LMFDB - Group of Dirichlet characters of modulus 2028

sage:H = DirichletGroup(2028)

pari:g = idealstar(,2028,2)

Character group

sage:G.order() pari:g.no
Order	=	624
sage:H.invariants() pari:g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{156}$
sage:H.gens() pari:g.gen
Generators	=	$\chi_{2028}(1015,\cdot)$, $\chi_{2028}(677,\cdot)$, $\chi_{2028}(1861,\cdot)$

First 32 of 624 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	$-1$	$1$	$5$	$7$	$11$	$17$	$19$	$23$	$25$	$29$	$31$	$35$
$\chi_{2028}(1,\cdot)$	2028.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{2028}(5,\cdot)$	2028.bi	52	no	$1$	$1$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{12}{13}\right)$	$-i$	$1$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{5}{26}\right)$
$\chi_{2028}(7,\cdot)$	2028.bs	156	no	$1$	$1$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{139}{156}\right)$	$e\left(\frac{23}{156}\right)$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{5}{78}\right)$
$\chi_{2028}(11,\cdot)$	2028.bv	156	yes	$-1$	$1$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{23}{156}\right)$	$e\left(\frac{1}{156}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{23}{39}\right)$
$\chi_{2028}(17,\cdot)$	2028.bm	78	no	$-1$	$1$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{5}{78}\right)$
$\chi_{2028}(19,\cdot)$	2028.w	12	no	$1$	$1$	$-i$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$i$	$e\left(\frac{5}{6}\right)$
$\chi_{2028}(23,\cdot)$	2028.r	6	no	$1$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{2}{3}\right)$
$\chi_{2028}(25,\cdot)$	2028.bf	26	no	$1$	$1$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{11}{13}\right)$	$-1$	$1$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{5}{13}\right)$
$\chi_{2028}(29,\cdot)$	2028.bq	78	no	$-1$	$1$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{19}{78}\right)$
$\chi_{2028}(31,\cdot)$	2028.bk	52	no	$1$	$1$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{17}{26}\right)$	$i$	$1$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{3}{26}\right)$
$\chi_{2028}(35,\cdot)$	2028.bp	78	yes	$1$	$1$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{10}{39}\right)$
$\chi_{2028}(37,\cdot)$	2028.bt	156	no	$-1$	$1$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{89}{156}\right)$	$e\left(\frac{109}{156}\right)$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{11}{39}\right)$
$\chi_{2028}(41,\cdot)$	2028.bu	156	no	$1$	$1$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{47}{156}\right)$	$e\left(\frac{97}{156}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{55}{78}\right)$
$\chi_{2028}(43,\cdot)$	2028.br	78	no	$-1$	$1$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{7}{39}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{17}{78}\right)$
$\chi_{2028}(47,\cdot)$	2028.bh	52	yes	$-1$	$1$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{6}{13}\right)$	$-i$	$-1$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{11}{13}\right)$
$\chi_{2028}(49,\cdot)$	2028.bo	78	no	$1$	$1$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{61}{78}\right)$	$e\left(\frac{23}{78}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{5}{39}\right)$
