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

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Results (displaying matches 1-50 of 364) 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
9.3.d.a	$2$	$0.245$	$\Q(\sqrt{-3}) $	None	$-3$	$-3$	$6$	$-2$		$q+(-1-\zeta_{6})q^{2}+(-3+3\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
9.4.a.a	$1$	$0.531$	$\Q$	$\Q(\sqrt{-3}) $	$0$	$0$	$0$	$20$	$+$	$q-8q^{4}+20q^{7}-70q^{13}+2^{6}q^{16}+\cdots$
9.4.c.a	$4$	$0.531$	$\Q(\sqrt{-3}, \sqrt{-11})$	None	$-3$	$-3$	$-15$	$-7$		$q+(-\beta _{1}-\beta _{3})q^{2}+(-1+\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots$
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	$-3$	$-3$	$-12$	$12$		$q+\beta _{2}q^{2}+(-3+\beta _{1}-3\beta _{3}+\beta _{4})q^{3}+\cdots$
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	$3$	$-12$	$78$	$28$		$q+(1-\beta _{1}+\beta _{4}+\beta _{5})q^{2}+(-3+3\beta _{1}+\cdots)q^{3}+\cdots$
9.7.b.a	$2$	$2.070$	$\Q(\sqrt{-2}) $	None	$0$	$0$	$0$	$1048$		$q+\beta q^{2}-98q^{4}+5\beta q^{5}+524q^{7}+\cdots$
9.7.d.a	$10$	$2.070$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	$-3$	$24$	$-219$	$-121$		$q-\beta _{1}q^{2}+(2+\beta _{1}-\beta _{2}+\beta _{3}+\beta _{6}+\cdots)q^{3}+\cdots$
9.8.a.a	$1$	$2.811$	$\Q$	None	$-6$	$0$	$-390$	$-64$	$-$	$q-6q^{2}-92q^{4}-390q^{5}-2^{6}q^{7}+\cdots$
9.8.a.b	$2$	$2.811$	$\Q(\sqrt{10}) $	None	$0$	$0$	$0$	$520$	$+$	$q+\beta q^{2}+232q^{4}-2^{4}\beta q^{5}+260q^{7}+\cdots$
9.8.c.a	$12$	$2.811$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	$-9$	$24$	$-180$	$-84$		$q+(-\beta _{2}-\beta _{3})q^{2}+(1-\beta _{1}-\beta _{4}+\beta _{6}+\cdots)q^{3}+\cdots$
9.9.b.a	$2$	$3.666$	$\Q(\sqrt{-2}) $	None	$0$	$0$	$0$	$3304$		$q+\beta q^{2}+238q^{4}+233\beta q^{5}+1652q^{7}+\cdots$
9.9.d.a	$14$	$3.666$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None	$-3$	$-93$	$438$	$922$		$q-\beta _{1}q^{2}+(-5-3\beta _{3}+\beta _{4}+\beta _{6})q^{3}+\cdots$
9.10.a.a	$1$	$4.635$	$\Q$	None	$-18$	$0$	$1530$	$9128$	$-$	$q-18q^{2}-188q^{4}+1530q^{5}+9128q^{7}+\cdots$
9.10.a.b	$1$	$4.635$	$\Q$	$\Q(\sqrt{-3}) $	$0$	$0$	$0$	$-12580$	$+$	$q-2^{9}q^{4}-12580q^{7}+118370q^{13}+\cdots$
