LMFDB - Newform Search Results

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Level	Weight	Analytic conductor	$Nk^2$	Dim.

Bad $p$	Char.	Primitive character	Character order	Coefficient field

Self-twists	CM/RM discriminant	Inner twist count*	Is self-dual?	Analytic rank

Coefficient ring index	Coefficient ring gens.	Only for weight 1:	Projective image	Projective image type
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Results (displaying matches 1-50 of at least 1000) Next

Label	Dim.	$A$	Field	CM	Traces				Fricke sign	$q$-expansion
Label	Dim.	$A$	Field	CM	$a_2$	$a_3$	$a_5$	$a_7$	Fricke sign	$q$-expansion
1.66.a.a	$5$	$26.757$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	None	$-3959709648$	$-2\!\cdots\!04$	$26\!\cdots\!50$	$-6\!\cdots\!08$	$+$	$q+(-791941930-\beta _{1})q^{2}+(-446261486940055+\cdots)q^{3}+\cdots$
1.68.a.a	$5$	$28.429$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	None	$5554901256$	$34\!\cdots\!72$	$33\!\cdots\!50$	$33\!\cdots\!56$	$+$	$q+(1110980251-\beta _{1})q^{2}+(688672053797479+\cdots)q^{3}+\cdots$
1.70.a.a	$5$	$30.151$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	None	$-18005734368$	$-4\!\cdots\!04$	$-1\!\cdots\!50$	$76\!\cdots\!92$	$+$	$q+(-3601146874-\beta _{1})q^{2}+(-971616465424800+\cdots)q^{3}+\cdots$
1.72.a.a	$6$	$31.925$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	$66157336440$	$89\!\cdots\!40$	$-4\!\cdots\!20$	$33\!\cdots\!00$	$+$	$q+(11026222740-\beta _{1})q^{2}+(14982825462961740+\cdots)q^{3}+\cdots$
1.74.a.a	$5$	$33.748$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	None	$-92089333488$	$-1\!\cdots\!04$	$23\!\cdots\!50$	$-4\!\cdots\!08$	$+$	$q+(-18417866698-\beta _{1})q^{2}+\cdots$
1.76.a.a	$6$	$35.623$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	$-57080822040$	$-7\!\cdots\!40$	$-3\!\cdots\!40$	$19\!\cdots\!00$	$+$	$q+(-9513470340+\beta _{1})q^{2}+\cdots$
1.78.a.a	$6$	$37.548$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	$264721893120$	$14\!\cdots\!80$	$-2\!\cdots\!00$	$27\!\cdots\!00$	$+$	$q+(44120315520-\beta _{1})q^{2}+(240268562631348180+\cdots)q^{3}+\cdots$
1.80.a.a	$6$	$39.524$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	$-16086577320$	$19\!\cdots\!80$	$60\!\cdots\!40$	$-2\!\cdots\!00$	$+$	$q+(-2681096220+\beta _{1})q^{2}+\cdots$
1.82.a.a	$6$	$41.550$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	$-460872026640$	$-1\!\cdots\!60$	$-1\!\cdots\!00$	$-3\!\cdots\!00$	$+$	$q+(-76812004440-\beta _{1})q^{2}+\cdots$
1.84.a.a	$7$	$43.627$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	$347450761416$	$92\!\cdots\!72$	$95\!\cdots\!70$	$41\!\cdots\!56$	$+$	$q+(49635823059+\beta _{1})q^{2}+\cdots$
