(\beta _{1}-\beta _{2})q^{7}+(1+\beta _{2})q^{9}+\cdots\)
575.1.d.b 575.d 23.b $3$ $0.287$ \(\Q(\zeta_{18})^+\) \(\Q(\sqrt{-23}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}+\beta _{2}q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{6}+\cdots\)
575.1.d.c 575.d 23.b $3$ $0.287$ \(\Q(\zeta_{18})^+\) \(\Q(\sqrt{-23}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}-\beta _{2}q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{6}+\cdots\)
587.1.b.a 587.b 587.b $3$ $0.293$ \(\Q(\zeta_{14})^+\) \(\Q(\sqrt{-587}) \) None \(0\) \(-1\) \(0\) \(-1\) \(q-\beta _{1}q^{3}+q^{4}+(-1+\beta _{1}-\beta _{2})q^{7}+\cdots\)
596.1.d.a 596.d 596.d $3$ $0.297$ \(\Q(\zeta_{14})^+\) \(\Q(\sqrt{-149}) \) None \(-3\) \(1\) \(-1\) \(0\) \(q-q^{2}+\beta _{1}q^{3}+q^{4}+(-1+\beta _{1}-\beta _{2})q^{5}+\cdots\)
596.1.d.b 596.d 596.d $3$ $0.297$ \(\Q(\zeta_{14})^+\) \(\Q(\sqrt{-149}) \) None \(3\) \(-1\) \(-1\) \(0\) \(q+q^{2}-\beta _{1}q^{3}+q^{4}+(-1+\beta _{1}-\beta _{2})q^{5}+\cdots\)
639.1.d.a 639.d 71.b $3$ $0.319$ \(\Q(\zeta_{14})^+\) \(\Q(\sqrt{-71}) \) None \(1\) \(0\) \(1\) \(0\) \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{2}q^{5}+(1+\beta _{2})q^{8}+\cdots\)
41.2.a.a 41.a 1.a $3$ $0.327$ 3.3.148.1 None None \(-1\) \(0\) \(-2\) \(6\) $-$ $\mathrm{SU}(2)$ \(q+(-\beta _{1}-\beta _{2})q^{2}+\beta _{2}q^{3}+(1+2\beta _{1}+\cdots)q^{4}+\cdots\)
679.1.c.c 679.c 679.c $3$ $0.339$ \(\Q(\zeta_{18})^+\) \(\Q(\sqrt{-679}) \) None \(0\) \(0\) \(-3\) \(3\) \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}+q^{7}+(-1+\cdots)q^{8}+\cdots\)
679.1.c.d 679.c 679.c $3$ $0.339$ \(\Q(\zeta_{18})^+\) \(\Q(\sqrt{-679}) \) None \(0\) \(0\) \(3\) \(-3\) \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{5}-q^{7}+(-1+\cdots)q^{8}+\cdots\)
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