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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Label	Dim.	$A$	Field	Image	CM	RM	Traces				$q$-expansion
Label	Dim.	$A$	Field	Image	CM	RM	$a_2$	$a_3$	$a_5$	$a_7$	$q$-expansion
2001.1.i.a	$2$	$0.999$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-23}) $	None	$-2$	$2$	$0$	$0$	$q+(-1+i)q^{2}+q^{3}-iq^{4}+(-1+i+\cdots)q^{6}+\cdots$
2001.1.i.b	$2$	$0.999$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-23}) $	None	$2$	$0$	$0$	$0$	$q+(1-i)q^{2}+iq^{3}-iq^{4}+(1+i)q^{6}+\cdots$
2001.1.i.c	$4$	$0.999$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-23}) $	None	$-2$	$0$	$0$	$0$	$q+(\zeta_{12}^{4}+\zeta_{12}^{5})q^{2}-\zeta_{12}^{5}q^{3}+(-\zeta_{12}^{2}+\cdots)q^{4}+\cdots$
2001.1.i.d	$4$	$0.999$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-23}) $	None	$2$	$-2$	$0$	$0$	$q+(-\zeta_{12}+\zeta_{12}^{2})q^{2}-\zeta_{12}^{2}q^{3}+(\zeta_{12}^{2}+\cdots)q^{4}+\cdots$
2001.1.bf.a	$12$	$0.999$	$\Q(\zeta_{28})$	$D_{28}$	$\Q(\sqrt{-23}) $	None	$-2$	$0$	$0$	$0$	$q+(-\zeta_{28}^{7}-\zeta_{28}^{10})q^{2}-\zeta_{28}^{9}q^{3}+\cdots$
2001.1.bf.b	$12$	$0.999$	$\Q(\zeta_{28})$	$D_{28}$	$\Q(\sqrt{-23}) $	None	$2$	$-2$	$0$	$0$	$q+(\zeta_{28}^{7}+\zeta_{28}^{10})q^{2}-\zeta_{28}^{6}q^{3}+(-1+\cdots)q^{4}+\cdots$
2001.1.bf.c	$24$	$0.999$	$\Q(\zeta_{84})$	$D_{84}$	$\Q(\sqrt{-23}) $	None	$-2$	$2$	$0$	$0$	$q+(-\zeta_{84}^{7}-\zeta_{84}^{20})q^{2}-\zeta_{84}^{26}q^{3}+\cdots$
2001.1.bf.d	$24$	$0.999$	$\Q(\zeta_{84})$	$D_{84}$	$\Q(\sqrt{-23}) $	None	$2$	$0$	$0$	$0$	$q+(\zeta_{84}^{7}+\zeta_{84}^{20})q^{2}+\zeta_{84}^{25}q^{3}+\cdots$
2003.1.b.a	$1$	$1.000$	$\Q$	$D_{3}$	$\Q(\sqrt{-2003}) $	None	$0$	$-1$	$0$	$0$	$q-q^{3}+q^{4}-q^{12}-q^{13}+q^{16}+2q^{19}+\cdots$
2003.1.b.b	$3$	$1.000$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-2003}) $	None	$0$	$0$	$0$	$0$	$q-\beta _{1}q^{3}+q^{4}+(1+\beta _{2})q^{9}-\beta _{1}q^{12}+\cdots$
2004.1.g.a	$1$	$1.000$	$\Q$	$D_{2}$	$\Q(\sqrt{-167}) $, $\Q(\sqrt{-501}) $	$\Q(\sqrt{3}) $	$-1$	$-1$	$0$	$0$	$q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots$
2004.1.g.b	$1$	$1.000$	$\Q$	$D_{2}$	$\Q(\sqrt{-167}) $, $\Q(\sqrt{-501}) $	$\Q(\sqrt{3}) $	$1$	$1$	$0$	$0$	$q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}+q^{9}+\cdots$
2004.1.g.c	$2$	$1.000$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-501}) $	None	$-2$	$2$	$0$	$0$	$q-q^{2}+q^{3}+q^{4}-\beta q^{5}-q^{6}-q^{8}+\cdots$
