LMFDB - Group of Dirichlet characters of modulus 3200

Show commands: PariGP / SageMath

sage: H = DirichletGroup(3200)

pari: g = idealstar(,3200,2)

Character group

sage: G.order() pari: g.no
Order	=	1280
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{4}\times C_{160}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{3200}(1151,\cdot)$, $\chi_{3200}(901,\cdot)$, $\chi_{3200}(2177,\cdot)$

First 32 of 1280 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	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$19$	$21$	$23$	$27$
$\chi_{3200}(1,\cdot)$	3200.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{3200}(3,\cdot)$	3200.di	160	yes	$1$	$1$	$e\left(\frac{37}{160}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{11}{160}\right)$	$e\left(\frac{9}{160}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{153}{160}\right)$	$e\left(\frac{67}{160}\right)$	$e\left(\frac{53}{80}\right)$	$e\left(\frac{111}{160}\right)$
$\chi_{3200}(7,\cdot)$	3200.br	16	no	$1$	$1$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{7}{16}\right)$	$1$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{9}{16}\right)$
$\chi_{3200}(9,\cdot)$	3200.cy	80	no	$1$	$1$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{11}{80}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{67}{80}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{31}{80}\right)$
$\chi_{3200}(11,\cdot)$	3200.de	160	yes	$-1$	$1$	$e\left(\frac{11}{160}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{11}{80}\right)$	$e\left(\frac{13}{160}\right)$	$e\left(\frac{7}{160}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{159}{160}\right)$	$e\left(\frac{21}{160}\right)$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{33}{160}\right)$
$\chi_{3200}(13,\cdot)$	3200.dj	160	yes	$-1$	$1$	$e\left(\frac{9}{160}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{7}{160}\right)$	$e\left(\frac{13}{160}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{141}{160}\right)$	$e\left(\frac{79}{160}\right)$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{27}{160}\right)$
$\chi_{3200}(17,\cdot)$	3200.cs	40	no	$-1$	$1$	$e\left(\frac{7}{40}\right)$	$1$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{21}{40}\right)$
$\chi_{3200}(19,\cdot)$	3200.dg	160	yes	$-1$	$1$	$e\left(\frac{153}{160}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{159}{160}\right)$	$e\left(\frac{141}{160}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{37}{160}\right)$	$e\left(\frac{23}{160}\right)$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{139}{160}\right)$
$\chi_{3200}(21,\cdot)$	3200.dh	160	yes	$1$	$1$	$e\left(\frac{67}{160}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{67}{80}\right)$	$e\left(\frac{21}{160}\right)$	$e\left(\frac{79}{160}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{23}{160}\right)$	$e\left(\frac{77}{160}\right)$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{41}{160}\right)$
$\chi_{3200}(23,\cdot)$	3200.cu	80	no	$1$	$1$	$e\left(\frac{53}{80}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{79}{80}\right)$
$\chi_{3200}(27,\cdot)$	3200.di	160	yes	$1$	$1$	$e\left(\frac{111}{160}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{31}{80}\right)$	$e\left(\frac{33}{160}\right)$	$e\left(\frac{27}{160}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{139}{160}\right)$	$e\left(\frac{41}{160}\right)$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{13}{160}\right)$
$\chi_{3200}(29,\cdot)$	3200.df	160	yes	$1$	$1$	$e\left(\frac{37}{160}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{51}{160}\right)$	$e\left(\frac{89}{160}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{33}{160}\right)$	$e\left(\frac{27}{160}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{111}{160}\right)$
$\chi_{3200}(31,\cdot)$	3200.ca	20	no	$-1$	$1$	$e\left(\frac{1}{20}\right)$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{20}\right)$
$\chi_{3200}(33,\cdot)$	3200.cd	20	no	$-1$	$1$	$e\left(\frac{3}{10}\right)$	$i$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{9}{10}\right)$
