LMFDB - Group of Dirichlet characters of modulus 833

sage:H = DirichletGroup(833)

pari:g = idealstar(,833,2)

Character group

sage:G.order() pari:g.no
Order	=	672
sage:H.invariants() pari:g.cyc
Structure	=	$C_{2}\times C_{336}$
sage:H.gens() pari:g.gen
Generators	=	$\chi_{833}(52,\cdot)$, $\chi_{833}(785,\cdot)$

First 32 of 672 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$8$	$9$	$10$	$11$	$12$
$\chi_{833}(1,\cdot)$	833.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{833}(2,\cdot)$	833.bl	168	yes	$1$	$1$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{83}{168}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{55}{168}\right)$	$e\left(\frac{47}{56}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{113}{168}\right)$	$e\left(\frac{149}{168}\right)$	$e\left(\frac{31}{168}\right)$
$\chi_{833}(3,\cdot)$	833.bn	336	yes	$1$	$1$	$e\left(\frac{83}{168}\right)$	$e\left(\frac{29}{336}\right)$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{1}{336}\right)$	$e\left(\frac{65}{112}\right)$	$e\left(\frac{27}{56}\right)$	$e\left(\frac{29}{168}\right)$	$e\left(\frac{167}{336}\right)$	$e\left(\frac{131}{336}\right)$	$e\left(\frac{25}{336}\right)$
$\chi_{833}(4,\cdot)$	833.bg	84	yes	$1$	$1$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{31}{84}\right)$
$\chi_{833}(5,\cdot)$	833.bn	336	yes	$1$	$1$	$e\left(\frac{55}{168}\right)$	$e\left(\frac{1}{336}\right)$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{197}{336}\right)$	$e\left(\frac{37}{112}\right)$	$e\left(\frac{55}{56}\right)$	$e\left(\frac{1}{168}\right)$	$e\left(\frac{307}{336}\right)$	$e\left(\frac{271}{336}\right)$	$e\left(\frac{221}{336}\right)$
$\chi_{833}(6,\cdot)$	833.bi	112	yes	$1$	$1$	$e\left(\frac{47}{56}\right)$	$e\left(\frac{65}{112}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{37}{112}\right)$	$e\left(\frac{47}{112}\right)$	$e\left(\frac{29}{56}\right)$	$e\left(\frac{9}{56}\right)$	$e\left(\frac{19}{112}\right)$	$e\left(\frac{31}{112}\right)$	$e\left(\frac{29}{112}\right)$
$\chi_{833}(8,\cdot)$	833.bf	56	yes	$1$	$1$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{27}{56}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{55}{56}\right)$	$e\left(\frac{29}{56}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{1}{56}\right)$	$e\left(\frac{37}{56}\right)$	$e\left(\frac{31}{56}\right)$
$\chi_{833}(9,\cdot)$	833.bl	168	yes	$1$	$1$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{29}{168}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{1}{168}\right)$	$e\left(\frac{9}{56}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{167}{168}\right)$	$e\left(\frac{131}{168}\right)$	$e\left(\frac{25}{168}\right)$
$\chi_{833}(10,\cdot)$	833.bn	336	yes	$1$	$1$	$e\left(\frac{113}{168}\right)$	$e\left(\frac{167}{336}\right)$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{307}{336}\right)$	$e\left(\frac{19}{112}\right)$	$e\left(\frac{1}{56}\right)$	$e\left(\frac{167}{168}\right)$	$e\left(\frac{197}{336}\right)$	$e\left(\frac{233}{336}\right)$	$e\left(\frac{283}{336}\right)$
$\chi_{833}(11,\cdot)$	833.bm	336	yes	$-1$	$1$	$e\left(\frac{149}{168}\right)$	$e\left(\frac{131}{336}\right)$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{271}{336}\right)$	$e\left(\frac{31}{112}\right)$	$e\left(\frac{37}{56}\right)$	$e\left(\frac{131}{168}\right)$	$e\left(\frac{233}{336}\right)$	$e\left(\frac{53}{336}\right)$	$e\left(\frac{55}{336}\right)$
$\chi_{833}(12,\cdot)$	833.bn	336	yes	$1$	$1$	$e\left(\frac{31}{168}\right)$	$e\left(\frac{25}{336}\right)$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{221}{336}\right)$	$e\left(\frac{29}{112}\right)$	$e\left(\frac{31}{56}\right)$	$e\left(\frac{25}{168}\right)$	$e\left(\frac{283}{336}\right)$	$e\left(\frac{55}{336}\right)$	$e\left(\frac{149}{336}\right)$
$\chi_{833}(13,\cdot)$	833.y	28	yes	$-1$	$1$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{25}{28}\right)$