2004.1.g.d	$2$	$1.000$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-501}) $	None	$2$	$-2$	$0$	$0$	$q+q^{2}-q^{3}+q^{4}-\beta q^{5}-q^{6}+q^{8}+\cdots$
2004.1.g.e	$10$	$1.000$	$\Q(\zeta_{22})$	$D_{22}$	$\Q(\sqrt{-167}) $	None	$-1$	$-1$	$0$	$0$	$q+\zeta_{22}^{6}q^{2}+\zeta_{22}^{2}q^{3}-\zeta_{22}q^{4}+\zeta_{22}^{8}q^{6}+\cdots$
2004.1.g.f	$10$	$1.000$	$\Q(\zeta_{22})$	$D_{22}$	$\Q(\sqrt{-167}) $	None	$1$	$1$	$0$	$0$	$q-\zeta_{22}^{6}q^{2}+\zeta_{22}^{9}q^{3}-\zeta_{22}q^{4}+\zeta_{22}^{4}q^{6}+\cdots$
2005.1.g.a	$2$	$1.001$	$\Q(\sqrt{-1}) $	$D_{4}$	None	$\Q(\sqrt{401}) $	$2$	$0$	$2$	$-2$	$q+(1-i)q^{2}-iq^{4}+q^{5}+(-1+i+\cdots)q^{7}+\cdots$
2005.1.g.b	$8$	$1.001$	$\Q(\zeta_{20})$	$D_{20}$	None	$\Q(\sqrt{401}) $	$-2$	$0$	$-2$	$2$	$q+(-\zeta_{20}+\zeta_{20}^{4})q^{2}+(\zeta_{20}^{2}-\zeta_{20}^{5}+\cdots)q^{4}+\cdots$
2007.1.d.a	$1$	$1.002$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-223}) $	$\Q(\sqrt{669}) $	$0$	$0$	$0$	$-2$	$q-q^{4}-2q^{7}+q^{16}+2q^{19}+q^{25}+\cdots$
2007.1.d.b	$3$	$1.002$	$\Q(\zeta_{14})^+$	$D_{7}$	$\Q(\sqrt{-223}) $	None	$1$	$0$	$0$	$-1$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1+\beta _{1}-\beta _{2})q^{7}+\cdots$
2007.1.d.c	$6$	$1.002$	$\Q(\zeta_{28})^+$	$D_{14}$	$\Q(\sqrt{-223}) $	None	$0$	$0$	$0$	$2$	$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(1-\beta _{2}-\beta _{4}+\cdots)q^{7}+\cdots$
2007.1.v.a	$36$	$1.002$	$\Q(\zeta_{74})$	$D_{74}$	$\Q(\sqrt{-3}) $	None	$0$	$0$	$0$	$2$	$q-\zeta_{74}^{20}q^{4}+(\zeta_{74}^{21}+\zeta_{74}^{27})q^{7}+\cdots$
2008.1.c.a	$3$	$1.002$	$\Q(\zeta_{14})^+$	$D_{7}$	$\Q(\sqrt{-502}) $	None	$-3$	$0$	$0$	$-1$	$q-q^{2}+q^{4}-\beta _{1}q^{7}-q^{8}+q^{9}-\beta _{2}q^{11}+\cdots$
2008.1.c.b	$3$	$1.002$	$\Q(\zeta_{14})^+$	$D_{7}$	$\Q(\sqrt{-502}) $	None	$3$	$0$	$0$	$-1$	$q+q^{2}+q^{4}-\beta _{1}q^{7}+q^{8}+q^{9}+\beta _{2}q^{11}+\cdots$
2008.1.j.a	$4$	$1.002$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-2}) $	None	$4$	$-2$	$0$	$0$	$q+q^{2}+(-\zeta_{10}+\zeta_{10}^{2})q^{3}+q^{4}+(-\zeta_{10}+\cdots)q^{6}+\cdots$
2008.1.w.a	$20$	$1.002$	$\Q(\zeta_{50})$	$D_{25}$	$\Q(\sqrt{-2}) $	None	$-5$	$0$	$0$	$0$	$q-\zeta_{50}^{5}q^{2}+(\zeta_{50}^{2}+\zeta_{50}^{4})q^{3}+\zeta_{50}^{10}q^{4}+\cdots$