9.10.a.c	$1$	$4.635$	$\Q$	None	$36$	$0$	$1314$	$-4480$	$-$	$q+6^{2}q^{2}+28^{2}q^{4}+1314q^{5}-4480q^{7}+\cdots$
9.10.c.a	$16$	$4.635$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	$15$	$-3$	$453$	$-343$		$q+(2+\beta _{2}-2\beta _{3})q^{2}+(9-18\beta _{3}+\beta _{5}+\cdots)q^{3}+\cdots$
9.11.b.a	$4$	$5.718$	$\Q(\sqrt{-2}, \sqrt{385})$	None	$0$	$0$	$0$	$-44464$		$q-\beta _{1}q^{2}+(-1073-\beta _{2})q^{4}+(-35\beta _{1}+\cdots)q^{5}+\cdots$
9.11.d.a	$18$	$5.718$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None	$-3$	$51$	$4956$	$-6120$		$q-\beta _{3}q^{2}+(3-\beta _{1}+\beta _{3}+\beta _{4}-\beta _{6}+\cdots)q^{3}+\cdots$
9.12.a.a	$1$	$6.915$	$\Q$	None	$-78$	$0$	$5370$	$-27760$	$-$	$q-78q^{2}+4036q^{4}+5370q^{5}-27760q^{7}+\cdots$
9.12.a.b	$1$	$6.915$	$\Q$	None	$24$	$0$	$-4830$	$-16744$	$-$	$q+24q^{2}-1472q^{4}-4830q^{5}-16744q^{7}+\cdots$
9.12.a.c	$2$	$6.915$	$\Q(\sqrt{70}) $	None	$0$	$0$	$0$	$116200$	$+$	$q+\beta q^{2}+472q^{4}+224\beta q^{5}+58100q^{7}+\cdots$
9.12.c.a	$20$	$6.915$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	None	$-33$	$-12$	$-7230$	$8512$		$q+(\beta _{1}-3\beta _{3})q^{2}+(24-51\beta _{3}+\beta _{4}+\cdots)q^{3}+\cdots$
9.13.b.a	$2$	$8.226$	$\Q(\sqrt{-2}) $	None	$0$	$0$	$0$	$-223736$		$q+8\beta q^{2}-6272q^{4}-2291\beta q^{5}-111868q^{7}+\cdots$
9.13.b.b	$2$	$8.226$	$\Q(\sqrt{-2}) $	None	$0$	$0$	$0$	$232456$		$q+\beta q^{2}+2638q^{4}-175\beta q^{5}+116228q^{7}+\cdots$
9.13.d.a	$22$	$8.226$		None	$-3$	$618$	$-15987$	$34319$
9.14.a.a	$1$	$9.651$	$\Q$	None	$12$	$0$	$30210$	$235088$	$-$	$q+12q^{2}-8048q^{4}+30210q^{5}+235088q^{7}+\cdots$
9.14.a.b	$2$	$9.651$	$\Q(\sqrt{55}) $	None	$0$	$0$	$0$	$-266600$	$+$	$q+\beta q^{2}-272q^{4}-520\beta q^{5}-133300q^{7}+\cdots$
9.14.a.c	$2$	$9.651$	$\Q(\sqrt{1969}) $	None	$54$	$0$	$-40716$	$-21008$	$-$	$q+(3^{3}-\beta )q^{2}+(10258-54\beta )q^{4}+(-20358+\cdots)q^{5}+\cdots$
9.14.c.a	$24$	$9.651$		None	$63$	$-732$	$52128$	$-93912$
9.15.b.a	$4$	$11.190$	$\Q(\sqrt{-2}, \sqrt{3745})$	None	$0$	$0$	$0$	$-1065904$		$q-\beta _{3}q^{2}+(-833-\beta _{2})q^{4}+(-7\beta _{1}+\cdots)q^{5}+\cdots$
9.15.d.a	$26$	$11.190$		None	$-3$	$-2199$	$-107994$	$-146330$
9.16.a.a	$1$	$12.842$	$\Q$	None	$-216$	$0$	$-52110$	$2822456$	$-$	$q-6^{3}q^{2}+13888q^{4}-52110q^{5}+\cdots$