$\chi_{833}(15,\cdot)$	833.bf	56	yes	$1$	$1$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{5}{56}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{33}{56}\right)$	$e\left(\frac{51}{56}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{23}{56}\right)$	$e\left(\frac{11}{56}\right)$	$e\left(\frac{41}{56}\right)$
$\chi_{833}(16,\cdot)$	833.z	42	yes	$1$	$1$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{31}{42}\right)$
$\chi_{833}(18,\cdot)$	833.e	3	no	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{833}(19,\cdot)$	833.w	24	no	$-1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{5}{8}\right)$	$-i$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{13}{24}\right)$
$\chi_{833}(20,\cdot)$	833.bi	112	yes	$1$	$1$	$e\left(\frac{1}{56}\right)$	$e\left(\frac{111}{112}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{27}{112}\right)$	$e\left(\frac{1}{112}\right)$	$e\left(\frac{3}{56}\right)$	$e\left(\frac{55}{56}\right)$	$e\left(\frac{29}{112}\right)$	$e\left(\frac{65}{112}\right)$	$e\left(\frac{3}{112}\right)$
$\chi_{833}(22,\cdot)$	833.bj	112	yes	$-1$	$1$	$e\left(\frac{13}{56}\right)$	$e\left(\frac{99}{112}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{15}{112}\right)$	$e\left(\frac{13}{112}\right)$	$e\left(\frac{39}{56}\right)$	$e\left(\frac{43}{56}\right)$	$e\left(\frac{41}{112}\right)$	$e\left(\frac{5}{112}\right)$	$e\left(\frac{39}{112}\right)$
$\chi_{833}(23,\cdot)$	833.bm	336	yes	$-1$	$1$	$e\left(\frac{109}{168}\right)$	$e\left(\frac{283}{336}\right)$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{311}{336}\right)$	$e\left(\frac{55}{112}\right)$	$e\left(\frac{53}{56}\right)$	$e\left(\frac{115}{168}\right)$	$e\left(\frac{193}{336}\right)$	$e\left(\frac{253}{336}\right)$	$e\left(\frac{47}{336}\right)$
$\chi_{833}(24,\cdot)$	833.bn	336	yes	$1$	$1$	$e\left(\frac{89}{168}\right)$	$e\left(\frac{191}{336}\right)$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{331}{336}\right)$	$e\left(\frac{11}{112}\right)$	$e\left(\frac{33}{56}\right)$	$e\left(\frac{23}{168}\right)$	$e\left(\frac{173}{336}\right)$	$e\left(\frac{17}{336}\right)$	$e\left(\frac{211}{336}\right)$
$\chi_{833}(25,\cdot)$	833.bl	168	yes	$1$	$1$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{1}{168}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{29}{168}\right)$	$e\left(\frac{37}{56}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{139}{168}\right)$	$e\left(\frac{103}{168}\right)$	$e\left(\frac{53}{168}\right)$
$\chi_{833}(26,\cdot)$	833.bk	168	yes	$-1$	$1$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{89}{168}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{61}{168}\right)$	$e\left(\frac{45}{56}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{107}{168}\right)$	$e\left(\frac{11}{168}\right)$	$e\left(\frac{13}{168}\right)$
$\chi_{833}(27,\cdot)$	833.bi	112	yes	$1$	$1$	$e\left(\frac{27}{56}\right)$	$e\left(\frac{29}{112}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{1}{112}\right)$	$e\left(\frac{83}{112}\right)$	$e\left(\frac{25}{56}\right)$	$e\left(\frac{29}{56}\right)$	$e\left(\frac{55}{112}\right)$	$e\left(\frac{19}{112}\right)$	$e\left(\frac{25}{112}\right)$
$\chi_{833}(29,\cdot)$	833.bj	112	yes	$-1$	$1$	$e\left(\frac{29}{56}\right)$	$e\left(\frac{27}{112}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{55}{112}\right)$	$e\left(\frac{85}{112}\right)$	$e\left(\frac{31}{56}\right)$	$e\left(\frac{27}{56}\right)$	$e\left(\frac{1}{112}\right)$	$e\left(\frac{93}{112}\right)$	$e\left(\frac{31}{112}\right)$
$\chi_{833}(30,\cdot)$	833.o	12	no	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$	$-i$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{833}(31,\cdot)$	833.bc	48	no	$1$	$1$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{7}{48}\right)$
