LMFDB - Newform Search Results

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Level	Weight	Analytic conductor	$Nk^2$	Dim.

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

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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
4.5.b.a	$1$	$0.413$	$\Q$	$\Q(\sqrt{-1}) $	$-4$	$0$	$-14$	$0$		$q-4q^{2}+2^{4}q^{4}-14q^{5}-2^{6}q^{8}+3^{4}q^{9}+\cdots$
3.6.a.a	$1$	$0.481$	$\Q$	None	$-6$	$9$	$6$	$-40$	$-$	$q-6q^{2}+9q^{3}+4q^{4}+6q^{5}-54q^{6}+\cdots$
5.5.c.a	$2$	$0.517$	$\Q(\sqrt{-1}) $	None	$-2$	$-12$	$40$	$-52$		$q+(-1-i)q^{2}+(-6+6i)q^{3}-14iq^{4}+\cdots$
6.5.b.a	$2$	$0.620$	$\Q(\sqrt{-2}) $	None	$0$	$-6$	$0$	$52$		$q+\beta q^{2}+(-3-3\beta )q^{3}-8q^{4}+6\beta q^{5}+\cdots$
2.8.a.a	$1$	$0.625$	$\Q$	None	$-8$	$12$	$-210$	$1016$	$+$	$q-8q^{2}+12q^{3}+2^{6}q^{4}-210q^{5}+\cdots$
4.6.a.a	$1$	$0.642$	$\Q$	None	$0$	$-12$	$54$	$-88$	$-$	$q-12q^{3}+54q^{5}-88q^{7}-99q^{9}+\cdots$
3.7.b.a	$1$	$0.690$	$\Q$	$\Q(\sqrt{-3}) $	$0$	$-27$	$0$	$-286$		$q-3^{3}q^{3}+2^{6}q^{4}-286q^{7}+3^{6}q^{9}+\cdots$
7.5.b.a	$1$	$0.724$	$\Q$	$\Q(\sqrt{-7}) $	$1$	$0$	$0$	$49$		$q+q^{2}-15q^{4}+7^{2}q^{7}-31q^{8}+3^{4}q^{9}+\cdots$
7.5.d.a	$4$	$0.724$	$\Q(\sqrt{-3}, \sqrt{22})$	None	$-4$	$6$	$-30$	$0$		$q+(-2+\beta _{1}-2\beta _{2})q^{2}+(2-\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots$
5.6.a.a	$1$	$0.802$	$\Q$	None	$2$	$-4$	$25$	$192$	$-$	$q+2q^{2}-4q^{3}-28q^{4}+5^{2}q^{5}-8q^{6}+\cdots$
5.6.b.a	$2$	$0.802$	$\Q(\sqrt{-11}) $	None	$0$	$0$	$-90$	$0$		$q-\beta q^{2}+3\beta q^{3}-12q^{4}+(-45-5\beta )q^{5}+\cdots$
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	$-2$	$12$	$0$	$0$		$q+(-1-\beta )q^{2}+6q^{3}+(-14+2\beta )q^{4}+\cdots$
4.7.b.a	$2$	$0.920$	$\Q(\sqrt{-15}) $	None	$4$	$0$	$20$	$0$		$q+(2+\beta )q^{2}-4\beta q^{3}+(-56+4\beta )q^{4}+\cdots$
9.5.b.a	$2$	$0.930$	$\Q(\sqrt{-2}) $	None	$0$	$0$	$0$	$-56$		$q+\beta q^{2}-2q^{4}-7\beta q^{5}-28q^{7}+14\beta q^{8}+\cdots$
9.5.d.a	$6$	$0.930$	6.0.39400128.1	None	$-3$	$-3$	$-12$	$12$		$q+\beta _{2}q^{2}+(-3+\beta _{1}-3\beta _{3}+\beta _{4})q^{3}+\cdots$
3.8.a.a	$1$	$0.937$	$\Q$	None	$6$	$-27$	$390$	$-64$	$+$	$q+6q^{2}-3^{3}q^{3}-92q^{4}+390q^{5}+\cdots$
6.6.a.a	$1$	$0.962$	$\Q$	None	$4$	$-9$	$-66$	$176$	$-$	$q+4q^{2}-9q^{3}+2^{4}q^{4}-66q^{5}-6^{2}q^{6}+\cdots$
