LMFDB - Group of Dirichlet characters of modulus 3888

Show commands: PariGP / SageMath

sage: H = DirichletGroup(3888)

pari: g = idealstar(,3888,2)

Character group

sage: G.order() pari: g.no
Order	=	1296
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{324}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{3888}(2431,\cdot)$, $\chi_{3888}(2917,\cdot)$, $\chi_{3888}(1217,\cdot)$

First 32 of 1296 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	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$
$\chi_{3888}(1,\cdot)$	3888.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{3888}(5,\cdot)$	3888.cg	324	yes	$-1$	$1$	$e\left(\frac{167}{324}\right)$	$e\left(\frac{71}{162}\right)$	$e\left(\frac{139}{324}\right)$	$e\left(\frac{287}{324}\right)$	$e\left(\frac{37}{54}\right)$	$e\left(\frac{97}{108}\right)$	$e\left(\frac{59}{81}\right)$	$e\left(\frac{5}{162}\right)$	$e\left(\frac{1}{324}\right)$	$e\left(\frac{68}{81}\right)$
$\chi_{3888}(7,\cdot)$	3888.bx	162	no	$-1$	$1$	$e\left(\frac{71}{162}\right)$	$e\left(\frac{121}{162}\right)$	$e\left(\frac{23}{81}\right)$	$e\left(\frac{155}{162}\right)$	$e\left(\frac{7}{27}\right)$	$e\left(\frac{11}{27}\right)$	$e\left(\frac{95}{162}\right)$	$e\left(\frac{71}{81}\right)$	$e\left(\frac{79}{162}\right)$	$e\left(\frac{23}{162}\right)$
$\chi_{3888}(11,\cdot)$	3888.ch	324	yes	$1$	$1$	$e\left(\frac{139}{324}\right)$	$e\left(\frac{23}{81}\right)$	$e\left(\frac{41}{324}\right)$	$e\left(\frac{235}{324}\right)$	$e\left(\frac{35}{54}\right)$	$e\left(\frac{83}{108}\right)$	$e\left(\frac{89}{162}\right)$	$e\left(\frac{139}{162}\right)$	$e\left(\frac{125}{324}\right)$	$e\left(\frac{71}{162}\right)$
$\chi_{3888}(13,\cdot)$	3888.ce	324	yes	$1$	$1$	$e\left(\frac{287}{324}\right)$	$e\left(\frac{155}{162}\right)$	$e\left(\frac{235}{324}\right)$	$e\left(\frac{209}{324}\right)$	$e\left(\frac{17}{27}\right)$	$e\left(\frac{103}{108}\right)$	$e\left(\frac{115}{162}\right)$	$e\left(\frac{125}{162}\right)$	$e\left(\frac{25}{324}\right)$	$e\left(\frac{80}{81}\right)$
$\chi_{3888}(17,\cdot)$	3888.bo	54	no	$-1$	$1$	$e\left(\frac{37}{54}\right)$	$e\left(\frac{7}{27}\right)$	$e\left(\frac{35}{54}\right)$	$e\left(\frac{17}{27}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{13}{54}\right)$	$e\left(\frac{10}{27}\right)$	$e\left(\frac{29}{54}\right)$	$e\left(\frac{2}{27}\right)$
$\chi_{3888}(19,\cdot)$	3888.bu	108	no	$-1$	$1$	$e\left(\frac{97}{108}\right)$	$e\left(\frac{11}{27}\right)$	$e\left(\frac{83}{108}\right)$	$e\left(\frac{103}{108}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{16}{27}\right)$	$e\left(\frac{43}{54}\right)$	$e\left(\frac{95}{108}\right)$	$e\left(\frac{41}{54}\right)$
