LMFDB - Group of Dirichlet characters of modulus 2347

Show commands: PariGP / SageMath

sage: H = DirichletGroup(2347)

pari: g = idealstar(,2347,2)

Character group

sage: G.order() pari: g.no
Order	=	2346
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2346}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{2347}(3,\cdot)$

First 32 of 2346 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{2347}(1,\cdot)$	2347.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{2347}(2,\cdot)$	2347.n	782	yes	$-1$	$1$	$e\left(\frac{351}{782}\right)$	$e\left(\frac{741}{782}\right)$	$e\left(\frac{351}{391}\right)$	$e\left(\frac{695}{782}\right)$	$e\left(\frac{155}{391}\right)$	$e\left(\frac{57}{782}\right)$	$e\left(\frac{271}{782}\right)$	$e\left(\frac{350}{391}\right)$	$e\left(\frac{132}{391}\right)$	$e\left(\frac{367}{782}\right)$
$\chi_{2347}(3,\cdot)$	2347.p	2346	yes	$-1$	$1$	$e\left(\frac{741}{782}\right)$	$e\left(\frac{1}{2346}\right)$	$e\left(\frac{350}{391}\right)$	$e\left(\frac{1795}{2346}\right)$	$e\left(\frac{1112}{1173}\right)$	$e\left(\frac{381}{782}\right)$	$e\left(\frac{659}{782}\right)$	$e\left(\frac{1}{1173}\right)$	$e\left(\frac{836}{1173}\right)$	$e\left(\frac{239}{2346}\right)$
$\chi_{2347}(4,\cdot)$	2347.m	391	yes	$1$	$1$	$e\left(\frac{351}{391}\right)$	$e\left(\frac{350}{391}\right)$	$e\left(\frac{311}{391}\right)$	$e\left(\frac{304}{391}\right)$	$e\left(\frac{310}{391}\right)$	$e\left(\frac{57}{391}\right)$	$e\left(\frac{271}{391}\right)$	$e\left(\frac{309}{391}\right)$	$e\left(\frac{264}{391}\right)$	$e\left(\frac{367}{391}\right)$
$\chi_{2347}(5,\cdot)$	2347.p	2346	yes	$-1$	$1$	$e\left(\frac{695}{782}\right)$	$e\left(\frac{1795}{2346}\right)$	$e\left(\frac{304}{391}\right)$	$e\left(\frac{967}{2346}\right)$	$e\left(\frac{767}{1173}\right)$	$e\left(\frac{427}{782}\right)$	$e\left(\frac{521}{782}\right)$	$e\left(\frac{622}{1173}\right)$	$e\left(\frac{353}{1173}\right)$	$e\left(\frac{2033}{2346}\right)$
$\chi_{2347}(6,\cdot)$	2347.o	1173	yes	$1$	$1$	$e\left(\frac{155}{391}\right)$	$e\left(\frac{1112}{1173}\right)$	$e\left(\frac{310}{391}\right)$	$e\left(\frac{767}{1173}\right)$	$e\left(\frac{404}{1173}\right)$	$e\left(\frac{219}{391}\right)$	$e\left(\frac{74}{391}\right)$	$e\left(\frac{1051}{1173}\right)$	$e\left(\frac{59}{1173}\right)$	$e\left(\frac{670}{1173}\right)$
$\chi_{2347}(7,\cdot)$	2347.n	782	yes	$-1$	$1$	$e\left(\frac{57}{782}\right)$	$e\left(\frac{381}{782}\right)$	$e\left(\frac{57}{391}\right)$	$e\left(\frac{427}{782}\right)$	$e\left(\frac{219}{391}\right)$	$e\left(\frac{691}{782}\right)$	$e\left(\frac{171}{782}\right)$	$e\left(\frac{381}{391}\right)$	$e\left(\frac{242}{391}\right)$	$e\left(\frac{347}{782}\right)$
$\chi_{2347}(8,\cdot)$	2347.n	782	yes	$-1$	$1$	$e\left(\frac{271}{782}\right)$	$e\left(\frac{659}{782}\right)$	$e\left(\frac{271}{391}\right)$	$e\left(\frac{521}{782}\right)$	$e\left(\frac{74}{391}\right)$	$e\left(\frac{171}{782}\right)$	$e\left(\frac{31}{782}\right)$	$e\left(\frac{268}{391}\right)$	$e\left(\frac{5}{391}\right)$	$e\left(\frac{319}{782}\right)$