9.16.a.b	$1$	$12.842$	$\Q$	$\Q(\sqrt{-3}) $	$0$	$0$	$0$	$1244900$	$+$	$q-2^{15}q^{4}+1244900q^{7}+397771850q^{13}+\cdots$
9.16.a.c	$1$	$12.842$	$\Q$	None	$72$	$0$	$221490$	$-2149000$	$-$	$q+72q^{2}-27584q^{4}+221490q^{5}+\cdots$
9.16.a.d	$1$	$12.842$	$\Q$	None	$234$	$0$	$-280710$	$-1373344$	$-$	$q+234q^{2}+21988q^{4}-280710q^{5}+\cdots$
9.16.a.e	$2$	$12.842$	$\Q(\sqrt{370}) $	None	$0$	$0$	$0$	$-5182520$	$+$	$q+\beta q^{2}+87112q^{4}+464\beta q^{5}-2591260q^{7}+\cdots$
9.16.c.a	$28$	$12.842$		None	$-129$	$3345$	$-152655$	$803705$
9.17.b.a	$6$	$14.609$	$\mathbb{Q}[x]/(x^{6} + \cdots)$	None	$0$	$0$	$0$	$5400696$		$q-\beta _{1}q^{2}+(-61382-\beta _{4})q^{4}+(-189\beta _{1}+\cdots)q^{5}+\cdots$
9.17.d.a	$30$	$14.609$		None	$-3$	$2049$	$507588$	$220596$
9.18.a.a	$1$	$16.490$	$\Q$	None	$-204$	$0$	$163554$	$-20846560$	$-$	$q-204q^{2}-89456q^{4}+163554q^{5}+\cdots$
9.18.a.b	$1$	$16.490$	$\Q$	None	$528$	$0$	$1025850$	$3225992$	$-$	$q+528q^{2}+147712q^{4}+1025850q^{5}+\cdots$
9.18.a.c	$2$	$16.490$	$\Q(\sqrt{14569}) $	None	$-594$	$0$	$-382860$	$24471568$	$-$	$q+(-297-\beta )q^{2}+(88258+594\beta )q^{4}+\cdots$
9.18.a.d	$2$	$16.490$	$\Q(\sqrt{910}) $	None	$0$	$0$	$0$	$-392840$	$+$	$q+\beta q^{2}-2^{5}q^{4}-280\beta q^{5}-196420q^{7}+\cdots$
9.18.c.a	$32$	$16.490$		None	$255$	$-2280$	$255678$	$-5846540$
9.19.b.a	$6$	$18.485$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	$0$	$0$	$0$	$19180488$		$q+\beta _{1}q^{2}+(-42038-\beta _{2})q^{4}+(1082\beta _{1}+\cdots)q^{5}+\cdots$
9.19.d.a	$34$	$18.485$		None	$-3$	$3804$	$2192181$	$4302359$
9.20.a.a	$1$	$20.594$	$\Q$	None	$-456$	$0$	$2377410$	$-16917544$	$-$	$q-456q^{2}-316352q^{4}+2377410q^{5}+\cdots$
9.20.a.b	$1$	$20.594$	$\Q$	None	$1104$	$0$	$-3516270$	$-195590584$	$-$	$q+1104q^{2}+694528q^{4}-3516270q^{5}+\cdots$

Introduction	Features
Universe	News

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
9.3.d.a	\(2\)	\(0.245\)	\(\Q(\sqrt{-3}) \)	None	\(-3\)	\(-3\)	\(6\)	\(-2\)		\(q+(-1-\zeta_{6})q^{2}+(-3+3\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
9.4.a.a	\(1\)	\(0.531\)	\(\Q\)	\(\Q(\sqrt{-3}) \)	\(0\)	\(0\)	\(0\)	\(20\)	\(+\)	\(q-8q^{4}+20q^{7}-70q^{13}+2^{6}q^{16}+\cdots\)