2008.1.bd.a	$100$	$1.002$	$\Q(\zeta_{250})$	$D_{125}$	$\Q(\sqrt{-2}) $	None	$0$	$0$	$0$	$0$	$q-\zeta_{250}^{35}q^{2}+(\zeta_{250}^{14}-\zeta_{250}^{53})q^{3}+\cdots$
2009.1.i.a	$6$	$1.003$	6.0.64827.1	$D_{7}$	$\Q(\sqrt{-287}) $	None	$1$	$-1$	$0$	$0$	$q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{2}-\beta _{3}-\beta _{4}-\beta _{5})q^{3}+\cdots$
2009.1.i.b	$6$	$1.003$	6.0.64827.1	$D_{7}$	$\Q(\sqrt{-287}) $	None	$1$	$1$	$0$	$0$	$q+\beta _{1}q^{2}+(\beta _{1}-\beta _{2}+\beta _{3}+\beta _{4}+\beta _{5})q^{3}+\cdots$
2011.1.b.a	$3$	$1.004$	$\Q(\zeta_{14})^+$	$D_{7}$	$\Q(\sqrt{-2011}) $	None	$0$	$0$	$-1$	$0$	$q+q^{4}-\beta _{1}q^{5}+q^{9}+(-1+\beta _{1}-\beta _{2})q^{13}+\cdots$
2013.1.bm.a	$4$	$1.005$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-183}) $	None	$-3$	$-1$	$0$	$0$	$q+(-1+\zeta_{10})q^{2}+\zeta_{10}^{4}q^{3}+(1-\zeta_{10}+\cdots)q^{4}+\cdots$
2013.1.bm.b	$4$	$1.005$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-183}) $	None	$3$	$-1$	$0$	$0$	$q+(1-\zeta_{10})q^{2}+\zeta_{10}^{4}q^{3}+(1-\zeta_{10}+\cdots)q^{4}+\cdots$
2013.1.bm.c	$8$	$1.005$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-183}) $	None	$0$	$-2$	$0$	$0$	$q+(\zeta_{20}^{5}+\zeta_{20}^{7})q^{2}+\zeta_{20}^{8}q^{3}+(-1+\cdots)q^{4}+\cdots$
2013.1.bm.d	$16$	$1.005$	$\Q(\zeta_{40})$	$D_{20}$	$\Q(\sqrt{-183}) $	None	$0$	$4$	$0$	$0$	$q+(\zeta_{40}^{9}+\zeta_{40}^{15})q^{2}-\zeta_{40}^{16}q^{3}+\cdots$
2015.1.h.a	$4$	$1.006$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-155}) $	None	$0$	$0$	$0$	$0$	$q+(\zeta_{8}-\zeta_{8}^{3})q^{3}-q^{4}+\zeta_{8}^{2}q^{5}+q^{9}+\cdots$
2015.1.h.b	$6$	$1.006$	$\Q(\zeta_{26})^+$	$D_{13}$	$\Q(\sqrt{-2015}) $	None	$-1$	$-1$	$6$	$-1$	$q-\beta _{1}q^{2}-\beta _{3}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots$
2015.1.h.c	$6$	$1.006$	$\Q(\zeta_{26})^+$	$D_{13}$	$\Q(\sqrt{-2015}) $	None	$-1$	$1$	$6$	$-1$	$q-\beta _{1}q^{2}+\beta _{3}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots$
2015.1.h.d	$6$	$1.006$	$\Q(\zeta_{26})^+$	$D_{13}$	$\Q(\sqrt{-2015}) $	None	$1$	$-1$	$-6$	$1$	$q+\beta _{1}q^{2}-\beta _{3}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots$
2015.1.h.e	$6$	$1.006$	$\Q(\zeta_{26})^+$	$D_{13}$	$\Q(\sqrt{-2015}) $	None	$1$	$1$	$-6$	$1$	$q+\beta _{1}q^{2}+\beta _{3}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots$