$\chi_{2347}(9,\cdot)$	2347.o	1173	yes	$1$	$1$	$e\left(\frac{350}{391}\right)$	$e\left(\frac{1}{1173}\right)$	$e\left(\frac{309}{391}\right)$	$e\left(\frac{622}{1173}\right)$	$e\left(\frac{1051}{1173}\right)$	$e\left(\frac{381}{391}\right)$	$e\left(\frac{268}{391}\right)$	$e\left(\frac{2}{1173}\right)$	$e\left(\frac{499}{1173}\right)$	$e\left(\frac{239}{1173}\right)$
$\chi_{2347}(10,\cdot)$	2347.o	1173	yes	$1$	$1$	$e\left(\frac{132}{391}\right)$	$e\left(\frac{836}{1173}\right)$	$e\left(\frac{264}{391}\right)$	$e\left(\frac{353}{1173}\right)$	$e\left(\frac{59}{1173}\right)$	$e\left(\frac{242}{391}\right)$	$e\left(\frac{5}{391}\right)$	$e\left(\frac{499}{1173}\right)$	$e\left(\frac{749}{1173}\right)$	$e\left(\frac{394}{1173}\right)$
$\chi_{2347}(11,\cdot)$	2347.p	2346	yes	$-1$	$1$	$e\left(\frac{367}{782}\right)$	$e\left(\frac{239}{2346}\right)$	$e\left(\frac{367}{391}\right)$	$e\left(\frac{2033}{2346}\right)$	$e\left(\frac{670}{1173}\right)$	$e\left(\frac{347}{782}\right)$	$e\left(\frac{319}{782}\right)$	$e\left(\frac{239}{1173}\right)$	$e\left(\frac{394}{1173}\right)$	$e\left(\frac{817}{2346}\right)$
$\chi_{2347}(12,\cdot)$	2347.p	2346	yes	$-1$	$1$	$e\left(\frac{661}{782}\right)$	$e\left(\frac{2101}{2346}\right)$	$e\left(\frac{270}{391}\right)$	$e\left(\frac{1273}{2346}\right)$	$e\left(\frac{869}{1173}\right)$	$e\left(\frac{495}{782}\right)$	$e\left(\frac{419}{782}\right)$	$e\left(\frac{928}{1173}\right)$	$e\left(\frac{455}{1173}\right)$	$e\left(\frac{95}{2346}\right)$
$\chi_{2347}(13,\cdot)$	2347.h	46	yes	$-1$	$1$	$e\left(\frac{41}{46}\right)$	$e\left(\frac{15}{46}\right)$	$e\left(\frac{18}{23}\right)$	$e\left(\frac{15}{46}\right)$	$e\left(\frac{5}{23}\right)$	$e\left(\frac{33}{46}\right)$	$e\left(\frac{31}{46}\right)$	$e\left(\frac{15}{23}\right)$	$e\left(\frac{5}{23}\right)$	$e\left(\frac{43}{46}\right)$
$\chi_{2347}(14,\cdot)$	2347.f	23	yes	$1$	$1$	$e\left(\frac{12}{23}\right)$	$e\left(\frac{10}{23}\right)$	$e\left(\frac{1}{23}\right)$	$e\left(\frac{10}{23}\right)$	$e\left(\frac{22}{23}\right)$	$e\left(\frac{22}{23}\right)$	$e\left(\frac{13}{23}\right)$	$e\left(\frac{20}{23}\right)$	$e\left(\frac{22}{23}\right)$	$e\left(\frac{21}{23}\right)$
$\chi_{2347}(15,\cdot)$	2347.o	1173	yes	$1$	$1$	$e\left(\frac{327}{391}\right)$	$e\left(\frac{898}{1173}\right)$	$e\left(\frac{263}{391}\right)$	$e\left(\frac{208}{1173}\right)$	$e\left(\frac{706}{1173}\right)$	$e\left(\frac{13}{391}\right)$	$e\left(\frac{199}{391}\right)$	$e\left(\frac{623}{1173}\right)$	$e\left(\frac{16}{1173}\right)$	$e\left(\frac{1136}{1173}\right)$
$\chi_{2347}(16,\cdot)$	2347.m	391	yes	$1$	$1$	$e\left(\frac{311}{391}\right)$	$e\left(\frac{309}{391}\right)$	$e\left(\frac{231}{391}\right)$	$e\left(\frac{217}{391}\right)$	$e\left(\frac{229}{391}\right)$	$e\left(\frac{114}{391}\right)$	$e\left(\frac{151}{391}\right)$	$e\left(\frac{227}{391}\right)$	$e\left(\frac{137}{391}\right)$	$e\left(\frac{343}{391}\right)$