$\chi_{3200}(37,\cdot)$	3200.dj	160	yes	$-1$	$1$	$e\left(\frac{79}{160}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{97}{160}\right)$	$e\left(\frac{43}{160}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{11}{160}\right)$	$e\left(\frac{89}{160}\right)$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{77}{160}\right)$
$\chi_{3200}(39,\cdot)$	3200.cw	80	no	$-1$	$1$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{11}{80}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{67}{80}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{69}{80}\right)$
$\chi_{3200}(41,\cdot)$	3200.cz	80	no	$1$	$1$	$e\left(\frac{17}{80}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{51}{80}\right)$
$\chi_{3200}(43,\cdot)$	3200.cl	32	no	$1$	$1$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{13}{32}\right)$
$\chi_{3200}(47,\cdot)$	3200.cn	40	no	$1$	$1$	$e\left(\frac{23}{40}\right)$	$-1$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{29}{40}\right)$
$\chi_{3200}(49,\cdot)$	3200.ba	8	no	$1$	$1$	$e\left(\frac{3}{8}\right)$	$-i$	$-i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{8}\right)$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{8}\right)$	$i$	$e\left(\frac{1}{8}\right)$
$\chi_{3200}(51,\cdot)$	3200.cj	32	no	$-1$	$1$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{7}{32}\right)$
$\chi_{3200}(53,\cdot)$	3200.dd	160	yes	$-1$	$1$	$e\left(\frac{147}{160}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{67}{80}\right)$	$e\left(\frac{141}{160}\right)$	$e\left(\frac{159}{160}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{143}{160}\right)$	$e\left(\frac{37}{160}\right)$	$e\left(\frac{3}{80}\right)$	$e\left(\frac{121}{160}\right)$
$\chi_{3200}(57,\cdot)$	3200.bq	16	no	$-1$	$1$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{15}{16}\right)$	$1$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{9}{16}\right)$
$\chi_{3200}(59,\cdot)$	3200.dg	160	yes	$-1$	$1$	$e\left(\frac{159}{160}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{137}{160}\right)$	$e\left(\frac{43}{160}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{51}{160}\right)$	$e\left(\frac{49}{160}\right)$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{157}{160}\right)$
$\chi_{3200}(61,\cdot)$	3200.dh	160	yes	$1$	$1$	$e\left(\frac{61}{160}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{43}{160}\right)$	$e\left(\frac{17}{160}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{9}{160}\right)$	$e\left(\frac{51}{160}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{23}{160}\right)$
$\chi_{3200}(63,\cdot)$	3200.bx	20	no	$1$	$1$	$e\left(\frac{13}{20}\right)$	$i$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{19}{20}\right)$
$\chi_{3200}(67,\cdot)$	3200.dc	160	yes	$1$	$1$	$e\left(\frac{133}{160}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{53}{80}\right)$	$e\left(\frac{59}{160}\right)$	$e\left(\frac{41}{160}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{137}{160}\right)$	$e\left(\frac{83}{160}\right)$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{79}{160}\right)$
$\chi_{3200}(69,\cdot)$	3200.df	160	yes	$1$	$1$	$e\left(\frac{143}{160}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{89}{160}\right)$	$e\left(\frac{11}{160}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{67}{160}\right)$	$e\left(\frac{113}{160}\right)$	$e\left(\frac{27}{80}\right)$	$e\left(\frac{109}{160}\right)$
$\chi_{3200}(71,\cdot)$	3200.cx	80	no	$-1$	$1$	$e\left(\frac{11}{80}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{33}{80}\right)$
$\chi_{3200}(73,\cdot)$	3200.cv	80	no	$-1$	$1$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{19}{80}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{57}{80}\right)$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{59}{80}\right)$
$\chi_{3200}(77,\cdot)$	3200.dd	160	yes	$-1$	$1$	$e\left(\frac{41}{160}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{23}{160}\right)$	$e\left(\frac{77}{160}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{29}{160}\right)$	$e\left(\frac{31}{160}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{123}{160}\right)$
$\chi_{3200}(79,\cdot)$	3200.cp	40	no	$-1$	$1$	$e\left(\frac{3}{40}\right)$	$i$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{9}{40}\right)$

