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-twist	CM/RM discriminant	Inner twist count	Is self-dual	Analytic rank

Coefficient ring index	Coefficient ring gens.		Projective image	Projective image type
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Results (displaying matches 1-50 of 271) 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
8.3.d.a	$1$	$0.218$	$\Q$	$\Q(\sqrt{-2}) $	$-2$	$-2$	$0$	$0$		$q-2q^{2}-2q^{3}+4q^{4}+4q^{6}-8q^{8}+\cdots$
8.4.a.a	$1$	$0.472$	$\Q$	None	$0$	$-4$	$-2$	$24$	$+$	$q-4q^{3}-2q^{5}+24q^{7}-11q^{9}-44q^{11}+\cdots$
8.4.b.a	$2$	$0.472$	$\Q(\sqrt{-7}) $	None	$-2$	$0$	$0$	$-16$		$q+(-1-\beta )q^{2}+2\beta q^{3}+(-6+2\beta )q^{4}+\cdots$
8.5.d.a	$1$	$0.827$	$\Q$	$\Q(\sqrt{-2}) $	$4$	$-14$	$0$	$0$		$q+4q^{2}-14q^{3}+2^{4}q^{4}-56q^{6}+2^{6}q^{8}+\cdots$
8.5.d.b	$2$	$0.827$	$\Q(\sqrt{-15}) $	None	$-2$	$12$	$0$	$0$		$q+(-1-\beta )q^{2}+6q^{3}+(-14+2\beta )q^{4}+\cdots$
8.6.a.a	$1$	$1.283$	$\Q$	None	$0$	$20$	$-74$	$-24$	$-$	$q+20q^{3}-74q^{5}-24q^{7}+157q^{9}+\cdots$
8.6.b.a	$4$	$1.283$	4.0.218489.1	None	$-2$	$0$	$0$	$96$		$q+(-1-\beta _{1})q^{2}+(-\beta _{1}+\beta _{3})q^{3}+(5+\cdots)q^{4}+\cdots$
8.7.d.a	$1$	$1.840$	$\Q$	$\Q(\sqrt{-2}) $	$-8$	$46$	$0$	$0$		$q-8q^{2}+46q^{3}+2^{6}q^{4}-368q^{6}+\cdots$
8.7.d.b	$4$	$1.840$	4.0.3803625.2	None	$2$	$-48$	$0$	$0$		$q+\beta _{1}q^{2}+(-13+2\beta _{1}+\beta _{2})q^{3}+(-12+\cdots)q^{4}+\cdots$
8.8.a.a	$1$	$2.499$	$\Q$	None	$0$	$-84$	$-82$	$-456$	$-$	$q-84q^{3}-82q^{5}-456q^{7}+4869q^{9}+\cdots$
8.8.a.b	$1$	$2.499$	$\Q$	None	$0$	$44$	$430$	$-1224$	$+$	$q+44q^{3}+430q^{5}-1224q^{7}-251q^{9}+\cdots$
8.8.b.a	$6$	$2.499$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	$6$	$0$	$0$	$-688$		$q+(1+\beta _{1})q^{2}+\beta _{4}q^{3}+(19+\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots$
8.9.d.a	$1$	$3.259$	$\Q$	$\Q(\sqrt{-2}) $	$16$	$34$	$0$	$0$		$q+2^{4}q^{2}+34q^{3}+2^{8}q^{4}+544q^{6}+\cdots$
8.9.d.b	$6$	$3.259$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	$-14$	$-36$	$0$	$0$		$q+(-2+\beta _{1})q^{2}+(-6-\beta _{1}-\beta _{2})q^{3}+\cdots$
8.10.a.a	$1$	$4.120$	$\Q$	None	$0$	$-60$	$-2074$	$-4344$	$+$	$q-60q^{3}-2074q^{5}-4344q^{7}-16083q^{9}+\cdots$