$\chi_{2347}(17,\cdot)$	2347.o	1173	yes	$1$	$1$	$e\left(\frac{218}{391}\right)$	$e\left(\frac{1120}{1173}\right)$	$e\left(\frac{45}{391}\right)$	$e\left(\frac{1051}{1173}\right)$	$e\left(\frac{601}{1173}\right)$	$e\left(\frac{139}{391}\right)$	$e\left(\frac{263}{391}\right)$	$e\left(\frac{1067}{1173}\right)$	$e\left(\frac{532}{1173}\right)$	$e\left(\frac{236}{1173}\right)$
$\chi_{2347}(18,\cdot)$	2347.p	2346	yes	$-1$	$1$	$e\left(\frac{269}{782}\right)$	$e\left(\frac{2225}{2346}\right)$	$e\left(\frac{269}{391}\right)$	$e\left(\frac{983}{2346}\right)$	$e\left(\frac{343}{1173}\right)$	$e\left(\frac{37}{782}\right)$	$e\left(\frac{25}{782}\right)$	$e\left(\frac{1052}{1173}\right)$	$e\left(\frac{895}{1173}\right)$	$e\left(\frac{1579}{2346}\right)$
$\chi_{2347}(19,\cdot)$	2347.f	23	yes	$1$	$1$	$e\left(\frac{7}{23}\right)$	$e\left(\frac{2}{23}\right)$	$e\left(\frac{14}{23}\right)$	$e\left(\frac{2}{23}\right)$	$e\left(\frac{9}{23}\right)$	$e\left(\frac{9}{23}\right)$	$e\left(\frac{21}{23}\right)$	$e\left(\frac{4}{23}\right)$	$e\left(\frac{9}{23}\right)$	$e\left(\frac{18}{23}\right)$
$\chi_{2347}(20,\cdot)$	2347.p	2346	yes	$-1$	$1$	$e\left(\frac{615}{782}\right)$	$e\left(\frac{1549}{2346}\right)$	$e\left(\frac{224}{391}\right)$	$e\left(\frac{445}{2346}\right)$	$e\left(\frac{524}{1173}\right)$	$e\left(\frac{541}{782}\right)$	$e\left(\frac{281}{782}\right)$	$e\left(\frac{376}{1173}\right)$	$e\left(\frac{1145}{1173}\right)$	$e\left(\frac{1889}{2346}\right)$
$\chi_{2347}(21,\cdot)$	2347.o	1173	yes	$1$	$1$	$e\left(\frac{8}{391}\right)$	$e\left(\frac{572}{1173}\right)$	$e\left(\frac{16}{391}\right)$	$e\left(\frac{365}{1173}\right)$	$e\left(\frac{596}{1173}\right)$	$e\left(\frac{145}{391}\right)$	$e\left(\frac{24}{391}\right)$	$e\left(\frac{1144}{1173}\right)$	$e\left(\frac{389}{1173}\right)$	$e\left(\frac{640}{1173}\right)$
$\chi_{2347}(22,\cdot)$	2347.o	1173	yes	$1$	$1$	$e\left(\frac{359}{391}\right)$	$e\left(\frac{58}{1173}\right)$	$e\left(\frac{327}{391}\right)$	$e\left(\frac{886}{1173}\right)$	$e\left(\frac{1135}{1173}\right)$	$e\left(\frac{202}{391}\right)$	$e\left(\frac{295}{391}\right)$	$e\left(\frac{116}{1173}\right)$	$e\left(\frac{790}{1173}\right)$	$e\left(\frac{959}{1173}\right)$
$\chi_{2347}(23,\cdot)$	2347.n	782	yes	$-1$	$1$	$e\left(\frac{427}{782}\right)$	$e\left(\frac{467}{782}\right)$	$e\left(\frac{36}{391}\right)$	$e\left(\frac{743}{782}\right)$	$e\left(\frac{56}{391}\right)$	$e\left(\frac{457}{782}\right)$	$e\left(\frac{499}{782}\right)$	$e\left(\frac{76}{391}\right)$	$e\left(\frac{194}{391}\right)$	$e\left(\frac{569}{782}\right)$
$\chi_{2347}(24,\cdot)$	2347.i	51	yes	$1$	$1$	$e\left(\frac{5}{17}\right)$	$e\left(\frac{43}{51}\right)$	$e\left(\frac{10}{17}\right)$	$e\left(\frac{22}{51}\right)$	$e\left(\frac{7}{51}\right)$	$e\left(\frac{12}{17}\right)$	$e\left(\frac{15}{17}\right)$	$e\left(\frac{35}{51}\right)$	$e\left(\frac{37}{51}\right)$	$e\left(\frac{26}{51}\right)$
$\chi_{2347}(25,\cdot)$	2347.o	1173	yes	$1$	$1$	$e\left(\frac{304}{391}\right)$	$e\left(\frac{622}{1173}\right)$	$e\left(\frac{217}{391}\right)$	$e\left(\frac{967}{1173}\right)$	$e\left(\frac{361}{1173}\right)$	$e\left(\frac{36}{391}\right)$	$e\left(\frac{130}{391}\right)$	$e\left(\frac{71}{1173}\right)$	$e\left(\frac{706}{1173}\right)$	$e\left(\frac{860}{1173}\right)$
