LMFDB - Group of Dirichlet characters of modulus 349

Show commands: PariGP / SageMath

sage: H = DirichletGroup(349)

pari: g = idealstar(,349,2)

Character group

sage: G.order() pari: g.no
Order	=	348
sage: H.invariants() pari: g.cyc
Structure	=	$C_{348}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{349}(2,\cdot)$

First 32 of 348 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{349}(1,\cdot)$	349.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{349}(2,\cdot)$	349.l	348	yes	$-1$	$1$	$e\left(\frac{1}{348}\right)$	$e\left(\frac{13}{174}\right)$	$e\left(\frac{1}{174}\right)$	$e\left(\frac{157}{174}\right)$	$e\left(\frac{9}{116}\right)$	$e\left(\frac{67}{348}\right)$	$e\left(\frac{1}{116}\right)$	$e\left(\frac{13}{87}\right)$	$e\left(\frac{105}{116}\right)$	$e\left(\frac{7}{116}\right)$
$\chi_{349}(3,\cdot)$	349.k	174	yes	$1$	$1$	$e\left(\frac{13}{174}\right)$	$e\left(\frac{82}{87}\right)$	$e\left(\frac{13}{87}\right)$	$e\left(\frac{40}{87}\right)$	$e\left(\frac{1}{58}\right)$	$e\left(\frac{1}{174}\right)$	$e\left(\frac{13}{58}\right)$	$e\left(\frac{77}{87}\right)$	$e\left(\frac{31}{58}\right)$	$e\left(\frac{33}{58}\right)$
$\chi_{349}(4,\cdot)$	349.k	174	yes	$1$	$1$	$e\left(\frac{1}{174}\right)$	$e\left(\frac{13}{87}\right)$	$e\left(\frac{1}{87}\right)$	$e\left(\frac{70}{87}\right)$	$e\left(\frac{9}{58}\right)$	$e\left(\frac{67}{174}\right)$	$e\left(\frac{1}{58}\right)$	$e\left(\frac{26}{87}\right)$	$e\left(\frac{47}{58}\right)$	$e\left(\frac{7}{58}\right)$
$\chi_{349}(5,\cdot)$	349.k	174	yes	$1$	$1$	$e\left(\frac{157}{174}\right)$	$e\left(\frac{40}{87}\right)$	$e\left(\frac{70}{87}\right)$	$e\left(\frac{28}{87}\right)$	$e\left(\frac{21}{58}\right)$	$e\left(\frac{79}{174}\right)$	$e\left(\frac{41}{58}\right)$	$e\left(\frac{80}{87}\right)$	$e\left(\frac{13}{58}\right)$	$e\left(\frac{55}{58}\right)$
$\chi_{349}(6,\cdot)$	349.j	116	yes	$-1$	$1$	$e\left(\frac{9}{116}\right)$	$e\left(\frac{1}{58}\right)$	$e\left(\frac{9}{58}\right)$	$e\left(\frac{21}{58}\right)$	$e\left(\frac{11}{116}\right)$	$e\left(\frac{23}{116}\right)$	$e\left(\frac{27}{116}\right)$	$e\left(\frac{1}{29}\right)$	$e\left(\frac{51}{116}\right)$	$e\left(\frac{73}{116}\right)$
$\chi_{349}(7,\cdot)$	349.l	348	yes	$-1$	$1$	$e\left(\frac{67}{348}\right)$	$e\left(\frac{1}{174}\right)$	$e\left(\frac{67}{174}\right)$	$e\left(\frac{79}{174}\right)$	$e\left(\frac{23}{116}\right)$	$e\left(\frac{313}{348}\right)$	$e\left(\frac{67}{116}\right)$	$e\left(\frac{1}{87}\right)$	$e\left(\frac{75}{116}\right)$	$e\left(\frac{5}{116}\right)$
$\chi_{349}(8,\cdot)$	349.j	116	yes	$-1$	$1$	$e\left(\frac{1}{116}\right)$	$e\left(\frac{13}{58}\right)$	$e\left(\frac{1}{58}\right)$	$e\left(\frac{41}{58}\right)$	$e\left(\frac{27}{116}\right)$	$e\left(\frac{67}{116}\right)$	$e\left(\frac{3}{116}\right)$	$e\left(\frac{13}{29}\right)$	$e\left(\frac{83}{116}\right)$	$e\left(\frac{21}{116}\right)$