1.86.a.a	$6$	$45.755$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	$-3\!\cdots\!00$	$-1\!\cdots\!00$	$-9\!\cdots\!00$	$37\!\cdots\!00$	$+$	$q+(-599485114800+\beta _{1})q^{2}+\cdots$
1.88.a.a	$7$	$47.933$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	$18\!\cdots\!36$	$-7\!\cdots\!48$	$33\!\cdots\!50$	$45\!\cdots\!56$	$+$	$q+(2599574577562+\beta _{1})q^{2}+\cdots$
1.90.a.a	$7$	$50.162$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	$-3\!\cdots\!08$	$-1\!\cdots\!64$	$10\!\cdots\!50$	$38\!\cdots\!92$	$+$	$q+(-4486761478773-\beta _{1})q^{2}+\cdots$
1.92.a.a	$7$	$52.442$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	$38\!\cdots\!56$	$62\!\cdots\!32$	$23\!\cdots\!30$	$-1\!\cdots\!44$	$+$	$q+(548816691151+\beta _{1})q^{2}+\cdots$
2.66.a.a	$2$	$53.514$	$\mathbb{Q}[x]/(x^{2} - \cdots)$	None	$-8589934592$	$11\!\cdots\!92$	$-7\!\cdots\!00$	$27\!\cdots\!24$	$+$	$q-2^{32}q^{2}+(574529980102596-111\beta )q^{3}+\cdots$
2.66.a.b	$3$	$53.514$	$\mathbb{Q}[x]/(x^{3} - \cdots)$	None	$12884901888$	$29\!\cdots\!12$	$39\!\cdots\!50$	$42\!\cdots\!64$	$-$	$q+2^{32}q^{2}+(994852866070404-\beta _{1}+\cdots)q^{3}+\cdots$
1.94.a.a	$7$	$54.773$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	$43\!\cdots\!92$	$-3\!\cdots\!84$	$-2\!\cdots\!50$	$-9\!\cdots\!08$	$+$	$q+(6247918101970+\beta _{1})q^{2}+\cdots$
2.68.a.a	$3$	$56.858$	$\mathbb{Q}[x]/(x^{3} - \cdots)$	None	$-25769803776$	$-5\!\cdots\!16$	$-2\!\cdots\!50$	$21\!\cdots\!12$	$+$	$q-2^{33}q^{2}+(-1741882068537572+\cdots)q^{3}+\cdots$
2.68.a.b	$3$	$56.858$	$\mathbb{Q}[x]/(x^{3} - \cdots)$	None	$25769803776$	$-2\!\cdots\!44$	$69\!\cdots\!90$	$-4\!\cdots\!92$	$-$	$q+2^{33}q^{2}+(-794134480773348+\cdots)q^{3}+\cdots$
1.96.a.a	$8$	$57.154$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	$-5\!\cdots\!80$	$-9\!\cdots\!80$	$19\!\cdots\!60$	$31\!\cdots\!00$	$+$	$q+(-729457392285+\beta _{1})q^{2}+\cdots$
1.98.a.a	$7$	$59.585$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	$-1\!\cdots\!08$	$10\!\cdots\!96$	$-3\!\cdots\!50$	$-1\!\cdots\!08$	$+$	$q+(-2385320155001+\beta _{1})q^{2}+\cdots$
2.70.a.a	$3$	$60.303$	$\mathbb{Q}[x]/(x^{3} - \cdots)$	None	$-51539607552$	$15\!\cdots\!12$	$20\!\cdots\!70$	$-2\!\cdots\!96$	$+$	$q-2^{34}q^{2}+(5160893455497204+\cdots)q^{3}+\cdots$
2.70.a.b	$3$	$60.303$	$\mathbb{Q}[x]/(x^{3} - \cdots)$	None	$51539607552$	$-2\!\cdots\!52$	$-5\!\cdots\!50$	$92\!\cdots\!16$	$-$	$q+2^{34}q^{2}+(-7866377652201484+\cdots)q^{3}+\cdots$
1.100.a.a	$8$	$62.068$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	$-2\!\cdots\!20$	$-2\!\cdots\!20$	$-4\!\cdots\!60$	$-5\!\cdots\!00$	$+$	$q+(-26005077112815+\beta _{1})q^{2}+\cdots$
