LMFDB - Group of Dirichlet characters of modulus 254

Show commands: PariGP / SageMath

sage: H = DirichletGroup(254)

pari: g = idealstar(,254,2)

Character group

sage: G.order() pari: g.no
Order	=	126
sage: H.invariants() pari: g.cyc
Structure	=	$C_{126}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{254}(3,\cdot)$

First 32 of 126 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	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{254}(1,\cdot)$	254.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{254}(3,\cdot)$	254.l	126	no	$-1$	$1$	$e\left(\frac{1}{126}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{115}{126}\right)$	$e\left(\frac{1}{63}\right)$	$e\left(\frac{34}{63}\right)$	$e\left(\frac{47}{63}\right)$	$e\left(\frac{44}{63}\right)$	$e\left(\frac{19}{63}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{58}{63}\right)$
$\chi_{254}(5,\cdot)$	254.j	42	no	$-1$	$1$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{5}{21}\right)$	$1$	$e\left(\frac{2}{21}\right)$
$\chi_{254}(7,\cdot)$	254.l	126	no	$-1$	$1$	$e\left(\frac{115}{126}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{121}{126}\right)$	$e\left(\frac{52}{63}\right)$	$e\left(\frac{4}{63}\right)$	$e\left(\frac{50}{63}\right)$	$e\left(\frac{20}{63}\right)$	$e\left(\frac{43}{63}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{55}{63}\right)$
$\chi_{254}(9,\cdot)$	254.k	63	no	$1$	$1$	$e\left(\frac{1}{63}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{52}{63}\right)$	$e\left(\frac{2}{63}\right)$	$e\left(\frac{5}{63}\right)$	$e\left(\frac{31}{63}\right)$	$e\left(\frac{25}{63}\right)$	$e\left(\frac{38}{63}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{53}{63}\right)$
$\chi_{254}(11,\cdot)$	254.k	63	no	$1$	$1$	$e\left(\frac{34}{63}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{4}{63}\right)$	$e\left(\frac{5}{63}\right)$	$e\left(\frac{44}{63}\right)$	$e\left(\frac{46}{63}\right)$	$e\left(\frac{31}{63}\right)$	$e\left(\frac{32}{63}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{38}{63}\right)$
$\chi_{254}(13,\cdot)$	254.k	63	no	$1$	$1$	$e\left(\frac{47}{63}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{50}{63}\right)$	$e\left(\frac{31}{63}\right)$	$e\left(\frac{46}{63}\right)$	$e\left(\frac{8}{63}\right)$	$e\left(\frac{41}{63}\right)$	$e\left(\frac{22}{63}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{34}{63}\right)$
$\chi_{254}(15,\cdot)$	254.k	63	no	$1$	$1$	$e\left(\frac{44}{63}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{20}{63}\right)$	$e\left(\frac{25}{63}\right)$	$e\left(\frac{31}{63}\right)$	$e\left(\frac{41}{63}\right)$	$e\left(\frac{29}{63}\right)$	$e\left(\frac{34}{63}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{63}\right)$
$\chi_{254}(17,\cdot)$	254.k	63	no	$1$	$1$	$e\left(\frac{19}{63}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{43}{63}\right)$	$e\left(\frac{38}{63}\right)$	$e\left(\frac{32}{63}\right)$	$e\left(\frac{22}{63}\right)$	$e\left(\frac{34}{63}\right)$	$e\left(\frac{29}{63}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{62}{63}\right)$
$\chi_{254}(19,\cdot)$	254.c	3	no	$1$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$
$\chi_{254}(21,\cdot)$	254.k	63	no	$1$	$1$	$e\left(\frac{58}{63}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{55}{63}\right)$	$e\left(\frac{53}{63}\right)$	$e\left(\frac{38}{63}\right)$	$e\left(\frac{34}{63}\right)$	$e\left(\frac{1}{63}\right)$	$e\left(\frac{62}{63}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{50}{63}\right)$
$\chi_{254}(23,\cdot)$	254.l	126	no	$-1$	$1$	$e\left(\frac{121}{126}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{55}{126}\right)$	$e\left(\frac{58}{63}\right)$	$e\left(\frac{19}{63}\right)$	$e\left(\frac{17}{63}\right)$	$e\left(\frac{32}{63}\right)$	$e\left(\frac{31}{63}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{25}{63}\right)$
$\chi_{254}(25,\cdot)$	254.i	21	no	$1$	$1$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{10}{21}\right)$	$1$	$e\left(\frac{4}{21}\right)$
$\chi_{254}(27,\cdot)$	254.j	42	no	$-1$	$1$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{19}{21}\right)$	$1$	$e\left(\frac{16}{21}\right)$
$\chi_{254}(29,\cdot)$	254.l	126	no	$-1$	$1$	$e\left(\frac{113}{126}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{17}{126}\right)$	$e\left(\frac{50}{63}\right)$	$e\left(\frac{62}{63}\right)$	$e\left(\frac{19}{63}\right)$	$e\left(\frac{58}{63}\right)$	$e\left(\frac{5}{63}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{63}\right)$
