LMFDB - Group of Dirichlet characters of modulus 178

Show commands: PariGP / SageMath

sage: H = DirichletGroup(178)

pari: g = idealstar(,178,2)

Character group

sage: G.order() pari: g.no
Order	=	88
sage: H.invariants() pari: g.cyc
Structure	=	$C_{88}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{178}(3,\cdot)$

First 32 of 88 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	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{178}(1,\cdot)$	178.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{178}(3,\cdot)$	178.h	88	no	$-1$	$1$	$e\left(\frac{1}{88}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{81}{88}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{23}{88}\right)$	$e\left(\frac{71}{88}\right)$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{35}{88}\right)$	$e\left(\frac{41}{44}\right)$
$\chi_{178}(5,\cdot)$	178.g	44	no	$1$	$1$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{5}{22}\right)$
$\chi_{178}(7,\cdot)$	178.h	88	no	$-1$	$1$	$e\left(\frac{81}{88}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{49}{88}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{15}{88}\right)$	$e\left(\frac{31}{88}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{19}{88}\right)$	$e\left(\frac{21}{44}\right)$
$\chi_{178}(9,\cdot)$	178.g	44	no	$1$	$1$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{19}{22}\right)$
$\chi_{178}(11,\cdot)$	178.f	22	no	$1$	$1$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{3}{11}\right)$
$\chi_{178}(13,\cdot)$	178.h	88	no	$-1$	$1$	$e\left(\frac{23}{88}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{15}{88}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{1}{88}\right)$	$e\left(\frac{49}{88}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{13}{88}\right)$	$e\left(\frac{19}{44}\right)$
$\chi_{178}(15,\cdot)$	178.h	88	no	$-1$	$1$	$e\left(\frac{71}{88}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{31}{88}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{49}{88}\right)$	$e\left(\frac{25}{88}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{21}{88}\right)$	$e\left(\frac{7}{44}\right)$
$\chi_{178}(17,\cdot)$	178.g	44	no	$1$	$1$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{13}{22}\right)$
$\chi_{178}(19,\cdot)$	178.h	88	no	$-1$	$1$	$e\left(\frac{35}{88}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{19}{88}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{13}{88}\right)$	$e\left(\frac{21}{88}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{81}{88}\right)$	$e\left(\frac{27}{44}\right)$
$\chi_{178}(21,\cdot)$	178.g	44	no	$1$	$1$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{9}{22}\right)$
$\chi_{178}(23,\cdot)$	178.h	88	no	$-1$	$1$	$e\left(\frac{57}{88}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{41}{88}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{79}{88}\right)$	$e\left(\frac{87}{88}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{59}{88}\right)$	$e\left(\frac{5}{44}\right)$
$\chi_{178}(25,\cdot)$	178.f	22	no	$1$	$1$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{5}{11}\right)$
$\chi_{178}(27,\cdot)$	178.h	88	no	$-1$	$1$	$e\left(\frac{3}{88}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{67}{88}\right)$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{69}{88}\right)$	$e\left(\frac{37}{88}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{17}{88}\right)$	$e\left(\frac{35}{44}\right)$
$\chi_{178}(29,\cdot)$	178.h	88	no	$-1$	$1$	$e\left(\frac{59}{88}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{27}{88}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{37}{88}\right)$	$e\left(\frac{53}{88}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{41}{88}\right)$	$e\left(\frac{43}{44}\right)$
$\chi_{178}(31,\cdot)$	178.h	88	no	$-1$	$1$	$e\left(\frac{31}{88}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{47}{88}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{9}{88}\right)$	$e\left(\frac{1}{88}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{29}{88}\right)$	$e\left(\frac{39}{44}\right)$
$\chi_{178}(33,\cdot)$	178.h	88	no	$-1$	$1$	$e\left(\frac{85}{88}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{21}{88}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{19}{88}\right)$	$e\left(\frac{51}{88}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{71}{88}\right)$	$e\left(\frac{9}{44}\right)$
$\chi_{178}(35,\cdot)$	178.h	88	no	$-1$	$1$	$e\left(\frac{63}{88}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{87}{88}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{41}{88}\right)$	$e\left(\frac{73}{88}\right)$	$e\left(\frac{13}{44}\right)$	$e\left(\frac{5}{88}\right)$	$e\left(\frac{31}{44}\right)$
$\chi_{178}(37,\cdot)$	178.d	8	no	$-1$	$1$	$e\left(\frac{1}{8}\right)$	$-i$	$e\left(\frac{1}{8}\right)$	$i$	$-1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{8}\right)$	$-i$	$e\left(\frac{3}{8}\right)$	$i$
$\chi_{178}(39,\cdot)$	178.e	11	no	$1$	$1$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{4}{11}\right)$
$\chi_{178}(41,\cdot)$	178.h	88	no	$-1$	$1$	$e\left(\frac{21}{88}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{29}{88}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{43}{88}\right)$	$e\left(\frac{83}{88}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{31}{88}\right)$	$e\left(\frac{25}{44}\right)$
$\chi_{178}(43,\cdot)$	178.h	88	no	$-1$	$1$	$e\left(\frac{29}{88}\right)$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{61}{88}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{51}{88}\right)$	$e\left(\frac{35}{88}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{47}{88}\right)$	$e\left(\frac{1}{44}\right)$
$\chi_{178}(45,\cdot)$	178.e	11	no	$1$	$1$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{1}{11}\right)$
$\chi_{178}(47,\cdot)$	178.g	44	no	$1$	$1$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{7}{22}\right)$
$\chi_{178}(49,\cdot)$	178.g	44	no	$1$	$1$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{21}{22}\right)$
$\chi_{178}(51,\cdot)$	178.h	88	no	$-1$	$1$	$e\left(\frac{7}{88}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{39}{88}\right)$	$e\left(\frac{7}{44}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{73}{88}\right)$	$e\left(\frac{57}{88}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{69}{88}\right)$	$e\left(\frac{23}{44}\right)$
$\chi_{178}(53,\cdot)$	178.g	44	no	$1$	$1$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{35}{44}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{15}{22}\right)$
$\chi_{178}(55,\cdot)$	178.c	4	no	$1$	$1$	$-i$	$-1$	$-i$	$-1$	$1$	$i$	$i$	$-1$	$i$	$-1$
$\chi_{178}(57,\cdot)$	178.f	22	no	$1$	$1$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{6}{11}\right)$
$\chi_{178}(59,\cdot)$	178.h	88	no	$-1$	$1$	$e\left(\frac{43}{88}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{51}{88}\right)$	$e\left(\frac{43}{44}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{21}{88}\right)$	$e\left(\frac{61}{88}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{9}{88}\right)$	$e\left(\frac{3}{44}\right)$
$\chi_{178}(61,\cdot)$	178.h	88	no	$-1$	$1$	$e\left(\frac{69}{88}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{45}{88}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{3}{88}\right)$	$e\left(\frac{59}{88}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{39}{88}\right)$	$e\left(\frac{13}{44}\right)$
$\chi_{178}(63,\cdot)$	178.h	88	no	$-1$	$1$	$e\left(\frac{83}{88}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{35}{88}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{61}{88}\right)$	$e\left(\frac{85}{88}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{1}{88}\right)$	$e\left(\frac{15}{44}\right)$

