LMFDB - Group of Dirichlet characters of modulus 242

Show commands: PariGP / SageMath

sage: H = DirichletGroup(242)

pari: g = idealstar(,242,2)

Character group

sage: G.order() pari: g.no
Order	=	110
sage: H.invariants() pari: g.cyc
Structure	=	$C_{110}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{242}(123,\cdot)$

First 32 of 110 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	$-1$	$1$	$3$	$5$	$7$	$9$	$13$	$15$	$17$	$19$	$21$	$23$
$\chi_{242}(1,\cdot)$	242.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{242}(3,\cdot)$	242.c	5	no	$1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{5}\right)$	$1$	$1$
$\chi_{242}(5,\cdot)$	242.g	55	no	$1$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{1}{11}\right)$
$\chi_{242}(7,\cdot)$	242.h	110	no	$-1$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{49}{110}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{47}{110}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{13}{110}\right)$	$e\left(\frac{31}{110}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{5}{11}\right)$
$\chi_{242}(9,\cdot)$	242.c	5	no	$1$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{5}\right)$	$1$	$1$
$\chi_{242}(13,\cdot)$	242.h	110	no	$-1$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{47}{110}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{81}{110}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{109}{110}\right)$	$e\left(\frac{23}{110}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{3}{11}\right)$
$\chi_{242}(15,\cdot)$	242.g	55	no	$1$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{1}{11}\right)$
$\chi_{242}(17,\cdot)$	242.h	110	no	$-1$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{13}{110}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{109}{110}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{91}{110}\right)$	$e\left(\frac{107}{110}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{2}{11}\right)$
$\chi_{242}(19,\cdot)$	242.h	110	no	$-1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{31}{110}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{23}{110}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{107}{110}\right)$	$e\left(\frac{69}{110}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{9}{11}\right)$
$\chi_{242}(21,\cdot)$	242.f	22	no	$-1$	$1$	$1$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{1}{22}\right)$	$1$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{5}{11}\right)$
$\chi_{242}(23,\cdot)$	242.e	11	no	$1$	$1$	$1$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{5}{11}\right)$	$1$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{6}{11}\right)$
$\chi_{242}(25,\cdot)$	242.g	55	no	$1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{2}{11}\right)$
$\chi_{242}(27,\cdot)$	242.c	5	no	$1$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{5}\right)$	$1$	$1$
$\chi_{242}(29,\cdot)$	242.h	110	no	$-1$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{67}{110}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{63}{110}\right)$	$e\left(\frac{91}{110}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{9}{11}\right)$
$\chi_{242}(31,\cdot)$	242.g	55	no	$1$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{8}{11}\right)$
$\chi_{242}(35,\cdot)$	242.h	110	no	$-1$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{17}{110}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{41}{110}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{13}{110}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{6}{11}\right)$
$\chi_{242}(37,\cdot)$	242.g	55	no	$1$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{37}{55}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{8}{11}\right)$
$\chi_{242}(39,\cdot)$	242.h	110	no	$-1$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{3}{110}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{59}{110}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{21}{110}\right)$	$e\left(\frac{67}{110}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{3}{11}\right)$
$\chi_{242}(41,\cdot)$	242.h	110	no	$-1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{51}{110}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{13}{110}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{27}{110}\right)$	$e\left(\frac{39}{110}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{7}{11}\right)$
$\chi_{242}(43,\cdot)$	242.f	22	no	$-1$	$1$	$1$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{13}{22}\right)$	$1$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{10}{11}\right)$
$\chi_{242}(45,\cdot)$	242.e	11	no	$1$	$1$	$1$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{10}{11}\right)$	$1$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{1}{11}\right)$
$\chi_{242}(47,\cdot)$	242.g	55	no	$1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{4}{11}\right)$
$\chi_{242}(49,\cdot)$	242.g	55	no	$1$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{23}{55}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{10}{11}\right)$
$\chi_{242}(51,\cdot)$	242.h	110	no	$-1$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{79}{110}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{87}{110}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{3}{110}\right)$	$e\left(\frac{41}{110}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{2}{11}\right)$
$\chi_{242}(53,\cdot)$	242.g	55	no	$1$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{5}{11}\right)$
$\chi_{242}(57,\cdot)$	242.h	110	no	$-1$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{97}{110}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{110}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{19}{110}\right)$	$e\left(\frac{3}{110}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{9}{11}\right)$
$\chi_{242}(59,\cdot)$	242.g	55	no	$1$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{4}{11}\right)$
$\chi_{242}(61,\cdot)$	242.h	110	no	$-1$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{103}{110}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{61}{110}\right)$	$e\left(\frac{27}{110}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{4}{11}\right)$
$\chi_{242}(63,\cdot)$	242.h	110	no	$-1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{71}{110}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{110}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{57}{110}\right)$	$e\left(\frac{9}{110}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{5}{11}\right)$
$\chi_{242}(65,\cdot)$	242.f	22	no	$-1$	$1$	$1$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{3}{22}\right)$	$1$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{4}{11}\right)$
$\chi_{242}(67,\cdot)$	242.e	11	no	$1$	$1$	$1$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{4}{11}\right)$	$1$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{7}{11}\right)$
$\chi_{242}(69,\cdot)$	242.g	55	no	$1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{6}{11}\right)$

