LMFDB - Group of Dirichlet characters of modulus 2112

Show commands: PariGP / SageMath

sage: H = DirichletGroup(2112)

pari: g = idealstar(,2112,2)

Character group

sage: G.order() pari: g.no
Order	=	640
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{2}\times C_{80}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{2112}(2047,\cdot)$, $\chi_{2112}(133,\cdot)$, $\chi_{2112}(1409,\cdot)$, $\chi_{2112}(1729,\cdot)$

First 32 of 640 characters

Each row describes a character. When available, the columns show the orbit label, order of the character, whether the character is primitive, and several values of the character.

Character	Orbit	Order	Primitive	$-1$	$1$	$5$	$7$	$13$	$17$	$19$	$23$	$25$	$29$	$31$	$35$
$\chi_{2112}(1,\cdot)$	2112.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{2112}(5,\cdot)$	2112.cy	80	yes	$-1$	$1$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{27}{80}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{47}{80}\right)$
$\chi_{2112}(7,\cdot)$	2112.co	40	no	$1$	$1$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{39}{40}\right)$	$i$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{40}\right)$
$\chi_{2112}(13,\cdot)$	2112.cz	80	no	$-1$	$1$	$e\left(\frac{27}{80}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{33}{80}\right)$
$\chi_{2112}(17,\cdot)$	2112.ce	20	no	$1$	$1$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{19}{20}\right)$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{13}{20}\right)$
$\chi_{2112}(19,\cdot)$	2112.cu	80	no	$1$	$1$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{49}{80}\right)$
$\chi_{2112}(23,\cdot)$	2112.bd	8	no	$1$	$1$	$e\left(\frac{3}{8}\right)$	$i$	$e\left(\frac{1}{8}\right)$	$1$	$e\left(\frac{5}{8}\right)$	$i$	$-i$	$e\left(\frac{1}{8}\right)$	$-1$	$e\left(\frac{5}{8}\right)$
$\chi_{2112}(25,\cdot)$	2112.cr	40	no	$1$	$1$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{11}{40}\right)$	$-i$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{40}\right)$
$\chi_{2112}(29,\cdot)$	2112.db	80	yes	$1$	$1$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{61}{80}\right)$
$\chi_{2112}(31,\cdot)$	2112.bu	10	no	$-1$	$1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{5}\right)$	$-1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{2112}(35,\cdot)$	2112.cw	80	yes	$-1$	$1$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{33}{80}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{49}{80}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{53}{80}\right)$
$\chi_{2112}(37,\cdot)$	2112.da	80	no	$1$	$1$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{31}{80}\right)$
$\chi_{2112}(41,\cdot)$	2112.cq	40	no	$1$	$1$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{40}\right)$	$-i$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{17}{40}\right)$
$\chi_{2112}(43,\cdot)$	2112.cb	16	no	$1$	$1$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{11}{16}\right)$	$i$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{16}\right)$	$1$	$e\left(\frac{15}{16}\right)$
$\chi_{2112}(47,\cdot)$	2112.ch	20	no	$1$	$1$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{20}\right)$	$-1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{20}\right)$
$\chi_{2112}(49,\cdot)$	2112.ci	20	no	$1$	$1$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{19}{20}\right)$	$-1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{20}\right)$
$\chi_{2112}(53,\cdot)$	2112.cy	80	yes	$-1$	$1$	$e\left(\frac{17}{80}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{11}{80}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{43}{80}\right)$
$\chi_{2112}(59,\cdot)$	2112.cv	80	yes	$1$	$1$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{11}{80}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{71}{80}\right)$
$\chi_{2112}(61,\cdot)$	2112.cz	80	no	$-1$	$1$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{57}{80}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{77}{80}\right)$
$\chi_{2112}(65,\cdot)$	2112.b	2	no	$1$	$1$	$-1$	$-1$	$-1$	$1$	$-1$	$-1$	$1$	$1$	$1$	$1$
$\chi_{2112}(67,\cdot)$	2112.cc	16	no	$-1$	$1$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{13}{16}\right)$	$i$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{16}\right)$	$1$	$e\left(\frac{9}{16}\right)$
$\chi_{2112}(71,\cdot)$	2112.cp	40	no	$1$	$1$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{40}\right)$	$-i$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{11}{40}\right)$
$\chi_{2112}(73,\cdot)$	2112.cn	40	no	$-1$	$1$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{29}{40}\right)$	$i$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{33}{40}\right)$
$\chi_{2112}(79,\cdot)$	2112.cl	20	no	$1$	$1$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{11}{20}\right)$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{20}\right)$
$\chi_{2112}(83,\cdot)$	2112.cw	80	yes	$-1$	$1$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{21}{80}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{49}{80}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{57}{80}\right)$
$\chi_{2112}(85,\cdot)$	2112.cz	80	no	$-1$	$1$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{3}{80}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{19}{80}\right)$
$\chi_{2112}(89,\cdot)$	2112.bg	8	no	$-1$	$1$	$e\left(\frac{5}{8}\right)$	$i$	$e\left(\frac{7}{8}\right)$	$1$	$e\left(\frac{7}{8}\right)$	$i$	$i$	$e\left(\frac{7}{8}\right)$	$1$	$e\left(\frac{7}{8}\right)$
$\chi_{2112}(91,\cdot)$	2112.cx	80	no	$-1$	$1$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{19}{80}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{67}{80}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{39}{80}\right)$
$\chi_{2112}(95,\cdot)$	2112.bh	10	no	$-1$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{10}\right)$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{2112}(97,\cdot)$	2112.br	10	no	$1$	$1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{10}\right)$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{10}\right)$
$\chi_{2112}(101,\cdot)$	2112.db	80	yes	$1$	$1$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{19}{80}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{31}{80}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{63}{80}\right)$
$\chi_{2112}(103,\cdot)$	2112.cs	40	no	$-1$	$1$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{39}{40}\right)$	$i$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{40}\right)$