$\chi_{833}(32,\cdot)$	833.bl	168	yes	$1$	$1$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{79}{168}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{107}{168}\right)$	$e\left(\frac{11}{56}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{61}{168}\right)$	$e\left(\frac{73}{168}\right)$	$e\left(\frac{155}{168}\right)$
$\chi_{833}(33,\cdot)$	833.bb	42	yes	$-1$	$1$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{5}{21}\right)$
$\chi_{833}(36,\cdot)$	833.bf	56	yes	$1$	$1$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{9}{56}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{37}{56}\right)$	$e\left(\frac{47}{56}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{19}{56}\right)$	$e\left(\frac{31}{56}\right)$	$e\left(\frac{29}{56}\right)$
$\chi_{833}(37,\cdot)$	833.bm	336	yes	$-1$	$1$	$e\left(\frac{115}{168}\right)$	$e\left(\frac{277}{336}\right)$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{137}{336}\right)$	$e\left(\frac{57}{112}\right)$	$e\left(\frac{3}{56}\right)$	$e\left(\frac{109}{168}\right)$	$e\left(\frac{31}{336}\right)$	$e\left(\frac{307}{336}\right)$	$e\left(\frac{65}{336}\right)$
$\chi_{833}(38,\cdot)$	833.bh	84	yes	$-1$	$1$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{61}{84}\right)$
$\chi_{833}(39,\cdot)$	833.bm	336	yes	$-1$	$1$	$e\left(\frac{71}{168}\right)$	$e\left(\frac{41}{336}\right)$	$e\left(\frac{71}{84}\right)$	$e\left(\frac{13}{336}\right)$	$e\left(\frac{61}{112}\right)$	$e\left(\frac{15}{56}\right)$	$e\left(\frac{41}{168}\right)$	$e\left(\frac{155}{336}\right)$	$e\left(\frac{191}{336}\right)$	$e\left(\frac{325}{336}\right)$

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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 $\F_{q}$
Belyi maps

Modulus	$833$
Structure	\(C_{2}\times C_{336}\)
Order	$672$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(8\)	\(9\)	\(10\)	\(11\)	\(12\)
\(\chi_{833}(1,\cdot)\)	833.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{833}(2,\cdot)\)	833.bl	168	yes	\(1\)	\(1\)	\(e\left(\frac{29}{84}\right)\)	\(e\left(\frac{83}{168}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{55}{168}\right)\)	\(e\left(\frac{47}{56}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{113}{168}\right)\)	\(e\left(\frac{149}{168}\right)\)	\(e\left(\frac{31}{168}\right)\)
\(\chi_{833}(3,\cdot)\)	833.bn	336	yes	\(1\)	\(1\)	\(e\left(\frac{83}{168}\right)\)	\(e\left(\frac{29}{336}\right)\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{1}{336}\right)\)	\(e\left(\frac{65}{112}\right)\)	\(e\left(\frac{27}{56}\right)\)	\(e\left(\frac{29}{168}\right)\)	\(e\left(\frac{167}{336}\right)\)	\(e\left(\frac{131}{336}\right)\)	\(e\left(\frac{25}{336}\right)\)
\(\chi_{833}(4,\cdot)\)	833.bg	84	yes	\(1\)	\(1\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{55}{84}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{29}{84}\right)\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{31}{84}\right)\)
\(\chi_{833}(5,\cdot)\)	833.bn	336	yes	\(1\)	\(1\)	\(e\left(\frac{55}{168}\right)\)	\(e\left(\frac{1}{336}\right)\)	\(e\left(\frac{55}{84}\right)\)	\(e\left(\frac{197}{336}\right)\)	\(e\left(\frac{37}{112}\right)\)	\(e\left(\frac{55}{56}\right)\)	\(e\left(\frac{1}{168}\right)\)	\(e\left(\frac{307}{336}\right)\)	\(e\left(\frac{271}{336}\right)\)	\(e\left(\frac{221}{336}\right)\)
\(\chi_{833}(6,\cdot)\)	833.bi	112	yes	\(1\)	\(1\)	\(e\left(\frac{47}{56}\right)\)	\(e\left(\frac{65}{112}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{37}{112}\right)\)	\(e\left(\frac{47}{112}\right)\)	\(e\left(\frac{29}{56}\right)\)	\(e\left(\frac{9}{56}\right)\)	\(e\left(\frac{19}{112}\right)\)	\(e\left(\frac{31}{112}\right)\)	\(e\left(\frac{29}{112}\right)\)