$\chi_{3888}(23,\cdot)$	3888.cb	162	no	$1$	$1$	$e\left(\frac{59}{81}\right)$	$e\left(\frac{95}{162}\right)$	$e\left(\frac{89}{162}\right)$	$e\left(\frac{115}{162}\right)$	$e\left(\frac{13}{54}\right)$	$e\left(\frac{16}{27}\right)$	$e\left(\frac{47}{81}\right)$	$e\left(\frac{37}{81}\right)$	$e\left(\frac{28}{81}\right)$	$e\left(\frac{85}{162}\right)$
$\chi_{3888}(25,\cdot)$	3888.bz	162	no	$1$	$1$	$e\left(\frac{5}{162}\right)$	$e\left(\frac{71}{81}\right)$	$e\left(\frac{139}{162}\right)$	$e\left(\frac{125}{162}\right)$	$e\left(\frac{10}{27}\right)$	$e\left(\frac{43}{54}\right)$	$e\left(\frac{37}{81}\right)$	$e\left(\frac{5}{81}\right)$	$e\left(\frac{1}{162}\right)$	$e\left(\frac{55}{81}\right)$
$\chi_{3888}(29,\cdot)$	3888.cg	324	yes	$-1$	$1$	$e\left(\frac{1}{324}\right)$	$e\left(\frac{79}{162}\right)$	$e\left(\frac{125}{324}\right)$	$e\left(\frac{25}{324}\right)$	$e\left(\frac{29}{54}\right)$	$e\left(\frac{95}{108}\right)$	$e\left(\frac{28}{81}\right)$	$e\left(\frac{1}{162}\right)$	$e\left(\frac{227}{324}\right)$	$e\left(\frac{46}{81}\right)$
$\chi_{3888}(31,\cdot)$	3888.by	162	no	$-1$	$1$	$e\left(\frac{68}{81}\right)$	$e\left(\frac{23}{162}\right)$	$e\left(\frac{71}{162}\right)$	$e\left(\frac{80}{81}\right)$	$e\left(\frac{2}{27}\right)$	$e\left(\frac{41}{54}\right)$	$e\left(\frac{85}{162}\right)$	$e\left(\frac{55}{81}\right)$	$e\left(\frac{46}{81}\right)$	$e\left(\frac{157}{162}\right)$
$\chi_{3888}(35,\cdot)$	3888.bt	108	no	$1$	$1$	$e\left(\frac{103}{108}\right)$	$e\left(\frac{5}{27}\right)$	$e\left(\frac{77}{108}\right)$	$e\left(\frac{91}{108}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{17}{54}\right)$	$e\left(\frac{49}{54}\right)$	$e\left(\frac{53}{108}\right)$	$e\left(\frac{53}{54}\right)$
$\chi_{3888}(37,\cdot)$	3888.bw	108	no	$1$	$1$	$e\left(\frac{95}{108}\right)$	$e\left(\frac{53}{54}\right)$	$e\left(\frac{103}{108}\right)$	$e\left(\frac{53}{108}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{1}{54}\right)$	$e\left(\frac{41}{54}\right)$	$e\left(\frac{73}{108}\right)$	$e\left(\frac{23}{27}\right)$
$\chi_{3888}(41,\cdot)$	3888.cd	162	no	$-1$	$1$	$e\left(\frac{2}{81}\right)$	$e\left(\frac{73}{81}\right)$	$e\left(\frac{7}{81}\right)$	$e\left(\frac{19}{162}\right)$	$e\left(\frac{43}{54}\right)$	$e\left(\frac{29}{54}\right)$	$e\left(\frac{43}{162}\right)$	$e\left(\frac{4}{81}\right)$	$e\left(\frac{49}{81}\right)$	$e\left(\frac{44}{81}\right)$
$\chi_{3888}(43,\cdot)$	3888.cf	324	yes	$-1$	$1$	$e\left(\frac{229}{324}\right)$	$e\left(\frac{14}{81}\right)$	$e\left(\frac{275}{324}\right)$	$e\left(\frac{55}{324}\right)$	$e\left(\frac{13}{27}\right)$	$e\left(\frac{47}{108}\right)$	$e\left(\frac{13}{81}\right)$	$e\left(\frac{67}{162}\right)$	$e\left(\frac{143}{324}\right)$	$e\left(\frac{89}{162}\right)$
