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
1.34.a.a	$2$	$6.898$	$\mathbb{Q}[x]/(x^{2} - \cdots)$	None	$-121680$	$37919880$	$-181061536500$	$-6\!\cdots\!00$	$+$	$q+(-60840-\beta )q^{2}+(18959940+312\beta )q^{3}+\cdots$
1.36.a.a	$3$	$7.760$	$\mathbb{Q}[x]/(x^{3} - \cdots)$	None	$139656$	$-104875308$	$892652054010$	$87\!\cdots\!56$	$+$	$q+(46552+\beta _{1})q^{2}+(-34958436+\cdots)q^{3}+\cdots$
1.38.a.a	$2$	$8.671$	$\mathbb{Q}[x]/(x^{2} - \cdots)$	None	$-194400$	$13991400$	$55\!\cdots\!00$	$-3\!\cdots\!00$	$+$	$q+(-97200-\beta )q^{2}+(6995700+72\beta )q^{3}+\cdots$
1.40.a.a	$3$	$9.634$	$\mathbb{Q}[x]/(x^{3} - \cdots)$	None	$548856$	$1109442852$	$17\!\cdots\!90$	$-1\!\cdots\!44$	$+$	$q+(182952-\beta _{1})q^{2}+(369814284+\cdots)q^{3}+\cdots$
1.42.a.a	$3$	$10.647$	$\mathbb{Q}[x]/(x^{3} - \cdots)$	None	$-344688$	$-10820953044$	$-2\!\cdots\!50$	$57\!\cdots\!92$	$+$	$q+(-114896+\beta _{1})q^{2}+(-3606984348+\cdots)q^{3}+\cdots$
1.44.a.a	$3$	$11.711$	$\mathbb{Q}[x]/(x^{3} - \cdots)$	None	$-2209944$	$24401437812$	$53\!\cdots\!70$	$30\!\cdots\!56$	$+$	$q+(-736648-\beta _{1})q^{2}+(8133812604+\cdots)q^{3}+\cdots$
1.46.a.a	$3$	$12.826$	$\mathbb{Q}[x]/(x^{3} - \cdots)$	None	$3814272$	$5359866876$	$-9\!\cdots\!50$	$-7\!\cdots\!08$	$+$	$q+(1271424+\beta _{1})q^{2}+(1786622292+\cdots)q^{3}+\cdots$
2.34.a.a	$1$	$13.797$	$\Q$	None	$-65536$	$-133005564$	$538799132550$	$-3\!\cdots\!68$	$+$	$q-2^{16}q^{2}-133005564q^{3}+2^{32}q^{4}+\cdots$
2.34.a.b	$2$	$13.797$	$\mathbb{Q}[x]/(x^{2} - \cdots)$	None	$131072$	$8356488$	$-5332476660$	$13\!\cdots\!56$	$-$	$q+2^{16}q^{2}+(4178244-\beta )q^{3}+2^{32}q^{4}+\cdots$
1.48.a.a	$4$	$13.991$	$\mathbb{Q}[x]/(x^{4} - \cdots)$	None	$5785560$	$38461494960$	$-3\!\cdots\!00$	$-3\!\cdots\!00$	$+$	$q+(1446390+\beta _{1})q^{2}+(9615373740+\cdots)q^{3}+\cdots$
1.50.a.a	$3$	$15.207$	$\mathbb{Q}[x]/(x^{3} - \cdots)$	None	$-24225168$	$-326954692404$	$63\!\cdots\!50$	$50\!\cdots\!92$	$+$	$q+(-8075056+\beta _{1})q^{2}+(-108984897468+\cdots)q^{3}+\cdots$
2.36.a.a	$1$	$15.519$	$\Q$	None	$-131072$	$36494748$	$389070858750$	$-1\!\cdots\!56$	$+$	$q-2^{17}q^{2}+36494748q^{3}+2^{34}q^{4}+\cdots$
2.36.a.b	$1$	$15.519$	$\Q$	None	$131072$	$159933852$	$-2\!\cdots\!90$	$-7\!\cdots\!44$	$-$	$q+2^{17}q^{2}+159933852q^{3}+2^{34}q^{4}+\cdots$
1.52.a.a	$4$	$16.473$	$\mathbb{Q}[x]/(x^{4} - \cdots)$	None	$32756040$	$403863773040$	$12\!\cdots\!80$	$65\!\cdots\!00$	$+$	$q+(8189010+\beta _{1})q^{2}+(100965943260+\cdots)q^{3}+\cdots$