8.10.a.b	$1$	$4.120$	$\Q$	None	$0$	$68$	$1510$	$10248$	$-$	$q+68q^{3}+1510q^{5}+10248q^{7}-15059q^{9}+\cdots$
8.10.b.a	$8$	$4.120$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	$-18$	$0$	$0$	$4800$		$q+(-2-\beta _{1})q^{2}+(\beta _{1}+\beta _{3})q^{3}+(-54+\cdots)q^{4}+\cdots$
8.11.d.a	$1$	$5.083$	$\Q$	$\Q(\sqrt{-2}) $	$-32$	$-482$	$0$	$0$		$q-2^{5}q^{2}-482q^{3}+2^{10}q^{4}+15424q^{6}+\cdots$
8.11.d.b	$8$	$5.083$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	$42$	$480$	$0$	$0$		$q+(5-\beta _{1})q^{2}+(60+\beta _{1}+\beta _{2})q^{3}+(5^{2}+\cdots)q^{4}+\cdots$
8.12.a.a	$1$	$6.147$	$\Q$	None	$0$	$-36$	$-3490$	$-55464$	$-$	$q-6^{2}q^{3}-3490q^{5}-55464q^{7}-175851q^{9}+\cdots$
8.12.a.b	$2$	$6.147$	$\Q(\sqrt{109}) $	None	$0$	$56$	$7868$	$91056$	$+$	$q+(28+\beta )q^{3}+(3934-12\beta )q^{5}+(45528+\cdots)q^{7}+\cdots$
8.12.b.a	$10$	$6.147$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	$22$	$0$	$0$	$-33616$		$q+(2+\beta _{1})q^{2}+(\beta _{1}+\beta _{3})q^{3}+(43+2\beta _{1}+\cdots)q^{4}+\cdots$
8.13.d.a	$1$	$7.312$	$\Q$	$\Q(\sqrt{-2}) $	$64$	$658$	$0$	$0$		$q+2^{6}q^{2}+658q^{3}+2^{12}q^{4}+42112q^{6}+\cdots$
8.13.d.b	$10$	$7.312$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	$-110$	$-660$	$0$	$0$		$q+(-11-\beta _{1})q^{2}+(-66+3\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots$
8.14.a.a	$1$	$8.578$	$\Q$	None	$0$	$-12$	$-4330$	$-139992$	$+$	$q-12q^{3}-4330q^{5}-139992q^{7}+\cdots$
8.14.a.b	$2$	$8.578$	$\Q(\sqrt{781}) $	None	$0$	$872$	$18476$	$110928$	$-$	$q+(436-\beta )q^{3}+(9238-12\beta )q^{5}+(55464+\cdots)q^{7}+\cdots$
8.14.b.a	$2$	$8.578$	$\Q(\sqrt{-79}) $	None	$-112$	$0$	$0$	$-351664$		$q+(-56-4\beta )q^{2}+129\beta q^{3}+(-1920+\cdots)q^{4}+\cdots$
8.14.b.b	$10$	$8.578$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	$110$	$0$	$0$	$586960$		$q+(11+\beta _{1})q^{2}+(3\beta _{1}+\beta _{3})q^{3}+(-472+\cdots)q^{4}+\cdots$
8.15.d.a	$1$	$9.946$	$\Q$	$\Q(\sqrt{-2}) $	$-128$	$3022$	$0$	$0$		$q-2^{7}q^{2}+3022q^{3}+2^{14}q^{4}-386816q^{6}+\cdots$
8.15.d.b	$12$	$9.946$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	$218$	$-3024$	$0$	$0$		$q+(18+\beta _{1})q^{2}+(-252+3\beta _{1}+\beta _{3}+\cdots)q^{3}+\cdots$