$\chi_{3888}(47,\cdot)$	3888.cc	162	no	$1$	$1$	$e\left(\frac{107}{162}\right)$	$e\left(\frac{139}{162}\right)$	$e\left(\frac{5}{81}\right)$	$e\left(\frac{1}{81}\right)$	$e\left(\frac{23}{54}\right)$	$e\left(\frac{13}{54}\right)$	$e\left(\frac{79}{81}\right)$	$e\left(\frac{26}{81}\right)$	$e\left(\frac{151}{162}\right)$	$e\left(\frac{5}{162}\right)$
$\chi_{3888}(49,\cdot)$	3888.bs	81	no	$1$	$1$	$e\left(\frac{71}{81}\right)$	$e\left(\frac{40}{81}\right)$	$e\left(\frac{46}{81}\right)$	$e\left(\frac{74}{81}\right)$	$e\left(\frac{14}{27}\right)$	$e\left(\frac{22}{27}\right)$	$e\left(\frac{14}{81}\right)$	$e\left(\frac{61}{81}\right)$	$e\left(\frac{79}{81}\right)$	$e\left(\frac{23}{81}\right)$
$\chi_{3888}(53,\cdot)$	3888.bj	36	no	$-1$	$1$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{2}{9}\right)$
$\chi_{3888}(55,\cdot)$	3888.z	18	no	$-1$	$1$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{5}{18}\right)$
$\chi_{3888}(59,\cdot)$	3888.ch	324	yes	$1$	$1$	$e\left(\frac{131}{324}\right)$	$e\left(\frac{31}{81}\right)$	$e\left(\frac{13}{324}\right)$	$e\left(\frac{35}{324}\right)$	$e\left(\frac{19}{54}\right)$	$e\left(\frac{79}{108}\right)$	$e\left(\frac{127}{162}\right)$	$e\left(\frac{131}{162}\right)$	$e\left(\frac{253}{324}\right)$	$e\left(\frac{145}{162}\right)$
$\chi_{3888}(61,\cdot)$	3888.ce	324	yes	$1$	$1$	$e\left(\frac{151}{324}\right)$	$e\left(\frac{103}{162}\right)$	$e\left(\frac{83}{324}\right)$	$e\left(\frac{49}{324}\right)$	$e\left(\frac{16}{27}\right)$	$e\left(\frac{35}{108}\right)$	$e\left(\frac{113}{162}\right)$	$e\left(\frac{151}{162}\right)$	$e\left(\frac{257}{324}\right)$	$e\left(\frac{61}{81}\right)$
$\chi_{3888}(65,\cdot)$	3888.ca	162	no	$-1$	$1$	$e\left(\frac{65}{162}\right)$	$e\left(\frac{32}{81}\right)$	$e\left(\frac{25}{162}\right)$	$e\left(\frac{43}{81}\right)$	$e\left(\frac{17}{54}\right)$	$e\left(\frac{23}{27}\right)$	$e\left(\frac{71}{162}\right)$	$e\left(\frac{65}{81}\right)$	$e\left(\frac{13}{162}\right)$	$e\left(\frac{67}{81}\right)$
$\chi_{3888}(67,\cdot)$	3888.cf	324	yes	$-1$	$1$	$e\left(\frac{323}{324}\right)$	$e\left(\frac{1}{81}\right)$	$e\left(\frac{37}{324}\right)$	$e\left(\frac{137}{324}\right)$	$e\left(\frac{26}{27}\right)$	$e\left(\frac{13}{108}\right)$	$e\left(\frac{53}{81}\right)$	$e\left(\frac{161}{162}\right)$	$e\left(\frac{97}{324}\right)$	$e\left(\frac{151}{162}\right)$
$\chi_{3888}(71,\cdot)$	3888.bn	54	no	$1$	$1$	$e\left(\frac{20}{27}\right)$	$e\left(\frac{29}{54}\right)$	$e\left(\frac{5}{54}\right)$	$e\left(\frac{1}{54}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{26}{27}\right)$	$e\left(\frac{13}{27}\right)$	$e\left(\frac{4}{27}\right)$	$e\left(\frac{43}{54}\right)$
$\chi_{3888}(73,\cdot)$	3888.bp	54	no	$1$	$1$	$e\left(\frac{5}{54}\right)$	$e\left(\frac{17}{27}\right)$	$e\left(\frac{31}{54}\right)$	$e\left(\frac{17}{54}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{10}{27}\right)$	$e\left(\frac{5}{27}\right)$	$e\left(\frac{1}{54}\right)$	$e\left(\frac{1}{27}\right)$