$\chi_{254}(31,\cdot)$	254.k	63	no	$1$	$1$	$e\left(\frac{23}{63}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{62}{63}\right)$	$e\left(\frac{46}{63}\right)$	$e\left(\frac{52}{63}\right)$	$e\left(\frac{20}{63}\right)$	$e\left(\frac{8}{63}\right)$	$e\left(\frac{55}{63}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{22}{63}\right)$
$\chi_{254}(33,\cdot)$	254.j	42	no	$-1$	$1$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{17}{21}\right)$	$1$	$e\left(\frac{11}{21}\right)$
$\chi_{254}(35,\cdot)$	254.k	63	no	$1$	$1$	$e\left(\frac{38}{63}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{23}{63}\right)$	$e\left(\frac{13}{63}\right)$	$e\left(\frac{1}{63}\right)$	$e\left(\frac{44}{63}\right)$	$e\left(\frac{5}{63}\right)$	$e\left(\frac{58}{63}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{61}{63}\right)$
$\chi_{254}(37,\cdot)$	254.f	9	no	$1$	$1$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{9}\right)$
$\chi_{254}(39,\cdot)$	254.l	126	no	$-1$	$1$	$e\left(\frac{95}{126}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{89}{126}\right)$	$e\left(\frac{32}{63}\right)$	$e\left(\frac{17}{63}\right)$	$e\left(\frac{55}{63}\right)$	$e\left(\frac{22}{63}\right)$	$e\left(\frac{41}{63}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{29}{63}\right)$
$\chi_{254}(41,\cdot)$	254.k	63	no	$1$	$1$	$e\left(\frac{40}{63}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{1}{63}\right)$	$e\left(\frac{17}{63}\right)$	$e\left(\frac{11}{63}\right)$	$e\left(\frac{43}{63}\right)$	$e\left(\frac{55}{63}\right)$	$e\left(\frac{8}{63}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{41}{63}\right)$
$\chi_{254}(43,\cdot)$	254.l	126	no	$-1$	$1$	$e\left(\frac{71}{126}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{101}{126}\right)$	$e\left(\frac{8}{63}\right)$	$e\left(\frac{20}{63}\right)$	$e\left(\frac{61}{63}\right)$	$e\left(\frac{37}{63}\right)$	$e\left(\frac{26}{63}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{23}{63}\right)$
$\chi_{254}(45,\cdot)$	254.l	126	no	$-1$	$1$	$e\left(\frac{89}{126}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{29}{126}\right)$	$e\left(\frac{26}{63}\right)$	$e\left(\frac{2}{63}\right)$	$e\left(\frac{25}{63}\right)$	$e\left(\frac{10}{63}\right)$	$e\left(\frac{53}{63}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{59}{63}\right)$
$\chi_{254}(47,\cdot)$	254.i	21	no	$1$	$1$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{2}{21}\right)$	$1$	$e\left(\frac{5}{21}\right)$
$\chi_{254}(49,\cdot)$	254.k	63	no	$1$	$1$	$e\left(\frac{52}{63}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{58}{63}\right)$	$e\left(\frac{41}{63}\right)$	$e\left(\frac{8}{63}\right)$	$e\left(\frac{37}{63}\right)$	$e\left(\frac{40}{63}\right)$	$e\left(\frac{23}{63}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{47}{63}\right)$
$\chi_{254}(51,\cdot)$	254.j	42	no	$-1$	$1$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{16}{21}\right)$	$1$	$e\left(\frac{19}{21}\right)$
$\chi_{254}(53,\cdot)$	254.l	126	no	$-1$	$1$	$e\left(\frac{107}{126}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{83}{126}\right)$	$e\left(\frac{44}{63}\right)$	$e\left(\frac{47}{63}\right)$	$e\left(\frac{52}{63}\right)$	$e\left(\frac{46}{63}\right)$	$e\left(\frac{17}{63}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{32}{63}\right)$
$\chi_{254}(55,\cdot)$	254.l	126	no	$-1$	$1$	$e\left(\frac{29}{126}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{59}{126}\right)$	$e\left(\frac{29}{63}\right)$	$e\left(\frac{41}{63}\right)$	$e\left(\frac{40}{63}\right)$	$e\left(\frac{16}{63}\right)$	$e\left(\frac{47}{63}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{44}{63}\right)$
$\chi_{254}(57,\cdot)$	254.l	126	no	$-1$	$1$	$e\left(\frac{85}{126}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{73}{126}\right)$	$e\left(\frac{22}{63}\right)$	$e\left(\frac{55}{63}\right)$	$e\left(\frac{26}{63}\right)$	$e\left(\frac{23}{63}\right)$	$e\left(\frac{40}{63}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{16}{63}\right)$
$\chi_{254}(59,\cdot)$	254.h	18	no	$-1$	$1$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{9}\right)$
$\chi_{254}(61,\cdot)$	254.i	21	no	$1$	$1$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{11}{21}\right)$	$1$	$e\left(\frac{17}{21}\right)$
$\chi_{254}(63,\cdot)$	254.g	14	no	$-1$	$1$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{2}{7}\right)$	$1$	$e\left(\frac{5}{7}\right)$