$\chi_{2347}(26,\cdot)$	2347.m	391	yes	$1$	$1$	$e\left(\frac{133}{391}\right)$	$e\left(\frac{107}{391}\right)$	$e\left(\frac{266}{391}\right)$	$e\left(\frac{84}{391}\right)$	$e\left(\frac{240}{391}\right)$	$e\left(\frac{309}{391}\right)$	$e\left(\frac{8}{391}\right)$	$e\left(\frac{214}{391}\right)$	$e\left(\frac{217}{391}\right)$	$e\left(\frac{158}{391}\right)$
$\chi_{2347}(27,\cdot)$	2347.n	782	yes	$-1$	$1$	$e\left(\frac{659}{782}\right)$	$e\left(\frac{1}{782}\right)$	$e\left(\frac{268}{391}\right)$	$e\left(\frac{231}{782}\right)$	$e\left(\frac{330}{391}\right)$	$e\left(\frac{361}{782}\right)$	$e\left(\frac{413}{782}\right)$	$e\left(\frac{1}{391}\right)$	$e\left(\frac{54}{391}\right)$	$e\left(\frac{239}{782}\right)$
$\chi_{2347}(28,\cdot)$	2347.g	34	yes	$-1$	$1$	$e\left(\frac{33}{34}\right)$	$e\left(\frac{13}{34}\right)$	$e\left(\frac{16}{17}\right)$	$e\left(\frac{11}{34}\right)$	$e\left(\frac{6}{17}\right)$	$e\left(\frac{1}{34}\right)$	$e\left(\frac{31}{34}\right)$	$e\left(\frac{13}{17}\right)$	$e\left(\frac{5}{17}\right)$	$e\left(\frac{13}{34}\right)$
$\chi_{2347}(29,\cdot)$	2347.p	2346	yes	$-1$	$1$	$e\left(\frac{515}{782}\right)$	$e\left(\frac{2219}{2346}\right)$	$e\left(\frac{124}{391}\right)$	$e\left(\frac{1943}{2346}\right)$	$e\left(\frac{709}{1173}\right)$	$e\left(\frac{97}{782}\right)$	$e\left(\frac{763}{782}\right)$	$e\left(\frac{1046}{1173}\right)$	$e\left(\frac{571}{1173}\right)$	$e\left(\frac{145}{2346}\right)$
$\chi_{2347}(30,\cdot)$	2347.p	2346	yes	$-1$	$1$	$e\left(\frac{223}{782}\right)$	$e\left(\frac{1673}{2346}\right)$	$e\left(\frac{223}{391}\right)$	$e\left(\frac{155}{2346}\right)$	$e\left(\frac{1171}{1173}\right)$	$e\left(\frac{83}{782}\right)$	$e\left(\frac{669}{782}\right)$	$e\left(\frac{500}{1173}\right)$	$e\left(\frac{412}{1173}\right)$	$e\left(\frac{1027}{2346}\right)$
$\chi_{2347}(31,\cdot)$	2347.o	1173	yes	$1$	$1$	$e\left(\frac{271}{391}\right)$	$e\left(\frac{22}{1173}\right)$	$e\left(\frac{151}{391}\right)$	$e\left(\frac{781}{1173}\right)$	$e\left(\frac{835}{1173}\right)$	$e\left(\frac{171}{391}\right)$	$e\left(\frac{31}{391}\right)$	$e\left(\frac{44}{1173}\right)$	$e\left(\frac{421}{1173}\right)$	$e\left(\frac{566}{1173}\right)$
$\chi_{2347}(32,\cdot)$	2347.n	782	yes	$-1$	$1$	$e\left(\frac{191}{782}\right)$	$e\left(\frac{577}{782}\right)$	$e\left(\frac{191}{391}\right)$	$e\left(\frac{347}{782}\right)$	$e\left(\frac{384}{391}\right)$	$e\left(\frac{285}{782}\right)$	$e\left(\frac{573}{782}\right)$	$e\left(\frac{186}{391}\right)$	$e\left(\frac{269}{391}\right)$	$e\left(\frac{271}{782}\right)$

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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	$2347$
Structure	\(C_{2346}\)