2.72.a.a	$2$	$63.849$	$\mathbb{Q}[x]/(x^{2} - \cdots)$	None	$68719476736$	$-7\!\cdots\!24$	$40\!\cdots\!00$	$-2\!\cdots\!52$	$-$	$q+2^{35}q^{2}+(-36645276287423412+\cdots)q^{3}+\cdots$
2.72.a.b	$3$	$63.849$	$\mathbb{Q}[x]/(x^{3} - \cdots)$	None	$-103079215104$	$23\!\cdots\!36$	$47\!\cdots\!50$	$-6\!\cdots\!72$	$+$	$q-2^{35}q^{2}+(787523430902412+\beta _{1}+\cdots)q^{3}+\cdots$
1.102.a.a	$8$	$64.601$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	$-4\!\cdots\!40$	$-1\!\cdots\!60$	$38\!\cdots\!00$	$-5\!\cdots\!00$	$+$	$q+(-54373636474380-\beta _{1})q^{2}+\cdots$
1.104.a.a	$8$	$67.184$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	$43\!\cdots\!40$	$50\!\cdots\!40$	$55\!\cdots\!20$	$41\!\cdots\!00$	$+$	$q+(548616194585055-\beta _{1})q^{2}+\cdots$
2.74.a.a	$3$	$67.497$	$\mathbb{Q}[x]/(x^{3} - \cdots)$	None	$-206158430208$	$-3\!\cdots\!72$	$-3\!\cdots\!50$	$-2\!\cdots\!64$	$+$	$q-2^{36}q^{2}+(-101346400339911324+\cdots)q^{3}+\cdots$
2.74.a.b	$4$	$67.497$	$\mathbb{Q}[x]/(x^{4} - \cdots)$	None	$274877906944$	$30\!\cdots\!76$	$-7\!\cdots\!60$	$36\!\cdots\!12$	$-$	$q+2^{36}q^{2}+(76266581430811044+\cdots)q^{3}+\cdots$
1.106.a.a	$8$	$69.819$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	$-9\!\cdots\!20$	$-3\!\cdots\!80$	$74\!\cdots\!00$	$70\!\cdots\!00$	$+$	$q+(-1146879061146990+\beta _{1})q^{2}+\cdots$
2.76.a.a	$3$	$71.246$	$\mathbb{Q}[x]/(x^{3} - \cdots)$	None	$-412316860416$	$12\!\cdots\!04$	$16\!\cdots\!50$	$49\!\cdots\!12$	$+$	$q-2^{37}q^{2}+(415752245544732668+\cdots)q^{3}+\cdots$
2.76.a.b	$3$	$71.246$	$\mathbb{Q}[x]/(x^{3} - \cdots)$	None	$412316860416$	$45\!\cdots\!16$	$-1\!\cdots\!90$	$-3\!\cdots\!52$	$-$	$q+2^{37}q^{2}+(152747388742936572+\cdots)q^{3}+\cdots$
1.108.a.a	$9$	$72.504$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	$54\!\cdots\!96$	$15\!\cdots\!12$	$24\!\cdots\!50$	$-9\!\cdots\!44$	$+$	$q+(607308845937277-\beta _{1})q^{2}+\cdots$
2.78.a.a	$3$	$75.096$	$\mathbb{Q}[x]/(x^{3} - \cdots)$	None	$-824633720832$	$-2\!\cdots\!88$	$30\!\cdots\!10$	$-2\!\cdots\!16$	$+$	$q-2^{38}q^{2}+(-842429601461527596+\cdots)q^{3}+\cdots$
2.78.a.b	$3$	$75.096$	$\mathbb{Q}[x]/(x^{3} - \cdots)$	None	$824633720832$	$-1\!\cdots\!92$	$64\!\cdots\!50$	$-1\!\cdots\!44$	$-$	$q+2^{38}q^{2}+(-37139225154949164+\cdots)q^{3}+\cdots$
1.110.a.a	$8$	$75.239$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	$22\!\cdots\!00$	$-7\!\cdots\!00$	$-2\!\cdots\!00$	$23\!\cdots\!00$	$+$	$q+(286049075864400-\beta _{1})q^{2}+\cdots$
3.65.b.a	$20$	$77.821$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	None	$0$	$-1\!\cdots\!92$	$0$	$68\!\cdots\!76$		$q+\beta _{1}q^{2}+(-71037898477915+13312\beta _{1}+\cdots)q^{3}+\cdots$