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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	$254$
Structure	\(C_{126}\)
Order	$126$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\(\chi_{254}(1,\cdot)\)	254.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{254}(3,\cdot)\)	254.l	126	no	\(-1\)	\(1\)	\(e\left(\frac{1}{126}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{115}{126}\right)\)	\(e\left(\frac{1}{63}\right)\)	\(e\left(\frac{34}{63}\right)\)	\(e\left(\frac{47}{63}\right)\)	\(e\left(\frac{44}{63}\right)\)	\(e\left(\frac{19}{63}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{58}{63}\right)\)
\(\chi_{254}(5,\cdot)\)	254.j	42	no	\(-1\)	\(1\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(1\)	\(e\left(\frac{2}{21}\right)\)
\(\chi_{254}(7,\cdot)\)	254.l	126	no	\(-1\)	\(1\)	\(e\left(\frac{115}{126}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{121}{126}\right)\)	\(e\left(\frac{52}{63}\right)\)	\(e\left(\frac{4}{63}\right)\)	\(e\left(\frac{50}{63}\right)\)	\(e\left(\frac{20}{63}\right)\)	\(e\left(\frac{43}{63}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{55}{63}\right)\)
\(\chi_{254}(9,\cdot)\)	254.k	63	no	\(1\)	\(1\)	\(e\left(\frac{1}{63}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{52}{63}\right)\)	\(e\left(\frac{2}{63}\right)\)	\(e\left(\frac{5}{63}\right)\)	\(e\left(\frac{31}{63}\right)\)	\(e\left(\frac{25}{63}\right)\)	\(e\left(\frac{38}{63}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{53}{63}\right)\)
\(\chi_{254}(11,\cdot)\)	254.k	63	no	\(1\)	\(1\)	\(e\left(\frac{34}{63}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{4}{63}\right)\)	\(e\left(\frac{5}{63}\right)\)	\(e\left(\frac{44}{63}\right)\)	\(e\left(\frac{46}{63}\right)\)	\(e\left(\frac{31}{63}\right)\)	\(e\left(\frac{32}{63}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{38}{63}\right)\)
\(\chi_{254}(13,\cdot)\)	254.k	63	no	\(1\)	\(1\)	\(e\left(\frac{47}{63}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{50}{63}\right)\)	\(e\left(\frac{31}{63}\right)\)	\(e\left(\frac{46}{63}\right)\)	\(e\left(\frac{8}{63}\right)\)	\(e\left(\frac{41}{63}\right)\)	\(e\left(\frac{22}{63}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{34}{63}\right)\)
\(\chi_{254}(15,\cdot)\)	254.k	63	no	\(1\)	\(1\)	\(e\left(\frac{44}{63}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{20}{63}\right)\)	\(e\left(\frac{25}{63}\right)\)	\(e\left(\frac{31}{63}\right)\)	\(e\left(\frac{41}{63}\right)\)	\(e\left(\frac{29}{63}\right)\)	\(e\left(\frac{34}{63}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{63}\right)\)
\(\chi_{254}(17,\cdot)\)	254.k	63	no	\(1\)	\(1\)	\(e\left(\frac{19}{63}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{43}{63}\right)\)	\(e\left(\frac{38}{63}\right)\)	\(e\left(\frac{32}{63}\right)\)	\(e\left(\frac{22}{63}\right)\)	\(e\left(\frac{34}{63}\right)\)	\(e\left(\frac{29}{63}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{62}{63}\right)\)
