LMFDB - Group of Dirichlet characters of modulus 925

sage:H = DirichletGroup(925)

pari:g = idealstar(,925,2)

Character group

sage:G.order() pari:g.no
Order	=	720
sage:H.invariants() pari:g.cyc
Structure	=	$C_{4}\times C_{180}$
sage:H.gens() pari:g.gen
Generators	=	$\chi_{925}(852,\cdot)$, $\chi_{925}(76,\cdot)$

First 32 of 720 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	$-1$	$1$	$2$	$3$	$4$	$6$	$7$	$8$	$9$	$11$	$12$	$13$
$\chi_{925}(1,\cdot)$	925.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{925}(2,\cdot)$	925.cd	180	yes	$1$	$1$	$e\left(\frac{7}{90}\right)$	$e\left(\frac{13}{180}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{41}{180}\right)$	$e\left(\frac{23}{90}\right)$
$\chi_{925}(3,\cdot)$	925.ch	180	yes	$-1$	$1$	$e\left(\frac{13}{180}\right)$	$e\left(\frac{41}{180}\right)$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{67}{180}\right)$	$e\left(\frac{107}{180}\right)$
$\chi_{925}(4,\cdot)$	925.cb	90	yes	$1$	$1$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{23}{45}\right)$
$\chi_{925}(6,\cdot)$	925.bh	20	yes	$-1$	$1$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{9}{20}\right)$	$1$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{17}{20}\right)$
$\chi_{925}(7,\cdot)$	925.br	36	no	$-1$	$1$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{5}{18}\right)$	$1$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{19}{36}\right)$
$\chi_{925}(8,\cdot)$	925.bt	60	yes	$1$	$1$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{23}{30}\right)$
$\chi_{925}(9,\cdot)$	925.bz	90	yes	$1$	$1$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{17}{90}\right)$
$\chi_{925}(11,\cdot)$	925.bk	30	yes	$1$	$1$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{11}{30}\right)$
$\chi_{925}(12,\cdot)$	925.cc	180	yes	$-1$	$1$	$e\left(\frac{41}{180}\right)$	$e\left(\frac{67}{180}\right)$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{149}{180}\right)$	$e\left(\frac{19}{180}\right)$
$\chi_{925}(13,\cdot)$	925.cd	180	yes	$1$	$1$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{107}{180}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{19}{180}\right)$	$e\left(\frac{37}{90}\right)$
$\chi_{925}(14,\cdot)$	925.bx	60	yes	$-1$	$1$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{47}{60}\right)$
$\chi_{925}(16,\cdot)$	925.bs	45	yes	$1$	$1$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{1}{45}\right)$
$\chi_{925}(17,\cdot)$	925.cg	180	yes	$1$	$1$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{109}{180}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{53}{180}\right)$	$e\left(\frac{22}{45}\right)$
$\chi_{925}(18,\cdot)$	925.bn	36	no	$1$	$1$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{4}{9}\right)$	$-i$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{4}{9}\right)$
$\chi_{925}(19,\cdot)$	925.cf	180	yes	$-1$	$1$	$e\left(\frac{157}{180}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{29}{90}\right)$	$e\left(\frac{143}{180}\right)$
$\chi_{925}(21,\cdot)$	925.ca	90	yes	$1$	$1$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{11}{90}\right)$
$\chi_{925}(22,\cdot)$	925.cg	180	yes	$1$	$1$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{61}{180}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{137}{180}\right)$	$e\left(\frac{28}{45}\right)$
$\chi_{925}(23,\cdot)$	925.bt	60	yes	$1$	$1$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{1}{30}\right)$
$\chi_{925}(24,\cdot)$	925.bo	36	no	$-1$	$1$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{11}{18}\right)$	$-i$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{13}{36}\right)$
$\chi_{925}(26,\cdot)$	925.e	3	no	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{925}(27,\cdot)$	925.bw	60	yes	$-1$	$1$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{47}{60}\right)$
$\chi_{925}(28,\cdot)$	925.ch	180	yes	$-1$	$1$	$e\left(\frac{53}{180}\right)$	$e\left(\frac{1}{180}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{1}{90}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{107}{180}\right)$	$e\left(\frac{7}{180}\right)$
$\chi_{925}(29,\cdot)$	925.bx	60	yes	$-1$	$1$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{19}{60}\right)$
$\chi_{925}(31,\cdot)$	925.bh	20	yes	$-1$	$1$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{19}{20}\right)$	$1$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{20}\right)$
$\chi_{925}(32,\cdot)$	925.bq	36	no	$1$	$1$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{7}{9}\right)$	$-i$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{5}{18}\right)$
$\chi_{925}(33,\cdot)$	925.cc	180	yes	$-1$	$1$	$e\left(\frac{127}{180}\right)$	$e\left(\frac{89}{180}\right)$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{163}{180}\right)$	$e\left(\frac{173}{180}\right)$
$\chi_{925}(34,\cdot)$	925.bz	90	yes	$1$	$1$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{67}{90}\right)$
$\chi_{925}(36,\cdot)$	925.r	10	yes	$1$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{9}{10}\right)$	$1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{925}(38,\cdot)$	925.bf	20	no	$-1$	$1$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{5}\right)$	$-i$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{1}{20}\right)$
$\chi_{925}(39,\cdot)$	925.cf	180	yes	$-1$	$1$	$e\left(\frac{59}{180}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{59}{90}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{1}{180}\right)$
$\chi_{925}(41,\cdot)$	925.ca	90	yes	$1$	$1$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{37}{90}\right)$