Order	$2346$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{2347}(1,\cdot)\)	2347.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{2347}(2,\cdot)\)	2347.n	782	yes	\(-1\)	\(1\)	\(e\left(\frac{351}{782}\right)\)	\(e\left(\frac{741}{782}\right)\)	\(e\left(\frac{351}{391}\right)\)	\(e\left(\frac{695}{782}\right)\)	\(e\left(\frac{155}{391}\right)\)	\(e\left(\frac{57}{782}\right)\)	\(e\left(\frac{271}{782}\right)\)	\(e\left(\frac{350}{391}\right)\)	\(e\left(\frac{132}{391}\right)\)	\(e\left(\frac{367}{782}\right)\)
\(\chi_{2347}(3,\cdot)\)	2347.p	2346	yes	\(-1\)	\(1\)	\(e\left(\frac{741}{782}\right)\)	\(e\left(\frac{1}{2346}\right)\)	\(e\left(\frac{350}{391}\right)\)	\(e\left(\frac{1795}{2346}\right)\)	\(e\left(\frac{1112}{1173}\right)\)	\(e\left(\frac{381}{782}\right)\)	\(e\left(\frac{659}{782}\right)\)	\(e\left(\frac{1}{1173}\right)\)	\(e\left(\frac{836}{1173}\right)\)	\(e\left(\frac{239}{2346}\right)\)
\(\chi_{2347}(4,\cdot)\)	2347.m	391	yes	\(1\)	\(1\)	\(e\left(\frac{351}{391}\right)\)	\(e\left(\frac{350}{391}\right)\)	\(e\left(\frac{311}{391}\right)\)	\(e\left(\frac{304}{391}\right)\)	\(e\left(\frac{310}{391}\right)\)	\(e\left(\frac{57}{391}\right)\)	\(e\left(\frac{271}{391}\right)\)	\(e\left(\frac{309}{391}\right)\)	\(e\left(\frac{264}{391}\right)\)	\(e\left(\frac{367}{391}\right)\)
\(\chi_{2347}(5,\cdot)\)	2347.p	2346	yes	\(-1\)	\(1\)	\(e\left(\frac{695}{782}\right)\)	\(e\left(\frac{1795}{2346}\right)\)	\(e\left(\frac{304}{391}\right)\)	\(e\left(\frac{967}{2346}\right)\)	\(e\left(\frac{767}{1173}\right)\)	\(e\left(\frac{427}{782}\right)\)	\(e\left(\frac{521}{782}\right)\)	\(e\left(\frac{622}{1173}\right)\)	\(e\left(\frac{353}{1173}\right)\)	\(e\left(\frac{2033}{2346}\right)\)
\(\chi_{2347}(6,\cdot)\)	2347.o	1173	yes	\(1\)	\(1\)	\(e\left(\frac{155}{391}\right)\)	\(e\left(\frac{1112}{1173}\right)\)	\(e\left(\frac{310}{391}\right)\)	\(e\left(\frac{767}{1173}\right)\)	\(e\left(\frac{404}{1173}\right)\)	\(e\left(\frac{219}{391}\right)\)	\(e\left(\frac{74}{391}\right)\)	\(e\left(\frac{1051}{1173}\right)\)	\(e\left(\frac{59}{1173}\right)\)	\(e\left(\frac{670}{1173}\right)\)
\(\chi_{2347}(7,\cdot)\)	2347.n	782	yes	\(-1\)	\(1\)	\(e\left(\frac{57}{782}\right)\)	\(e\left(\frac{381}{782}\right)\)	\(e\left(\frac{57}{391}\right)\)	\(e\left(\frac{427}{782}\right)\)	\(e\left(\frac{219}{391}\right)\)	\(e\left(\frac{691}{782}\right)\)	\(e\left(\frac{171}{782}\right)\)	\(e\left(\frac{381}{391}\right)\)	\(e\left(\frac{242}{391}\right)\)	\(e\left(\frac{347}{782}\right)\)
\(\chi_{2347}(8,\cdot)\)	2347.n	782	yes	\(-1\)	\(1\)	\(e\left(\frac{271}{782}\right)\)	\(e\left(\frac{659}{782}\right)\)	\(e\left(\frac{271}{391}\right)\)	\(e\left(\frac{521}{782}\right)\)	\(e\left(\frac{74}{391}\right)\)	\(e\left(\frac{171}{782}\right)\)	\(e\left(\frac{31}{782}\right)\)	\(e\left(\frac{268}{391}\right)\)	\(e\left(\frac{5}{391}\right)\)	\(e\left(\frac{319}{782}\right)\)
\(\chi_{2347}(9,\cdot)\)	2347.o	1173	yes	\(1\)	\(1\)	\(e\left(\frac{350}{391}\right)\)	\(e\left(\frac{1}{1173}\right)\)	\(e\left(\frac{309}{391}\right)\)	\(e\left(\frac{622}{1173}\right)\)	\(e\left(\frac{1051}{1173}\right)\)	\(e\left(\frac{381}{391}\right)\)	\(e\left(\frac{268}{391}\right)\)	\(e\left(\frac{2}{1173}\right)\)	\(e\left(\frac{499}{1173}\right)\)	\(e\left(\frac{239}{1173}\right)\)