10.5.c.a	$2$	$1.034$	$\Q(\sqrt{-1}) $	None	$-4$	$18$	$-30$	$58$		$q+(-2-2i)q^{2}+(9-9i)q^{3}+8iq^{4}+\cdots$
10.5.c.b	$2$	$1.034$	$\Q(\sqrt{-1}) $	None	$4$	$2$	$-30$	$-38$		$q+(2+2i)q^{2}+(1-i)q^{3}+8iq^{4}+(-15+\cdots)q^{5}+\cdots$
7.6.a.a	$1$	$1.123$	$\Q$	None	$-10$	$-14$	$-56$	$-49$	$+$	$q-10q^{2}-14q^{3}+68q^{4}-56q^{5}+\cdots$
7.6.a.b	$2$	$1.123$	$\Q(\sqrt{57}) $	None	$9$	$-6$	$-18$	$98$	$-$	$q+(5-\beta )q^{2}+(-6+6\beta )q^{3}+(7-9\beta )q^{4}+\cdots$
7.6.c.a	$4$	$1.123$	$\Q(\sqrt{-3}, \sqrt{37})$	None	$-2$	$8$	$38$	$-168$		$q+(-\beta _{1}-\beta _{2})q^{2}+(4-4\beta _{1}-\beta _{2}-\beta _{3})q^{3}+\cdots$
11.5.b.a	$1$	$1.137$	$\Q$	$\Q(\sqrt{-11}) $	$0$	$7$	$-49$	$0$		$q+7q^{3}+2^{4}q^{4}-7^{2}q^{5}-2^{5}q^{9}+11^{2}q^{11}+\cdots$
11.5.b.b	$2$	$1.137$	$\Q(\sqrt{-30}) $	None	$0$	$-6$	$62$	$0$		$q+\beta q^{2}-3q^{3}-14q^{4}+31q^{5}-3\beta q^{6}+\cdots$
11.5.d.a	$12$	$1.137$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None	$-5$	$-6$	$-18$	$-80$		$q+(-1-\beta _{2}-2\beta _{3}-\beta _{4}+\beta _{7})q^{2}+\cdots$
5.7.c.a	$4$	$1.150$	$\Q(i, \sqrt{201})$	None	$-10$	$30$	$-70$	$550$		$q+(-2+2\beta _{1}+\beta _{3})q^{2}+(7+8\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots$
12.5.c.a	$1$	$1.240$	$\Q$	$\Q(\sqrt{-3}) $	$0$	$9$	$0$	$-94$		$q+9q^{3}-94q^{7}+3^{4}q^{9}+146q^{13}+\cdots$
12.5.d.a	$4$	$1.240$	$\Q(\sqrt{-3}, \sqrt{13})$	None	$6$	$0$	$24$	$0$		$q+(2-\beta _{1})q^{2}-\beta _{2}q^{3}+(-4-3\beta _{1}+\cdots)q^{4}+\cdots$
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	$-2$	$0$	$0$	$96$		$q+(-1-\beta _{1})q^{2}+(-\beta _{1}+\beta _{3})q^{3}+(5+\cdots)q^{4}+\cdots$
13.5.d.a	$6$	$1.344$	6.0.$\cdots$.1	None	$-2$	$-4$	$-14$	$48$		$q-\beta _{1}q^{2}+(-1+\beta _{4})q^{3}+(-\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots$
13.5.f.a	$16$	$1.344$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None	$-4$	$-2$	$8$	$56$		$q-\beta _{12}q^{2}+(-1-\beta _{8}+\beta _{9}+\beta _{12}+\cdots)q^{3}+\cdots$
6.7.b.a	$2$	$1.380$	$\Q(\sqrt{-2}) $	None	$0$	$42$	$0$	$4$		$q+\beta q^{2}+(21+3\beta )q^{3}-2^{5}q^{4}-30\beta q^{5}+\cdots$
9.6.a.a	$1$	$1.443$	$\Q$	None	$6$	$0$	$-6$	$-40$	$-$	$q+6q^{2}+4q^{4}-6q^{5}-40q^{7}-168q^{8}+\cdots$
9.6.c.a	$8$	$1.443$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None	$3$	$-12$	$78$	$28$		$q+(1-\beta _{1}+\beta _{4}+\beta _{5})q^{2}+(-3+3\beta _{1}+\cdots)q^{3}+\cdots$