$\chi_{3888}(77,\cdot)$	3888.cg	324	yes	$-1$	$1$	$e\left(\frac{281}{324}\right)$	$e\left(\frac{5}{162}\right)$	$e\left(\frac{133}{324}\right)$	$e\left(\frac{221}{324}\right)$	$e\left(\frac{49}{54}\right)$	$e\left(\frac{19}{108}\right)$	$e\left(\frac{11}{81}\right)$	$e\left(\frac{119}{162}\right)$	$e\left(\frac{283}{324}\right)$	$e\left(\frac{47}{81}\right)$
$\chi_{3888}(79,\cdot)$	3888.by	162	no	$-1$	$1$	$e\left(\frac{25}{81}\right)$	$e\left(\frac{43}{162}\right)$	$e\left(\frac{13}{162}\right)$	$e\left(\frac{58}{81}\right)$	$e\left(\frac{19}{27}\right)$	$e\left(\frac{25}{54}\right)$	$e\left(\frac{11}{162}\right)$	$e\left(\frac{50}{81}\right)$	$e\left(\frac{5}{81}\right)$	$e\left(\frac{47}{162}\right)$
$\chi_{3888}(83,\cdot)$	3888.ch	324	yes	$1$	$1$	$e\left(\frac{73}{324}\right)$	$e\left(\frac{8}{81}\right)$	$e\left(\frac{215}{324}\right)$	$e\left(\frac{205}{324}\right)$	$e\left(\frac{11}{54}\right)$	$e\left(\frac{77}{108}\right)$	$e\left(\frac{119}{162}\right)$	$e\left(\frac{73}{162}\right)$	$e\left(\frac{47}{324}\right)$	$e\left(\frac{155}{162}\right)$
$\chi_{3888}(85,\cdot)$	3888.ce	324	yes	$1$	$1$	$e\left(\frac{65}{324}\right)$	$e\left(\frac{113}{162}\right)$	$e\left(\frac{25}{324}\right)$	$e\left(\frac{167}{324}\right)$	$e\left(\frac{11}{27}\right)$	$e\left(\frac{73}{108}\right)$	$e\left(\frac{157}{162}\right)$	$e\left(\frac{65}{162}\right)$	$e\left(\frac{175}{324}\right)$	$e\left(\frac{74}{81}\right)$
$\chi_{3888}(89,\cdot)$	3888.bl	54	no	$-1$	$1$	$e\left(\frac{7}{27}\right)$	$e\left(\frac{26}{27}\right)$	$e\left(\frac{11}{27}\right)$	$e\left(\frac{53}{54}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{29}{54}\right)$	$e\left(\frac{14}{27}\right)$	$e\left(\frac{23}{27}\right)$	$e\left(\frac{19}{27}\right)$
$\chi_{3888}(91,\cdot)$	3888.bu	108	no	$-1$	$1$	$e\left(\frac{35}{108}\right)$	$e\left(\frac{19}{27}\right)$	$e\left(\frac{1}{108}\right)$	$e\left(\frac{65}{108}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{8}{27}\right)$	$e\left(\frac{35}{54}\right)$	$e\left(\frac{61}{108}\right)$	$e\left(\frac{7}{54}\right)$
$\chi_{3888}(95,\cdot)$	3888.cc	162	no	$1$	$1$	$e\left(\frac{67}{162}\right)$	$e\left(\frac{137}{162}\right)$	$e\left(\frac{16}{81}\right)$	$e\left(\frac{68}{81}\right)$	$e\left(\frac{25}{54}\right)$	$e\left(\frac{47}{54}\right)$	$e\left(\frac{26}{81}\right)$	$e\left(\frac{67}{81}\right)$	$e\left(\frac{143}{162}\right)$	$e\left(\frac{97}{162}\right)$

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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	$3888$
Structure	\(C_{2}\times C_{2}\times C_{324}\)
Order	$1296$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)