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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	$178$
Structure	\(C_{88}\)
Order	$88$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\(\chi_{178}(1,\cdot)\)	178.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{178}(3,\cdot)\)	178.h	88	no	\(-1\)	\(1\)	\(e\left(\frac{1}{88}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{81}{88}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{23}{88}\right)\)	\(e\left(\frac{71}{88}\right)\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{35}{88}\right)\)	\(e\left(\frac{41}{44}\right)\)
\(\chi_{178}(5,\cdot)\)	178.g	44	no	\(1\)	\(1\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{5}{22}\right)\)
\(\chi_{178}(7,\cdot)\)	178.h	88	no	\(-1\)	\(1\)	\(e\left(\frac{81}{88}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{49}{88}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{15}{88}\right)\)	\(e\left(\frac{31}{88}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{19}{88}\right)\)	\(e\left(\frac{21}{44}\right)\)
\(\chi_{178}(9,\cdot)\)	178.g	44	no	\(1\)	\(1\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{19}{22}\right)\)
\(\chi_{178}(11,\cdot)\)	178.f	22	no	\(1\)	\(1\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)
\(\chi_{178}(13,\cdot)\)	178.h	88	no	\(-1\)	\(1\)	\(e\left(\frac{23}{88}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{15}{88}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{1}{88}\right)\)	\(e\left(\frac{49}{88}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{13}{88}\right)\)	\(e\left(\frac{19}{44}\right)\)
\(\chi_{178}(15,\cdot)\)	178.h	88	no	\(-1\)	\(1\)	\(e\left(\frac{71}{88}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{31}{88}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{49}{88}\right)\)	\(e\left(\frac{25}{88}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{21}{88}\right)\)	\(e\left(\frac{7}{44}\right)\)
\(\chi_{178}(17,\cdot)\)	178.g	44	no	\(1\)	\(1\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{13}{22}\right)\)
\(\chi_{178}(19,\cdot)\)	178.h	88	no	\(-1\)	\(1\)	\(e\left(\frac{35}{88}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{19}{88}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{13}{88}\right)\)	\(e\left(\frac{21}{88}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{81}{88}\right)\)	\(e\left(\frac{27}{44}\right)\)
\(\chi_{178}(21,\cdot)\)	178.g	44	no	\(1\)	\(1\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{9}{22}\right)\)
\(\chi_{178}(23,\cdot)\)	178.h	88	no	\(-1\)	\(1\)	\(e\left(\frac{57}{88}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{41}{88}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{79}{88}\right)\)	\(e\left(\frac{87}{88}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{59}{88}\right)\)	\(e\left(\frac{5}{44}\right)\)
\(\chi_{178}(25,\cdot)\)	178.f	22	no	\(1\)	\(1\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{5}{11}\right)\)
\(\chi_{178}(27,\cdot)\)	178.h	88	no	\(-1\)	\(1\)	\(e\left(\frac{3}{88}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{67}{88}\right)\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{69}{88}\right)\)	\(e\left(\frac{37}{88}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{17}{88}\right)\)	\(e\left(\frac{35}{44}\right)\)
\(\chi_{178}(29,\cdot)\)	178.h	88	no	\(-1\)	\(1\)	\(e\left(\frac{59}{88}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{27}{88}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{37}{88}\right)\)	\(e\left(\frac{53}{88}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{41}{88}\right)\)	\(e\left(\frac{43}{44}\right)\)
\(\chi_{178}(31,\cdot)\)	178.h	88	no	\(-1\)	\(1\)	\(e\left(\frac{31}{88}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{47}{88}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{9}{88}\right)\)	\(e\left(\frac{1}{88}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{29}{88}\right)\)	\(e\left(\frac{39}{44}\right)\)