14.5.b.a	$4$	$1.447$	4.0.1308672.3	None	$0$	$0$	$0$	$-76$		$q+\beta _{2}q^{2}-\beta _{1}q^{3}+8q^{4}+(\beta _{1}+\beta _{3})q^{5}+\cdots$
14.5.d.a	$4$	$1.447$	$\Q(\sqrt{2}, \sqrt{-3})$	None	$0$	$-18$	$54$	$-28$		$q+\beta _{1}q^{2}+(-6+2\beta _{1}-3\beta _{2}-2\beta _{3})q^{3}+\cdots$
15.5.c.a	$6$	$1.551$	$\mathbb{Q}[x]/(x^{6} + \cdots)$	None	$0$	$8$	$0$	$76$		$q+\beta _{1}q^{2}+(1-\beta _{2})q^{3}+(-8+\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots$
15.5.d.a	$1$	$1.551$	$\Q$	$\Q(\sqrt{-15}) $	$-7$	$9$	$25$	$0$		$q-7q^{2}+9q^{3}+33q^{4}+5^{2}q^{5}-63q^{6}+\cdots$
15.5.d.b	$1$	$1.551$	$\Q$	$\Q(\sqrt{-15}) $	$7$	$-9$	$-25$	$0$		$q+7q^{2}-9q^{3}+33q^{4}-5^{2}q^{5}-63q^{6}+\cdots$
15.5.d.c	$4$	$1.551$	$\Q(\sqrt{10}, \sqrt{-26})$	None	$0$	$0$	$0$	$0$		$q+\beta _{2}q^{2}+(\beta _{1}+\beta _{2})q^{3}-6q^{4}+(2\beta _{2}+\cdots)q^{5}+\cdots$
15.5.f.a	$8$	$1.551$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	$0$	$0$	$-84$	$20$		$q+\beta _{1}q^{2}+\beta _{5}q^{3}+(-\beta _{1}-12\beta _{2}-2\beta _{3}+\cdots)q^{4}+\cdots$
5.8.a.a	$1$	$1.562$	$\Q$	None	$-14$	$-48$	$125$	$-1644$	$-$	$q-14q^{2}-48q^{3}+68q^{4}+5^{3}q^{5}+\cdots$
5.8.a.b	$2$	$1.562$	$\Q(\sqrt{19}) $	None	$20$	$20$	$-250$	$-100$	$+$	$q+(10+\beta )q^{2}+(10-8\beta )q^{3}+(48+20\beta )q^{4}+\cdots$
5.8.b.a	$2$	$1.562$	$\Q(\sqrt{-29}) $	None	$0$	$0$	$150$	$0$		$q+\beta q^{2}+3\beta q^{3}+12q^{4}+(75-5^{2}\beta )q^{5}+\cdots$
10.6.a.a	$1$	$1.604$	$\Q$	None	$-4$	$-26$	$-25$	$-22$	$+$	$q-4q^{2}-26q^{3}+2^{4}q^{4}-5^{2}q^{5}+104q^{6}+\cdots$
10.6.a.b	$1$	$1.604$	$\Q$	None	$-4$	$24$	$25$	$-172$	$-$	$q-4q^{2}+24q^{3}+2^{4}q^{4}+5^{2}q^{5}-96q^{6}+\cdots$
10.6.a.c	$1$	$1.604$	$\Q$	None	$4$	$6$	$-25$	$-118$	$-$	$q+4q^{2}+6q^{3}+2^{4}q^{4}-5^{2}q^{5}+24q^{6}+\cdots$
10.6.b.a	$2$	$1.604$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$110$	$0$		$q+2iq^{2}+7iq^{3}-2^{4}q^{4}+(55+5i)q^{5}+\cdots$

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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
4.5.b.a	\(1\)	\(0.413\)	\(\Q\)	\(\Q(\sqrt{-1}) \)	\(-4\)	\(0\)	\(-14\)	\(0\)		\(q-4q^{2}+2^{4}q^{4}-14q^{5}-2^{6}q^{8}+3^{4}q^{9}+\cdots\)
3.6.a.a	\(1\)	\(0.481\)	\(\Q\)	None	\(-6\)	\(9\)	\(6\)	\(-40\)	\(-\)	\(q-6q^{2}+9q^{3}+4q^{4}+6q^{5}-54q^{6}+\cdots\)