9.4.c.a	\(4\)	\(0.531\)	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None	\(-3\)	\(-3\)	\(-15\)	\(-7\)		\(q+(-\beta _{1}-\beta _{3})q^{2}+(-1+\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
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	\(-3\)	\(-3\)	\(-12\)	\(12\)		\(q+\beta _{2}q^{2}+(-3+\beta _{1}-3\beta _{3}+\beta _{4})q^{3}+\cdots\)
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	\(3\)	\(-12\)	\(78\)	\(28\)		\(q+(1-\beta _{1}+\beta _{4}+\beta _{5})q^{2}+(-3+3\beta _{1}+\cdots)q^{3}+\cdots\)
9.7.b.a	\(2\)	\(2.070\)	\(\Q(\sqrt{-2}) \)	None	\(0\)	\(0\)	\(0\)	\(1048\)		\(q+\beta q^{2}-98q^{4}+5\beta q^{5}+524q^{7}+\cdots\)
9.7.d.a	\(10\)	\(2.070\)	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	\(-3\)	\(24\)	\(-219\)	\(-121\)		\(q-\beta _{1}q^{2}+(2+\beta _{1}-\beta _{2}+\beta _{3}+\beta _{6}+\cdots)q^{3}+\cdots\)
9.8.a.a	\(1\)	\(2.811\)	\(\Q\)	None	\(-6\)	\(0\)	\(-390\)	\(-64\)	\(-\)	\(q-6q^{2}-92q^{4}-390q^{5}-2^{6}q^{7}+\cdots\)
9.8.a.b	\(2\)	\(2.811\)	\(\Q(\sqrt{10}) \)	None	\(0\)	\(0\)	\(0\)	\(520\)	\(+\)	\(q+\beta q^{2}+232q^{4}-2^{4}\beta q^{5}+260q^{7}+\cdots\)
9.8.c.a	\(12\)	\(2.811\)	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	\(-9\)	\(24\)	\(-180\)	\(-84\)		\(q+(-\beta _{2}-\beta _{3})q^{2}+(1-\beta _{1}-\beta _{4}+\beta _{6}+\cdots)q^{3}+\cdots\)
9.9.b.a	\(2\)	\(3.666\)	\(\Q(\sqrt{-2}) \)	None	\(0\)	\(0\)	\(0\)	\(3304\)		\(q+\beta q^{2}+238q^{4}+233\beta q^{5}+1652q^{7}+\cdots\)
9.9.d.a	\(14\)	\(3.666\)	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	\(-3\)	\(-93\)	\(438\)	\(922\)		\(q-\beta _{1}q^{2}+(-5-3\beta _{3}+\beta _{4}+\beta _{6})q^{3}+\cdots\)
9.10.a.a	\(1\)	\(4.635\)	\(\Q\)	None	\(-18\)	\(0\)	\(1530\)	\(9128\)	\(-\)	\(q-18q^{2}-188q^{4}+1530q^{5}+9128q^{7}+\cdots\)
9.10.a.b	\(1\)	\(4.635\)	\(\Q\)	\(\Q(\sqrt{-3}) \)	\(0\)	\(0\)	\(0\)	\(-12580\)	\(+\)	\(q-2^{9}q^{4}-12580q^{7}+118370q^{13}+\cdots\)
9.10.a.c	\(1\)	\(4.635\)	\(\Q\)	None	\(36\)	\(0\)	\(1314\)	\(-4480\)	\(-\)	\(q+6^{2}q^{2}+28^{2}q^{4}+1314q^{5}-4480q^{7}+\cdots\)
9.10.c.a	\(16\)	\(4.635\)	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	\(15\)	\(-3\)	\(453\)	\(-343\)		\(q+(2+\beta _{2}-2\beta _{3})q^{2}+(9-18\beta _{3}+\beta _{5}+\cdots)q^{3}+\cdots\)