8.16.a.a	$1$	$11.415$	$\Q$	None	$0$	$-3444$	$313358$	$-2324616$	$-$	$q-3444q^{3}+313358q^{5}-2324616q^{7}+\cdots$
8.16.a.b	$1$	$11.415$	$\Q$	None	$0$	$2700$	$-251890$	$1374072$	$-$	$q+2700q^{3}-251890q^{5}+1374072q^{7}+\cdots$
8.16.a.c	$2$	$11.415$	$\Q(\sqrt{58}) $	None	$0$	$-4072$	$-140260$	$126192$	$+$	$q+(-2036+\beta )q^{3}+(-70130+6^{2}\beta )q^{5}+\cdots$
8.16.b.a	$14$	$11.415$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None	$-90$	$0$	$0$	$-1647088$		$q+(-6-\beta _{1})q^{2}+\beta _{2}q^{3}+(3672+5\beta _{1}+\cdots)q^{4}+\cdots$
8.17.d.a	$1$	$12.986$	$\Q$	$\Q(\sqrt{-2}) $	$256$	$-11966$	$0$	$0$		$q+2^{8}q^{2}-11966q^{3}+2^{16}q^{4}-3063296q^{6}+\cdots$
8.17.d.b	$14$	$12.986$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None	$-350$	$11964$	$0$	$0$		$q+(-5^{2}-\beta _{1})q^{2}+(855-6\beta _{1}+\beta _{3}+\cdots)q^{3}+\cdots$
8.18.a.a	$2$	$14.658$	$\Q(\sqrt{2146}) $	None	$0$	$-952$	$-53620$	$-333168$	$-$	$q+(-476+\beta )q^{3}+(-26810+60\beta )q^{5}+\cdots$
8.18.a.b	$2$	$14.658$	$\Q(\sqrt{114}) $	None	$0$	$11592$	$-791924$	$-18932592$	$+$	$q+(5796+\beta )q^{3}+(-395962-68\beta )q^{5}+\cdots$
8.18.b.a	$16$	$14.658$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	$270$	$0$	$0$	$11529600$		$q+(17-\beta _{1})q^{2}+(3\beta _{1}-\beta _{2})q^{3}+(-1712+\cdots)q^{4}+\cdots$
8.19.d.a	$1$	$16.431$	$\Q$	$\Q(\sqrt{-2}) $	$-512$	$-3266$	$0$	$0$		$q-2^{9}q^{2}-3266q^{3}+2^{18}q^{4}+1672192q^{6}+\cdots$
8.19.d.b	$16$	$16.431$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	$426$	$3264$	$0$	$0$		$q+(3^{3}+\beta _{1})q^{2}+(203-4\beta _{1}-\beta _{2})q^{3}+\cdots$
8.20.a.a	$2$	$18.305$	$\Q(\sqrt{1453}) $	None	$0$	$-27912$	$1226620$	$88510512$	$-$	$q+(-13956-\beta )q^{3}+(613310+44\beta )q^{5}+\cdots$
8.20.a.b	$3$	$18.305$	$\mathbb{Q}[x]/(x^{3} - \cdots)$	None	$0$	$23732$	$2140218$	$55851720$	$+$	$q+(7911-\beta _{1})q^{3}+(713429-70\beta _{1}+\cdots)q^{5}+\cdots$
8.20.b.a	$18$	$18.305$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None	$-458$	$0$	$0$	$-80707216$		$q+(-5^{2}+\beta _{1})q^{2}+(2+5\beta _{1}-\beta _{2})q^{3}+\cdots$
8.21.d.a	$1$	$20.281$	$\Q$	$\Q(\sqrt{-2}) $	$1024$	$114226$	$0$	$0$		$q+2^{10}q^{2}+114226q^{3}+2^{20}q^{4}+\cdots$