5.5.c.a	\(2\)	\(0.517\)	\(\Q(\sqrt{-1}) \)	None	\(-2\)	\(-12\)	\(40\)	\(-52\)		\(q+(-1-i)q^{2}+(-6+6i)q^{3}-14iq^{4}+\cdots\)
6.5.b.a	\(2\)	\(0.620\)	\(\Q(\sqrt{-2}) \)	None	\(0\)	\(-6\)	\(0\)	\(52\)		\(q+\beta q^{2}+(-3-3\beta )q^{3}-8q^{4}+6\beta q^{5}+\cdots\)
2.8.a.a	\(1\)	\(0.625\)	\(\Q\)	None	\(-8\)	\(12\)	\(-210\)	\(1016\)	\(+\)	\(q-8q^{2}+12q^{3}+2^{6}q^{4}-210q^{5}+\cdots\)
4.6.a.a	\(1\)	\(0.642\)	\(\Q\)	None	\(0\)	\(-12\)	\(54\)	\(-88\)	\(-\)	\(q-12q^{3}+54q^{5}-88q^{7}-99q^{9}+\cdots\)
3.7.b.a	\(1\)	\(0.690\)	\(\Q\)	\(\Q(\sqrt{-3}) \)	\(0\)	\(-27\)	\(0\)	\(-286\)		\(q-3^{3}q^{3}+2^{6}q^{4}-286q^{7}+3^{6}q^{9}+\cdots\)
7.5.b.a	\(1\)	\(0.724\)	\(\Q\)	\(\Q(\sqrt{-7}) \)	\(1\)	\(0\)	\(0\)	\(49\)		\(q+q^{2}-15q^{4}+7^{2}q^{7}-31q^{8}+3^{4}q^{9}+\cdots\)
7.5.d.a	\(4\)	\(0.724\)	\(\Q(\sqrt{-3}, \sqrt{22})\)	None	\(-4\)	\(6\)	\(-30\)	\(0\)		\(q+(-2+\beta _{1}-2\beta _{2})q^{2}+(2-\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
5.6.a.a	\(1\)	\(0.802\)	\(\Q\)	None	\(2\)	\(-4\)	\(25\)	\(192\)	\(-\)	\(q+2q^{2}-4q^{3}-28q^{4}+5^{2}q^{5}-8q^{6}+\cdots\)
5.6.b.a	\(2\)	\(0.802\)	\(\Q(\sqrt{-11}) \)	None	\(0\)	\(0\)	\(-90\)	\(0\)		\(q-\beta q^{2}+3\beta q^{3}-12q^{4}+(-45-5\beta )q^{5}+\cdots\)
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	\(-2\)	\(12\)	\(0\)	\(0\)		\(q+(-1-\beta )q^{2}+6q^{3}+(-14+2\beta )q^{4}+\cdots\)
4.7.b.a	\(2\)	\(0.920\)	\(\Q(\sqrt{-15}) \)	None	\(4\)	\(0\)	\(20\)	\(0\)		\(q+(2+\beta )q^{2}-4\beta q^{3}+(-56+4\beta )q^{4}+\cdots\)
9.5.b.a	\(2\)	\(0.930\)	\(\Q(\sqrt{-2}) \)	None	\(0\)	\(0\)	\(0\)	\(-56\)		\(q+\beta q^{2}-2q^{4}-7\beta q^{5}-28q^{7}+14\beta q^{8}+\cdots\)
9.5.d.a	\(6\)	\(0.930\)	6.0.39400128.1	None	\(-3\)	\(-3\)	\(-12\)	\(12\)		\(q+\beta _{2}q^{2}+(-3+\beta _{1}-3\beta _{3}+\beta _{4})q^{3}+\cdots\)
3.8.a.a	\(1\)	\(0.937\)	\(\Q\)	None	\(6\)	\(-27\)	\(390\)	\(-64\)	\(+\)	\(q+6q^{2}-3^{3}q^{3}-92q^{4}+390q^{5}+\cdots\)
6.6.a.a	\(1\)	\(0.962\)	\(\Q\)	None	\(4\)	\(-9\)	\(-66\)	\(176\)	\(-\)	\(q+4q^{2}-9q^{3}+2^{4}q^{4}-66q^{5}-6^{2}q^{6}+\cdots\)
10.5.c.a	\(2\)	\(1.034\)	\(\Q(\sqrt{-1}) \)	None	\(-4\)	\(18\)	\(-30\)	\(58\)		\(q+(-2-2i)q^{2}+(9-9i)q^{3}+8iq^{4}+\cdots\)
10.5.c.b	\(2\)	\(1.034\)	\(\Q(\sqrt{-1}) \)	None	\(4\)	\(2\)	\(-30\)	\(-38\)		\(q+(2+2i)q^{2}+(1-i)q^{3}+8iq^{4}+(-15+\cdots)q^{5}+\cdots\)