2.38.a.a	$2$	$17.343$	$\mathbb{Q}[x]/(x^{2} - \cdots)$	None	$-524288$	$423071208$	$-1\!\cdots\!40$	$31\!\cdots\!56$	$+$	$q-2^{18}q^{2}+(211535604-\beta )q^{3}+2^{36}q^{4}+\cdots$
2.38.a.b	$2$	$17.343$	$\mathbb{Q}[x]/(x^{2} - \cdots)$	None	$524288$	$-501686808$	$41\!\cdots\!00$	$-3\!\cdots\!56$	$-$	$q+2^{18}q^{2}+(-250843404-\beta )q^{3}+\cdots$
1.54.a.a	$4$	$17.790$	$\mathbb{Q}[x]/(x^{4} - \cdots)$	None	$-68476320$	$-1\!\cdots\!80$	$-4\!\cdots\!00$	$-2\!\cdots\!00$	$+$	$q+(-17119080+\beta _{1})q^{2}+(-262102751820+\cdots)q^{3}+\cdots$
1.56.a.a	$4$	$19.158$	$\mathbb{Q}[x]/(x^{4} - \cdots)$	None	$208622520$	$-6\!\cdots\!80$	$14\!\cdots\!60$	$-2\!\cdots\!00$	$+$	$q+(52155630+\beta _{1})q^{2}+(-1705367672820+\cdots)q^{3}+\cdots$
2.40.a.a	$1$	$19.268$	$\Q$	None	$524288$	$-735458292$	$-1\!\cdots\!50$	$16\!\cdots\!64$	$-$	$q+2^{19}q^{2}-735458292q^{3}+2^{38}q^{4}+\cdots$
2.40.a.b	$2$	$19.268$	$\mathbb{Q}[x]/(x^{2} - \cdots)$	None	$-1048576$	$287418264$	$53\!\cdots\!20$	$74\!\cdots\!12$	$+$	$q-2^{19}q^{2}+(143709132-\beta )q^{3}+2^{38}q^{4}+\cdots$
3.33.b.a	$10$	$19.460$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	None	$0$	$-21387150$	$0$	$-5\!\cdots\!40$		$q+\beta _{1}q^{2}+(-2138715+35\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots$
1.58.a.a	$4$	$20.577$	$\mathbb{Q}[x]/(x^{4} - \cdots)$	None	$-217744560$	$37\!\cdots\!60$	$-1\!\cdots\!00$	$95\!\cdots\!00$	$+$	$q+(-54436140+\beta _{1})q^{2}+(9368965543140+\cdots)q^{3}+\cdots$
3.34.a.a	$3$	$20.695$	$\mathbb{Q}[x]/(x^{3} - \cdots)$	None	$41202$	$129140163$	$51261823890$	$76\!\cdots\!56$	$-$	$q+(13734-\beta _{1})q^{2}+3^{16}q^{3}+(-369155924+\cdots)q^{4}+\cdots$
3.34.a.b	$3$	$20.695$	$\mathbb{Q}[x]/(x^{3} - \cdots)$	None	$136620$	$-129140163$	$-260488036134$	$10\!\cdots\!32$	$+$	$q+(45540-\beta _{1})q^{2}-3^{16}q^{3}+(4863185200+\cdots)q^{4}+\cdots$
2.42.a.a	$1$	$21.294$	$\Q$	None	$-1048576$	$5043516516$	$-4\!\cdots\!50$	$-1\!\cdots\!68$	$+$	$q-2^{20}q^{2}+5043516516q^{3}+2^{40}q^{4}+\cdots$
2.42.a.b	$2$	$21.294$	$\mathbb{Q}[x]/(x^{2} - \cdots)$	None	$2097152$	$8863347528$	$97\!\cdots\!80$	$21\!\cdots\!56$	$-$	$q+2^{20}q^{2}+(4431673764-\beta )q^{3}+\cdots$
3.35.b.a	$10$	$21.968$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	None	$0$	$119369106$	$0$	$-1\!\cdots\!72$		$q+\beta _{1}q^{2}+(11936911+41\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots$