$\chi_{349}(9,\cdot)$	349.i	87	yes	$1$	$1$	$e\left(\frac{13}{87}\right)$	$e\left(\frac{77}{87}\right)$	$e\left(\frac{26}{87}\right)$	$e\left(\frac{80}{87}\right)$	$e\left(\frac{1}{29}\right)$	$e\left(\frac{1}{87}\right)$	$e\left(\frac{13}{29}\right)$	$e\left(\frac{67}{87}\right)$	$e\left(\frac{2}{29}\right)$	$e\left(\frac{4}{29}\right)$
$\chi_{349}(10,\cdot)$	349.j	116	yes	$-1$	$1$	$e\left(\frac{105}{116}\right)$	$e\left(\frac{31}{58}\right)$	$e\left(\frac{47}{58}\right)$	$e\left(\frac{13}{58}\right)$	$e\left(\frac{51}{116}\right)$	$e\left(\frac{75}{116}\right)$	$e\left(\frac{83}{116}\right)$	$e\left(\frac{2}{29}\right)$	$e\left(\frac{15}{116}\right)$	$e\left(\frac{1}{116}\right)$
$\chi_{349}(11,\cdot)$	349.j	116	yes	$-1$	$1$	$e\left(\frac{7}{116}\right)$	$e\left(\frac{33}{58}\right)$	$e\left(\frac{7}{58}\right)$	$e\left(\frac{55}{58}\right)$	$e\left(\frac{73}{116}\right)$	$e\left(\frac{5}{116}\right)$	$e\left(\frac{21}{116}\right)$	$e\left(\frac{4}{29}\right)$	$e\left(\frac{1}{116}\right)$	$e\left(\frac{31}{116}\right)$
$\chi_{349}(12,\cdot)$	349.i	87	yes	$1$	$1$	$e\left(\frac{7}{87}\right)$	$e\left(\frac{8}{87}\right)$	$e\left(\frac{14}{87}\right)$	$e\left(\frac{23}{87}\right)$	$e\left(\frac{5}{29}\right)$	$e\left(\frac{34}{87}\right)$	$e\left(\frac{7}{29}\right)$	$e\left(\frac{16}{87}\right)$	$e\left(\frac{10}{29}\right)$	$e\left(\frac{20}{29}\right)$
$\chi_{349}(13,\cdot)$	349.l	348	yes	$-1$	$1$	$e\left(\frac{271}{348}\right)$	$e\left(\frac{43}{174}\right)$	$e\left(\frac{97}{174}\right)$	$e\left(\frac{91}{174}\right)$	$e\left(\frac{3}{116}\right)$	$e\left(\frac{61}{348}\right)$	$e\left(\frac{39}{116}\right)$	$e\left(\frac{43}{87}\right)$	$e\left(\frac{35}{116}\right)$	$e\left(\frac{41}{116}\right)$
$\chi_{349}(14,\cdot)$	349.i	87	yes	$1$	$1$	$e\left(\frac{17}{87}\right)$	$e\left(\frac{7}{87}\right)$	$e\left(\frac{34}{87}\right)$	$e\left(\frac{31}{87}\right)$	$e\left(\frac{8}{29}\right)$	$e\left(\frac{8}{87}\right)$	$e\left(\frac{17}{29}\right)$	$e\left(\frac{14}{87}\right)$	$e\left(\frac{16}{29}\right)$	$e\left(\frac{3}{29}\right)$
$\chi_{349}(15,\cdot)$	349.i	87	yes	$1$	$1$	$e\left(\frac{85}{87}\right)$	$e\left(\frac{35}{87}\right)$	$e\left(\frac{83}{87}\right)$	$e\left(\frac{68}{87}\right)$	$e\left(\frac{11}{29}\right)$	$e\left(\frac{40}{87}\right)$	$e\left(\frac{27}{29}\right)$	$e\left(\frac{70}{87}\right)$	$e\left(\frac{22}{29}\right)$	$e\left(\frac{15}{29}\right)$
$\chi_{349}(16,\cdot)$	349.i	87	yes	$1$	$1$	$e\left(\frac{1}{87}\right)$	$e\left(\frac{26}{87}\right)$	$e\left(\frac{2}{87}\right)$	$e\left(\frac{53}{87}\right)$	$e\left(\frac{9}{29}\right)$	$e\left(\frac{67}{87}\right)$	$e\left(\frac{1}{29}\right)$	$e\left(\frac{52}{87}\right)$	$e\left(\frac{18}{29}\right)$	$e\left(\frac{7}{29}\right)$