$\chi_{2028}(53,\cdot)$	2028.bd	26	no	$-1$	$1$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{21}{26}\right)$	$1$	$-1$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{19}{26}\right)$
$\chi_{2028}(55,\cdot)$	2028.bl	78	no	$-1$	$1$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{61}{78}\right)$
$\chi_{2028}(59,\cdot)$	2028.bv	156	yes	$-1$	$1$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{79}{156}\right)$	$e\left(\frac{17}{156}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{1}{39}\right)$
$\chi_{2028}(61,\cdot)$	2028.bg	39	no	$1$	$1$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{4}{39}\right)$
$\chi_{2028}(67,\cdot)$	2028.bs	156	no	$1$	$1$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{137}{156}\right)$	$e\left(\frac{145}{156}\right)$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{1}{78}\right)$
$\chi_{2028}(71,\cdot)$	2028.bv	156	yes	$-1$	$1$	$e\left(\frac{21}{52}\right)$	$e\left(\frac{73}{156}\right)$	$e\left(\frac{71}{156}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{34}{39}\right)$
$\chi_{2028}(73,\cdot)$	2028.bj	52	no	$-1$	$1$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{19}{26}\right)$	$i$	$-1$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{12}{13}\right)$
$\chi_{2028}(77,\cdot)$	2028.ba	26	no	$-1$	$1$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{1}{26}\right)$	$-1$	$-1$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{17}{26}\right)$
$\chi_{2028}(79,\cdot)$	2028.bb	26	no	$-1$	$1$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{6}{13}\right)$	$-1$	$-1$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{9}{26}\right)$
$\chi_{2028}(83,\cdot)$	2028.bh	52	yes	$-1$	$1$	$e\left(\frac{5}{52}\right)$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{8}{13}\right)$	$i$	$-1$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{29}{52}\right)$	$e\left(\frac{6}{13}\right)$
$\chi_{2028}(85,\cdot)$	2028.bt	156	no	$-1$	$1$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{49}{156}\right)$	$e\left(\frac{53}{156}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{10}{39}\right)$
$\chi_{2028}(89,\cdot)$	2028.u	12	no	$1$	$1$	$-i$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{5}{6}\right)$	$i$	$e\left(\frac{1}{6}\right)$
$\chi_{2028}(95,\cdot)$	2028.bn	78	yes	$1$	$1$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{67}{78}\right)$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{1}{39}\right)$
$\chi_{2028}(97,\cdot)$	2028.bt	156	no	$-1$	$1$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{103}{156}\right)$	$e\left(\frac{35}{156}\right)$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{25}{39}\right)$
$\chi_{2028}(101,\cdot)$	2028.bm	78	no	$-1$	$1$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{1}{78}\right)$	$e\left(\frac{28}{39}\right)$	$e\left(\frac{1}{78}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{43}{78}\right)$
$\chi_{2028}(103,\cdot)$	2028.bc	26	no	$-1$	$1$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{5}{13}\right)$	$1$	$-1$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{1}{26}\right)$