8.21.d.b	$18$	$20.281$	$\mathbb{Q}[x]/(x^{18} + \cdots)$	None	$-398$	$-114228$	$0$	$0$		$q+(-22+\beta _{1})q^{2}+(-6347-5\beta _{1}+\cdots)q^{3}+\cdots$
8.22.a.a	$2$	$22.358$	$\Q(\sqrt{358549}) $	None	$0$	$-105432$	$2108140$	$444771792$	$+$	$q+(-52716-\beta )q^{3}+(1054070+20\beta )q^{5}+\cdots$
8.22.a.b	$3$	$22.358$	$\mathbb{Q}[x]/(x^{3} - \cdots)$	None	$0$	$96764$	$-24111774$	$295988280$	$-$	$q+(32255-\beta _{1})q^{3}+(-8037261+9\beta _{1}+\cdots)q^{5}+\cdots$
8.22.b.a	$20$	$22.358$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None	$286$	$0$	$0$	$564950496$		$q+(14-\beta _{1})q^{2}+(1+3\beta _{1}-\beta _{2})q^{3}+\cdots$
8.23.d.a	$1$	$24.537$	$\Q$	$\Q(\sqrt{-2}) $	$-2048$	$-199058$	$0$	$0$		$q-2^{11}q^{2}-199058q^{3}+2^{22}q^{4}+\cdots$

Overview	Features
Universe	Knowledge

Degree 1	Degree 2
Degree 3	Degree 4
$\zeta$ zeros

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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
8.3.d.a	\(1\)	\(0.218\)	\(\Q\)	\(\Q(\sqrt{-2}) \)	\(-2\)	\(-2\)	\(0\)	\(0\)		\(q-2q^{2}-2q^{3}+4q^{4}+4q^{6}-8q^{8}+\cdots\)
8.4.a.a	\(1\)	\(0.472\)	\(\Q\)	None	\(0\)	\(-4\)	\(-2\)	\(24\)	\(+\)	\(q-4q^{3}-2q^{5}+24q^{7}-11q^{9}-44q^{11}+\cdots\)
8.4.b.a	\(2\)	\(0.472\)	\(\Q(\sqrt{-7}) \)	None	\(-2\)	\(0\)	\(0\)	\(-16\)		\(q+(-1-\beta )q^{2}+2\beta q^{3}+(-6+2\beta )q^{4}+\cdots\)
8.5.d.a	\(1\)	\(0.827\)	\(\Q\)	\(\Q(\sqrt{-2}) \)	\(4\)	\(-14\)	\(0\)	\(0\)		\(q+4q^{2}-14q^{3}+2^{4}q^{4}-56q^{6}+2^{6}q^{8}+\cdots\)
8.5.d.b	\(2\)	\(0.827\)	\(\Q(\sqrt{-15}) \)	None	\(-2\)	\(12\)	\(0\)	\(0\)		\(q+(-1-\beta )q^{2}+6q^{3}+(-14+2\beta )q^{4}+\cdots\)
8.6.a.a	\(1\)	\(1.283\)	\(\Q\)	None	\(0\)	\(20\)	\(-74\)	\(-24\)	\(-\)	\(q+20q^{3}-74q^{5}-24q^{7}+157q^{9}+\cdots\)
8.6.b.a	\(4\)	\(1.283\)	4.0.218489.1	None	\(-2\)	\(0\)	\(0\)	\(96\)		\(q+(-1-\beta _{1})q^{2}+(-\beta _{1}+\beta _{3})q^{3}+(5+\cdots)q^{4}+\cdots\)
8.7.d.a	\(1\)	\(1.840\)	\(\Q\)	\(\Q(\sqrt{-2}) \)	\(-8\)	\(46\)	\(0\)	\(0\)		\(q-8q^{2}+46q^{3}+2^{6}q^{4}-368q^{6}+\cdots\)
8.7.d.b	\(4\)	\(1.840\)	4.0.3803625.2	None	\(2\)	\(-48\)	\(0\)	\(0\)		\(q+\beta _{1}q^{2}+(-13+2\beta _{1}+\beta _{2})q^{3}+(-12+\cdots)q^{4}+\cdots\)
8.8.a.a	\(1\)	\(2.499\)	\(\Q\)	None	\(0\)	\(-84\)	\(-82\)	\(-456\)	\(-\)	\(q-84q^{3}-82q^{5}-456q^{7}+4869q^{9}+\cdots\)