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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	$3200$
Structure	\(C_{2}\times C_{4}\times C_{160}\)
Order	$1280$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)
\(\chi_{3200}(1,\cdot)\)	3200.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{3200}(3,\cdot)\)	3200.di	160	yes	\(1\)	\(1\)	\(e\left(\frac{37}{160}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{11}{160}\right)\)	\(e\left(\frac{9}{160}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{153}{160}\right)\)	\(e\left(\frac{67}{160}\right)\)	\(e\left(\frac{53}{80}\right)\)	\(e\left(\frac{111}{160}\right)\)
\(\chi_{3200}(7,\cdot)\)	3200.br	16	no	\(1\)	\(1\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(1\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{9}{16}\right)\)
\(\chi_{3200}(9,\cdot)\)	3200.cy	80	no	\(1\)	\(1\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{11}{80}\right)\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{67}{80}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{31}{80}\right)\)
\(\chi_{3200}(11,\cdot)\)	3200.de	160	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{160}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{11}{80}\right)\)	\(e\left(\frac{13}{160}\right)\)	\(e\left(\frac{7}{160}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{159}{160}\right)\)	\(e\left(\frac{21}{160}\right)\)	\(e\left(\frac{39}{80}\right)\)	\(e\left(\frac{33}{160}\right)\)
\(\chi_{3200}(13,\cdot)\)	3200.dj	160	yes	\(-1\)	\(1\)	\(e\left(\frac{9}{160}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{7}{160}\right)\)	\(e\left(\frac{13}{160}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{141}{160}\right)\)	\(e\left(\frac{79}{160}\right)\)	\(e\left(\frac{1}{80}\right)\)	\(e\left(\frac{27}{160}\right)\)
\(\chi_{3200}(17,\cdot)\)	3200.cs	40	no	\(-1\)	\(1\)	\(e\left(\frac{7}{40}\right)\)	\(1\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{21}{40}\right)\)
\(\chi_{3200}(19,\cdot)\)	3200.dg	160	yes	\(-1\)	\(1\)	\(e\left(\frac{153}{160}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{159}{160}\right)\)	\(e\left(\frac{141}{160}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{37}{160}\right)\)	\(e\left(\frac{23}{160}\right)\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{139}{160}\right)\)
\(\chi_{3200}(21,\cdot)\)	3200.dh	160	yes	\(1\)	\(1\)	\(e\left(\frac{67}{160}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{67}{80}\right)\)	\(e\left(\frac{21}{160}\right)\)	\(e\left(\frac{79}{160}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{23}{160}\right)\)	\(e\left(\frac{77}{160}\right)\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{41}{160}\right)\)
\(\chi_{3200}(23,\cdot)\)	3200.cu	80	no	\(1\)	\(1\)	\(e\left(\frac{53}{80}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{39}{80}\right)\)	\(e\left(\frac{1}{80}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{79}{80}\right)\)
\(\chi_{3200}(27,\cdot)\)	3200.di	160	yes	\(1\)	\(1\)	\(e\left(\frac{111}{160}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{31}{80}\right)\)	\(e\left(\frac{33}{160}\right)\)	\(e\left(\frac{27}{160}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{139}{160}\right)\)	\(e\left(\frac{41}{160}\right)\)	\(e\left(\frac{79}{80}\right)\)	\(e\left(\frac{13}{160}\right)\)
\(\chi_{3200}(29,\cdot)\)	3200.df	160	yes	\(1\)	\(1\)	\(e\left(\frac{37}{160}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{51}{160}\right)\)	\(e\left(\frac{89}{160}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{33}{160}\right)\)	\(e\left(\frac{27}{160}\right)\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{111}{160}\right)\)
\(\chi_{3200}(31,\cdot)\)	3200.ca	20	no	\(-1\)	\(1\)	\(e\left(\frac{1}{20}\right)\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{20}\right)\)
\(\chi_{3200}(33,\cdot)\)	3200.cd	20	no	\(-1\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(i\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)
\(\chi_{3200}(37,\cdot)\)	3200.dj	160	yes	\(-1\)	\(1\)	\(e\left(\frac{79}{160}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{79}{80}\right)\)	\(e\left(\frac{97}{160}\right)\)	\(e\left(\frac{43}{160}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{11}{160}\right)\)	\(e\left(\frac{89}{160}\right)\)	\(e\left(\frac{71}{80}\right)\)	\(e\left(\frac{77}{160}\right)\)