1.60.a.a	$5$	$22.046$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	None	$-449691864$	$84\!\cdots\!32$	$17\!\cdots\!90$	$14\!\cdots\!56$	$+$	$q+(-89938373-\beta _{1})q^{2}+(16803326335969+\cdots)q^{3}+\cdots$
3.36.a.a	$2$	$23.279$	$\Q(\sqrt{2196841}) $	None	$-60912$	$258280326$	$-1\!\cdots\!40$	$-1\!\cdots\!44$	$-$	$q+(-30456-\beta )q^{2}+3^{17}q^{3}+(28571469952+\cdots)q^{4}+\cdots$
3.36.a.b	$3$	$23.279$	$\mathbb{Q}[x]/(x^{3} - \cdots)$	None	$-87330$	$-387420489$	$27\!\cdots\!10$	$48\!\cdots\!64$	$+$	$q+(-29110+\beta _{1})q^{2}-3^{17}q^{3}+(10829584300+\cdots)q^{4}+\cdots$
2.44.a.a	$2$	$23.422$	$\mathbb{Q}[x]/(x^{2} - \cdots)$	None	$-4194304$	$-12981630984$	$-3\!\cdots\!00$	$11\!\cdots\!08$	$+$	$q-2^{21}q^{2}+(-6490815492-\beta )q^{3}+\cdots$
2.44.a.b	$2$	$23.422$	$\mathbb{Q}[x]/(x^{2} - \cdots)$	None	$4194304$	$-22341634056$	$-4\!\cdots\!20$	$-2\!\cdots\!28$	$-$	$q+2^{21}q^{2}+(-11170817028-\beta )q^{3}+\cdots$
1.62.a.a	$4$	$23.566$	$\mathbb{Q}[x]/(x^{4} - \cdots)$	None	$1146312000$	$-5\!\cdots\!00$	$-5\!\cdots\!00$	$-6\!\cdots\!00$	$+$	$q+(286578000-\beta _{1})q^{2}+(-143430899755500+\cdots)q^{3}+\cdots$
3.37.b.a	$1$	$24.627$	$\Q$	$\Q(\sqrt{-3}) $	$0$	$387420489$	$0$	$27\!\cdots\!98$		$q+3^{18}q^{3}+2^{36}q^{4}+2757049053441698q^{7}+\cdots$
3.37.b.b	$10$	$24.627$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	None	$0$	$-552156750$	$0$	$-1\!\cdots\!00$		$q+\beta _{1}q^{2}+(-55215675-69\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots$
1.64.a.a	$5$	$25.136$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	None	$507315096$	$95\!\cdots\!52$	$-5\!\cdots\!30$	$37\!\cdots\!56$	$+$	$q+(101463019-\beta _{1})q^{2}+(190649070219572+\cdots)q^{3}+\cdots$
2.46.a.a	$2$	$25.651$	$\mathbb{Q}[x]/(x^{2} - \cdots)$	None	$-8388608$	$-69766206552$	$-4\!\cdots\!00$	$-9\!\cdots\!44$	$+$	$q-2^{22}q^{2}+(-34883103276-\beta )q^{3}+\cdots$
2.46.a.b	$2$	$25.651$	$\mathbb{Q}[x]/(x^{2} - \cdots)$	None	$8388608$	$59861217192$	$43\!\cdots\!00$	$79\!\cdots\!24$	$-$	$q+2^{22}q^{2}+(29930608596-\beta )q^{3}+\cdots$
4.33.b.a	$1$	$25.947$	$\Q$	$\Q(\sqrt{-1}) $	$65536$	$0$	$-196496109694$	$0$		$q+2^{16}q^{2}+2^{32}q^{4}-196496109694q^{5}+\cdots$
4.33.b.b	$14$	$25.947$	$\mathbb{Q}[x]/(x^{14} + \cdots)$	None	$-23780$	$0$	$138121491740$	$0$		$q+(-1699+\beta _{1})q^{2}+(9-21\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots$
3.38.a.a	$3$	$26.014$	$\mathbb{Q}[x]/(x^{3} - \cdots)$	None	$-310908$	$-1162261467$	$-9\!\cdots\!90$	$-4\!\cdots\!44$	$+$	$q+(-103636-\beta _{1})q^{2}-3^{18}q^{3}+(112825533616+\cdots)q^{4}+\cdots$