1.112.a.a	$9$	$78.026$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	$73\!\cdots\!76$	$23\!\cdots\!52$	$81\!\cdots\!30$	$78\!\cdots\!56$	$+$	$q+(811166749386264+\beta _{1})q^{2}+\cdots$
2.80.a.a	$3$	$79.047$	$\mathbb{Q}[x]/(x^{3} - \cdots)$	None	$16\!\cdots\!64$	$-4\!\cdots\!36$	$-4\!\cdots\!50$	$14\!\cdots\!12$	$-$	$q+2^{39}q^{2}+(-1528323113916241812+\cdots)q^{3}+\cdots$
2.80.a.b	$4$	$79.047$	$\mathbb{Q}[x]/(x^{4} - \cdots)$	None	$-2\!\cdots\!52$	$43\!\cdots\!88$	$-2\!\cdots\!80$	$25\!\cdots\!04$	$+$	$q-2^{39}q^{2}+(1099291558848636972+\cdots)q^{3}+\cdots$
3.66.a.a	$5$	$80.272$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	None	$-2586530964$	$-9\!\cdots\!05$	$-8\!\cdots\!94$	$57\!\cdots\!24$	$+$	$q+(-517306193-\beta _{1})q^{2}-3^{32}q^{3}+\cdots$
3.66.a.b	$6$	$80.272$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	$6210982962$	$11\!\cdots\!46$	$35\!\cdots\!00$	$13\!\cdots\!04$	$-$	$q+(1035163827+\beta _{1})q^{2}+3^{32}q^{3}+\cdots$
1.114.a.a	$9$	$80.863$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	$49\!\cdots\!32$	$-1\!\cdots\!24$	$-3\!\cdots\!50$	$-1\!\cdots\!08$	$+$	$q+(552636039763781+\beta _{1})q^{2}+\cdots$
3.67.b.a	$1$	$82.760$	$\Q$	$\Q(\sqrt{-3}) $	$0$	$-5\!\cdots\!23$	$0$	$-1\!\cdots\!14$		$q-3^{33}q^{3}+2^{66}q^{4}+\cdots$
3.67.b.b	$20$	$82.760$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	None	$0$	$48\!\cdots\!16$	$0$	$12\!\cdots\!88$		$q+\beta _{1}q^{2}+(243548779847726+15513\beta _{1}+\cdots)q^{3}+\cdots$
2.82.a.a	$3$	$83.100$	$\mathbb{Q}[x]/(x^{3} - \cdots)$	None	$-3\!\cdots\!28$	$12\!\cdots\!88$	$-2\!\cdots\!50$	$-5\!\cdots\!24$	$+$	$q-2^{40}q^{2}+(4201453557463404996+\cdots)q^{3}+\cdots$
2.82.a.b	$4$	$83.100$	$\mathbb{Q}[x]/(x^{4} - \cdots)$	None	$43\!\cdots\!04$	$-7\!\cdots\!04$	$24\!\cdots\!80$	$18\!\cdots\!92$	$-$	$q+2^{40}q^{2}+(-1777934344659239676+\cdots)q^{3}+\cdots$
1.116.a.a	$9$	$83.750$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	$-1\!\cdots\!44$	$34\!\cdots\!92$	$-9\!\cdots\!90$	$18\!\cdots\!56$	$+$	$q+(-12908974454383949-\beta _{1}+\cdots)q^{2}+\cdots$
3.68.a.a	$5$	$85.287$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	None	$-16255223088$	$27\!\cdots\!15$	$-7\!\cdots\!10$	$28\!\cdots\!08$	$-$	$q+(-3251044618-\beta _{1})q^{2}+3^{33}q^{3}+\cdots$

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Introduction	Features
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Label	Dim.	\(A\)	Field	CM	Traces				Fricke sign	$q$-expansion
Label	Dim.	\(A\)	Field	CM	\(a_2\)	\(a_3\)	\(a_5\)	\(a_7\)	Fricke sign	$q$-expansion