$\chi_{349}(17,\cdot)$	349.h	58	yes	$1$	$1$	$e\left(\frac{43}{58}\right)$	$e\left(\frac{8}{29}\right)$	$e\left(\frac{14}{29}\right)$	$e\left(\frac{23}{29}\right)$	$e\left(\frac{1}{58}\right)$	$e\left(\frac{39}{58}\right)$	$e\left(\frac{13}{58}\right)$	$e\left(\frac{16}{29}\right)$	$e\left(\frac{31}{58}\right)$	$e\left(\frac{33}{58}\right)$
$\chi_{349}(18,\cdot)$	349.l	348	yes	$-1$	$1$	$e\left(\frac{53}{348}\right)$	$e\left(\frac{167}{174}\right)$	$e\left(\frac{53}{174}\right)$	$e\left(\frac{143}{174}\right)$	$e\left(\frac{13}{116}\right)$	$e\left(\frac{71}{348}\right)$	$e\left(\frac{53}{116}\right)$	$e\left(\frac{80}{87}\right)$	$e\left(\frac{113}{116}\right)$	$e\left(\frac{23}{116}\right)$
$\chi_{349}(19,\cdot)$	349.i	87	yes	$1$	$1$	$e\left(\frac{47}{87}\right)$	$e\left(\frac{4}{87}\right)$	$e\left(\frac{7}{87}\right)$	$e\left(\frac{55}{87}\right)$	$e\left(\frac{17}{29}\right)$	$e\left(\frac{17}{87}\right)$	$e\left(\frac{18}{29}\right)$	$e\left(\frac{8}{87}\right)$	$e\left(\frac{5}{29}\right)$	$e\left(\frac{10}{29}\right)$
$\chi_{349}(20,\cdot)$	349.i	87	yes	$1$	$1$	$e\left(\frac{79}{87}\right)$	$e\left(\frac{53}{87}\right)$	$e\left(\frac{71}{87}\right)$	$e\left(\frac{11}{87}\right)$	$e\left(\frac{15}{29}\right)$	$e\left(\frac{73}{87}\right)$	$e\left(\frac{21}{29}\right)$	$e\left(\frac{19}{87}\right)$	$e\left(\frac{1}{29}\right)$	$e\left(\frac{2}{29}\right)$
$\chi_{349}(21,\cdot)$	349.j	116	yes	$-1$	$1$	$e\left(\frac{31}{116}\right)$	$e\left(\frac{55}{58}\right)$	$e\left(\frac{31}{58}\right)$	$e\left(\frac{53}{58}\right)$	$e\left(\frac{25}{116}\right)$	$e\left(\frac{105}{116}\right)$	$e\left(\frac{93}{116}\right)$	$e\left(\frac{26}{29}\right)$	$e\left(\frac{21}{116}\right)$	$e\left(\frac{71}{116}\right)$
$\chi_{349}(22,\cdot)$	349.k	174	yes	$1$	$1$	$e\left(\frac{11}{174}\right)$	$e\left(\frac{56}{87}\right)$	$e\left(\frac{11}{87}\right)$	$e\left(\frac{74}{87}\right)$	$e\left(\frac{41}{58}\right)$	$e\left(\frac{41}{174}\right)$	$e\left(\frac{11}{58}\right)$	$e\left(\frac{25}{87}\right)$	$e\left(\frac{53}{58}\right)$	$e\left(\frac{19}{58}\right)$
$\chi_{349}(23,\cdot)$	349.i	87	yes	$1$	$1$	$e\left(\frac{46}{87}\right)$	$e\left(\frac{65}{87}\right)$	$e\left(\frac{5}{87}\right)$	$e\left(\frac{2}{87}\right)$	$e\left(\frac{8}{29}\right)$	$e\left(\frac{37}{87}\right)$	$e\left(\frac{17}{29}\right)$	$e\left(\frac{43}{87}\right)$	$e\left(\frac{16}{29}\right)$	$e\left(\frac{3}{29}\right)$
$\chi_{349}(24,\cdot)$	349.f	12	yes	$-1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$i$	$e\left(\frac{7}{12}\right)$	$i$	$e\left(\frac{1}{3}\right)$	$i$	$-i$
$\chi_{349}(25,\cdot)$	349.i	87	yes	$1$	$1$	$e\left(\frac{70}{87}\right)$	$e\left(\frac{80}{87}\right)$	$e\left(\frac{53}{87}\right)$	$e\left(\frac{56}{87}\right)$	$e\left(\frac{21}{29}\right)$	$e\left(\frac{79}{87}\right)$	$e\left(\frac{12}{29}\right)$	$e\left(\frac{73}{87}\right)$	$e\left(\frac{13}{29}\right)$	$e\left(\frac{26}{29}\right)$