\(\chi_{3200}(39,\cdot)\)	3200.cw	80	no	\(-1\)	\(1\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{11}{80}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{67}{80}\right)\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{69}{80}\right)\)
\(\chi_{3200}(41,\cdot)\)	3200.cz	80	no	\(1\)	\(1\)	\(e\left(\frac{17}{80}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{71}{80}\right)\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{47}{80}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{51}{80}\right)\)
\(\chi_{3200}(43,\cdot)\)	3200.cl	32	no	\(1\)	\(1\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{13}{32}\right)\)
\(\chi_{3200}(47,\cdot)\)	3200.cn	40	no	\(1\)	\(1\)	\(e\left(\frac{23}{40}\right)\)	\(-1\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{29}{40}\right)\)
\(\chi_{3200}(49,\cdot)\)	3200.ba	8	no	\(1\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(-i\)	\(-i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(i\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{3200}(51,\cdot)\)	3200.cj	32	no	\(-1\)	\(1\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{7}{32}\right)\)
\(\chi_{3200}(53,\cdot)\)	3200.dd	160	yes	\(-1\)	\(1\)	\(e\left(\frac{147}{160}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{67}{80}\right)\)	\(e\left(\frac{141}{160}\right)\)	\(e\left(\frac{159}{160}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{143}{160}\right)\)	\(e\left(\frac{37}{160}\right)\)	\(e\left(\frac{3}{80}\right)\)	\(e\left(\frac{121}{160}\right)\)
\(\chi_{3200}(57,\cdot)\)	3200.bq	16	no	\(-1\)	\(1\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(1\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{9}{16}\right)\)
\(\chi_{3200}(59,\cdot)\)	3200.dg	160	yes	\(-1\)	\(1\)	\(e\left(\frac{159}{160}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{79}{80}\right)\)	\(e\left(\frac{137}{160}\right)\)	\(e\left(\frac{43}{160}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{51}{160}\right)\)	\(e\left(\frac{49}{160}\right)\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{157}{160}\right)\)
\(\chi_{3200}(61,\cdot)\)	3200.dh	160	yes	\(1\)	\(1\)	\(e\left(\frac{61}{160}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{43}{160}\right)\)	\(e\left(\frac{17}{160}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{9}{160}\right)\)	\(e\left(\frac{51}{160}\right)\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{23}{160}\right)\)
\(\chi_{3200}(63,\cdot)\)	3200.bx	20	no	\(1\)	\(1\)	\(e\left(\frac{13}{20}\right)\)	\(i\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)
\(\chi_{3200}(67,\cdot)\)	3200.dc	160	yes	\(1\)	\(1\)	\(e\left(\frac{133}{160}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{53}{80}\right)\)	\(e\left(\frac{59}{160}\right)\)	\(e\left(\frac{41}{160}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{137}{160}\right)\)	\(e\left(\frac{83}{160}\right)\)	\(e\left(\frac{77}{80}\right)\)	\(e\left(\frac{79}{160}\right)\)
\(\chi_{3200}(69,\cdot)\)	3200.df	160	yes	\(1\)	\(1\)	\(e\left(\frac{143}{160}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{63}{80}\right)\)	\(e\left(\frac{89}{160}\right)\)	\(e\left(\frac{11}{160}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{67}{160}\right)\)	\(e\left(\frac{113}{160}\right)\)	\(e\left(\frac{27}{80}\right)\)	\(e\left(\frac{109}{160}\right)\)
\(\chi_{3200}(71,\cdot)\)	3200.cx	80	no	\(-1\)	\(1\)	\(e\left(\frac{11}{80}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{47}{80}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{79}{80}\right)\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{33}{80}\right)\)
\(\chi_{3200}(73,\cdot)\)	3200.cv	80	no	\(-1\)	\(1\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{19}{80}\right)\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{57}{80}\right)\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{59}{80}\right)\)
\(\chi_{3200}(77,\cdot)\)	3200.dd	160	yes	\(-1\)	\(1\)	\(e\left(\frac{41}{160}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{23}{160}\right)\)	\(e\left(\frac{77}{160}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{29}{160}\right)\)	\(e\left(\frac{31}{160}\right)\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{123}{160}\right)\)
\(\chi_{3200}(79,\cdot)\)	3200.cp	40	no	\(-1\)	\(1\)	\(e\left(\frac{3}{40}\right)\)	\(i\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{9}{40}\right)\)

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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.