3.38.a.b	$4$	$26.014$	$\mathbb{Q}[x]/(x^{4} - \cdots)$	None	$437562$	$1549681956$	$-4\!\cdots\!04$	$66\!\cdots\!84$	$-$	$q+(109391-\beta _{1})q^{2}+3^{18}q^{3}+(86524834843+\cdots)q^{4}+\cdots$
3.39.b.a	$12$	$27.439$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None	$0$	$-114742404$	$0$	$81\!\cdots\!48$		$q+\beta _{1}q^{2}+(-9561867+97\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots$
4.34.a.a	$3$	$27.593$	$\mathbb{Q}[x]/(x^{3} - \cdots)$	None	$0$	$92491788$	$-53880683886$	$45\!\cdots\!92$	$-$	$q+(30830596+\beta _{1})q^{3}+(-17960227962+\cdots)q^{5}+\cdots$
2.48.a.a	$1$	$27.982$	$\Q$	None	$8388608$	$-196634580372$	$20\!\cdots\!50$	$-5\!\cdots\!96$	$-$	$q+2^{23}q^{2}-196634580372q^{3}+2^{46}q^{4}+\cdots$
2.48.a.b	$2$	$27.982$	$\mathbb{Q}[x]/(x^{2} - \cdots)$	None	$-16777216$	$122289844824$	$18\!\cdots\!40$	$16\!\cdots\!32$	$+$	$q-2^{23}q^{2}+(61144922412-5\beta )q^{3}+\cdots$
3.40.a.a	$3$	$28.902$	$\mathbb{Q}[x]/(x^{3} - \cdots)$	None	$-1107000$	$3486784401$	$93\!\cdots\!90$	$13\!\cdots\!04$	$-$	$q+(-369000-\beta _{1})q^{2}+3^{19}q^{3}+(335300075200+\cdots)q^{4}+\cdots$
3.40.a.b	$3$	$28.902$	$\mathbb{Q}[x]/(x^{3} - \cdots)$	None	$533574$	$-3486784401$	$-5\!\cdots\!30$	$-1\!\cdots\!28$	$+$	$q+(177858-\beta _{1})q^{2}-3^{19}q^{3}+(319147551244+\cdots)q^{4}+\cdots$
4.35.b.a	$16$	$29.290$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	$-27372$	$0$	$-21372255840$	$0$		$q+(-1711+\beta _{1})q^{2}+(19-76\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots$
3.41.b.a	$12$	$30.403$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None	$0$	$-372082572$	$0$	$-9\!\cdots\!84$		$q+\beta _{1}q^{2}+(-31006881-471\beta _{1}+\cdots)q^{3}+\cdots$

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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
1.34.a.a	\(2\)	\(6.898\)	\(\mathbb{Q}[x]/(x^{2} - \cdots)\)	None	\(-121680\)	\(37919880\)	\(-181061536500\)	\(-6\!\cdots\!00\)	\(+\)	\(q+(-60840-\beta )q^{2}+(18959940+312\beta )q^{3}+\cdots\)
1.36.a.a	\(3\)	\(7.760\)	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	\(139656\)	\(-104875308\)	\(892652054010\)	\(87\!\cdots\!56\)	\(+\)	\(q+(46552+\beta _{1})q^{2}+(-34958436+\cdots)q^{3}+\cdots\)
1.38.a.a	\(2\)	\(8.671\)	\(\mathbb{Q}[x]/(x^{2} - \cdots)\)	None	\(-194400\)	\(13991400\)	\(55\!\cdots\!00\)	\(-3\!\cdots\!00\)	\(+\)	\(q+(-97200-\beta )q^{2}+(6995700+72\beta )q^{3}+\cdots\)