$\chi_{349}(26,\cdot)$	349.i	87	yes	$1$	$1$	$e\left(\frac{68}{87}\right)$	$e\left(\frac{28}{87}\right)$	$e\left(\frac{49}{87}\right)$	$e\left(\frac{37}{87}\right)$	$e\left(\frac{3}{29}\right)$	$e\left(\frac{32}{87}\right)$	$e\left(\frac{10}{29}\right)$	$e\left(\frac{56}{87}\right)$	$e\left(\frac{6}{29}\right)$	$e\left(\frac{12}{29}\right)$
$\chi_{349}(27,\cdot)$	349.h	58	yes	$1$	$1$	$e\left(\frac{13}{58}\right)$	$e\left(\frac{24}{29}\right)$	$e\left(\frac{13}{29}\right)$	$e\left(\frac{11}{29}\right)$	$e\left(\frac{3}{58}\right)$	$e\left(\frac{1}{58}\right)$	$e\left(\frac{39}{58}\right)$	$e\left(\frac{19}{29}\right)$	$e\left(\frac{35}{58}\right)$	$e\left(\frac{41}{58}\right)$
$\chi_{349}(28,\cdot)$	349.j	116	yes	$-1$	$1$	$e\left(\frac{23}{116}\right)$	$e\left(\frac{9}{58}\right)$	$e\left(\frac{23}{58}\right)$	$e\left(\frac{15}{58}\right)$	$e\left(\frac{41}{116}\right)$	$e\left(\frac{33}{116}\right)$	$e\left(\frac{69}{116}\right)$	$e\left(\frac{9}{29}\right)$	$e\left(\frac{53}{116}\right)$	$e\left(\frac{19}{116}\right)$
$\chi_{349}(29,\cdot)$	349.k	174	yes	$1$	$1$	$e\left(\frac{73}{174}\right)$	$e\left(\frac{79}{87}\right)$	$e\left(\frac{73}{87}\right)$	$e\left(\frac{64}{87}\right)$	$e\left(\frac{19}{58}\right)$	$e\left(\frac{19}{174}\right)$	$e\left(\frac{15}{58}\right)$	$e\left(\frac{71}{87}\right)$	$e\left(\frac{9}{58}\right)$	$e\left(\frac{47}{58}\right)$
$\chi_{349}(30,\cdot)$	349.l	348	yes	$-1$	$1$	$e\left(\frac{341}{348}\right)$	$e\left(\frac{83}{174}\right)$	$e\left(\frac{167}{174}\right)$	$e\left(\frac{119}{174}\right)$	$e\left(\frac{53}{116}\right)$	$e\left(\frac{227}{348}\right)$	$e\left(\frac{109}{116}\right)$	$e\left(\frac{83}{87}\right)$	$e\left(\frac{77}{116}\right)$	$e\left(\frac{67}{116}\right)$
$\chi_{349}(31,\cdot)$	349.g	29	yes	$1$	$1$	$e\left(\frac{13}{29}\right)$	$e\left(\frac{19}{29}\right)$	$e\left(\frac{26}{29}\right)$	$e\left(\frac{22}{29}\right)$	$e\left(\frac{3}{29}\right)$	$e\left(\frac{1}{29}\right)$	$e\left(\frac{10}{29}\right)$	$e\left(\frac{9}{29}\right)$	$e\left(\frac{6}{29}\right)$	$e\left(\frac{12}{29}\right)$
$\chi_{349}(32,\cdot)$	349.l	348	yes	$-1$	$1$	$e\left(\frac{5}{348}\right)$	$e\left(\frac{65}{174}\right)$	$e\left(\frac{5}{174}\right)$	$e\left(\frac{89}{174}\right)$	$e\left(\frac{45}{116}\right)$	$e\left(\frac{335}{348}\right)$	$e\left(\frac{5}{116}\right)$	$e\left(\frac{65}{87}\right)$	$e\left(\frac{61}{116}\right)$	$e\left(\frac{35}{116}\right)$

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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	$349$
Structure	\(C_{348}\)
Order	$348$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{349}(1,\cdot)\)	349.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{349}(2,\cdot)\)	349.l	348	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{348}\right)\)	\(e\left(\frac{13}{174}\right)\)	\(e\left(\frac{1}{174}\right)\)	\(e\left(\frac{157}{174}\right)\)	\(e\left(\frac{9}{116}\right)\)	\(e\left(\frac{67}{348}\right)\)	\(e\left(\frac{1}{116}\right)\)	\(e\left(\frac{13}{87}\right)\)	\(e\left(\frac{105}{116}\right)\)	\(e\left(\frac{7}{116}\right)\)