\(\chi_{3888}(1,\cdot)\)	3888.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{3888}(5,\cdot)\)	3888.cg	324	yes	\(-1\)	\(1\)	\(e\left(\frac{167}{324}\right)\)	\(e\left(\frac{71}{162}\right)\)	\(e\left(\frac{139}{324}\right)\)	\(e\left(\frac{287}{324}\right)\)	\(e\left(\frac{37}{54}\right)\)	\(e\left(\frac{97}{108}\right)\)	\(e\left(\frac{59}{81}\right)\)	\(e\left(\frac{5}{162}\right)\)	\(e\left(\frac{1}{324}\right)\)	\(e\left(\frac{68}{81}\right)\)
\(\chi_{3888}(7,\cdot)\)	3888.bx	162	no	\(-1\)	\(1\)	\(e\left(\frac{71}{162}\right)\)	\(e\left(\frac{121}{162}\right)\)	\(e\left(\frac{23}{81}\right)\)	\(e\left(\frac{155}{162}\right)\)	\(e\left(\frac{7}{27}\right)\)	\(e\left(\frac{11}{27}\right)\)	\(e\left(\frac{95}{162}\right)\)	\(e\left(\frac{71}{81}\right)\)	\(e\left(\frac{79}{162}\right)\)	\(e\left(\frac{23}{162}\right)\)
\(\chi_{3888}(11,\cdot)\)	3888.ch	324	yes	\(1\)	\(1\)	\(e\left(\frac{139}{324}\right)\)	\(e\left(\frac{23}{81}\right)\)	\(e\left(\frac{41}{324}\right)\)	\(e\left(\frac{235}{324}\right)\)	\(e\left(\frac{35}{54}\right)\)	\(e\left(\frac{83}{108}\right)\)	\(e\left(\frac{89}{162}\right)\)	\(e\left(\frac{139}{162}\right)\)	\(e\left(\frac{125}{324}\right)\)	\(e\left(\frac{71}{162}\right)\)
\(\chi_{3888}(13,\cdot)\)	3888.ce	324	yes	\(1\)	\(1\)	\(e\left(\frac{287}{324}\right)\)	\(e\left(\frac{155}{162}\right)\)	\(e\left(\frac{235}{324}\right)\)	\(e\left(\frac{209}{324}\right)\)	\(e\left(\frac{17}{27}\right)\)	\(e\left(\frac{103}{108}\right)\)	\(e\left(\frac{115}{162}\right)\)	\(e\left(\frac{125}{162}\right)\)	\(e\left(\frac{25}{324}\right)\)	\(e\left(\frac{80}{81}\right)\)
\(\chi_{3888}(17,\cdot)\)	3888.bo	54	no	\(-1\)	\(1\)	\(e\left(\frac{37}{54}\right)\)	\(e\left(\frac{7}{27}\right)\)	\(e\left(\frac{35}{54}\right)\)	\(e\left(\frac{17}{27}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{13}{54}\right)\)	\(e\left(\frac{10}{27}\right)\)	\(e\left(\frac{29}{54}\right)\)	\(e\left(\frac{2}{27}\right)\)
\(\chi_{3888}(19,\cdot)\)	3888.bu	108	no	\(-1\)	\(1\)	\(e\left(\frac{97}{108}\right)\)	\(e\left(\frac{11}{27}\right)\)	\(e\left(\frac{83}{108}\right)\)	\(e\left(\frac{103}{108}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{16}{27}\right)\)	\(e\left(\frac{43}{54}\right)\)	\(e\left(\frac{95}{108}\right)\)	\(e\left(\frac{41}{54}\right)\)
\(\chi_{3888}(23,\cdot)\)	3888.cb	162	no	\(1\)	\(1\)	\(e\left(\frac{59}{81}\right)\)	\(e\left(\frac{95}{162}\right)\)	\(e\left(\frac{89}{162}\right)\)	\(e\left(\frac{115}{162}\right)\)	\(e\left(\frac{13}{54}\right)\)	\(e\left(\frac{16}{27}\right)\)	\(e\left(\frac{47}{81}\right)\)	\(e\left(\frac{37}{81}\right)\)	\(e\left(\frac{28}{81}\right)\)	\(e\left(\frac{85}{162}\right)\)
\(\chi_{3888}(25,\cdot)\)	3888.bz	162	no	\(1\)	\(1\)	\(e\left(\frac{5}{162}\right)\)	\(e\left(\frac{71}{81}\right)\)	\(e\left(\frac{139}{162}\right)\)	\(e\left(\frac{125}{162}\right)\)	\(e\left(\frac{10}{27}\right)\)	\(e\left(\frac{43}{54}\right)\)	\(e\left(\frac{37}{81}\right)\)	\(e\left(\frac{5}{81}\right)\)	\(e\left(\frac{1}{162}\right)\)	\(e\left(\frac{55}{81}\right)\)