1.40.a.a	\(3\)	\(9.634\)	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	\(548856\)	\(1109442852\)	\(17\!\cdots\!90\)	\(-1\!\cdots\!44\)	\(+\)	\(q+(182952-\beta _{1})q^{2}+(369814284+\cdots)q^{3}+\cdots\)
1.42.a.a	\(3\)	\(10.647\)	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	\(-344688\)	\(-10820953044\)	\(-2\!\cdots\!50\)	\(57\!\cdots\!92\)	\(+\)	\(q+(-114896+\beta _{1})q^{2}+(-3606984348+\cdots)q^{3}+\cdots\)
1.44.a.a	\(3\)	\(11.711\)	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	\(-2209944\)	\(24401437812\)	\(53\!\cdots\!70\)	\(30\!\cdots\!56\)	\(+\)	\(q+(-736648-\beta _{1})q^{2}+(8133812604+\cdots)q^{3}+\cdots\)
1.46.a.a	\(3\)	\(12.826\)	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	\(3814272\)	\(5359866876\)	\(-9\!\cdots\!50\)	\(-7\!\cdots\!08\)	\(+\)	\(q+(1271424+\beta _{1})q^{2}+(1786622292+\cdots)q^{3}+\cdots\)
2.34.a.a	\(1\)	\(13.797\)	\(\Q\)	None	\(-65536\)	\(-133005564\)	\(538799132550\)	\(-3\!\cdots\!68\)	\(+\)	\(q-2^{16}q^{2}-133005564q^{3}+2^{32}q^{4}+\cdots\)
2.34.a.b	\(2\)	\(13.797\)	\(\mathbb{Q}[x]/(x^{2} - \cdots)\)	None	\(131072\)	\(8356488\)	\(-5332476660\)	\(13\!\cdots\!56\)	\(-\)	\(q+2^{16}q^{2}+(4178244-\beta )q^{3}+2^{32}q^{4}+\cdots\)
1.48.a.a	\(4\)	\(13.991\)	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	\(5785560\)	\(38461494960\)	\(-3\!\cdots\!00\)	\(-3\!\cdots\!00\)	\(+\)	\(q+(1446390+\beta _{1})q^{2}+(9615373740+\cdots)q^{3}+\cdots\)
1.50.a.a	\(3\)	\(15.207\)	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	\(-24225168\)	\(-326954692404\)	\(63\!\cdots\!50\)	\(50\!\cdots\!92\)	\(+\)	\(q+(-8075056+\beta _{1})q^{2}+(-108984897468+\cdots)q^{3}+\cdots\)
2.36.a.a	\(1\)	\(15.519\)	\(\Q\)	None	\(-131072\)	\(36494748\)	\(389070858750\)	\(-1\!\cdots\!56\)	\(+\)	\(q-2^{17}q^{2}+36494748q^{3}+2^{34}q^{4}+\cdots\)
2.36.a.b	\(1\)	\(15.519\)	\(\Q\)	None	\(131072\)	\(159933852\)	\(-2\!\cdots\!90\)	\(-7\!\cdots\!44\)	\(-\)	\(q+2^{17}q^{2}+159933852q^{3}+2^{34}q^{4}+\cdots\)
1.52.a.a	\(4\)	\(16.473\)	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	\(32756040\)	\(403863773040\)	\(12\!\cdots\!80\)	\(65\!\cdots\!00\)	\(+\)	\(q+(8189010+\beta _{1})q^{2}+(100965943260+\cdots)q^{3}+\cdots\)
2.38.a.a	\(2\)	\(17.343\)	\(\mathbb{Q}[x]/(x^{2} - \cdots)\)	None	\(-524288\)	\(423071208\)	\(-1\!\cdots\!40\)	\(31\!\cdots\!56\)	\(+\)	\(q-2^{18}q^{2}+(211535604-\beta )q^{3}+2^{36}q^{4}+\cdots\)