9.11.b.a	\(4\)	\(5.718\)	\(\Q(\sqrt{-2}, \sqrt{385})\)	None	\(0\)	\(0\)	\(0\)	\(-44464\)		\(q-\beta _{1}q^{2}+(-1073-\beta _{2})q^{4}+(-35\beta _{1}+\cdots)q^{5}+\cdots\)
9.11.d.a	\(18\)	\(5.718\)	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	\(-3\)	\(51\)	\(4956\)	\(-6120\)		\(q-\beta _{3}q^{2}+(3-\beta _{1}+\beta _{3}+\beta _{4}-\beta _{6}+\cdots)q^{3}+\cdots\)
9.12.a.a	\(1\)	\(6.915\)	\(\Q\)	None	\(-78\)	\(0\)	\(5370\)	\(-27760\)	\(-\)	\(q-78q^{2}+4036q^{4}+5370q^{5}-27760q^{7}+\cdots\)
9.12.a.b	\(1\)	\(6.915\)	\(\Q\)	None	\(24\)	\(0\)	\(-4830\)	\(-16744\)	\(-\)	\(q+24q^{2}-1472q^{4}-4830q^{5}-16744q^{7}+\cdots\)
9.12.a.c	\(2\)	\(6.915\)	\(\Q(\sqrt{70}) \)	None	\(0\)	\(0\)	\(0\)	\(116200\)	\(+\)	\(q+\beta q^{2}+472q^{4}+224\beta q^{5}+58100q^{7}+\cdots\)
9.12.c.a	\(20\)	\(6.915\)	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None	\(-33\)	\(-12\)	\(-7230\)	\(8512\)		\(q+(\beta _{1}-3\beta _{3})q^{2}+(24-51\beta _{3}+\beta _{4}+\cdots)q^{3}+\cdots\)
9.13.b.a	\(2\)	\(8.226\)	\(\Q(\sqrt{-2}) \)	None	\(0\)	\(0\)	\(0\)	\(-223736\)		\(q+8\beta q^{2}-6272q^{4}-2291\beta q^{5}-111868q^{7}+\cdots\)
9.13.b.b	\(2\)	\(8.226\)	\(\Q(\sqrt{-2}) \)	None	\(0\)	\(0\)	\(0\)	\(232456\)		\(q+\beta q^{2}+2638q^{4}-175\beta q^{5}+116228q^{7}+\cdots\)
9.13.d.a	\(22\)	\(8.226\)		None	\(-3\)	\(618\)	\(-15987\)	\(34319\)
9.14.a.a	\(1\)	\(9.651\)	\(\Q\)	None	\(12\)	\(0\)	\(30210\)	\(235088\)	\(-\)	\(q+12q^{2}-8048q^{4}+30210q^{5}+235088q^{7}+\cdots\)
9.14.a.b	\(2\)	\(9.651\)	\(\Q(\sqrt{55}) \)	None	\(0\)	\(0\)	\(0\)	\(-266600\)	\(+\)	\(q+\beta q^{2}-272q^{4}-520\beta q^{5}-133300q^{7}+\cdots\)
9.14.a.c	\(2\)	\(9.651\)	\(\Q(\sqrt{1969}) \)	None	\(54\)	\(0\)	\(-40716\)	\(-21008\)	\(-\)	\(q+(3^{3}-\beta )q^{2}+(10258-54\beta )q^{4}+(-20358+\cdots)q^{5}+\cdots\)
9.14.c.a	\(24\)	\(9.651\)		None	\(63\)	\(-732\)	\(52128\)	\(-93912\)
9.15.b.a	\(4\)	\(11.190\)	\(\Q(\sqrt{-2}, \sqrt{3745})\)	None	\(0\)	\(0\)	\(0\)	\(-1065904\)		\(q-\beta _{3}q^{2}+(-833-\beta _{2})q^{4}+(-7\beta _{1}+\cdots)q^{5}+\cdots\)
9.15.d.a	\(26\)	\(11.190\)		None	\(-3\)	\(-2199\)	\(-107994\)	\(-146330\)
9.16.a.a	\(1\)	\(12.842\)	\(\Q\)	None	\(-216\)	\(0\)	\(-52110\)	\(2822456\)	\(-\)	\(q-6^{3}q^{2}+13888q^{4}-52110q^{5}+\cdots\)