8.8.a.b	\(1\)	\(2.499\)	\(\Q\)	None	\(0\)	\(44\)	\(430\)	\(-1224\)	\(+\)	\(q+44q^{3}+430q^{5}-1224q^{7}-251q^{9}+\cdots\)
8.8.b.a	\(6\)	\(2.499\)	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	\(6\)	\(0\)	\(0\)	\(-688\)		\(q+(1+\beta _{1})q^{2}+\beta _{4}q^{3}+(19+\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots\)
8.9.d.a	\(1\)	\(3.259\)	\(\Q\)	\(\Q(\sqrt{-2}) \)	\(16\)	\(34\)	\(0\)	\(0\)		\(q+2^{4}q^{2}+34q^{3}+2^{8}q^{4}+544q^{6}+\cdots\)
8.9.d.b	\(6\)	\(3.259\)	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	\(-14\)	\(-36\)	\(0\)	\(0\)		\(q+(-2+\beta _{1})q^{2}+(-6-\beta _{1}-\beta _{2})q^{3}+\cdots\)
8.10.a.a	\(1\)	\(4.120\)	\(\Q\)	None	\(0\)	\(-60\)	\(-2074\)	\(-4344\)	\(+\)	\(q-60q^{3}-2074q^{5}-4344q^{7}-16083q^{9}+\cdots\)
8.10.a.b	\(1\)	\(4.120\)	\(\Q\)	None	\(0\)	\(68\)	\(1510\)	\(10248\)	\(-\)	\(q+68q^{3}+1510q^{5}+10248q^{7}-15059q^{9}+\cdots\)
8.10.b.a	\(8\)	\(4.120\)	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	\(-18\)	\(0\)	\(0\)	\(4800\)		\(q+(-2-\beta _{1})q^{2}+(\beta _{1}+\beta _{3})q^{3}+(-54+\cdots)q^{4}+\cdots\)
8.11.d.a	\(1\)	\(5.083\)	\(\Q\)	\(\Q(\sqrt{-2}) \)	\(-32\)	\(-482\)	\(0\)	\(0\)		\(q-2^{5}q^{2}-482q^{3}+2^{10}q^{4}+15424q^{6}+\cdots\)
8.11.d.b	\(8\)	\(5.083\)	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	\(42\)	\(480\)	\(0\)	\(0\)		\(q+(5-\beta _{1})q^{2}+(60+\beta _{1}+\beta _{2})q^{3}+(5^{2}+\cdots)q^{4}+\cdots\)
8.12.a.a	\(1\)	\(6.147\)	\(\Q\)	None	\(0\)	\(-36\)	\(-3490\)	\(-55464\)	\(-\)	\(q-6^{2}q^{3}-3490q^{5}-55464q^{7}-175851q^{9}+\cdots\)
8.12.a.b	\(2\)	\(6.147\)	\(\Q(\sqrt{109}) \)	None	\(0\)	\(56\)	\(7868\)	\(91056\)	\(+\)	\(q+(28+\beta )q^{3}+(3934-12\beta )q^{5}+(45528+\cdots)q^{7}+\cdots\)
8.12.b.a	\(10\)	\(6.147\)	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	\(22\)	\(0\)	\(0\)	\(-33616\)		\(q+(2+\beta _{1})q^{2}+(\beta _{1}+\beta _{3})q^{3}+(43+2\beta _{1}+\cdots)q^{4}+\cdots\)
8.13.d.a	\(1\)	\(7.312\)	\(\Q\)	\(\Q(\sqrt{-2}) \)	\(64\)	\(658\)	\(0\)	\(0\)		\(q+2^{6}q^{2}+658q^{3}+2^{12}q^{4}+42112q^{6}+\cdots\)
8.13.d.b	\(10\)	\(7.312\)	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	\(-110\)	\(-660\)	\(0\)	\(0\)		\(q+(-11-\beta _{1})q^{2}+(-66+3\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)