2.38.a.b	\(2\)	\(17.343\)	\(\mathbb{Q}[x]/(x^{2} - \cdots)\)	None	\(524288\)	\(-501686808\)	\(41\!\cdots\!00\)	\(-3\!\cdots\!56\)	\(-\)	\(q+2^{18}q^{2}+(-250843404-\beta )q^{3}+\cdots\)
1.54.a.a	\(4\)	\(17.790\)	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	\(-68476320\)	\(-1\!\cdots\!80\)	\(-4\!\cdots\!00\)	\(-2\!\cdots\!00\)	\(+\)	\(q+(-17119080+\beta _{1})q^{2}+(-262102751820+\cdots)q^{3}+\cdots\)
1.56.a.a	\(4\)	\(19.158\)	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	\(208622520\)	\(-6\!\cdots\!80\)	\(14\!\cdots\!60\)	\(-2\!\cdots\!00\)	\(+\)	\(q+(52155630+\beta _{1})q^{2}+(-1705367672820+\cdots)q^{3}+\cdots\)
2.40.a.a	\(1\)	\(19.268\)	\(\Q\)	None	\(524288\)	\(-735458292\)	\(-1\!\cdots\!50\)	\(16\!\cdots\!64\)	\(-\)	\(q+2^{19}q^{2}-735458292q^{3}+2^{38}q^{4}+\cdots\)
2.40.a.b	\(2\)	\(19.268\)	\(\mathbb{Q}[x]/(x^{2} - \cdots)\)	None	\(-1048576\)	\(287418264\)	\(53\!\cdots\!20\)	\(74\!\cdots\!12\)	\(+\)	\(q-2^{19}q^{2}+(143709132-\beta )q^{3}+2^{38}q^{4}+\cdots\)
3.33.b.a	\(10\)	\(19.460\)	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None	\(0\)	\(-21387150\)	\(0\)	\(-5\!\cdots\!40\)		\(q+\beta _{1}q^{2}+(-2138715+35\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)
1.58.a.a	\(4\)	\(20.577\)	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	\(-217744560\)	\(37\!\cdots\!60\)	\(-1\!\cdots\!00\)	\(95\!\cdots\!00\)	\(+\)	\(q+(-54436140+\beta _{1})q^{2}+(9368965543140+\cdots)q^{3}+\cdots\)
3.34.a.a	\(3\)	\(20.695\)	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	\(41202\)	\(129140163\)	\(51261823890\)	\(76\!\cdots\!56\)	\(-\)	\(q+(13734-\beta _{1})q^{2}+3^{16}q^{3}+(-369155924+\cdots)q^{4}+\cdots\)
3.34.a.b	\(3\)	\(20.695\)	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	\(136620\)	\(-129140163\)	\(-260488036134\)	\(10\!\cdots\!32\)	\(+\)	\(q+(45540-\beta _{1})q^{2}-3^{16}q^{3}+(4863185200+\cdots)q^{4}+\cdots\)
2.42.a.a	\(1\)	\(21.294\)	\(\Q\)	None	\(-1048576\)	\(5043516516\)	\(-4\!\cdots\!50\)	\(-1\!\cdots\!68\)	\(+\)	\(q-2^{20}q^{2}+5043516516q^{3}+2^{40}q^{4}+\cdots\)
2.42.a.b	\(2\)	\(21.294\)	\(\mathbb{Q}[x]/(x^{2} - \cdots)\)	None	\(2097152\)	\(8863347528\)	\(97\!\cdots\!80\)	\(21\!\cdots\!56\)	\(-\)	\(q+2^{20}q^{2}+(4431673764-\beta )q^{3}+\cdots\)
3.35.b.a	\(10\)	\(21.968\)	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None	\(0\)	\(119369106\)	\(0\)	\(-1\!\cdots\!72\)		\(q+\beta _{1}q^{2}+(11936911+41\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)