7.6.a.a	\(1\)	\(1.123\)	\(\Q\)	None	\(-10\)	\(-14\)	\(-56\)	\(-49\)	\(+\)	\(q-10q^{2}-14q^{3}+68q^{4}-56q^{5}+\cdots\)
7.6.a.b	\(2\)	\(1.123\)	\(\Q(\sqrt{57}) \)	None	\(9\)	\(-6\)	\(-18\)	\(98\)	\(-\)	\(q+(5-\beta )q^{2}+(-6+6\beta )q^{3}+(7-9\beta )q^{4}+\cdots\)
7.6.c.a	\(4\)	\(1.123\)	\(\Q(\sqrt{-3}, \sqrt{37})\)	None	\(-2\)	\(8\)	\(38\)	\(-168\)		\(q+(-\beta _{1}-\beta _{2})q^{2}+(4-4\beta _{1}-\beta _{2}-\beta _{3})q^{3}+\cdots\)
11.5.b.a	\(1\)	\(1.137\)	\(\Q\)	\(\Q(\sqrt{-11}) \)	\(0\)	\(7\)	\(-49\)	\(0\)		\(q+7q^{3}+2^{4}q^{4}-7^{2}q^{5}-2^{5}q^{9}+11^{2}q^{11}+\cdots\)
11.5.b.b	\(2\)	\(1.137\)	\(\Q(\sqrt{-30}) \)	None	\(0\)	\(-6\)	\(62\)	\(0\)		\(q+\beta q^{2}-3q^{3}-14q^{4}+31q^{5}-3\beta q^{6}+\cdots\)
11.5.d.a	\(12\)	\(1.137\)	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None	\(-5\)	\(-6\)	\(-18\)	\(-80\)		\(q+(-1-\beta _{2}-2\beta _{3}-\beta _{4}+\beta _{7})q^{2}+\cdots\)
5.7.c.a	\(4\)	\(1.150\)	\(\Q(i, \sqrt{201})\)	None	\(-10\)	\(30\)	\(-70\)	\(550\)		\(q+(-2+2\beta _{1}+\beta _{3})q^{2}+(7+8\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
12.5.c.a	\(1\)	\(1.240\)	\(\Q\)	\(\Q(\sqrt{-3}) \)	\(0\)	\(9\)	\(0\)	\(-94\)		\(q+9q^{3}-94q^{7}+3^{4}q^{9}+146q^{13}+\cdots\)
12.5.d.a	\(4\)	\(1.240\)	\(\Q(\sqrt{-3}, \sqrt{13})\)	None	\(6\)	\(0\)	\(24\)	\(0\)		\(q+(2-\beta _{1})q^{2}-\beta _{2}q^{3}+(-4-3\beta _{1}+\cdots)q^{4}+\cdots\)
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	\(-2\)	\(0\)	\(0\)	\(96\)		\(q+(-1-\beta _{1})q^{2}+(-\beta _{1}+\beta _{3})q^{3}+(5+\cdots)q^{4}+\cdots\)
13.5.d.a	\(6\)	\(1.344\)	6.0.\(\cdots\).1	None	\(-2\)	\(-4\)	\(-14\)	\(48\)		\(q-\beta _{1}q^{2}+(-1+\beta _{4})q^{3}+(-\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
13.5.f.a	\(16\)	\(1.344\)	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None	\(-4\)	\(-2\)	\(8\)	\(56\)		\(q-\beta _{12}q^{2}+(-1-\beta _{8}+\beta _{9}+\beta _{12}+\cdots)q^{3}+\cdots\)
6.7.b.a	\(2\)	\(1.380\)	\(\Q(\sqrt{-2}) \)	None	\(0\)	\(42\)	\(0\)	\(4\)		\(q+\beta q^{2}+(21+3\beta )q^{3}-2^{5}q^{4}-30\beta q^{5}+\cdots\)
9.6.a.a	\(1\)	\(1.443\)	\(\Q\)	None	\(6\)	\(0\)	\(-6\)	\(-40\)	\(-\)	\(q+6q^{2}+4q^{4}-6q^{5}-40q^{7}-168q^{8}+\cdots\)
9.6.c.a	\(8\)	\(1.443\)	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None	\(3\)	\(-12\)	\(78\)	\(28\)		\(q+(1-\beta _{1}+\beta _{4}+\beta _{5})q^{2}+(-3+3\beta _{1}+\cdots)q^{3}+\cdots\)