\(\chi_{349}(3,\cdot)\)	349.k	174	yes	\(1\)	\(1\)	\(e\left(\frac{13}{174}\right)\)	\(e\left(\frac{82}{87}\right)\)	\(e\left(\frac{13}{87}\right)\)	\(e\left(\frac{40}{87}\right)\)	\(e\left(\frac{1}{58}\right)\)	\(e\left(\frac{1}{174}\right)\)	\(e\left(\frac{13}{58}\right)\)	\(e\left(\frac{77}{87}\right)\)	\(e\left(\frac{31}{58}\right)\)	\(e\left(\frac{33}{58}\right)\)
\(\chi_{349}(4,\cdot)\)	349.k	174	yes	\(1\)	\(1\)	\(e\left(\frac{1}{174}\right)\)	\(e\left(\frac{13}{87}\right)\)	\(e\left(\frac{1}{87}\right)\)	\(e\left(\frac{70}{87}\right)\)	\(e\left(\frac{9}{58}\right)\)	\(e\left(\frac{67}{174}\right)\)	\(e\left(\frac{1}{58}\right)\)	\(e\left(\frac{26}{87}\right)\)	\(e\left(\frac{47}{58}\right)\)	\(e\left(\frac{7}{58}\right)\)
\(\chi_{349}(5,\cdot)\)	349.k	174	yes	\(1\)	\(1\)	\(e\left(\frac{157}{174}\right)\)	\(e\left(\frac{40}{87}\right)\)	\(e\left(\frac{70}{87}\right)\)	\(e\left(\frac{28}{87}\right)\)	\(e\left(\frac{21}{58}\right)\)	\(e\left(\frac{79}{174}\right)\)	\(e\left(\frac{41}{58}\right)\)	\(e\left(\frac{80}{87}\right)\)	\(e\left(\frac{13}{58}\right)\)	\(e\left(\frac{55}{58}\right)\)
\(\chi_{349}(6,\cdot)\)	349.j	116	yes	\(-1\)	\(1\)	\(e\left(\frac{9}{116}\right)\)	\(e\left(\frac{1}{58}\right)\)	\(e\left(\frac{9}{58}\right)\)	\(e\left(\frac{21}{58}\right)\)	\(e\left(\frac{11}{116}\right)\)	\(e\left(\frac{23}{116}\right)\)	\(e\left(\frac{27}{116}\right)\)	\(e\left(\frac{1}{29}\right)\)	\(e\left(\frac{51}{116}\right)\)	\(e\left(\frac{73}{116}\right)\)
\(\chi_{349}(7,\cdot)\)	349.l	348	yes	\(-1\)	\(1\)	\(e\left(\frac{67}{348}\right)\)	\(e\left(\frac{1}{174}\right)\)	\(e\left(\frac{67}{174}\right)\)	\(e\left(\frac{79}{174}\right)\)	\(e\left(\frac{23}{116}\right)\)	\(e\left(\frac{313}{348}\right)\)	\(e\left(\frac{67}{116}\right)\)	\(e\left(\frac{1}{87}\right)\)	\(e\left(\frac{75}{116}\right)\)	\(e\left(\frac{5}{116}\right)\)
\(\chi_{349}(8,\cdot)\)	349.j	116	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{116}\right)\)	\(e\left(\frac{13}{58}\right)\)	\(e\left(\frac{1}{58}\right)\)	\(e\left(\frac{41}{58}\right)\)	\(e\left(\frac{27}{116}\right)\)	\(e\left(\frac{67}{116}\right)\)	\(e\left(\frac{3}{116}\right)\)	\(e\left(\frac{13}{29}\right)\)	\(e\left(\frac{83}{116}\right)\)	\(e\left(\frac{21}{116}\right)\)
\(\chi_{349}(9,\cdot)\)	349.i	87	yes	\(1\)	\(1\)	\(e\left(\frac{13}{87}\right)\)	\(e\left(\frac{77}{87}\right)\)	\(e\left(\frac{26}{87}\right)\)	\(e\left(\frac{80}{87}\right)\)	\(e\left(\frac{1}{29}\right)\)	\(e\left(\frac{1}{87}\right)\)	\(e\left(\frac{13}{29}\right)\)	\(e\left(\frac{67}{87}\right)\)	\(e\left(\frac{2}{29}\right)\)	\(e\left(\frac{4}{29}\right)\)