1.60.a.a	\(5\)	\(22.046\)	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	\(-449691864\)	\(84\!\cdots\!32\)	\(17\!\cdots\!90\)	\(14\!\cdots\!56\)	\(+\)	\(q+(-89938373-\beta _{1})q^{2}+(16803326335969+\cdots)q^{3}+\cdots\)
3.36.a.a	\(2\)	\(23.279\)	\(\Q(\sqrt{2196841}) \)	None	\(-60912\)	\(258280326\)	\(-1\!\cdots\!40\)	\(-1\!\cdots\!44\)	\(-\)	\(q+(-30456-\beta )q^{2}+3^{17}q^{3}+(28571469952+\cdots)q^{4}+\cdots\)
3.36.a.b	\(3\)	\(23.279\)	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	\(-87330\)	\(-387420489\)	\(27\!\cdots\!10\)	\(48\!\cdots\!64\)	\(+\)	\(q+(-29110+\beta _{1})q^{2}-3^{17}q^{3}+(10829584300+\cdots)q^{4}+\cdots\)
2.44.a.a	\(2\)	\(23.422\)	\(\mathbb{Q}[x]/(x^{2} - \cdots)\)	None	\(-4194304\)	\(-12981630984\)	\(-3\!\cdots\!00\)	\(11\!\cdots\!08\)	\(+\)	\(q-2^{21}q^{2}+(-6490815492-\beta )q^{3}+\cdots\)
2.44.a.b	\(2\)	\(23.422\)	\(\mathbb{Q}[x]/(x^{2} - \cdots)\)	None	\(4194304\)	\(-22341634056\)	\(-4\!\cdots\!20\)	\(-2\!\cdots\!28\)	\(-\)	\(q+2^{21}q^{2}+(-11170817028-\beta )q^{3}+\cdots\)
1.62.a.a	\(4\)	\(23.566\)	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	\(1146312000\)	\(-5\!\cdots\!00\)	\(-5\!\cdots\!00\)	\(-6\!\cdots\!00\)	\(+\)	\(q+(286578000-\beta _{1})q^{2}+(-143430899755500+\cdots)q^{3}+\cdots\)
3.37.b.a	\(1\)	\(24.627\)	\(\Q\)	\(\Q(\sqrt{-3}) \)	\(0\)	\(387420489\)	\(0\)	\(27\!\cdots\!98\)		\(q+3^{18}q^{3}+2^{36}q^{4}+2757049053441698q^{7}+\cdots\)
3.37.b.b	\(10\)	\(24.627\)	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None	\(0\)	\(-552156750\)	\(0\)	\(-1\!\cdots\!00\)		\(q+\beta _{1}q^{2}+(-55215675-69\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)
1.64.a.a	\(5\)	\(25.136\)	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	\(507315096\)	\(95\!\cdots\!52\)	\(-5\!\cdots\!30\)	\(37\!\cdots\!56\)	\(+\)	\(q+(101463019-\beta _{1})q^{2}+(190649070219572+\cdots)q^{3}+\cdots\)
2.46.a.a	\(2\)	\(25.651\)	\(\mathbb{Q}[x]/(x^{2} - \cdots)\)	None	\(-8388608\)	\(-69766206552\)	\(-4\!\cdots\!00\)	\(-9\!\cdots\!44\)	\(+\)	\(q-2^{22}q^{2}+(-34883103276-\beta )q^{3}+\cdots\)
2.46.a.b	\(2\)	\(25.651\)	\(\mathbb{Q}[x]/(x^{2} - \cdots)\)	None	\(8388608\)	\(59861217192\)	\(43\!\cdots\!00\)	\(79\!\cdots\!24\)	\(-\)	\(q+2^{22}q^{2}+(29930608596-\beta )q^{3}+\cdots\)
4.33.b.a	\(1\)	\(25.947\)	\(\Q\)	\(\Q(\sqrt{-1}) \)	\(65536\)	\(0\)	\(-196496109694\)	\(0\)		\(q+2^{16}q^{2}+2^{32}q^{4}-196496109694q^{5}+\cdots\)