\(\chi_{254}(19,\cdot)\)	254.c	3	no	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{254}(21,\cdot)\)	254.k	63	no	\(1\)	\(1\)	\(e\left(\frac{58}{63}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{55}{63}\right)\)	\(e\left(\frac{53}{63}\right)\)	\(e\left(\frac{38}{63}\right)\)	\(e\left(\frac{34}{63}\right)\)	\(e\left(\frac{1}{63}\right)\)	\(e\left(\frac{62}{63}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{50}{63}\right)\)
\(\chi_{254}(23,\cdot)\)	254.l	126	no	\(-1\)	\(1\)	\(e\left(\frac{121}{126}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{55}{126}\right)\)	\(e\left(\frac{58}{63}\right)\)	\(e\left(\frac{19}{63}\right)\)	\(e\left(\frac{17}{63}\right)\)	\(e\left(\frac{32}{63}\right)\)	\(e\left(\frac{31}{63}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{25}{63}\right)\)
\(\chi_{254}(25,\cdot)\)	254.i	21	no	\(1\)	\(1\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(1\)	\(e\left(\frac{4}{21}\right)\)
\(\chi_{254}(27,\cdot)\)	254.j	42	no	\(-1\)	\(1\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(1\)	\(e\left(\frac{16}{21}\right)\)
\(\chi_{254}(29,\cdot)\)	254.l	126	no	\(-1\)	\(1\)	\(e\left(\frac{113}{126}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{17}{126}\right)\)	\(e\left(\frac{50}{63}\right)\)	\(e\left(\frac{62}{63}\right)\)	\(e\left(\frac{19}{63}\right)\)	\(e\left(\frac{58}{63}\right)\)	\(e\left(\frac{5}{63}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{63}\right)\)
\(\chi_{254}(31,\cdot)\)	254.k	63	no	\(1\)	\(1\)	\(e\left(\frac{23}{63}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{62}{63}\right)\)	\(e\left(\frac{46}{63}\right)\)	\(e\left(\frac{52}{63}\right)\)	\(e\left(\frac{20}{63}\right)\)	\(e\left(\frac{8}{63}\right)\)	\(e\left(\frac{55}{63}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{22}{63}\right)\)
\(\chi_{254}(33,\cdot)\)	254.j	42	no	\(-1\)	\(1\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(1\)	\(e\left(\frac{11}{21}\right)\)
\(\chi_{254}(35,\cdot)\)	254.k	63	no	\(1\)	\(1\)	\(e\left(\frac{38}{63}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{23}{63}\right)\)	\(e\left(\frac{13}{63}\right)\)	\(e\left(\frac{1}{63}\right)\)	\(e\left(\frac{44}{63}\right)\)	\(e\left(\frac{5}{63}\right)\)	\(e\left(\frac{58}{63}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{61}{63}\right)\)
\(\chi_{254}(37,\cdot)\)	254.f	9	no	\(1\)	\(1\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{9}\right)\)
\(\chi_{254}(39,\cdot)\)	254.l	126	no	\(-1\)	\(1\)	\(e\left(\frac{95}{126}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{89}{126}\right)\)	\(e\left(\frac{32}{63}\right)\)	\(e\left(\frac{17}{63}\right)\)	\(e\left(\frac{55}{63}\right)\)	\(e\left(\frac{22}{63}\right)\)	\(e\left(\frac{41}{63}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{29}{63}\right)\)
\(\chi_{254}(41,\cdot)\)	254.k	63	no	\(1\)	\(1\)	\(e\left(\frac{40}{63}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{1}{63}\right)\)	\(e\left(\frac{17}{63}\right)\)	\(e\left(\frac{11}{63}\right)\)	\(e\left(\frac{43}{63}\right)\)	\(e\left(\frac{55}{63}\right)\)	\(e\left(\frac{8}{63}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{41}{63}\right)\)