\(\chi_{349}(10,\cdot)\)	349.j	116	yes	\(-1\)	\(1\)	\(e\left(\frac{105}{116}\right)\)	\(e\left(\frac{31}{58}\right)\)	\(e\left(\frac{47}{58}\right)\)	\(e\left(\frac{13}{58}\right)\)	\(e\left(\frac{51}{116}\right)\)	\(e\left(\frac{75}{116}\right)\)	\(e\left(\frac{83}{116}\right)\)	\(e\left(\frac{2}{29}\right)\)	\(e\left(\frac{15}{116}\right)\)	\(e\left(\frac{1}{116}\right)\)
\(\chi_{349}(11,\cdot)\)	349.j	116	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{116}\right)\)	\(e\left(\frac{33}{58}\right)\)	\(e\left(\frac{7}{58}\right)\)	\(e\left(\frac{55}{58}\right)\)	\(e\left(\frac{73}{116}\right)\)	\(e\left(\frac{5}{116}\right)\)	\(e\left(\frac{21}{116}\right)\)	\(e\left(\frac{4}{29}\right)\)	\(e\left(\frac{1}{116}\right)\)	\(e\left(\frac{31}{116}\right)\)
\(\chi_{349}(12,\cdot)\)	349.i	87	yes	\(1\)	\(1\)	\(e\left(\frac{7}{87}\right)\)	\(e\left(\frac{8}{87}\right)\)	\(e\left(\frac{14}{87}\right)\)	\(e\left(\frac{23}{87}\right)\)	\(e\left(\frac{5}{29}\right)\)	\(e\left(\frac{34}{87}\right)\)	\(e\left(\frac{7}{29}\right)\)	\(e\left(\frac{16}{87}\right)\)	\(e\left(\frac{10}{29}\right)\)	\(e\left(\frac{20}{29}\right)\)
\(\chi_{349}(13,\cdot)\)	349.l	348	yes	\(-1\)	\(1\)	\(e\left(\frac{271}{348}\right)\)	\(e\left(\frac{43}{174}\right)\)	\(e\left(\frac{97}{174}\right)\)	\(e\left(\frac{91}{174}\right)\)	\(e\left(\frac{3}{116}\right)\)	\(e\left(\frac{61}{348}\right)\)	\(e\left(\frac{39}{116}\right)\)	\(e\left(\frac{43}{87}\right)\)	\(e\left(\frac{35}{116}\right)\)	\(e\left(\frac{41}{116}\right)\)
\(\chi_{349}(14,\cdot)\)	349.i	87	yes	\(1\)	\(1\)	\(e\left(\frac{17}{87}\right)\)	\(e\left(\frac{7}{87}\right)\)	\(e\left(\frac{34}{87}\right)\)	\(e\left(\frac{31}{87}\right)\)	\(e\left(\frac{8}{29}\right)\)	\(e\left(\frac{8}{87}\right)\)	\(e\left(\frac{17}{29}\right)\)	\(e\left(\frac{14}{87}\right)\)	\(e\left(\frac{16}{29}\right)\)	\(e\left(\frac{3}{29}\right)\)
\(\chi_{349}(15,\cdot)\)	349.i	87	yes	\(1\)	\(1\)	\(e\left(\frac{85}{87}\right)\)	\(e\left(\frac{35}{87}\right)\)	\(e\left(\frac{83}{87}\right)\)	\(e\left(\frac{68}{87}\right)\)	\(e\left(\frac{11}{29}\right)\)	\(e\left(\frac{40}{87}\right)\)	\(e\left(\frac{27}{29}\right)\)	\(e\left(\frac{70}{87}\right)\)	\(e\left(\frac{22}{29}\right)\)	\(e\left(\frac{15}{29}\right)\)
\(\chi_{349}(16,\cdot)\)	349.i	87	yes	\(1\)	\(1\)	\(e\left(\frac{1}{87}\right)\)	\(e\left(\frac{26}{87}\right)\)	\(e\left(\frac{2}{87}\right)\)	\(e\left(\frac{53}{87}\right)\)	\(e\left(\frac{9}{29}\right)\)	\(e\left(\frac{67}{87}\right)\)	\(e\left(\frac{1}{29}\right)\)	\(e\left(\frac{52}{87}\right)\)	\(e\left(\frac{18}{29}\right)\)	\(e\left(\frac{7}{29}\right)\)
\(\chi_{349}(17,\cdot)\)	349.h	58	yes	\(1\)	\(1\)	\(e\left(\frac{43}{58}\right)\)	\(e\left(\frac{8}{29}\right)\)	\(e\left(\frac{14}{29}\right)\)	\(e\left(\frac{23}{29}\right)\)	\(e\left(\frac{1}{58}\right)\)	\(e\left(\frac{39}{58}\right)\)	\(e\left(\frac{13}{58}\right)\)	\(e\left(\frac{16}{29}\right)\)	\(e\left(\frac{31}{58}\right)\)	\(e\left(\frac{33}{58}\right)\)