\(\chi_{833}(8,\cdot)\)	833.bf	56	yes	\(1\)	\(1\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{27}{56}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{55}{56}\right)\)	\(e\left(\frac{29}{56}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{1}{56}\right)\)	\(e\left(\frac{37}{56}\right)\)	\(e\left(\frac{31}{56}\right)\)
\(\chi_{833}(9,\cdot)\)	833.bl	168	yes	\(1\)	\(1\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{29}{168}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{1}{168}\right)\)	\(e\left(\frac{9}{56}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{29}{84}\right)\)	\(e\left(\frac{167}{168}\right)\)	\(e\left(\frac{131}{168}\right)\)	\(e\left(\frac{25}{168}\right)\)
\(\chi_{833}(10,\cdot)\)	833.bn	336	yes	\(1\)	\(1\)	\(e\left(\frac{113}{168}\right)\)	\(e\left(\frac{167}{336}\right)\)	\(e\left(\frac{29}{84}\right)\)	\(e\left(\frac{307}{336}\right)\)	\(e\left(\frac{19}{112}\right)\)	\(e\left(\frac{1}{56}\right)\)	\(e\left(\frac{167}{168}\right)\)	\(e\left(\frac{197}{336}\right)\)	\(e\left(\frac{233}{336}\right)\)	\(e\left(\frac{283}{336}\right)\)
\(\chi_{833}(11,\cdot)\)	833.bm	336	yes	\(-1\)	\(1\)	\(e\left(\frac{149}{168}\right)\)	\(e\left(\frac{131}{336}\right)\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{271}{336}\right)\)	\(e\left(\frac{31}{112}\right)\)	\(e\left(\frac{37}{56}\right)\)	\(e\left(\frac{131}{168}\right)\)	\(e\left(\frac{233}{336}\right)\)	\(e\left(\frac{53}{336}\right)\)	\(e\left(\frac{55}{336}\right)\)
\(\chi_{833}(12,\cdot)\)	833.bn	336	yes	\(1\)	\(1\)	\(e\left(\frac{31}{168}\right)\)	\(e\left(\frac{25}{336}\right)\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{221}{336}\right)\)	\(e\left(\frac{29}{112}\right)\)	\(e\left(\frac{31}{56}\right)\)	\(e\left(\frac{25}{168}\right)\)	\(e\left(\frac{283}{336}\right)\)	\(e\left(\frac{55}{336}\right)\)	\(e\left(\frac{149}{336}\right)\)
\(\chi_{833}(13,\cdot)\)	833.y	28	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{25}{28}\right)\)
\(\chi_{833}(15,\cdot)\)	833.bf	56	yes	\(1\)	\(1\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{5}{56}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{33}{56}\right)\)	\(e\left(\frac{51}{56}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{23}{56}\right)\)	\(e\left(\frac{11}{56}\right)\)	\(e\left(\frac{41}{56}\right)\)
\(\chi_{833}(16,\cdot)\)	833.z	42	yes	\(1\)	\(1\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{31}{42}\right)\)
\(\chi_{833}(18,\cdot)\)	833.e	3	no	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{833}(19,\cdot)\)	833.w	24	no	\(-1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(-i\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{13}{24}\right)\)
\(\chi_{833}(20,\cdot)\)	833.bi	112	yes	\(1\)	\(1\)	\(e\left(\frac{1}{56}\right)\)	\(e\left(\frac{111}{112}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{27}{112}\right)\)	\(e\left(\frac{1}{112}\right)\)	\(e\left(\frac{3}{56}\right)\)	\(e\left(\frac{55}{56}\right)\)	\(e\left(\frac{29}{112}\right)\)	\(e\left(\frac{65}{112}\right)\)	\(e\left(\frac{3}{112}\right)\)
\(\chi_{833}(22,\cdot)\)	833.bj	112	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{56}\right)\)	\(e\left(\frac{99}{112}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{15}{112}\right)\)	\(e\left(\frac{13}{112}\right)\)	\(e\left(\frac{39}{56}\right)\)	\(e\left(\frac{43}{56}\right)\)	\(e\left(\frac{41}{112}\right)\)	\(e\left(\frac{5}{112}\right)\)	\(e\left(\frac{39}{112}\right)\)
\(\chi_{833}(23,\cdot)\)	833.bm	336	yes	\(-1\)	\(1\)	\(e\left(\frac{109}{168}\right)\)	\(e\left(\frac{283}{336}\right)\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{311}{336}\right)\)	\(e\left(\frac{55}{112}\right)\)	\(e\left(\frac{53}{56}\right)\)	\(e\left(\frac{115}{168}\right)\)	\(e\left(\frac{193}{336}\right)\)	\(e\left(\frac{253}{336}\right)\)	\(e\left(\frac{47}{336}\right)\)