\(\chi_{3888}(29,\cdot)\)	3888.cg	324	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{324}\right)\)	\(e\left(\frac{79}{162}\right)\)	\(e\left(\frac{125}{324}\right)\)	\(e\left(\frac{25}{324}\right)\)	\(e\left(\frac{29}{54}\right)\)	\(e\left(\frac{95}{108}\right)\)	\(e\left(\frac{28}{81}\right)\)	\(e\left(\frac{1}{162}\right)\)	\(e\left(\frac{227}{324}\right)\)	\(e\left(\frac{46}{81}\right)\)
\(\chi_{3888}(31,\cdot)\)	3888.by	162	no	\(-1\)	\(1\)	\(e\left(\frac{68}{81}\right)\)	\(e\left(\frac{23}{162}\right)\)	\(e\left(\frac{71}{162}\right)\)	\(e\left(\frac{80}{81}\right)\)	\(e\left(\frac{2}{27}\right)\)	\(e\left(\frac{41}{54}\right)\)	\(e\left(\frac{85}{162}\right)\)	\(e\left(\frac{55}{81}\right)\)	\(e\left(\frac{46}{81}\right)\)	\(e\left(\frac{157}{162}\right)\)
\(\chi_{3888}(35,\cdot)\)	3888.bt	108	no	\(1\)	\(1\)	\(e\left(\frac{103}{108}\right)\)	\(e\left(\frac{5}{27}\right)\)	\(e\left(\frac{77}{108}\right)\)	\(e\left(\frac{91}{108}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{17}{54}\right)\)	\(e\left(\frac{49}{54}\right)\)	\(e\left(\frac{53}{108}\right)\)	\(e\left(\frac{53}{54}\right)\)
\(\chi_{3888}(37,\cdot)\)	3888.bw	108	no	\(1\)	\(1\)	\(e\left(\frac{95}{108}\right)\)	\(e\left(\frac{53}{54}\right)\)	\(e\left(\frac{103}{108}\right)\)	\(e\left(\frac{53}{108}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{1}{54}\right)\)	\(e\left(\frac{41}{54}\right)\)	\(e\left(\frac{73}{108}\right)\)	\(e\left(\frac{23}{27}\right)\)
\(\chi_{3888}(41,\cdot)\)	3888.cd	162	no	\(-1\)	\(1\)	\(e\left(\frac{2}{81}\right)\)	\(e\left(\frac{73}{81}\right)\)	\(e\left(\frac{7}{81}\right)\)	\(e\left(\frac{19}{162}\right)\)	\(e\left(\frac{43}{54}\right)\)	\(e\left(\frac{29}{54}\right)\)	\(e\left(\frac{43}{162}\right)\)	\(e\left(\frac{4}{81}\right)\)	\(e\left(\frac{49}{81}\right)\)	\(e\left(\frac{44}{81}\right)\)
\(\chi_{3888}(43,\cdot)\)	3888.cf	324	yes	\(-1\)	\(1\)	\(e\left(\frac{229}{324}\right)\)	\(e\left(\frac{14}{81}\right)\)	\(e\left(\frac{275}{324}\right)\)	\(e\left(\frac{55}{324}\right)\)	\(e\left(\frac{13}{27}\right)\)	\(e\left(\frac{47}{108}\right)\)	\(e\left(\frac{13}{81}\right)\)	\(e\left(\frac{67}{162}\right)\)	\(e\left(\frac{143}{324}\right)\)	\(e\left(\frac{89}{162}\right)\)
\(\chi_{3888}(47,\cdot)\)	3888.cc	162	no	\(1\)	\(1\)	\(e\left(\frac{107}{162}\right)\)	\(e\left(\frac{139}{162}\right)\)	\(e\left(\frac{5}{81}\right)\)	\(e\left(\frac{1}{81}\right)\)	\(e\left(\frac{23}{54}\right)\)	\(e\left(\frac{13}{54}\right)\)	\(e\left(\frac{79}{81}\right)\)	\(e\left(\frac{26}{81}\right)\)	\(e\left(\frac{151}{162}\right)\)	\(e\left(\frac{5}{162}\right)\)