\(\chi_{349}(18,\cdot)\)	349.l	348	yes	\(-1\)	\(1\)	\(e\left(\frac{53}{348}\right)\)	\(e\left(\frac{167}{174}\right)\)	\(e\left(\frac{53}{174}\right)\)	\(e\left(\frac{143}{174}\right)\)	\(e\left(\frac{13}{116}\right)\)	\(e\left(\frac{71}{348}\right)\)	\(e\left(\frac{53}{116}\right)\)	\(e\left(\frac{80}{87}\right)\)	\(e\left(\frac{113}{116}\right)\)	\(e\left(\frac{23}{116}\right)\)
\(\chi_{349}(19,\cdot)\)	349.i	87	yes	\(1\)	\(1\)	\(e\left(\frac{47}{87}\right)\)	\(e\left(\frac{4}{87}\right)\)	\(e\left(\frac{7}{87}\right)\)	\(e\left(\frac{55}{87}\right)\)	\(e\left(\frac{17}{29}\right)\)	\(e\left(\frac{17}{87}\right)\)	\(e\left(\frac{18}{29}\right)\)	\(e\left(\frac{8}{87}\right)\)	\(e\left(\frac{5}{29}\right)\)	\(e\left(\frac{10}{29}\right)\)
\(\chi_{349}(20,\cdot)\)	349.i	87	yes	\(1\)	\(1\)	\(e\left(\frac{79}{87}\right)\)	\(e\left(\frac{53}{87}\right)\)	\(e\left(\frac{71}{87}\right)\)	\(e\left(\frac{11}{87}\right)\)	\(e\left(\frac{15}{29}\right)\)	\(e\left(\frac{73}{87}\right)\)	\(e\left(\frac{21}{29}\right)\)	\(e\left(\frac{19}{87}\right)\)	\(e\left(\frac{1}{29}\right)\)	\(e\left(\frac{2}{29}\right)\)
\(\chi_{349}(21,\cdot)\)	349.j	116	yes	\(-1\)	\(1\)	\(e\left(\frac{31}{116}\right)\)	\(e\left(\frac{55}{58}\right)\)	\(e\left(\frac{31}{58}\right)\)	\(e\left(\frac{53}{58}\right)\)	\(e\left(\frac{25}{116}\right)\)	\(e\left(\frac{105}{116}\right)\)	\(e\left(\frac{93}{116}\right)\)	\(e\left(\frac{26}{29}\right)\)	\(e\left(\frac{21}{116}\right)\)	\(e\left(\frac{71}{116}\right)\)
\(\chi_{349}(22,\cdot)\)	349.k	174	yes	\(1\)	\(1\)	\(e\left(\frac{11}{174}\right)\)	\(e\left(\frac{56}{87}\right)\)	\(e\left(\frac{11}{87}\right)\)	\(e\left(\frac{74}{87}\right)\)	\(e\left(\frac{41}{58}\right)\)	\(e\left(\frac{41}{174}\right)\)	\(e\left(\frac{11}{58}\right)\)	\(e\left(\frac{25}{87}\right)\)	\(e\left(\frac{53}{58}\right)\)	\(e\left(\frac{19}{58}\right)\)
\(\chi_{349}(23,\cdot)\)	349.i	87	yes	\(1\)	\(1\)	\(e\left(\frac{46}{87}\right)\)	\(e\left(\frac{65}{87}\right)\)	\(e\left(\frac{5}{87}\right)\)	\(e\left(\frac{2}{87}\right)\)	\(e\left(\frac{8}{29}\right)\)	\(e\left(\frac{37}{87}\right)\)	\(e\left(\frac{17}{29}\right)\)	\(e\left(\frac{43}{87}\right)\)	\(e\left(\frac{16}{29}\right)\)	\(e\left(\frac{3}{29}\right)\)
\(\chi_{349}(24,\cdot)\)	349.f	12	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(i\)	\(e\left(\frac{7}{12}\right)\)	\(i\)	\(e\left(\frac{1}{3}\right)\)	\(i\)	\(-i\)
\(\chi_{349}(25,\cdot)\)	349.i	87	yes	\(1\)	\(1\)	\(e\left(\frac{70}{87}\right)\)	\(e\left(\frac{80}{87}\right)\)	\(e\left(\frac{53}{87}\right)\)	\(e\left(\frac{56}{87}\right)\)	\(e\left(\frac{21}{29}\right)\)	\(e\left(\frac{79}{87}\right)\)	\(e\left(\frac{12}{29}\right)\)	\(e\left(\frac{73}{87}\right)\)	\(e\left(\frac{13}{29}\right)\)	\(e\left(\frac{26}{29}\right)\)