2015.1.bf.a	$8$	$1.006$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-155}) $	None	$0$	$0$	$0$	$0$	$q+(\zeta_{24}^{5}+\zeta_{24}^{11})q^{3}+\zeta_{24}^{4}q^{4}-\zeta_{24}^{6}q^{5}+\cdots$
2015.1.bq.a	$2$	$1.006$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-155}) $	None	$0$	$-2$	$2$	$0$	$q-\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}+q^{5}+3\zeta_{6}^{2}q^{9}+\cdots$
2015.1.bq.b	$2$	$1.006$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-155}) $	None	$0$	$2$	$2$	$0$	$q+\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}+q^{5}+3\zeta_{6}^{2}q^{9}+\cdots$
2015.1.bq.c	$4$	$1.006$	$\Q(\zeta_{12})$	$A_{4}$	None	None	$0$	$-2$	$0$	$0$	$q+\zeta_{12}q^{2}+\zeta_{12}^{4}q^{3}+\zeta_{12}^{3}q^{5}+\zeta_{12}^{5}q^{6}+\cdots$
2015.1.bq.d	$4$	$1.006$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-155}) $	None	$0$	$0$	$-4$	$0$	$q-\zeta_{12}^{2}q^{4}-q^{5}+\zeta_{12}^{2}q^{9}+\zeta_{12}^{5}q^{13}+\cdots$
2015.1.bq.e	$4$	$1.006$	$\Q(\zeta_{12})$	$A_{4}$	None	None	$0$	$2$	$0$	$0$	$q-\zeta_{12}q^{2}-\zeta_{12}^{4}q^{3}-\zeta_{12}^{3}q^{5}+\zeta_{12}^{5}q^{6}+\cdots$
2016.1.e.a	$4$	$1.006$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-7}) $	None	$0$	$0$	$0$	$0$	$q+\zeta_{8}^{2}q^{7}+(\zeta_{8}+\zeta_{8}^{3})q^{11}+(-\zeta_{8}+\cdots)q^{23}+\cdots$
2016.1.f.a	$4$	$1.006$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-21}) $	None	$0$	$0$	$0$	$0$	$q+(-\zeta_{8}-\zeta_{8}^{3})q^{5}+\zeta_{8}^{2}q^{7}+(-\zeta_{8}+\cdots)q^{11}+\cdots$
2016.1.l.a	$1$	$1.006$	$\Q$	$D_{2}$	$\Q(\sqrt{-7}) $, $\Q(\sqrt{-14}) $	$\Q(\sqrt{2}) $	$0$	$0$	$0$	$1$	$q+q^{7}+2q^{23}-q^{25}+q^{49}-2q^{71}+\cdots$
2016.1.l.b	$2$	$1.006$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-7}) $, $\Q(\sqrt{-6}) $	$\Q(\sqrt{42}) $	$0$	$0$	$0$	$-2$	$q-q^{7}-iq^{11}-q^{25}-iq^{29}+q^{49}+\cdots$
2016.1.bi.a	$4$	$1.006$	$\Q(\zeta_{12})$	$A_{4}$	None	None	$0$	$-2$	$0$	$0$	$q-\zeta_{12}^{2}q^{3}-\zeta_{12}^{3}q^{5}+\zeta_{12}q^{7}+\zeta_{12}^{4}q^{9}+\cdots$

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Introduction	Features
Universe	News

Label	Dim.	\(A\)	Field	Image	CM	RM	Traces				$q$-expansion
Label	Dim.	\(A\)	Field	Image	CM	RM	\(a_2\)	\(a_3\)	\(a_5\)	\(a_7\)	$q$-expansion
2001.1.i.a	\(2\)	\(0.999\)	\(\Q(\sqrt{-1}) \)	\(D_{4}\)	\(\Q(\sqrt{-23}) \)	None	\(-2\)	\(2\)	\(0\)	\(0\)	\(q+(-1+i)q^{2}+q^{3}-iq^{4}+(-1+i+\cdots)q^{6}+\cdots\)