1.66.a.a	\(5\)	\(26.757\)	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	\(-3959709648\)	\(-2\!\cdots\!04\)	\(26\!\cdots\!50\)	\(-6\!\cdots\!08\)	\(+\)	\(q+(-791941930-\beta _{1})q^{2}+(-446261486940055+\cdots)q^{3}+\cdots\)
1.68.a.a	\(5\)	\(28.429\)	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	\(5554901256\)	\(34\!\cdots\!72\)	\(33\!\cdots\!50\)	\(33\!\cdots\!56\)	\(+\)	\(q+(1110980251-\beta _{1})q^{2}+(688672053797479+\cdots)q^{3}+\cdots\)
1.70.a.a	\(5\)	\(30.151\)	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	\(-18005734368\)	\(-4\!\cdots\!04\)	\(-1\!\cdots\!50\)	\(76\!\cdots\!92\)	\(+\)	\(q+(-3601146874-\beta _{1})q^{2}+(-971616465424800+\cdots)q^{3}+\cdots\)
1.72.a.a	\(6\)	\(31.925\)	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	\(66157336440\)	\(89\!\cdots\!40\)	\(-4\!\cdots\!20\)	\(33\!\cdots\!00\)	\(+\)	\(q+(11026222740-\beta _{1})q^{2}+(14982825462961740+\cdots)q^{3}+\cdots\)
1.74.a.a	\(5\)	\(33.748\)	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	\(-92089333488\)	\(-1\!\cdots\!04\)	\(23\!\cdots\!50\)	\(-4\!\cdots\!08\)	\(+\)	\(q+(-18417866698-\beta _{1})q^{2}+\cdots\)
1.76.a.a	\(6\)	\(35.623\)	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	\(-57080822040\)	\(-7\!\cdots\!40\)	\(-3\!\cdots\!40\)	\(19\!\cdots\!00\)	\(+\)	\(q+(-9513470340+\beta _{1})q^{2}+\cdots\)
1.78.a.a	\(6\)	\(37.548\)	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	\(264721893120\)	\(14\!\cdots\!80\)	\(-2\!\cdots\!00\)	\(27\!\cdots\!00\)	\(+\)	\(q+(44120315520-\beta _{1})q^{2}+(240268562631348180+\cdots)q^{3}+\cdots\)
1.80.a.a	\(6\)	\(39.524\)	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	\(-16086577320\)	\(19\!\cdots\!80\)	\(60\!\cdots\!40\)	\(-2\!\cdots\!00\)	\(+\)	\(q+(-2681096220+\beta _{1})q^{2}+\cdots\)
1.82.a.a	\(6\)	\(41.550\)	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	\(-460872026640\)	\(-1\!\cdots\!60\)	\(-1\!\cdots\!00\)	\(-3\!\cdots\!00\)	\(+\)	\(q+(-76812004440-\beta _{1})q^{2}+\cdots\)
1.84.a.a	\(7\)	\(43.627\)	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	\(347450761416\)	\(92\!\cdots\!72\)	\(95\!\cdots\!70\)	\(41\!\cdots\!56\)	\(+\)	\(q+(49635823059+\beta _{1})q^{2}+\cdots\)
1.86.a.a	\(6\)	\(45.755\)	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	\(-3\!\cdots\!00\)	\(-1\!\cdots\!00\)	\(-9\!\cdots\!00\)	\(37\!\cdots\!00\)	\(+\)	\(q+(-599485114800+\beta _{1})q^{2}+\cdots\)
1.88.a.a	\(7\)	\(47.933\)	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	\(18\!\cdots\!36\)	\(-7\!\cdots\!48\)	\(33\!\cdots\!50\)	\(45\!\cdots\!56\)	\(+\)	\(q+(2599574577562+\beta _{1})q^{2}+\cdots\)
1.90.a.a	\(7\)	\(50.162\)	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	\(-3\!\cdots\!08\)	\(-1\!\cdots\!64\)	\(10\!\cdots\!50\)	\(38\!\cdots\!92\)	\(+\)	\(q+(-4486761478773-\beta _{1})q^{2}+\cdots\)