\(\chi_{178}(33,\cdot)\)	178.h	88	no	\(-1\)	\(1\)	\(e\left(\frac{85}{88}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{21}{88}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{19}{88}\right)\)	\(e\left(\frac{51}{88}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{71}{88}\right)\)	\(e\left(\frac{9}{44}\right)\)
\(\chi_{178}(35,\cdot)\)	178.h	88	no	\(-1\)	\(1\)	\(e\left(\frac{63}{88}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{87}{88}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{41}{88}\right)\)	\(e\left(\frac{73}{88}\right)\)	\(e\left(\frac{13}{44}\right)\)	\(e\left(\frac{5}{88}\right)\)	\(e\left(\frac{31}{44}\right)\)
\(\chi_{178}(37,\cdot)\)	178.d	8	no	\(-1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(-i\)	\(e\left(\frac{1}{8}\right)\)	\(i\)	\(-1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(-i\)	\(e\left(\frac{3}{8}\right)\)	\(i\)
\(\chi_{178}(39,\cdot)\)	178.e	11	no	\(1\)	\(1\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)
\(\chi_{178}(41,\cdot)\)	178.h	88	no	\(-1\)	\(1\)	\(e\left(\frac{21}{88}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{29}{88}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{43}{88}\right)\)	\(e\left(\frac{83}{88}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{31}{88}\right)\)	\(e\left(\frac{25}{44}\right)\)
\(\chi_{178}(43,\cdot)\)	178.h	88	no	\(-1\)	\(1\)	\(e\left(\frac{29}{88}\right)\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{61}{88}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{51}{88}\right)\)	\(e\left(\frac{35}{88}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{47}{88}\right)\)	\(e\left(\frac{1}{44}\right)\)
\(\chi_{178}(45,\cdot)\)	178.e	11	no	\(1\)	\(1\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)
\(\chi_{178}(47,\cdot)\)	178.g	44	no	\(1\)	\(1\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{7}{22}\right)\)
\(\chi_{178}(49,\cdot)\)	178.g	44	no	\(1\)	\(1\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{21}{22}\right)\)
\(\chi_{178}(51,\cdot)\)	178.h	88	no	\(-1\)	\(1\)	\(e\left(\frac{7}{88}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{39}{88}\right)\)	\(e\left(\frac{7}{44}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{73}{88}\right)\)	\(e\left(\frac{57}{88}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{69}{88}\right)\)	\(e\left(\frac{23}{44}\right)\)
\(\chi_{178}(53,\cdot)\)	178.g	44	no	\(1\)	\(1\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{35}{44}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{15}{22}\right)\)
\(\chi_{178}(55,\cdot)\)	178.c	4	no	\(1\)	\(1\)	\(-i\)	\(-1\)	\(-i\)	\(-1\)	\(1\)	\(i\)	\(i\)	\(-1\)	\(i\)	\(-1\)
\(\chi_{178}(57,\cdot)\)	178.f	22	no	\(1\)	\(1\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)
\(\chi_{178}(59,\cdot)\)	178.h	88	no	\(-1\)	\(1\)	\(e\left(\frac{43}{88}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{51}{88}\right)\)	\(e\left(\frac{43}{44}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{21}{88}\right)\)	\(e\left(\frac{61}{88}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{9}{88}\right)\)	\(e\left(\frac{3}{44}\right)\)
\(\chi_{178}(61,\cdot)\)	178.h	88	no	\(-1\)	\(1\)	\(e\left(\frac{69}{88}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{45}{88}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{3}{88}\right)\)	\(e\left(\frac{59}{88}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{39}{88}\right)\)	\(e\left(\frac{13}{44}\right)\)
\(\chi_{178}(63,\cdot)\)	178.h	88	no	\(-1\)	\(1\)	\(e\left(\frac{83}{88}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{35}{88}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{61}{88}\right)\)	\(e\left(\frac{85}{88}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{1}{88}\right)\)	\(e\left(\frac{15}{44}\right)\)

Introduction

L-functions

Modular forms

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Character group

First 32 of 88 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.