2001.1.i.b	\(2\)	\(0.999\)	\(\Q(\sqrt{-1}) \)	\(D_{4}\)	\(\Q(\sqrt{-23}) \)	None	\(2\)	\(0\)	\(0\)	\(0\)	\(q+(1-i)q^{2}+iq^{3}-iq^{4}+(1+i)q^{6}+\cdots\)
2001.1.i.c	\(4\)	\(0.999\)	\(\Q(\zeta_{12})\)	\(D_{12}\)	\(\Q(\sqrt{-23}) \)	None	\(-2\)	\(0\)	\(0\)	\(0\)	\(q+(\zeta_{12}^{4}+\zeta_{12}^{5})q^{2}-\zeta_{12}^{5}q^{3}+(-\zeta_{12}^{2}+\cdots)q^{4}+\cdots\)
2001.1.i.d	\(4\)	\(0.999\)	\(\Q(\zeta_{12})\)	\(D_{12}\)	\(\Q(\sqrt{-23}) \)	None	\(2\)	\(-2\)	\(0\)	\(0\)	\(q+(-\zeta_{12}+\zeta_{12}^{2})q^{2}-\zeta_{12}^{2}q^{3}+(\zeta_{12}^{2}+\cdots)q^{4}+\cdots\)
2001.1.bf.a	\(12\)	\(0.999\)	\(\Q(\zeta_{28})\)	\(D_{28}\)	\(\Q(\sqrt{-23}) \)	None	\(-2\)	\(0\)	\(0\)	\(0\)	\(q+(-\zeta_{28}^{7}-\zeta_{28}^{10})q^{2}-\zeta_{28}^{9}q^{3}+\cdots\)
2001.1.bf.b	\(12\)	\(0.999\)	\(\Q(\zeta_{28})\)	\(D_{28}\)	\(\Q(\sqrt{-23}) \)	None	\(2\)	\(-2\)	\(0\)	\(0\)	\(q+(\zeta_{28}^{7}+\zeta_{28}^{10})q^{2}-\zeta_{28}^{6}q^{3}+(-1+\cdots)q^{4}+\cdots\)
2001.1.bf.c	\(24\)	\(0.999\)	\(\Q(\zeta_{84})\)	\(D_{84}\)	\(\Q(\sqrt{-23}) \)	None	\(-2\)	\(2\)	\(0\)	\(0\)	\(q+(-\zeta_{84}^{7}-\zeta_{84}^{20})q^{2}-\zeta_{84}^{26}q^{3}+\cdots\)
2001.1.bf.d	\(24\)	\(0.999\)	\(\Q(\zeta_{84})\)	\(D_{84}\)	\(\Q(\sqrt{-23}) \)	None	\(2\)	\(0\)	\(0\)	\(0\)	\(q+(\zeta_{84}^{7}+\zeta_{84}^{20})q^{2}+\zeta_{84}^{25}q^{3}+\cdots\)
2003.1.b.a	\(1\)	\(1.000\)	\(\Q\)	\(D_{3}\)	\(\Q(\sqrt{-2003}) \)	None	\(0\)	\(-1\)	\(0\)	\(0\)	\(q-q^{3}+q^{4}-q^{12}-q^{13}+q^{16}+2q^{19}+\cdots\)
2003.1.b.b	\(3\)	\(1.000\)	\(\Q(\zeta_{18})^+\)	\(D_{9}\)	\(\Q(\sqrt{-2003}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(q-\beta _{1}q^{3}+q^{4}+(1+\beta _{2})q^{9}-\beta _{1}q^{12}+\cdots\)
2004.1.g.a	\(1\)	\(1.000\)	\(\Q\)	\(D_{2}\)	\(\Q(\sqrt{-167}) \), \(\Q(\sqrt{-501}) \)	\(\Q(\sqrt{3}) \)	\(-1\)	\(-1\)	\(0\)	\(0\)	\(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots\)
2004.1.g.b	\(1\)	\(1.000\)	\(\Q\)	\(D_{2}\)	\(\Q(\sqrt{-167}) \), \(\Q(\sqrt{-501}) \)	\(\Q(\sqrt{3}) \)	\(1\)	\(1\)	\(0\)	\(0\)	\(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}+q^{9}+\cdots\)
2004.1.g.c	\(2\)	\(1.000\)	\(\Q(\sqrt{2}) \)	\(D_{4}\)	\(\Q(\sqrt{-501}) \)	None	\(-2\)	\(2\)	\(0\)	\(0\)	\(q-q^{2}+q^{3}+q^{4}-\beta q^{5}-q^{6}-q^{8}+\cdots\)
2004.1.g.d	\(2\)	\(1.000\)	\(\Q(\sqrt{2}) \)	\(D_{4}\)	\(\Q(\sqrt{-501}) \)	None	\(2\)	\(-2\)	\(0\)	\(0\)	\(q+q^{2}-q^{3}+q^{4}-\beta q^{5}-q^{6}+q^{8}+\cdots\)