1.92.a.a	\(7\)	\(52.442\)	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	\(38\!\cdots\!56\)	\(62\!\cdots\!32\)	\(23\!\cdots\!30\)	\(-1\!\cdots\!44\)	\(+\)	\(q+(548816691151+\beta _{1})q^{2}+\cdots\)
2.66.a.a	\(2\)	\(53.514\)	\(\mathbb{Q}[x]/(x^{2} - \cdots)\)	None	\(-8589934592\)	\(11\!\cdots\!92\)	\(-7\!\cdots\!00\)	\(27\!\cdots\!24\)	\(+\)	\(q-2^{32}q^{2}+(574529980102596-111\beta )q^{3}+\cdots\)
2.66.a.b	\(3\)	\(53.514\)	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	\(12884901888\)	\(29\!\cdots\!12\)	\(39\!\cdots\!50\)	\(42\!\cdots\!64\)	\(-\)	\(q+2^{32}q^{2}+(994852866070404-\beta _{1}+\cdots)q^{3}+\cdots\)
1.94.a.a	\(7\)	\(54.773\)	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	\(43\!\cdots\!92\)	\(-3\!\cdots\!84\)	\(-2\!\cdots\!50\)	\(-9\!\cdots\!08\)	\(+\)	\(q+(6247918101970+\beta _{1})q^{2}+\cdots\)
2.68.a.a	\(3\)	\(56.858\)	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	\(-25769803776\)	\(-5\!\cdots\!16\)	\(-2\!\cdots\!50\)	\(21\!\cdots\!12\)	\(+\)	\(q-2^{33}q^{2}+(-1741882068537572+\cdots)q^{3}+\cdots\)
2.68.a.b	\(3\)	\(56.858\)	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	\(25769803776\)	\(-2\!\cdots\!44\)	\(69\!\cdots\!90\)	\(-4\!\cdots\!92\)	\(-\)	\(q+2^{33}q^{2}+(-794134480773348+\cdots)q^{3}+\cdots\)
1.96.a.a	\(8\)	\(57.154\)	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	\(-5\!\cdots\!80\)	\(-9\!\cdots\!80\)	\(19\!\cdots\!60\)	\(31\!\cdots\!00\)	\(+\)	\(q+(-729457392285+\beta _{1})q^{2}+\cdots\)
1.98.a.a	\(7\)	\(59.585\)	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	\(-1\!\cdots\!08\)	\(10\!\cdots\!96\)	\(-3\!\cdots\!50\)	\(-1\!\cdots\!08\)	\(+\)	\(q+(-2385320155001+\beta _{1})q^{2}+\cdots\)
2.70.a.a	\(3\)	\(60.303\)	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	\(-51539607552\)	\(15\!\cdots\!12\)	\(20\!\cdots\!70\)	\(-2\!\cdots\!96\)	\(+\)	\(q-2^{34}q^{2}+(5160893455497204+\cdots)q^{3}+\cdots\)
2.70.a.b	\(3\)	\(60.303\)	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	\(51539607552\)	\(-2\!\cdots\!52\)	\(-5\!\cdots\!50\)	\(92\!\cdots\!16\)	\(-\)	\(q+2^{34}q^{2}+(-7866377652201484+\cdots)q^{3}+\cdots\)
1.100.a.a	\(8\)	\(62.068\)	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	\(-2\!\cdots\!20\)	\(-2\!\cdots\!20\)	\(-4\!\cdots\!60\)	\(-5\!\cdots\!00\)	\(+\)	\(q+(-26005077112815+\beta _{1})q^{2}+\cdots\)
2.72.a.a	\(2\)	\(63.849\)	\(\mathbb{Q}[x]/(x^{2} - \cdots)\)	None	\(68719476736\)	\(-7\!\cdots\!24\)	\(40\!\cdots\!00\)	\(-2\!\cdots\!52\)	\(-\)	\(q+2^{35}q^{2}+(-36645276287423412+\cdots)q^{3}+\cdots\)