\(\chi_{3888}(49,\cdot)\)	3888.bs	81	no	\(1\)	\(1\)	\(e\left(\frac{71}{81}\right)\)	\(e\left(\frac{40}{81}\right)\)	\(e\left(\frac{46}{81}\right)\)	\(e\left(\frac{74}{81}\right)\)	\(e\left(\frac{14}{27}\right)\)	\(e\left(\frac{22}{27}\right)\)	\(e\left(\frac{14}{81}\right)\)	\(e\left(\frac{61}{81}\right)\)	\(e\left(\frac{79}{81}\right)\)	\(e\left(\frac{23}{81}\right)\)
\(\chi_{3888}(53,\cdot)\)	3888.bj	36	no	\(-1\)	\(1\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{2}{9}\right)\)
\(\chi_{3888}(55,\cdot)\)	3888.z	18	no	\(-1\)	\(1\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{5}{18}\right)\)
\(\chi_{3888}(59,\cdot)\)	3888.ch	324	yes	\(1\)	\(1\)	\(e\left(\frac{131}{324}\right)\)	\(e\left(\frac{31}{81}\right)\)	\(e\left(\frac{13}{324}\right)\)	\(e\left(\frac{35}{324}\right)\)	\(e\left(\frac{19}{54}\right)\)	\(e\left(\frac{79}{108}\right)\)	\(e\left(\frac{127}{162}\right)\)	\(e\left(\frac{131}{162}\right)\)	\(e\left(\frac{253}{324}\right)\)	\(e\left(\frac{145}{162}\right)\)
\(\chi_{3888}(61,\cdot)\)	3888.ce	324	yes	\(1\)	\(1\)	\(e\left(\frac{151}{324}\right)\)	\(e\left(\frac{103}{162}\right)\)	\(e\left(\frac{83}{324}\right)\)	\(e\left(\frac{49}{324}\right)\)	\(e\left(\frac{16}{27}\right)\)	\(e\left(\frac{35}{108}\right)\)	\(e\left(\frac{113}{162}\right)\)	\(e\left(\frac{151}{162}\right)\)	\(e\left(\frac{257}{324}\right)\)	\(e\left(\frac{61}{81}\right)\)
\(\chi_{3888}(65,\cdot)\)	3888.ca	162	no	\(-1\)	\(1\)	\(e\left(\frac{65}{162}\right)\)	\(e\left(\frac{32}{81}\right)\)	\(e\left(\frac{25}{162}\right)\)	\(e\left(\frac{43}{81}\right)\)	\(e\left(\frac{17}{54}\right)\)	\(e\left(\frac{23}{27}\right)\)	\(e\left(\frac{71}{162}\right)\)	\(e\left(\frac{65}{81}\right)\)	\(e\left(\frac{13}{162}\right)\)	\(e\left(\frac{67}{81}\right)\)
\(\chi_{3888}(67,\cdot)\)	3888.cf	324	yes	\(-1\)	\(1\)	\(e\left(\frac{323}{324}\right)\)	\(e\left(\frac{1}{81}\right)\)	\(e\left(\frac{37}{324}\right)\)	\(e\left(\frac{137}{324}\right)\)	\(e\left(\frac{26}{27}\right)\)	\(e\left(\frac{13}{108}\right)\)	\(e\left(\frac{53}{81}\right)\)	\(e\left(\frac{161}{162}\right)\)	\(e\left(\frac{97}{324}\right)\)	\(e\left(\frac{151}{162}\right)\)
\(\chi_{3888}(71,\cdot)\)	3888.bn	54	no	\(1\)	\(1\)	\(e\left(\frac{20}{27}\right)\)	\(e\left(\frac{29}{54}\right)\)	\(e\left(\frac{5}{54}\right)\)	\(e\left(\frac{1}{54}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{26}{27}\right)\)	\(e\left(\frac{13}{27}\right)\)	\(e\left(\frac{4}{27}\right)\)	\(e\left(\frac{43}{54}\right)\)
\(\chi_{3888}(73,\cdot)\)	3888.bp	54	no	\(1\)	\(1\)	\(e\left(\frac{5}{54}\right)\)	\(e\left(\frac{17}{27}\right)\)	\(e\left(\frac{31}{54}\right)\)	\(e\left(\frac{17}{54}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{10}{27}\right)\)	\(e\left(\frac{5}{27}\right)\)	\(e\left(\frac{1}{54}\right)\)	\(e\left(\frac{1}{27}\right)\)