8.14.a.a	\(1\)	\(8.578\)	\(\Q\)	None	\(0\)	\(-12\)	\(-4330\)	\(-139992\)	\(+\)	\(q-12q^{3}-4330q^{5}-139992q^{7}+\cdots\)
8.14.a.b	\(2\)	\(8.578\)	\(\Q(\sqrt{781}) \)	None	\(0\)	\(872\)	\(18476\)	\(110928\)	\(-\)	\(q+(436-\beta )q^{3}+(9238-12\beta )q^{5}+(55464+\cdots)q^{7}+\cdots\)
8.14.b.a	\(2\)	\(8.578\)	\(\Q(\sqrt{-79}) \)	None	\(-112\)	\(0\)	\(0\)	\(-351664\)		\(q+(-56-4\beta )q^{2}+129\beta q^{3}+(-1920+\cdots)q^{4}+\cdots\)
8.14.b.b	\(10\)	\(8.578\)	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	\(110\)	\(0\)	\(0\)	\(586960\)		\(q+(11+\beta _{1})q^{2}+(3\beta _{1}+\beta _{3})q^{3}+(-472+\cdots)q^{4}+\cdots\)
8.15.d.a	\(1\)	\(9.946\)	\(\Q\)	\(\Q(\sqrt{-2}) \)	\(-128\)	\(3022\)	\(0\)	\(0\)		\(q-2^{7}q^{2}+3022q^{3}+2^{14}q^{4}-386816q^{6}+\cdots\)
8.15.d.b	\(12\)	\(9.946\)	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	\(218\)	\(-3024\)	\(0\)	\(0\)		\(q+(18+\beta _{1})q^{2}+(-252+3\beta _{1}+\beta _{3}+\cdots)q^{3}+\cdots\)
8.16.a.a	\(1\)	\(11.415\)	\(\Q\)	None	\(0\)	\(-3444\)	\(313358\)	\(-2324616\)	\(-\)	\(q-3444q^{3}+313358q^{5}-2324616q^{7}+\cdots\)
8.16.a.b	\(1\)	\(11.415\)	\(\Q\)	None	\(0\)	\(2700\)	\(-251890\)	\(1374072\)	\(-\)	\(q+2700q^{3}-251890q^{5}+1374072q^{7}+\cdots\)
8.16.a.c	\(2\)	\(11.415\)	\(\Q(\sqrt{58}) \)	None	\(0\)	\(-4072\)	\(-140260\)	\(126192\)	\(+\)	\(q+(-2036+\beta )q^{3}+(-70130+6^{2}\beta )q^{5}+\cdots\)
8.16.b.a	\(14\)	\(11.415\)	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	\(-90\)	\(0\)	\(0\)	\(-1647088\)		\(q+(-6-\beta _{1})q^{2}+\beta _{2}q^{3}+(3672+5\beta _{1}+\cdots)q^{4}+\cdots\)
8.17.d.a	\(1\)	\(12.986\)	\(\Q\)	\(\Q(\sqrt{-2}) \)	\(256\)	\(-11966\)	\(0\)	\(0\)		\(q+2^{8}q^{2}-11966q^{3}+2^{16}q^{4}-3063296q^{6}+\cdots\)
8.17.d.b	\(14\)	\(12.986\)	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	\(-350\)	\(11964\)	\(0\)	\(0\)		\(q+(-5^{2}-\beta _{1})q^{2}+(855-6\beta _{1}+\beta _{3}+\cdots)q^{3}+\cdots\)
8.18.a.a	\(2\)	\(14.658\)	\(\Q(\sqrt{2146}) \)	None	\(0\)	\(-952\)	\(-53620\)	\(-333168\)	\(-\)	\(q+(-476+\beta )q^{3}+(-26810+60\beta )q^{5}+\cdots\)
8.18.a.b	\(2\)	\(14.658\)	\(\Q(\sqrt{114}) \)	None	\(0\)	\(11592\)	\(-791924\)	\(-18932592\)	\(+\)	\(q+(5796+\beta )q^{3}+(-395962-68\beta )q^{5}+\cdots\)