9.16.a.b	\(1\)	\(12.842\)	\(\Q\)	\(\Q(\sqrt{-3}) \)	\(0\)	\(0\)	\(0\)	\(1244900\)	\(+\)	\(q-2^{15}q^{4}+1244900q^{7}+397771850q^{13}+\cdots\)
9.16.a.c	\(1\)	\(12.842\)	\(\Q\)	None	\(72\)	\(0\)	\(221490\)	\(-2149000\)	\(-\)	\(q+72q^{2}-27584q^{4}+221490q^{5}+\cdots\)
9.16.a.d	\(1\)	\(12.842\)	\(\Q\)	None	\(234\)	\(0\)	\(-280710\)	\(-1373344\)	\(-\)	\(q+234q^{2}+21988q^{4}-280710q^{5}+\cdots\)
9.16.a.e	\(2\)	\(12.842\)	\(\Q(\sqrt{370}) \)	None	\(0\)	\(0\)	\(0\)	\(-5182520\)	\(+\)	\(q+\beta q^{2}+87112q^{4}+464\beta q^{5}-2591260q^{7}+\cdots\)
9.16.c.a	\(28\)	\(12.842\)		None	\(-129\)	\(3345\)	\(-152655\)	\(803705\)
9.17.b.a	\(6\)	\(14.609\)	\(\mathbb{Q}[x]/(x^{6} + \cdots)\)	None	\(0\)	\(0\)	\(0\)	\(5400696\)		\(q-\beta _{1}q^{2}+(-61382-\beta _{4})q^{4}+(-189\beta _{1}+\cdots)q^{5}+\cdots\)
9.17.d.a	\(30\)	\(14.609\)		None	\(-3\)	\(2049\)	\(507588\)	\(220596\)
9.18.a.a	\(1\)	\(16.490\)	\(\Q\)	None	\(-204\)	\(0\)	\(163554\)	\(-20846560\)	\(-\)	\(q-204q^{2}-89456q^{4}+163554q^{5}+\cdots\)
9.18.a.b	\(1\)	\(16.490\)	\(\Q\)	None	\(528\)	\(0\)	\(1025850\)	\(3225992\)	\(-\)	\(q+528q^{2}+147712q^{4}+1025850q^{5}+\cdots\)
9.18.a.c	\(2\)	\(16.490\)	\(\Q(\sqrt{14569}) \)	None	\(-594\)	\(0\)	\(-382860\)	\(24471568\)	\(-\)	\(q+(-297-\beta )q^{2}+(88258+594\beta )q^{4}+\cdots\)
9.18.a.d	\(2\)	\(16.490\)	\(\Q(\sqrt{910}) \)	None	\(0\)	\(0\)	\(0\)	\(-392840\)	\(+\)	\(q+\beta q^{2}-2^{5}q^{4}-280\beta q^{5}-196420q^{7}+\cdots\)
9.18.c.a	\(32\)	\(16.490\)		None	\(255\)	\(-2280\)	\(255678\)	\(-5846540\)
9.19.b.a	\(6\)	\(18.485\)	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	\(0\)	\(0\)	\(0\)	\(19180488\)		\(q+\beta _{1}q^{2}+(-42038-\beta _{2})q^{4}+(1082\beta _{1}+\cdots)q^{5}+\cdots\)
9.19.d.a	\(34\)	\(18.485\)		None	\(-3\)	\(3804\)	\(2192181\)	\(4302359\)
9.20.a.a	\(1\)	\(20.594\)	\(\Q\)	None	\(-456\)	\(0\)	\(2377410\)	\(-16917544\)	\(-\)	\(q-456q^{2}-316352q^{4}+2377410q^{5}+\cdots\)
9.20.a.b	\(1\)	\(20.594\)	\(\Q\)	None	\(1104\)	\(0\)	\(-3516270\)	\(-195590584\)	\(-\)	\(q+1104q^{2}+694528q^{4}-3516270q^{5}+\cdots\)

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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.