2004.1.g.e	\(10\)	\(1.000\)	\(\Q(\zeta_{22})\)	\(D_{22}\)	\(\Q(\sqrt{-167}) \)	None	\(-1\)	\(-1\)	\(0\)	\(0\)	\(q+\zeta_{22}^{6}q^{2}+\zeta_{22}^{2}q^{3}-\zeta_{22}q^{4}+\zeta_{22}^{8}q^{6}+\cdots\)
2004.1.g.f	\(10\)	\(1.000\)	\(\Q(\zeta_{22})\)	\(D_{22}\)	\(\Q(\sqrt{-167}) \)	None	\(1\)	\(1\)	\(0\)	\(0\)	\(q-\zeta_{22}^{6}q^{2}+\zeta_{22}^{9}q^{3}-\zeta_{22}q^{4}+\zeta_{22}^{4}q^{6}+\cdots\)
2005.1.g.a	\(2\)	\(1.001\)	\(\Q(\sqrt{-1}) \)	\(D_{4}\)	None	\(\Q(\sqrt{401}) \)	\(2\)	\(0\)	\(2\)	\(-2\)	\(q+(1-i)q^{2}-iq^{4}+q^{5}+(-1+i+\cdots)q^{7}+\cdots\)
2005.1.g.b	\(8\)	\(1.001\)	\(\Q(\zeta_{20})\)	\(D_{20}\)	None	\(\Q(\sqrt{401}) \)	\(-2\)	\(0\)	\(-2\)	\(2\)	\(q+(-\zeta_{20}+\zeta_{20}^{4})q^{2}+(\zeta_{20}^{2}-\zeta_{20}^{5}+\cdots)q^{4}+\cdots\)
2007.1.d.a	\(1\)	\(1.002\)	\(\Q\)	\(D_{2}\)	\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-223}) \)	\(\Q(\sqrt{669}) \)	\(0\)	\(0\)	\(0\)	\(-2\)	\(q-q^{4}-2q^{7}+q^{16}+2q^{19}+q^{25}+\cdots\)
2007.1.d.b	\(3\)	\(1.002\)	\(\Q(\zeta_{14})^+\)	\(D_{7}\)	\(\Q(\sqrt{-223}) \)	None	\(1\)	\(0\)	\(0\)	\(-1\)	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1+\beta _{1}-\beta _{2})q^{7}+\cdots\)
2007.1.d.c	\(6\)	\(1.002\)	\(\Q(\zeta_{28})^+\)	\(D_{14}\)	\(\Q(\sqrt{-223}) \)	None	\(0\)	\(0\)	\(0\)	\(2\)	\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(1-\beta _{2}-\beta _{4}+\cdots)q^{7}+\cdots\)
2007.1.v.a	\(36\)	\(1.002\)	\(\Q(\zeta_{74})\)	\(D_{74}\)	\(\Q(\sqrt{-3}) \)	None	\(0\)	\(0\)	\(0\)	\(2\)	\(q-\zeta_{74}^{20}q^{4}+(\zeta_{74}^{21}+\zeta_{74}^{27})q^{7}+\cdots\)
2008.1.c.a	\(3\)	\(1.002\)	\(\Q(\zeta_{14})^+\)	\(D_{7}\)	\(\Q(\sqrt{-502}) \)	None	\(-3\)	\(0\)	\(0\)	\(-1\)	\(q-q^{2}+q^{4}-\beta _{1}q^{7}-q^{8}+q^{9}-\beta _{2}q^{11}+\cdots\)
2008.1.c.b	\(3\)	\(1.002\)	\(\Q(\zeta_{14})^+\)	\(D_{7}\)	\(\Q(\sqrt{-502}) \)	None	\(3\)	\(0\)	\(0\)	\(-1\)	\(q+q^{2}+q^{4}-\beta _{1}q^{7}+q^{8}+q^{9}+\beta _{2}q^{11}+\cdots\)
2008.1.j.a	\(4\)	\(1.002\)	\(\Q(\zeta_{10})\)	\(D_{5}\)	\(\Q(\sqrt{-2}) \)	None	\(4\)	\(-2\)	\(0\)	\(0\)	\(q+q^{2}+(-\zeta_{10}+\zeta_{10}^{2})q^{3}+q^{4}+(-\zeta_{10}+\cdots)q^{6}+\cdots\)
2008.1.w.a	\(20\)	\(1.002\)	\(\Q(\zeta_{50})\)	\(D_{25}\)	\(\Q(\sqrt{-2}) \)	None	\(-5\)	\(0\)	\(0\)	\(0\)	\(q-\zeta_{50}^{5}q^{2}+(\zeta_{50}^{2}+\zeta_{50}^{4})q^{3}+\zeta_{50}^{10}q^{4}+\cdots\)
2008.1.bd.a	\(100\)	\(1.002\)	\(\Q(\zeta_{250})\)	\(D_{125}\)	\(\Q(\sqrt{-2}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(q-\zeta_{250}^{35}q^{2}+(\zeta_{250}^{14}-\zeta_{250}^{53})q^{3}+\cdots\)