\(\chi_{833}(24,\cdot)\)	833.bn	336	yes	\(1\)	\(1\)	\(e\left(\frac{89}{168}\right)\)	\(e\left(\frac{191}{336}\right)\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{331}{336}\right)\)	\(e\left(\frac{11}{112}\right)\)	\(e\left(\frac{33}{56}\right)\)	\(e\left(\frac{23}{168}\right)\)	\(e\left(\frac{173}{336}\right)\)	\(e\left(\frac{17}{336}\right)\)	\(e\left(\frac{211}{336}\right)\)
\(\chi_{833}(25,\cdot)\)	833.bl	168	yes	\(1\)	\(1\)	\(e\left(\frac{55}{84}\right)\)	\(e\left(\frac{1}{168}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{29}{168}\right)\)	\(e\left(\frac{37}{56}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{139}{168}\right)\)	\(e\left(\frac{103}{168}\right)\)	\(e\left(\frac{53}{168}\right)\)
\(\chi_{833}(26,\cdot)\)	833.bk	168	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{89}{168}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{61}{168}\right)\)	\(e\left(\frac{45}{56}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{107}{168}\right)\)	\(e\left(\frac{11}{168}\right)\)	\(e\left(\frac{13}{168}\right)\)
\(\chi_{833}(27,\cdot)\)	833.bi	112	yes	\(1\)	\(1\)	\(e\left(\frac{27}{56}\right)\)	\(e\left(\frac{29}{112}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{1}{112}\right)\)	\(e\left(\frac{83}{112}\right)\)	\(e\left(\frac{25}{56}\right)\)	\(e\left(\frac{29}{56}\right)\)	\(e\left(\frac{55}{112}\right)\)	\(e\left(\frac{19}{112}\right)\)	\(e\left(\frac{25}{112}\right)\)
\(\chi_{833}(29,\cdot)\)	833.bj	112	yes	\(-1\)	\(1\)	\(e\left(\frac{29}{56}\right)\)	\(e\left(\frac{27}{112}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{55}{112}\right)\)	\(e\left(\frac{85}{112}\right)\)	\(e\left(\frac{31}{56}\right)\)	\(e\left(\frac{27}{56}\right)\)	\(e\left(\frac{1}{112}\right)\)	\(e\left(\frac{93}{112}\right)\)	\(e\left(\frac{31}{112}\right)\)
\(\chi_{833}(30,\cdot)\)	833.o	12	no	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(-i\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{833}(31,\cdot)\)	833.bc	48	no	\(1\)	\(1\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{7}{48}\right)\)
\(\chi_{833}(32,\cdot)\)	833.bl	168	yes	\(1\)	\(1\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{79}{168}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{107}{168}\right)\)	\(e\left(\frac{11}{56}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{61}{168}\right)\)	\(e\left(\frac{73}{168}\right)\)	\(e\left(\frac{155}{168}\right)\)
\(\chi_{833}(33,\cdot)\)	833.bb	42	yes	\(-1\)	\(1\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{5}{21}\right)\)
\(\chi_{833}(36,\cdot)\)	833.bf	56	yes	\(1\)	\(1\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{9}{56}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{37}{56}\right)\)	\(e\left(\frac{47}{56}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{19}{56}\right)\)	\(e\left(\frac{31}{56}\right)\)	\(e\left(\frac{29}{56}\right)\)
\(\chi_{833}(37,\cdot)\)	833.bm	336	yes	\(-1\)	\(1\)	\(e\left(\frac{115}{168}\right)\)	\(e\left(\frac{277}{336}\right)\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{137}{336}\right)\)	\(e\left(\frac{57}{112}\right)\)	\(e\left(\frac{3}{56}\right)\)	\(e\left(\frac{109}{168}\right)\)	\(e\left(\frac{31}{336}\right)\)	\(e\left(\frac{307}{336}\right)\)	\(e\left(\frac{65}{336}\right)\)
\(\chi_{833}(38,\cdot)\)	833.bh	84	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{17}{84}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{29}{84}\right)\)	\(e\left(\frac{61}{84}\right)\)
\(\chi_{833}(39,\cdot)\)	833.bm	336	yes	\(-1\)	\(1\)	\(e\left(\frac{71}{168}\right)\)	\(e\left(\frac{41}{336}\right)\)	\(e\left(\frac{71}{84}\right)\)	\(e\left(\frac{13}{336}\right)\)	\(e\left(\frac{61}{112}\right)\)	\(e\left(\frac{15}{56}\right)\)	\(e\left(\frac{41}{168}\right)\)	\(e\left(\frac{155}{336}\right)\)	\(e\left(\frac{191}{336}\right)\)	\(e\left(\frac{325}{336}\right)\)

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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.