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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	$242$
Structure	\(C_{110}\)
Order	$110$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)	\(23\)
\(\chi_{242}(1,\cdot)\)	242.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{242}(3,\cdot)\)	242.c	5	no	\(1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(1\)	\(1\)
\(\chi_{242}(5,\cdot)\)	242.g	55	no	\(1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{52}{55}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)
\(\chi_{242}(7,\cdot)\)	242.h	110	no	\(-1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{49}{110}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{47}{110}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{13}{110}\right)\)	\(e\left(\frac{31}{110}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{5}{11}\right)\)
\(\chi_{242}(9,\cdot)\)	242.c	5	no	\(1\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(1\)	\(1\)
\(\chi_{242}(13,\cdot)\)	242.h	110	no	\(-1\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{52}{55}\right)\)	\(e\left(\frac{47}{110}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{81}{110}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{109}{110}\right)\)	\(e\left(\frac{23}{110}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)
\(\chi_{242}(15,\cdot)\)	242.g	55	no	\(1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{9}{55}\right)\)	\(e\left(\frac{13}{55}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)
\(\chi_{242}(17,\cdot)\)	242.h	110	no	\(-1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{13}{110}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{109}{110}\right)\)	\(e\left(\frac{9}{55}\right)\)	\(e\left(\frac{91}{110}\right)\)	\(e\left(\frac{107}{110}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{2}{11}\right)\)
\(\chi_{242}(19,\cdot)\)	242.h	110	no	\(-1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{31}{110}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{23}{110}\right)\)	\(e\left(\frac{13}{55}\right)\)	\(e\left(\frac{107}{110}\right)\)	\(e\left(\frac{69}{110}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{9}{11}\right)\)
\(\chi_{242}(21,\cdot)\)	242.f	22	no	\(-1\)	\(1\)	\(1\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(1\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{5}{11}\right)\)
\(\chi_{242}(23,\cdot)\)	242.e	11	no	\(1\)	\(1\)	\(1\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(1\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)
\(\chi_{242}(25,\cdot)\)	242.g	55	no	\(1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)
\(\chi_{242}(27,\cdot)\)	242.c	5	no	\(1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(1\)	\(1\)
\(\chi_{242}(29,\cdot)\)	242.h	110	no	\(-1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{9}{110}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{67}{110}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{63}{110}\right)\)	\(e\left(\frac{91}{110}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{9}{11}\right)\)
\(\chi_{242}(31,\cdot)\)	242.g	55	no	\(1\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)
\(\chi_{242}(35,\cdot)\)	242.h	110	no	\(-1\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{17}{110}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{41}{110}\right)\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{9}{110}\right)\)	\(e\left(\frac{13}{110}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)
\(\chi_{242}(37,\cdot)\)	242.g	55	no	\(1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{37}{55}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{38}{55}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)
\(\chi_{242}(39,\cdot)\)	242.h	110	no	\(-1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{3}{110}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{59}{110}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{21}{110}\right)\)	\(e\left(\frac{67}{110}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)
\(\chi_{242}(41,\cdot)\)	242.h	110	no	\(-1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{51}{110}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{13}{110}\right)\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{27}{110}\right)\)	\(e\left(\frac{39}{110}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{7}{11}\right)\)
\(\chi_{242}(43,\cdot)\)	242.f	22	no	\(-1\)	\(1\)	\(1\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(1\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)
\(\chi_{242}(45,\cdot)\)	242.e	11	no	\(1\)	\(1\)	\(1\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(1\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)
\(\chi_{242}(47,\cdot)\)	242.g	55	no	\(1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{13}{55}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{36}{55}\right)\)	\(e\left(\frac{52}{55}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)
\(\chi_{242}(49,\cdot)\)	242.g	55	no	\(1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{23}{55}\right)\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{13}{55}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)
\(\chi_{242}(51,\cdot)\)	242.h	110	no	\(-1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{9}{55}\right)\)	\(e\left(\frac{79}{110}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{87}{110}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{3}{110}\right)\)	\(e\left(\frac{41}{110}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{2}{11}\right)\)
\(\chi_{242}(53,\cdot)\)	242.g	55	no	\(1\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{12}{55}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)
\(\chi_{242}(57,\cdot)\)	242.h	110	no	\(-1\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{97}{110}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{110}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{19}{110}\right)\)	\(e\left(\frac{3}{110}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{9}{11}\right)\)
\(\chi_{242}(59,\cdot)\)	242.g	55	no	\(1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)
\(\chi_{242}(61,\cdot)\)	242.h	110	no	\(-1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{103}{110}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{9}{110}\right)\)	\(e\left(\frac{29}{55}\right)\)	\(e\left(\frac{61}{110}\right)\)	\(e\left(\frac{27}{110}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)
\(\chi_{242}(63,\cdot)\)	242.h	110	no	\(-1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{71}{110}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{110}\right)\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{57}{110}\right)\)	\(e\left(\frac{9}{110}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{5}{11}\right)\)
\(\chi_{242}(65,\cdot)\)	242.f	22	no	\(-1\)	\(1\)	\(1\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(1\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)
\(\chi_{242}(67,\cdot)\)	242.e	11	no	\(1\)	\(1\)	\(1\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(1\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)
\(\chi_{242}(69,\cdot)\)	242.g	55	no	\(1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{4}{55}\right)\)	\(e\left(\frac{38}{55}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{12}{55}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)

Introduction

L-functions

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Character group

First 32 of 110 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.