2.72.a.b	\(3\)	\(63.849\)	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	\(-103079215104\)	\(23\!\cdots\!36\)	\(47\!\cdots\!50\)	\(-6\!\cdots\!72\)	\(+\)	\(q-2^{35}q^{2}+(787523430902412+\beta _{1}+\cdots)q^{3}+\cdots\)
1.102.a.a	\(8\)	\(64.601\)	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	\(-4\!\cdots\!40\)	\(-1\!\cdots\!60\)	\(38\!\cdots\!00\)	\(-5\!\cdots\!00\)	\(+\)	\(q+(-54373636474380-\beta _{1})q^{2}+\cdots\)
1.104.a.a	\(8\)	\(67.184\)	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	\(43\!\cdots\!40\)	\(50\!\cdots\!40\)	\(55\!\cdots\!20\)	\(41\!\cdots\!00\)	\(+\)	\(q+(548616194585055-\beta _{1})q^{2}+\cdots\)
2.74.a.a	\(3\)	\(67.497\)	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	\(-206158430208\)	\(-3\!\cdots\!72\)	\(-3\!\cdots\!50\)	\(-2\!\cdots\!64\)	\(+\)	\(q-2^{36}q^{2}+(-101346400339911324+\cdots)q^{3}+\cdots\)
2.74.a.b	\(4\)	\(67.497\)	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	\(274877906944\)	\(30\!\cdots\!76\)	\(-7\!\cdots\!60\)	\(36\!\cdots\!12\)	\(-\)	\(q+2^{36}q^{2}+(76266581430811044+\cdots)q^{3}+\cdots\)
1.106.a.a	\(8\)	\(69.819\)	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	\(-9\!\cdots\!20\)	\(-3\!\cdots\!80\)	\(74\!\cdots\!00\)	\(70\!\cdots\!00\)	\(+\)	\(q+(-1146879061146990+\beta _{1})q^{2}+\cdots\)
2.76.a.a	\(3\)	\(71.246\)	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	\(-412316860416\)	\(12\!\cdots\!04\)	\(16\!\cdots\!50\)	\(49\!\cdots\!12\)	\(+\)	\(q-2^{37}q^{2}+(415752245544732668+\cdots)q^{3}+\cdots\)
2.76.a.b	\(3\)	\(71.246\)	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	\(412316860416\)	\(45\!\cdots\!16\)	\(-1\!\cdots\!90\)	\(-3\!\cdots\!52\)	\(-\)	\(q+2^{37}q^{2}+(152747388742936572+\cdots)q^{3}+\cdots\)
1.108.a.a	\(9\)	\(72.504\)	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	\(54\!\cdots\!96\)	\(15\!\cdots\!12\)	\(24\!\cdots\!50\)	\(-9\!\cdots\!44\)	\(+\)	\(q+(607308845937277-\beta _{1})q^{2}+\cdots\)
2.78.a.a	\(3\)	\(75.096\)	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	\(-824633720832\)	\(-2\!\cdots\!88\)	\(30\!\cdots\!10\)	\(-2\!\cdots\!16\)	\(+\)	\(q-2^{38}q^{2}+(-842429601461527596+\cdots)q^{3}+\cdots\)
2.78.a.b	\(3\)	\(75.096\)	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	\(824633720832\)	\(-1\!\cdots\!92\)	\(64\!\cdots\!50\)	\(-1\!\cdots\!44\)	\(-\)	\(q+2^{38}q^{2}+(-37139225154949164+\cdots)q^{3}+\cdots\)
1.110.a.a	\(8\)	\(75.239\)	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	\(22\!\cdots\!00\)	\(-7\!\cdots\!00\)	\(-2\!\cdots\!00\)	\(23\!\cdots\!00\)	\(+\)	\(q+(286049075864400-\beta _{1})q^{2}+\cdots\)
3.65.b.a	\(20\)	\(77.821\)	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None	\(0\)	\(-1\!\cdots\!92\)	\(0\)	\(68\!\cdots\!76\)		\(q+\beta _{1}q^{2}+(-71037898477915+13312\beta _{1}+\cdots)q^{3}+\cdots\)