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Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Modulus	$2112$
Structure	\(C_{2}\times C_{2}\times C_{2}\times C_{80}\)
Order	$640$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(7\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(35\)
\(\chi_{2112}(1,\cdot)\)	2112.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{2112}(5,\cdot)\)	2112.cy	80	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{27}{80}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{79}{80}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{47}{80}\right)\)
\(\chi_{2112}(7,\cdot)\)	2112.co	40	no	\(1\)	\(1\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(i\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{40}\right)\)
\(\chi_{2112}(13,\cdot)\)	2112.cz	80	no	\(-1\)	\(1\)	\(e\left(\frac{27}{80}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{1}{80}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{33}{80}\right)\)
\(\chi_{2112}(17,\cdot)\)	2112.ce	20	no	\(1\)	\(1\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{13}{20}\right)\)
\(\chi_{2112}(19,\cdot)\)	2112.cu	80	no	\(1\)	\(1\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{49}{80}\right)\)
\(\chi_{2112}(23,\cdot)\)	2112.bd	8	no	\(1\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(i\)	\(e\left(\frac{1}{8}\right)\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(i\)	\(-i\)	\(e\left(\frac{1}{8}\right)\)	\(-1\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{2112}(25,\cdot)\)	2112.cr	40	no	\(1\)	\(1\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(-i\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{40}\right)\)
\(\chi_{2112}(29,\cdot)\)	2112.db	80	yes	\(1\)	\(1\)	\(e\left(\frac{79}{80}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{1}{80}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{77}{80}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{61}{80}\right)\)
\(\chi_{2112}(31,\cdot)\)	2112.bu	10	no	\(-1\)	\(1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(-1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{2112}(35,\cdot)\)	2112.cw	80	yes	\(-1\)	\(1\)	\(e\left(\frac{47}{80}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{33}{80}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{49}{80}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{53}{80}\right)\)
\(\chi_{2112}(37,\cdot)\)	2112.da	80	no	\(1\)	\(1\)	\(e\left(\frac{29}{80}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{47}{80}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{31}{80}\right)\)
\(\chi_{2112}(41,\cdot)\)	2112.cq	40	no	\(1\)	\(1\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(-i\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{17}{40}\right)\)
\(\chi_{2112}(43,\cdot)\)	2112.cb	16	no	\(1\)	\(1\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(i\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(1\)	\(e\left(\frac{15}{16}\right)\)
\(\chi_{2112}(47,\cdot)\)	2112.ch	20	no	\(1\)	\(1\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(-1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{20}\right)\)
\(\chi_{2112}(49,\cdot)\)	2112.ci	20	no	\(1\)	\(1\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(-1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{20}\right)\)
\(\chi_{2112}(53,\cdot)\)	2112.cy	80	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{80}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{79}{80}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{11}{80}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{43}{80}\right)\)
\(\chi_{2112}(59,\cdot)\)	2112.cv	80	yes	\(1\)	\(1\)	\(e\left(\frac{29}{80}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{11}{80}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{47}{80}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{71}{80}\right)\)
\(\chi_{2112}(61,\cdot)\)	2112.cz	80	no	\(-1\)	\(1\)	\(e\left(\frac{63}{80}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{57}{80}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{80}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{29}{80}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{77}{80}\right)\)
\(\chi_{2112}(65,\cdot)\)	2112.b	2	no	\(1\)	\(1\)	\(-1\)	\(-1\)	\(-1\)	\(1\)	\(-1\)	\(-1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{2112}(67,\cdot)\)	2112.cc	16	no	\(-1\)	\(1\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(i\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(1\)	\(e\left(\frac{9}{16}\right)\)
\(\chi_{2112}(71,\cdot)\)	2112.cp	40	no	\(1\)	\(1\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(-i\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{11}{40}\right)\)
\(\chi_{2112}(73,\cdot)\)	2112.cn	40	no	\(-1\)	\(1\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(i\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{33}{40}\right)\)
\(\chi_{2112}(79,\cdot)\)	2112.cl	20	no	\(1\)	\(1\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{20}\right)\)
\(\chi_{2112}(83,\cdot)\)	2112.cw	80	yes	\(-1\)	\(1\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{21}{80}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{49}{80}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{57}{80}\right)\)
\(\chi_{2112}(85,\cdot)\)	2112.cz	80	no	\(-1\)	\(1\)	\(e\left(\frac{1}{80}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{39}{80}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{47}{80}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{3}{80}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{19}{80}\right)\)
\(\chi_{2112}(89,\cdot)\)	2112.bg	8	no	\(-1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(i\)	\(e\left(\frac{7}{8}\right)\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(i\)	\(i\)	\(e\left(\frac{7}{8}\right)\)	\(1\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{2112}(91,\cdot)\)	2112.cx	80	no	\(-1\)	\(1\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{19}{80}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{67}{80}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{63}{80}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{39}{80}\right)\)
\(\chi_{2112}(95,\cdot)\)	2112.bh	10	no	\(-1\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{2112}(97,\cdot)\)	2112.br	10	no	\(1\)	\(1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)
\(\chi_{2112}(101,\cdot)\)	2112.db	80	yes	\(1\)	\(1\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{19}{80}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{31}{80}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{63}{80}\right)\)
\(\chi_{2112}(103,\cdot)\)	2112.cs	40	no	\(-1\)	\(1\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(i\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{40}\right)\)

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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.