\(\chi_{2347}(10,\cdot)\)	2347.o	1173	yes	\(1\)	\(1\)	\(e\left(\frac{132}{391}\right)\)	\(e\left(\frac{836}{1173}\right)\)	\(e\left(\frac{264}{391}\right)\)	\(e\left(\frac{353}{1173}\right)\)	\(e\left(\frac{59}{1173}\right)\)	\(e\left(\frac{242}{391}\right)\)	\(e\left(\frac{5}{391}\right)\)	\(e\left(\frac{499}{1173}\right)\)	\(e\left(\frac{749}{1173}\right)\)	\(e\left(\frac{394}{1173}\right)\)
\(\chi_{2347}(11,\cdot)\)	2347.p	2346	yes	\(-1\)	\(1\)	\(e\left(\frac{367}{782}\right)\)	\(e\left(\frac{239}{2346}\right)\)	\(e\left(\frac{367}{391}\right)\)	\(e\left(\frac{2033}{2346}\right)\)	\(e\left(\frac{670}{1173}\right)\)	\(e\left(\frac{347}{782}\right)\)	\(e\left(\frac{319}{782}\right)\)	\(e\left(\frac{239}{1173}\right)\)	\(e\left(\frac{394}{1173}\right)\)	\(e\left(\frac{817}{2346}\right)\)
\(\chi_{2347}(12,\cdot)\)	2347.p	2346	yes	\(-1\)	\(1\)	\(e\left(\frac{661}{782}\right)\)	\(e\left(\frac{2101}{2346}\right)\)	\(e\left(\frac{270}{391}\right)\)	\(e\left(\frac{1273}{2346}\right)\)	\(e\left(\frac{869}{1173}\right)\)	\(e\left(\frac{495}{782}\right)\)	\(e\left(\frac{419}{782}\right)\)	\(e\left(\frac{928}{1173}\right)\)	\(e\left(\frac{455}{1173}\right)\)	\(e\left(\frac{95}{2346}\right)\)
\(\chi_{2347}(13,\cdot)\)	2347.h	46	yes	\(-1\)	\(1\)	\(e\left(\frac{41}{46}\right)\)	\(e\left(\frac{15}{46}\right)\)	\(e\left(\frac{18}{23}\right)\)	\(e\left(\frac{15}{46}\right)\)	\(e\left(\frac{5}{23}\right)\)	\(e\left(\frac{33}{46}\right)\)	\(e\left(\frac{31}{46}\right)\)	\(e\left(\frac{15}{23}\right)\)	\(e\left(\frac{5}{23}\right)\)	\(e\left(\frac{43}{46}\right)\)
\(\chi_{2347}(14,\cdot)\)	2347.f	23	yes	\(1\)	\(1\)	\(e\left(\frac{12}{23}\right)\)	\(e\left(\frac{10}{23}\right)\)	\(e\left(\frac{1}{23}\right)\)	\(e\left(\frac{10}{23}\right)\)	\(e\left(\frac{22}{23}\right)\)	\(e\left(\frac{22}{23}\right)\)	\(e\left(\frac{13}{23}\right)\)	\(e\left(\frac{20}{23}\right)\)	\(e\left(\frac{22}{23}\right)\)	\(e\left(\frac{21}{23}\right)\)
\(\chi_{2347}(15,\cdot)\)	2347.o	1173	yes	\(1\)	\(1\)	\(e\left(\frac{327}{391}\right)\)	\(e\left(\frac{898}{1173}\right)\)	\(e\left(\frac{263}{391}\right)\)	\(e\left(\frac{208}{1173}\right)\)	\(e\left(\frac{706}{1173}\right)\)	\(e\left(\frac{13}{391}\right)\)	\(e\left(\frac{199}{391}\right)\)	\(e\left(\frac{623}{1173}\right)\)	\(e\left(\frac{16}{1173}\right)\)	\(e\left(\frac{1136}{1173}\right)\)
\(\chi_{2347}(16,\cdot)\)	2347.m	391	yes	\(1\)	\(1\)	\(e\left(\frac{311}{391}\right)\)	\(e\left(\frac{309}{391}\right)\)	\(e\left(\frac{231}{391}\right)\)	\(e\left(\frac{217}{391}\right)\)	\(e\left(\frac{229}{391}\right)\)	\(e\left(\frac{114}{391}\right)\)	\(e\left(\frac{151}{391}\right)\)	\(e\left(\frac{227}{391}\right)\)	\(e\left(\frac{137}{391}\right)\)	\(e\left(\frac{343}{391}\right)\)
\(\chi_{2347}(17,\cdot)\)	2347.o	1173	yes	\(1\)	\(1\)	\(e\left(\frac{218}{391}\right)\)	\(e\left(\frac{1120}{1173}\right)\)	\(e\left(\frac{45}{391}\right)\)	\(e\left(\frac{1051}{1173}\right)\)	\(e\left(\frac{601}{1173}\right)\)	\(e\left(\frac{139}{391}\right)\)	\(e\left(\frac{263}{391}\right)\)	\(e\left(\frac{1067}{1173}\right)\)	\(e\left(\frac{532}{1173}\right)\)	\(e\left(\frac{236}{1173}\right)\)