\(\chi_{3888}(77,\cdot)\)	3888.cg	324	yes	\(-1\)	\(1\)	\(e\left(\frac{281}{324}\right)\)	\(e\left(\frac{5}{162}\right)\)	\(e\left(\frac{133}{324}\right)\)	\(e\left(\frac{221}{324}\right)\)	\(e\left(\frac{49}{54}\right)\)	\(e\left(\frac{19}{108}\right)\)	\(e\left(\frac{11}{81}\right)\)	\(e\left(\frac{119}{162}\right)\)	\(e\left(\frac{283}{324}\right)\)	\(e\left(\frac{47}{81}\right)\)
\(\chi_{3888}(79,\cdot)\)	3888.by	162	no	\(-1\)	\(1\)	\(e\left(\frac{25}{81}\right)\)	\(e\left(\frac{43}{162}\right)\)	\(e\left(\frac{13}{162}\right)\)	\(e\left(\frac{58}{81}\right)\)	\(e\left(\frac{19}{27}\right)\)	\(e\left(\frac{25}{54}\right)\)	\(e\left(\frac{11}{162}\right)\)	\(e\left(\frac{50}{81}\right)\)	\(e\left(\frac{5}{81}\right)\)	\(e\left(\frac{47}{162}\right)\)
\(\chi_{3888}(83,\cdot)\)	3888.ch	324	yes	\(1\)	\(1\)	\(e\left(\frac{73}{324}\right)\)	\(e\left(\frac{8}{81}\right)\)	\(e\left(\frac{215}{324}\right)\)	\(e\left(\frac{205}{324}\right)\)	\(e\left(\frac{11}{54}\right)\)	\(e\left(\frac{77}{108}\right)\)	\(e\left(\frac{119}{162}\right)\)	\(e\left(\frac{73}{162}\right)\)	\(e\left(\frac{47}{324}\right)\)	\(e\left(\frac{155}{162}\right)\)
\(\chi_{3888}(85,\cdot)\)	3888.ce	324	yes	\(1\)	\(1\)	\(e\left(\frac{65}{324}\right)\)	\(e\left(\frac{113}{162}\right)\)	\(e\left(\frac{25}{324}\right)\)	\(e\left(\frac{167}{324}\right)\)	\(e\left(\frac{11}{27}\right)\)	\(e\left(\frac{73}{108}\right)\)	\(e\left(\frac{157}{162}\right)\)	\(e\left(\frac{65}{162}\right)\)	\(e\left(\frac{175}{324}\right)\)	\(e\left(\frac{74}{81}\right)\)
\(\chi_{3888}(89,\cdot)\)	3888.bl	54	no	\(-1\)	\(1\)	\(e\left(\frac{7}{27}\right)\)	\(e\left(\frac{26}{27}\right)\)	\(e\left(\frac{11}{27}\right)\)	\(e\left(\frac{53}{54}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{29}{54}\right)\)	\(e\left(\frac{14}{27}\right)\)	\(e\left(\frac{23}{27}\right)\)	\(e\left(\frac{19}{27}\right)\)
\(\chi_{3888}(91,\cdot)\)	3888.bu	108	no	\(-1\)	\(1\)	\(e\left(\frac{35}{108}\right)\)	\(e\left(\frac{19}{27}\right)\)	\(e\left(\frac{1}{108}\right)\)	\(e\left(\frac{65}{108}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{8}{27}\right)\)	\(e\left(\frac{35}{54}\right)\)	\(e\left(\frac{61}{108}\right)\)	\(e\left(\frac{7}{54}\right)\)
\(\chi_{3888}(95,\cdot)\)	3888.cc	162	no	\(1\)	\(1\)	\(e\left(\frac{67}{162}\right)\)	\(e\left(\frac{137}{162}\right)\)	\(e\left(\frac{16}{81}\right)\)	\(e\left(\frac{68}{81}\right)\)	\(e\left(\frac{25}{54}\right)\)	\(e\left(\frac{47}{54}\right)\)	\(e\left(\frac{26}{81}\right)\)	\(e\left(\frac{67}{81}\right)\)	\(e\left(\frac{143}{162}\right)\)	\(e\left(\frac{97}{162}\right)\)

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L-functions

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Character group

First 32 of 1296 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.