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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 $\F_{q}$
Belyi maps

Modulus	$2028$
Structure	\(C_{2}\times C_{2}\times C_{156}\)
Order	$624$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(35\)
\(\chi_{2028}(1,\cdot)\)	2028.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{2028}(5,\cdot)\)	2028.bi	52	no	\(1\)	\(1\)	\(e\left(\frac{1}{52}\right)\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(-i\)	\(1\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{5}{26}\right)\)
\(\chi_{2028}(7,\cdot)\)	2028.bs	156	no	\(1\)	\(1\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{139}{156}\right)\)	\(e\left(\frac{23}{156}\right)\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{5}{78}\right)\)
\(\chi_{2028}(11,\cdot)\)	2028.bv	156	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{23}{156}\right)\)	\(e\left(\frac{1}{156}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{23}{39}\right)\)
\(\chi_{2028}(17,\cdot)\)	2028.bm	78	no	\(-1\)	\(1\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{5}{78}\right)\)
\(\chi_{2028}(19,\cdot)\)	2028.w	12	no	\(1\)	\(1\)	\(-i\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(i\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{2028}(23,\cdot)\)	2028.r	6	no	\(1\)	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{2028}(25,\cdot)\)	2028.bf	26	no	\(1\)	\(1\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{5}{13}\right)\)
\(\chi_{2028}(29,\cdot)\)	2028.bq	78	no	\(-1\)	\(1\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{19}{78}\right)\)
\(\chi_{2028}(31,\cdot)\)	2028.bk	52	no	\(1\)	\(1\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(i\)	\(1\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{3}{26}\right)\)
\(\chi_{2028}(35,\cdot)\)	2028.bp	78	yes	\(1\)	\(1\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{10}{39}\right)\)
\(\chi_{2028}(37,\cdot)\)	2028.bt	156	no	\(-1\)	\(1\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{89}{156}\right)\)	\(e\left(\frac{109}{156}\right)\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{11}{39}\right)\)
\(\chi_{2028}(41,\cdot)\)	2028.bu	156	no	\(1\)	\(1\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{47}{156}\right)\)	\(e\left(\frac{97}{156}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{55}{78}\right)\)
\(\chi_{2028}(43,\cdot)\)	2028.br	78	no	\(-1\)	\(1\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{7}{39}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{17}{78}\right)\)
\(\chi_{2028}(47,\cdot)\)	2028.bh	52	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(-i\)	\(-1\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{11}{13}\right)\)
\(\chi_{2028}(49,\cdot)\)	2028.bo	78	no	\(1\)	\(1\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{61}{78}\right)\)	\(e\left(\frac{23}{78}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{5}{39}\right)\)
\(\chi_{2028}(53,\cdot)\)	2028.bd	26	no	\(-1\)	\(1\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{19}{26}\right)\)
\(\chi_{2028}(55,\cdot)\)	2028.bl	78	no	\(-1\)	\(1\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{61}{78}\right)\)
\(\chi_{2028}(59,\cdot)\)	2028.bv	156	yes	\(-1\)	\(1\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{79}{156}\right)\)	\(e\left(\frac{17}{156}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{1}{39}\right)\)
\(\chi_{2028}(61,\cdot)\)	2028.bg	39	no	\(1\)	\(1\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{4}{39}\right)\)
\(\chi_{2028}(67,\cdot)\)	2028.bs	156	no	\(1\)	\(1\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{137}{156}\right)\)	\(e\left(\frac{145}{156}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{1}{78}\right)\)
\(\chi_{2028}(71,\cdot)\)	2028.bv	156	yes	\(-1\)	\(1\)	\(e\left(\frac{21}{52}\right)\)	\(e\left(\frac{73}{156}\right)\)	\(e\left(\frac{71}{156}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{34}{39}\right)\)
\(\chi_{2028}(73,\cdot)\)	2028.bj	52	no	\(-1\)	\(1\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(i\)	\(-1\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{12}{13}\right)\)
\(\chi_{2028}(77,\cdot)\)	2028.ba	26	no	\(-1\)	\(1\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(-1\)	\(-1\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{17}{26}\right)\)
\(\chi_{2028}(79,\cdot)\)	2028.bb	26	no	\(-1\)	\(1\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(-1\)	\(-1\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{9}{26}\right)\)
\(\chi_{2028}(83,\cdot)\)	2028.bh	52	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{52}\right)\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(i\)	\(-1\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{29}{52}\right)\)	\(e\left(\frac{6}{13}\right)\)
\(\chi_{2028}(85,\cdot)\)	2028.bt	156	no	\(-1\)	\(1\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{49}{156}\right)\)	\(e\left(\frac{53}{156}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{10}{39}\right)\)
\(\chi_{2028}(89,\cdot)\)	2028.u	12	no	\(1\)	\(1\)	\(-i\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(i\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{2028}(95,\cdot)\)	2028.bn	78	yes	\(1\)	\(1\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{67}{78}\right)\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{1}{39}\right)\)
\(\chi_{2028}(97,\cdot)\)	2028.bt	156	no	\(-1\)	\(1\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{103}{156}\right)\)	\(e\left(\frac{35}{156}\right)\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{25}{39}\right)\)
\(\chi_{2028}(101,\cdot)\)	2028.bm	78	no	\(-1\)	\(1\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{1}{78}\right)\)	\(e\left(\frac{28}{39}\right)\)	\(e\left(\frac{1}{78}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{43}{78}\right)\)
\(\chi_{2028}(103,\cdot)\)	2028.bc	26	no	\(-1\)	\(1\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{1}{26}\right)\)

Introduction

L-functions

Modular forms

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Properties

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Character group

First 32 of 624 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.