2009.1.i.a	\(6\)	\(1.003\)	6.0.64827.1	\(D_{7}\)	\(\Q(\sqrt{-287}) \)	None	\(1\)	\(-1\)	\(0\)	\(0\)	\(q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{2}-\beta _{3}-\beta _{4}-\beta _{5})q^{3}+\cdots\)
2009.1.i.b	\(6\)	\(1.003\)	6.0.64827.1	\(D_{7}\)	\(\Q(\sqrt{-287}) \)	None	\(1\)	\(1\)	\(0\)	\(0\)	\(q+\beta _{1}q^{2}+(\beta _{1}-\beta _{2}+\beta _{3}+\beta _{4}+\beta _{5})q^{3}+\cdots\)
2011.1.b.a	\(3\)	\(1.004\)	\(\Q(\zeta_{14})^+\)	\(D_{7}\)	\(\Q(\sqrt{-2011}) \)	None	\(0\)	\(0\)	\(-1\)	\(0\)	\(q+q^{4}-\beta _{1}q^{5}+q^{9}+(-1+\beta _{1}-\beta _{2})q^{13}+\cdots\)
2013.1.bm.a	\(4\)	\(1.005\)	\(\Q(\zeta_{10})\)	\(D_{5}\)	\(\Q(\sqrt{-183}) \)	None	\(-3\)	\(-1\)	\(0\)	\(0\)	\(q+(-1+\zeta_{10})q^{2}+\zeta_{10}^{4}q^{3}+(1-\zeta_{10}+\cdots)q^{4}+\cdots\)
2013.1.bm.b	\(4\)	\(1.005\)	\(\Q(\zeta_{10})\)	\(D_{5}\)	\(\Q(\sqrt{-183}) \)	None	\(3\)	\(-1\)	\(0\)	\(0\)	\(q+(1-\zeta_{10})q^{2}+\zeta_{10}^{4}q^{3}+(1-\zeta_{10}+\cdots)q^{4}+\cdots\)
2013.1.bm.c	\(8\)	\(1.005\)	\(\Q(\zeta_{20})\)	\(D_{10}\)	\(\Q(\sqrt{-183}) \)	None	\(0\)	\(-2\)	\(0\)	\(0\)	\(q+(\zeta_{20}^{5}+\zeta_{20}^{7})q^{2}+\zeta_{20}^{8}q^{3}+(-1+\cdots)q^{4}+\cdots\)
2013.1.bm.d	\(16\)	\(1.005\)	\(\Q(\zeta_{40})\)	\(D_{20}\)	\(\Q(\sqrt{-183}) \)	None	\(0\)	\(4\)	\(0\)	\(0\)	\(q+(\zeta_{40}^{9}+\zeta_{40}^{15})q^{2}-\zeta_{40}^{16}q^{3}+\cdots\)
2015.1.h.a	\(4\)	\(1.006\)	\(\Q(\zeta_{8})\)	\(D_{4}\)	\(\Q(\sqrt{-155}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(q+(\zeta_{8}-\zeta_{8}^{3})q^{3}-q^{4}+\zeta_{8}^{2}q^{5}+q^{9}+\cdots\)
2015.1.h.b	\(6\)	\(1.006\)	\(\Q(\zeta_{26})^+\)	\(D_{13}\)	\(\Q(\sqrt{-2015}) \)	None	\(-1\)	\(-1\)	\(6\)	\(-1\)	\(q-\beta _{1}q^{2}-\beta _{3}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots\)
2015.1.h.c	\(6\)	\(1.006\)	\(\Q(\zeta_{26})^+\)	\(D_{13}\)	\(\Q(\sqrt{-2015}) \)	None	\(-1\)	\(1\)	\(6\)	\(-1\)	\(q-\beta _{1}q^{2}+\beta _{3}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots\)
2015.1.h.d	\(6\)	\(1.006\)	\(\Q(\zeta_{26})^+\)	\(D_{13}\)	\(\Q(\sqrt{-2015}) \)	None	\(1\)	\(-1\)	\(-6\)	\(1\)	\(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots\)
2015.1.h.e	\(6\)	\(1.006\)	\(\Q(\zeta_{26})^+\)	\(D_{13}\)	\(\Q(\sqrt{-2015}) \)	None	\(1\)	\(1\)	\(-6\)	\(1\)	\(q+\beta _{1}q^{2}+\beta _{3}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots\)