4.33.b.b	\(14\)	\(25.947\)	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	None	\(-23780\)	\(0\)	\(138121491740\)	\(0\)		\(q+(-1699+\beta _{1})q^{2}+(9-21\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
3.38.a.a	\(3\)	\(26.014\)	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	\(-310908\)	\(-1162261467\)	\(-9\!\cdots\!90\)	\(-4\!\cdots\!44\)	\(+\)	\(q+(-103636-\beta _{1})q^{2}-3^{18}q^{3}+(112825533616+\cdots)q^{4}+\cdots\)
3.38.a.b	\(4\)	\(26.014\)	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	\(437562\)	\(1549681956\)	\(-4\!\cdots\!04\)	\(66\!\cdots\!84\)	\(-\)	\(q+(109391-\beta _{1})q^{2}+3^{18}q^{3}+(86524834843+\cdots)q^{4}+\cdots\)
3.39.b.a	\(12\)	\(27.439\)	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None	\(0\)	\(-114742404\)	\(0\)	\(81\!\cdots\!48\)		\(q+\beta _{1}q^{2}+(-9561867+97\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
4.34.a.a	\(3\)	\(27.593\)	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	\(0\)	\(92491788\)	\(-53880683886\)	\(45\!\cdots\!92\)	\(-\)	\(q+(30830596+\beta _{1})q^{3}+(-17960227962+\cdots)q^{5}+\cdots\)
2.48.a.a	\(1\)	\(27.982\)	\(\Q\)	None	\(8388608\)	\(-196634580372\)	\(20\!\cdots\!50\)	\(-5\!\cdots\!96\)	\(-\)	\(q+2^{23}q^{2}-196634580372q^{3}+2^{46}q^{4}+\cdots\)
2.48.a.b	\(2\)	\(27.982\)	\(\mathbb{Q}[x]/(x^{2} - \cdots)\)	None	\(-16777216\)	\(122289844824\)	\(18\!\cdots\!40\)	\(16\!\cdots\!32\)	\(+\)	\(q-2^{23}q^{2}+(61144922412-5\beta )q^{3}+\cdots\)
3.40.a.a	\(3\)	\(28.902\)	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	\(-1107000\)	\(3486784401\)	\(93\!\cdots\!90\)	\(13\!\cdots\!04\)	\(-\)	\(q+(-369000-\beta _{1})q^{2}+3^{19}q^{3}+(335300075200+\cdots)q^{4}+\cdots\)
3.40.a.b	\(3\)	\(28.902\)	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	\(533574\)	\(-3486784401\)	\(-5\!\cdots\!30\)	\(-1\!\cdots\!28\)	\(+\)	\(q+(177858-\beta _{1})q^{2}-3^{19}q^{3}+(319147551244+\cdots)q^{4}+\cdots\)
4.35.b.a	\(16\)	\(29.290\)	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	\(-27372\)	\(0\)	\(-21372255840\)	\(0\)		\(q+(-1711+\beta _{1})q^{2}+(19-76\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)
3.41.b.a	\(12\)	\(30.403\)	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None	\(0\)	\(-372082572\)	\(0\)	\(-9\!\cdots\!84\)		\(q+\beta _{1}q^{2}+(-31006881-471\beta _{1}+\cdots)q^{3}+\cdots\)

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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.