\(\chi_{254}(43,\cdot)\)	254.l	126	no	\(-1\)	\(1\)	\(e\left(\frac{71}{126}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{101}{126}\right)\)	\(e\left(\frac{8}{63}\right)\)	\(e\left(\frac{20}{63}\right)\)	\(e\left(\frac{61}{63}\right)\)	\(e\left(\frac{37}{63}\right)\)	\(e\left(\frac{26}{63}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{23}{63}\right)\)
\(\chi_{254}(45,\cdot)\)	254.l	126	no	\(-1\)	\(1\)	\(e\left(\frac{89}{126}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{29}{126}\right)\)	\(e\left(\frac{26}{63}\right)\)	\(e\left(\frac{2}{63}\right)\)	\(e\left(\frac{25}{63}\right)\)	\(e\left(\frac{10}{63}\right)\)	\(e\left(\frac{53}{63}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{59}{63}\right)\)
\(\chi_{254}(47,\cdot)\)	254.i	21	no	\(1\)	\(1\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(1\)	\(e\left(\frac{5}{21}\right)\)
\(\chi_{254}(49,\cdot)\)	254.k	63	no	\(1\)	\(1\)	\(e\left(\frac{52}{63}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{58}{63}\right)\)	\(e\left(\frac{41}{63}\right)\)	\(e\left(\frac{8}{63}\right)\)	\(e\left(\frac{37}{63}\right)\)	\(e\left(\frac{40}{63}\right)\)	\(e\left(\frac{23}{63}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{47}{63}\right)\)
\(\chi_{254}(51,\cdot)\)	254.j	42	no	\(-1\)	\(1\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(1\)	\(e\left(\frac{19}{21}\right)\)
\(\chi_{254}(53,\cdot)\)	254.l	126	no	\(-1\)	\(1\)	\(e\left(\frac{107}{126}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{83}{126}\right)\)	\(e\left(\frac{44}{63}\right)\)	\(e\left(\frac{47}{63}\right)\)	\(e\left(\frac{52}{63}\right)\)	\(e\left(\frac{46}{63}\right)\)	\(e\left(\frac{17}{63}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{32}{63}\right)\)
\(\chi_{254}(55,\cdot)\)	254.l	126	no	\(-1\)	\(1\)	\(e\left(\frac{29}{126}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{59}{126}\right)\)	\(e\left(\frac{29}{63}\right)\)	\(e\left(\frac{41}{63}\right)\)	\(e\left(\frac{40}{63}\right)\)	\(e\left(\frac{16}{63}\right)\)	\(e\left(\frac{47}{63}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{44}{63}\right)\)
\(\chi_{254}(57,\cdot)\)	254.l	126	no	\(-1\)	\(1\)	\(e\left(\frac{85}{126}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{73}{126}\right)\)	\(e\left(\frac{22}{63}\right)\)	\(e\left(\frac{55}{63}\right)\)	\(e\left(\frac{26}{63}\right)\)	\(e\left(\frac{23}{63}\right)\)	\(e\left(\frac{40}{63}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{16}{63}\right)\)
\(\chi_{254}(59,\cdot)\)	254.h	18	no	\(-1\)	\(1\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{9}\right)\)
\(\chi_{254}(61,\cdot)\)	254.i	21	no	\(1\)	\(1\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(1\)	\(e\left(\frac{17}{21}\right)\)
\(\chi_{254}(63,\cdot)\)	254.g	14	no	\(-1\)	\(1\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(1\)	\(e\left(\frac{5}{7}\right)\)

Introduction

L-functions

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Character group

First 32 of 126 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.