2015.1.bf.a	\(8\)	\(1.006\)	\(\Q(\zeta_{24})\)	\(D_{12}\)	\(\Q(\sqrt{-155}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(q+(\zeta_{24}^{5}+\zeta_{24}^{11})q^{3}+\zeta_{24}^{4}q^{4}-\zeta_{24}^{6}q^{5}+\cdots\)
2015.1.bq.a	\(2\)	\(1.006\)	\(\Q(\sqrt{-3}) \)	\(D_{3}\)	\(\Q(\sqrt{-155}) \)	None	\(0\)	\(-2\)	\(2\)	\(0\)	\(q-\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}+q^{5}+3\zeta_{6}^{2}q^{9}+\cdots\)
2015.1.bq.b	\(2\)	\(1.006\)	\(\Q(\sqrt{-3}) \)	\(D_{3}\)	\(\Q(\sqrt{-155}) \)	None	\(0\)	\(2\)	\(2\)	\(0\)	\(q+\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}+q^{5}+3\zeta_{6}^{2}q^{9}+\cdots\)
2015.1.bq.c	\(4\)	\(1.006\)	\(\Q(\zeta_{12})\)	\(A_{4}\)	None	None	\(0\)	\(-2\)	\(0\)	\(0\)	\(q+\zeta_{12}q^{2}+\zeta_{12}^{4}q^{3}+\zeta_{12}^{3}q^{5}+\zeta_{12}^{5}q^{6}+\cdots\)
2015.1.bq.d	\(4\)	\(1.006\)	\(\Q(\zeta_{12})\)	\(D_{6}\)	\(\Q(\sqrt{-155}) \)	None	\(0\)	\(0\)	\(-4\)	\(0\)	\(q-\zeta_{12}^{2}q^{4}-q^{5}+\zeta_{12}^{2}q^{9}+\zeta_{12}^{5}q^{13}+\cdots\)
2015.1.bq.e	\(4\)	\(1.006\)	\(\Q(\zeta_{12})\)	\(A_{4}\)	None	None	\(0\)	\(2\)	\(0\)	\(0\)	\(q-\zeta_{12}q^{2}-\zeta_{12}^{4}q^{3}-\zeta_{12}^{3}q^{5}+\zeta_{12}^{5}q^{6}+\cdots\)
2016.1.e.a	\(4\)	\(1.006\)	\(\Q(\zeta_{8})\)	\(D_{4}\)	\(\Q(\sqrt{-7}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(q+\zeta_{8}^{2}q^{7}+(\zeta_{8}+\zeta_{8}^{3})q^{11}+(-\zeta_{8}+\cdots)q^{23}+\cdots\)
2016.1.f.a	\(4\)	\(1.006\)	\(\Q(\zeta_{8})\)	\(D_{4}\)	\(\Q(\sqrt{-21}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(q+(-\zeta_{8}-\zeta_{8}^{3})q^{5}+\zeta_{8}^{2}q^{7}+(-\zeta_{8}+\cdots)q^{11}+\cdots\)
2016.1.l.a	\(1\)	\(1.006\)	\(\Q\)	\(D_{2}\)	\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-14}) \)	\(\Q(\sqrt{2}) \)	\(0\)	\(0\)	\(0\)	\(1\)	\(q+q^{7}+2q^{23}-q^{25}+q^{49}-2q^{71}+\cdots\)
2016.1.l.b	\(2\)	\(1.006\)	\(\Q(\sqrt{-1}) \)	\(D_{2}\)	\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-6}) \)	\(\Q(\sqrt{42}) \)	\(0\)	\(0\)	\(0\)	\(-2\)	\(q-q^{7}-iq^{11}-q^{25}-iq^{29}+q^{49}+\cdots\)
2016.1.bi.a	\(4\)	\(1.006\)	\(\Q(\zeta_{12})\)	\(A_{4}\)	None	None	\(0\)	\(-2\)	\(0\)	\(0\)	\(q-\zeta_{12}^{2}q^{3}-\zeta_{12}^{3}q^{5}+\zeta_{12}q^{7}+\zeta_{12}^{4}q^{9}+\cdots\)

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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.