\(\chi_{349}(26,\cdot)\)	349.i	87	yes	\(1\)	\(1\)	\(e\left(\frac{68}{87}\right)\)	\(e\left(\frac{28}{87}\right)\)	\(e\left(\frac{49}{87}\right)\)	\(e\left(\frac{37}{87}\right)\)	\(e\left(\frac{3}{29}\right)\)	\(e\left(\frac{32}{87}\right)\)	\(e\left(\frac{10}{29}\right)\)	\(e\left(\frac{56}{87}\right)\)	\(e\left(\frac{6}{29}\right)\)	\(e\left(\frac{12}{29}\right)\)
\(\chi_{349}(27,\cdot)\)	349.h	58	yes	\(1\)	\(1\)	\(e\left(\frac{13}{58}\right)\)	\(e\left(\frac{24}{29}\right)\)	\(e\left(\frac{13}{29}\right)\)	\(e\left(\frac{11}{29}\right)\)	\(e\left(\frac{3}{58}\right)\)	\(e\left(\frac{1}{58}\right)\)	\(e\left(\frac{39}{58}\right)\)	\(e\left(\frac{19}{29}\right)\)	\(e\left(\frac{35}{58}\right)\)	\(e\left(\frac{41}{58}\right)\)
\(\chi_{349}(28,\cdot)\)	349.j	116	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{116}\right)\)	\(e\left(\frac{9}{58}\right)\)	\(e\left(\frac{23}{58}\right)\)	\(e\left(\frac{15}{58}\right)\)	\(e\left(\frac{41}{116}\right)\)	\(e\left(\frac{33}{116}\right)\)	\(e\left(\frac{69}{116}\right)\)	\(e\left(\frac{9}{29}\right)\)	\(e\left(\frac{53}{116}\right)\)	\(e\left(\frac{19}{116}\right)\)
\(\chi_{349}(29,\cdot)\)	349.k	174	yes	\(1\)	\(1\)	\(e\left(\frac{73}{174}\right)\)	\(e\left(\frac{79}{87}\right)\)	\(e\left(\frac{73}{87}\right)\)	\(e\left(\frac{64}{87}\right)\)	\(e\left(\frac{19}{58}\right)\)	\(e\left(\frac{19}{174}\right)\)	\(e\left(\frac{15}{58}\right)\)	\(e\left(\frac{71}{87}\right)\)	\(e\left(\frac{9}{58}\right)\)	\(e\left(\frac{47}{58}\right)\)
\(\chi_{349}(30,\cdot)\)	349.l	348	yes	\(-1\)	\(1\)	\(e\left(\frac{341}{348}\right)\)	\(e\left(\frac{83}{174}\right)\)	\(e\left(\frac{167}{174}\right)\)	\(e\left(\frac{119}{174}\right)\)	\(e\left(\frac{53}{116}\right)\)	\(e\left(\frac{227}{348}\right)\)	\(e\left(\frac{109}{116}\right)\)	\(e\left(\frac{83}{87}\right)\)	\(e\left(\frac{77}{116}\right)\)	\(e\left(\frac{67}{116}\right)\)
\(\chi_{349}(31,\cdot)\)	349.g	29	yes	\(1\)	\(1\)	\(e\left(\frac{13}{29}\right)\)	\(e\left(\frac{19}{29}\right)\)	\(e\left(\frac{26}{29}\right)\)	\(e\left(\frac{22}{29}\right)\)	\(e\left(\frac{3}{29}\right)\)	\(e\left(\frac{1}{29}\right)\)	\(e\left(\frac{10}{29}\right)\)	\(e\left(\frac{9}{29}\right)\)	\(e\left(\frac{6}{29}\right)\)	\(e\left(\frac{12}{29}\right)\)
\(\chi_{349}(32,\cdot)\)	349.l	348	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{348}\right)\)	\(e\left(\frac{65}{174}\right)\)	\(e\left(\frac{5}{174}\right)\)	\(e\left(\frac{89}{174}\right)\)	\(e\left(\frac{45}{116}\right)\)	\(e\left(\frac{335}{348}\right)\)	\(e\left(\frac{5}{116}\right)\)	\(e\left(\frac{65}{87}\right)\)	\(e\left(\frac{61}{116}\right)\)	\(e\left(\frac{35}{116}\right)\)

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Character group

First 32 of 348 characters

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.