14.5.b.a	\(4\)	\(1.447\)	4.0.1308672.3	None	\(0\)	\(0\)	\(0\)	\(-76\)		\(q+\beta _{2}q^{2}-\beta _{1}q^{3}+8q^{4}+(\beta _{1}+\beta _{3})q^{5}+\cdots\)
14.5.d.a	\(4\)	\(1.447\)	\(\Q(\sqrt{2}, \sqrt{-3})\)	None	\(0\)	\(-18\)	\(54\)	\(-28\)		\(q+\beta _{1}q^{2}+(-6+2\beta _{1}-3\beta _{2}-2\beta _{3})q^{3}+\cdots\)
15.5.c.a	\(6\)	\(1.551\)	\(\mathbb{Q}[x]/(x^{6} + \cdots)\)	None	\(0\)	\(8\)	\(0\)	\(76\)		\(q+\beta _{1}q^{2}+(1-\beta _{2})q^{3}+(-8+\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots\)
15.5.d.a	\(1\)	\(1.551\)	\(\Q\)	\(\Q(\sqrt{-15}) \)	\(-7\)	\(9\)	\(25\)	\(0\)		\(q-7q^{2}+9q^{3}+33q^{4}+5^{2}q^{5}-63q^{6}+\cdots\)
15.5.d.b	\(1\)	\(1.551\)	\(\Q\)	\(\Q(\sqrt{-15}) \)	\(7\)	\(-9\)	\(-25\)	\(0\)		\(q+7q^{2}-9q^{3}+33q^{4}-5^{2}q^{5}-63q^{6}+\cdots\)
15.5.d.c	\(4\)	\(1.551\)	\(\Q(\sqrt{10}, \sqrt{-26})\)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\beta _{2}q^{2}+(\beta _{1}+\beta _{2})q^{3}-6q^{4}+(2\beta _{2}+\cdots)q^{5}+\cdots\)
15.5.f.a	\(8\)	\(1.551\)	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	\(0\)	\(0\)	\(-84\)	\(20\)		\(q+\beta _{1}q^{2}+\beta _{5}q^{3}+(-\beta _{1}-12\beta _{2}-2\beta _{3}+\cdots)q^{4}+\cdots\)
5.8.a.a	\(1\)	\(1.562\)	\(\Q\)	None	\(-14\)	\(-48\)	\(125\)	\(-1644\)	\(-\)	\(q-14q^{2}-48q^{3}+68q^{4}+5^{3}q^{5}+\cdots\)
5.8.a.b	\(2\)	\(1.562\)	\(\Q(\sqrt{19}) \)	None	\(20\)	\(20\)	\(-250\)	\(-100\)	\(+\)	\(q+(10+\beta )q^{2}+(10-8\beta )q^{3}+(48+20\beta )q^{4}+\cdots\)
5.8.b.a	\(2\)	\(1.562\)	\(\Q(\sqrt{-29}) \)	None	\(0\)	\(0\)	\(150\)	\(0\)		\(q+\beta q^{2}+3\beta q^{3}+12q^{4}+(75-5^{2}\beta )q^{5}+\cdots\)
10.6.a.a	\(1\)	\(1.604\)	\(\Q\)	None	\(-4\)	\(-26\)	\(-25\)	\(-22\)	\(+\)	\(q-4q^{2}-26q^{3}+2^{4}q^{4}-5^{2}q^{5}+104q^{6}+\cdots\)
10.6.a.b	\(1\)	\(1.604\)	\(\Q\)	None	\(-4\)	\(24\)	\(25\)	\(-172\)	\(-\)	\(q-4q^{2}+24q^{3}+2^{4}q^{4}+5^{2}q^{5}-96q^{6}+\cdots\)
10.6.a.c	\(1\)	\(1.604\)	\(\Q\)	None	\(4\)	\(6\)	\(-25\)	\(-118\)	\(-\)	\(q+4q^{2}+6q^{3}+2^{4}q^{4}-5^{2}q^{5}+24q^{6}+\cdots\)
10.6.b.a	\(2\)	\(1.604\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(110\)	\(0\)		\(q+2iq^{2}+7iq^{3}-2^{4}q^{4}+(55+5i)q^{5}+\cdots\)

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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.