\(\chi_{2347}(18,\cdot)\)	2347.p	2346	yes	\(-1\)	\(1\)	\(e\left(\frac{269}{782}\right)\)	\(e\left(\frac{2225}{2346}\right)\)	\(e\left(\frac{269}{391}\right)\)	\(e\left(\frac{983}{2346}\right)\)	\(e\left(\frac{343}{1173}\right)\)	\(e\left(\frac{37}{782}\right)\)	\(e\left(\frac{25}{782}\right)\)	\(e\left(\frac{1052}{1173}\right)\)	\(e\left(\frac{895}{1173}\right)\)	\(e\left(\frac{1579}{2346}\right)\)
\(\chi_{2347}(19,\cdot)\)	2347.f	23	yes	\(1\)	\(1\)	\(e\left(\frac{7}{23}\right)\)	\(e\left(\frac{2}{23}\right)\)	\(e\left(\frac{14}{23}\right)\)	\(e\left(\frac{2}{23}\right)\)	\(e\left(\frac{9}{23}\right)\)	\(e\left(\frac{9}{23}\right)\)	\(e\left(\frac{21}{23}\right)\)	\(e\left(\frac{4}{23}\right)\)	\(e\left(\frac{9}{23}\right)\)	\(e\left(\frac{18}{23}\right)\)
\(\chi_{2347}(20,\cdot)\)	2347.p	2346	yes	\(-1\)	\(1\)	\(e\left(\frac{615}{782}\right)\)	\(e\left(\frac{1549}{2346}\right)\)	\(e\left(\frac{224}{391}\right)\)	\(e\left(\frac{445}{2346}\right)\)	\(e\left(\frac{524}{1173}\right)\)	\(e\left(\frac{541}{782}\right)\)	\(e\left(\frac{281}{782}\right)\)	\(e\left(\frac{376}{1173}\right)\)	\(e\left(\frac{1145}{1173}\right)\)	\(e\left(\frac{1889}{2346}\right)\)
\(\chi_{2347}(21,\cdot)\)	2347.o	1173	yes	\(1\)	\(1\)	\(e\left(\frac{8}{391}\right)\)	\(e\left(\frac{572}{1173}\right)\)	\(e\left(\frac{16}{391}\right)\)	\(e\left(\frac{365}{1173}\right)\)	\(e\left(\frac{596}{1173}\right)\)	\(e\left(\frac{145}{391}\right)\)	\(e\left(\frac{24}{391}\right)\)	\(e\left(\frac{1144}{1173}\right)\)	\(e\left(\frac{389}{1173}\right)\)	\(e\left(\frac{640}{1173}\right)\)
\(\chi_{2347}(22,\cdot)\)	2347.o	1173	yes	\(1\)	\(1\)	\(e\left(\frac{359}{391}\right)\)	\(e\left(\frac{58}{1173}\right)\)	\(e\left(\frac{327}{391}\right)\)	\(e\left(\frac{886}{1173}\right)\)	\(e\left(\frac{1135}{1173}\right)\)	\(e\left(\frac{202}{391}\right)\)	\(e\left(\frac{295}{391}\right)\)	\(e\left(\frac{116}{1173}\right)\)	\(e\left(\frac{790}{1173}\right)\)	\(e\left(\frac{959}{1173}\right)\)
\(\chi_{2347}(23,\cdot)\)	2347.n	782	yes	\(-1\)	\(1\)	\(e\left(\frac{427}{782}\right)\)	\(e\left(\frac{467}{782}\right)\)	\(e\left(\frac{36}{391}\right)\)	\(e\left(\frac{743}{782}\right)\)	\(e\left(\frac{56}{391}\right)\)	\(e\left(\frac{457}{782}\right)\)	\(e\left(\frac{499}{782}\right)\)	\(e\left(\frac{76}{391}\right)\)	\(e\left(\frac{194}{391}\right)\)	\(e\left(\frac{569}{782}\right)\)
\(\chi_{2347}(24,\cdot)\)	2347.i	51	yes	\(1\)	\(1\)	\(e\left(\frac{5}{17}\right)\)	\(e\left(\frac{43}{51}\right)\)	\(e\left(\frac{10}{17}\right)\)	\(e\left(\frac{22}{51}\right)\)	\(e\left(\frac{7}{51}\right)\)	\(e\left(\frac{12}{17}\right)\)	\(e\left(\frac{15}{17}\right)\)	\(e\left(\frac{35}{51}\right)\)	\(e\left(\frac{37}{51}\right)\)	\(e\left(\frac{26}{51}\right)\)
\(\chi_{2347}(25,\cdot)\)	2347.o	1173	yes	\(1\)	\(1\)	\(e\left(\frac{304}{391}\right)\)	\(e\left(\frac{622}{1173}\right)\)	\(e\left(\frac{217}{391}\right)\)	\(e\left(\frac{967}{1173}\right)\)	\(e\left(\frac{361}{1173}\right)\)	\(e\left(\frac{36}{391}\right)\)	\(e\left(\frac{130}{391}\right)\)	\(e\left(\frac{71}{1173}\right)\)	\(e\left(\frac{706}{1173}\right)\)	\(e\left(\frac{860}{1173}\right)\)