8.18.b.a	\(16\)	\(14.658\)	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	\(270\)	\(0\)	\(0\)	\(11529600\)		\(q+(17-\beta _{1})q^{2}+(3\beta _{1}-\beta _{2})q^{3}+(-1712+\cdots)q^{4}+\cdots\)
8.19.d.a	\(1\)	\(16.431\)	\(\Q\)	\(\Q(\sqrt{-2}) \)	\(-512\)	\(-3266\)	\(0\)	\(0\)		\(q-2^{9}q^{2}-3266q^{3}+2^{18}q^{4}+1672192q^{6}+\cdots\)
8.19.d.b	\(16\)	\(16.431\)	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	\(426\)	\(3264\)	\(0\)	\(0\)		\(q+(3^{3}+\beta _{1})q^{2}+(203-4\beta _{1}-\beta _{2})q^{3}+\cdots\)
8.20.a.a	\(2\)	\(18.305\)	\(\Q(\sqrt{1453}) \)	None	\(0\)	\(-27912\)	\(1226620\)	\(88510512\)	\(-\)	\(q+(-13956-\beta )q^{3}+(613310+44\beta )q^{5}+\cdots\)
8.20.a.b	\(3\)	\(18.305\)	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	\(0\)	\(23732\)	\(2140218\)	\(55851720\)	\(+\)	\(q+(7911-\beta _{1})q^{3}+(713429-70\beta _{1}+\cdots)q^{5}+\cdots\)
8.20.b.a	\(18\)	\(18.305\)	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	\(-458\)	\(0\)	\(0\)	\(-80707216\)		\(q+(-5^{2}+\beta _{1})q^{2}+(2+5\beta _{1}-\beta _{2})q^{3}+\cdots\)
8.21.d.a	\(1\)	\(20.281\)	\(\Q\)	\(\Q(\sqrt{-2}) \)	\(1024\)	\(114226\)	\(0\)	\(0\)		\(q+2^{10}q^{2}+114226q^{3}+2^{20}q^{4}+\cdots\)
8.21.d.b	\(18\)	\(20.281\)	\(\mathbb{Q}[x]/(x^{18} + \cdots)\)	None	\(-398\)	\(-114228\)	\(0\)	\(0\)		\(q+(-22+\beta _{1})q^{2}+(-6347-5\beta _{1}+\cdots)q^{3}+\cdots\)
8.22.a.a	\(2\)	\(22.358\)	\(\Q(\sqrt{358549}) \)	None	\(0\)	\(-105432\)	\(2108140\)	\(444771792\)	\(+\)	\(q+(-52716-\beta )q^{3}+(1054070+20\beta )q^{5}+\cdots\)
8.22.a.b	\(3\)	\(22.358\)	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	\(0\)	\(96764\)	\(-24111774\)	\(295988280\)	\(-\)	\(q+(32255-\beta _{1})q^{3}+(-8037261+9\beta _{1}+\cdots)q^{5}+\cdots\)
8.22.b.a	\(20\)	\(22.358\)	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	\(286\)	\(0\)	\(0\)	\(564950496\)		\(q+(14-\beta _{1})q^{2}+(1+3\beta _{1}-\beta _{2})q^{3}+\cdots\)
8.23.d.a	\(1\)	\(24.537\)	\(\Q\)	\(\Q(\sqrt{-2}) \)	\(-2048\)	\(-199058\)	\(0\)	\(0\)		\(q-2^{11}q^{2}-199058q^{3}+2^{22}q^{4}+\cdots\)

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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.