1.112.a.a	\(9\)	\(78.026\)	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	\(73\!\cdots\!76\)	\(23\!\cdots\!52\)	\(81\!\cdots\!30\)	\(78\!\cdots\!56\)	\(+\)	\(q+(811166749386264+\beta _{1})q^{2}+\cdots\)
2.80.a.a	\(3\)	\(79.047\)	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	\(16\!\cdots\!64\)	\(-4\!\cdots\!36\)	\(-4\!\cdots\!50\)	\(14\!\cdots\!12\)	\(-\)	\(q+2^{39}q^{2}+(-1528323113916241812+\cdots)q^{3}+\cdots\)
2.80.a.b	\(4\)	\(79.047\)	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	\(-2\!\cdots\!52\)	\(43\!\cdots\!88\)	\(-2\!\cdots\!80\)	\(25\!\cdots\!04\)	\(+\)	\(q-2^{39}q^{2}+(1099291558848636972+\cdots)q^{3}+\cdots\)
3.66.a.a	\(5\)	\(80.272\)	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	\(-2586530964\)	\(-9\!\cdots\!05\)	\(-8\!\cdots\!94\)	\(57\!\cdots\!24\)	\(+\)	\(q+(-517306193-\beta _{1})q^{2}-3^{32}q^{3}+\cdots\)
3.66.a.b	\(6\)	\(80.272\)	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	\(6210982962\)	\(11\!\cdots\!46\)	\(35\!\cdots\!00\)	\(13\!\cdots\!04\)	\(-\)	\(q+(1035163827+\beta _{1})q^{2}+3^{32}q^{3}+\cdots\)
1.114.a.a	\(9\)	\(80.863\)	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	\(49\!\cdots\!32\)	\(-1\!\cdots\!24\)	\(-3\!\cdots\!50\)	\(-1\!\cdots\!08\)	\(+\)	\(q+(552636039763781+\beta _{1})q^{2}+\cdots\)
3.67.b.a	\(1\)	\(82.760\)	\(\Q\)	\(\Q(\sqrt{-3}) \)	\(0\)	\(-5\!\cdots\!23\)	\(0\)	\(-1\!\cdots\!14\)		\(q-3^{33}q^{3}+2^{66}q^{4}+\cdots\)
3.67.b.b	\(20\)	\(82.760\)	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None	\(0\)	\(48\!\cdots\!16\)	\(0\)	\(12\!\cdots\!88\)		\(q+\beta _{1}q^{2}+(243548779847726+15513\beta _{1}+\cdots)q^{3}+\cdots\)
2.82.a.a	\(3\)	\(83.100\)	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	\(-3\!\cdots\!28\)	\(12\!\cdots\!88\)	\(-2\!\cdots\!50\)	\(-5\!\cdots\!24\)	\(+\)	\(q-2^{40}q^{2}+(4201453557463404996+\cdots)q^{3}+\cdots\)
2.82.a.b	\(4\)	\(83.100\)	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	\(43\!\cdots\!04\)	\(-7\!\cdots\!04\)	\(24\!\cdots\!80\)	\(18\!\cdots\!92\)	\(-\)	\(q+2^{40}q^{2}+(-1777934344659239676+\cdots)q^{3}+\cdots\)
1.116.a.a	\(9\)	\(83.750\)	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	\(-1\!\cdots\!44\)	\(34\!\cdots\!92\)	\(-9\!\cdots\!90\)	\(18\!\cdots\!56\)	\(+\)	\(q+(-12908974454383949-\beta _{1}+\cdots)q^{2}+\cdots\)
3.68.a.a	\(5\)	\(85.287\)	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	\(-16255223088\)	\(27\!\cdots\!15\)	\(-7\!\cdots\!10\)	\(28\!\cdots\!08\)	\(-\)	\(q+(-3251044618-\beta _{1})q^{2}+3^{33}q^{3}+\cdots\)

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.