\(\chi_{2347}(26,\cdot)\)	2347.m	391	yes	\(1\)	\(1\)	\(e\left(\frac{133}{391}\right)\)	\(e\left(\frac{107}{391}\right)\)	\(e\left(\frac{266}{391}\right)\)	\(e\left(\frac{84}{391}\right)\)	\(e\left(\frac{240}{391}\right)\)	\(e\left(\frac{309}{391}\right)\)	\(e\left(\frac{8}{391}\right)\)	\(e\left(\frac{214}{391}\right)\)	\(e\left(\frac{217}{391}\right)\)	\(e\left(\frac{158}{391}\right)\)
\(\chi_{2347}(27,\cdot)\)	2347.n	782	yes	\(-1\)	\(1\)	\(e\left(\frac{659}{782}\right)\)	\(e\left(\frac{1}{782}\right)\)	\(e\left(\frac{268}{391}\right)\)	\(e\left(\frac{231}{782}\right)\)	\(e\left(\frac{330}{391}\right)\)	\(e\left(\frac{361}{782}\right)\)	\(e\left(\frac{413}{782}\right)\)	\(e\left(\frac{1}{391}\right)\)	\(e\left(\frac{54}{391}\right)\)	\(e\left(\frac{239}{782}\right)\)
\(\chi_{2347}(28,\cdot)\)	2347.g	34	yes	\(-1\)	\(1\)	\(e\left(\frac{33}{34}\right)\)	\(e\left(\frac{13}{34}\right)\)	\(e\left(\frac{16}{17}\right)\)	\(e\left(\frac{11}{34}\right)\)	\(e\left(\frac{6}{17}\right)\)	\(e\left(\frac{1}{34}\right)\)	\(e\left(\frac{31}{34}\right)\)	\(e\left(\frac{13}{17}\right)\)	\(e\left(\frac{5}{17}\right)\)	\(e\left(\frac{13}{34}\right)\)
\(\chi_{2347}(29,\cdot)\)	2347.p	2346	yes	\(-1\)	\(1\)	\(e\left(\frac{515}{782}\right)\)	\(e\left(\frac{2219}{2346}\right)\)	\(e\left(\frac{124}{391}\right)\)	\(e\left(\frac{1943}{2346}\right)\)	\(e\left(\frac{709}{1173}\right)\)	\(e\left(\frac{97}{782}\right)\)	\(e\left(\frac{763}{782}\right)\)	\(e\left(\frac{1046}{1173}\right)\)	\(e\left(\frac{571}{1173}\right)\)	\(e\left(\frac{145}{2346}\right)\)
\(\chi_{2347}(30,\cdot)\)	2347.p	2346	yes	\(-1\)	\(1\)	\(e\left(\frac{223}{782}\right)\)	\(e\left(\frac{1673}{2346}\right)\)	\(e\left(\frac{223}{391}\right)\)	\(e\left(\frac{155}{2346}\right)\)	\(e\left(\frac{1171}{1173}\right)\)	\(e\left(\frac{83}{782}\right)\)	\(e\left(\frac{669}{782}\right)\)	\(e\left(\frac{500}{1173}\right)\)	\(e\left(\frac{412}{1173}\right)\)	\(e\left(\frac{1027}{2346}\right)\)
\(\chi_{2347}(31,\cdot)\)	2347.o	1173	yes	\(1\)	\(1\)	\(e\left(\frac{271}{391}\right)\)	\(e\left(\frac{22}{1173}\right)\)	\(e\left(\frac{151}{391}\right)\)	\(e\left(\frac{781}{1173}\right)\)	\(e\left(\frac{835}{1173}\right)\)	\(e\left(\frac{171}{391}\right)\)	\(e\left(\frac{31}{391}\right)\)	\(e\left(\frac{44}{1173}\right)\)	\(e\left(\frac{421}{1173}\right)\)	\(e\left(\frac{566}{1173}\right)\)
\(\chi_{2347}(32,\cdot)\)	2347.n	782	yes	\(-1\)	\(1\)	\(e\left(\frac{191}{782}\right)\)	\(e\left(\frac{577}{782}\right)\)	\(e\left(\frac{191}{391}\right)\)	\(e\left(\frac{347}{782}\right)\)	\(e\left(\frac{384}{391}\right)\)	\(e\left(\frac{285}{782}\right)\)	\(e\left(\frac{573}{782}\right)\)	\(e\left(\frac{186}{391}\right)\)	\(e\left(\frac{269}{391}\right)\)	\(e\left(\frac{271}{782}\right)\)

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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.