Click here to search among the remaining 688 characters.

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	$925$
Structure	\(C_{4}\times C_{180}\)
Order	$720$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(7\)	\(8\)	\(9\)	\(11\)	\(12\)	\(13\)
\(\chi_{925}(1,\cdot)\)	925.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{925}(2,\cdot)\)	925.cd	180	yes	\(1\)	\(1\)	\(e\left(\frac{7}{90}\right)\)	\(e\left(\frac{13}{180}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{13}{90}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{41}{180}\right)\)	\(e\left(\frac{23}{90}\right)\)
\(\chi_{925}(3,\cdot)\)	925.ch	180	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{180}\right)\)	\(e\left(\frac{41}{180}\right)\)	\(e\left(\frac{13}{90}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{41}{90}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{67}{180}\right)\)	\(e\left(\frac{107}{180}\right)\)
\(\chi_{925}(4,\cdot)\)	925.cb	90	yes	\(1\)	\(1\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{13}{90}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{41}{90}\right)\)	\(e\left(\frac{23}{45}\right)\)
\(\chi_{925}(6,\cdot)\)	925.bh	20	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(1\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{17}{20}\right)\)
\(\chi_{925}(7,\cdot)\)	925.br	36	no	\(-1\)	\(1\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(1\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{19}{36}\right)\)
\(\chi_{925}(8,\cdot)\)	925.bt	60	yes	\(1\)	\(1\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{23}{30}\right)\)
\(\chi_{925}(9,\cdot)\)	925.bz	90	yes	\(1\)	\(1\)	\(e\left(\frac{13}{90}\right)\)	\(e\left(\frac{41}{90}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{67}{90}\right)\)	\(e\left(\frac{17}{90}\right)\)
\(\chi_{925}(11,\cdot)\)	925.bk	30	yes	\(1\)	\(1\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{11}{30}\right)\)
\(\chi_{925}(12,\cdot)\)	925.cc	180	yes	\(-1\)	\(1\)	\(e\left(\frac{41}{180}\right)\)	\(e\left(\frac{67}{180}\right)\)	\(e\left(\frac{41}{90}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{67}{90}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{149}{180}\right)\)	\(e\left(\frac{19}{180}\right)\)
\(\chi_{925}(13,\cdot)\)	925.cd	180	yes	\(1\)	\(1\)	\(e\left(\frac{23}{90}\right)\)	\(e\left(\frac{107}{180}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{17}{90}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{19}{180}\right)\)	\(e\left(\frac{37}{90}\right)\)
\(\chi_{925}(14,\cdot)\)	925.bx	60	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{47}{60}\right)\)
\(\chi_{925}(16,\cdot)\)	925.bs	45	yes	\(1\)	\(1\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{1}{45}\right)\)
\(\chi_{925}(17,\cdot)\)	925.cg	180	yes	\(1\)	\(1\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{109}{180}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{53}{180}\right)\)	\(e\left(\frac{22}{45}\right)\)
\(\chi_{925}(18,\cdot)\)	925.bn	36	no	\(1\)	\(1\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(-i\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{4}{9}\right)\)
\(\chi_{925}(19,\cdot)\)	925.cf	180	yes	\(-1\)	\(1\)	\(e\left(\frac{157}{180}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{67}{90}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{29}{90}\right)\)	\(e\left(\frac{143}{180}\right)\)
\(\chi_{925}(21,\cdot)\)	925.ca	90	yes	\(1\)	\(1\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{11}{90}\right)\)
\(\chi_{925}(22,\cdot)\)	925.cg	180	yes	\(1\)	\(1\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{61}{180}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{61}{90}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{137}{180}\right)\)	\(e\left(\frac{28}{45}\right)\)
\(\chi_{925}(23,\cdot)\)	925.bt	60	yes	\(1\)	\(1\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{1}{30}\right)\)
\(\chi_{925}(24,\cdot)\)	925.bo	36	no	\(-1\)	\(1\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(-i\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{13}{36}\right)\)
\(\chi_{925}(26,\cdot)\)	925.e	3	no	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{925}(27,\cdot)\)	925.bw	60	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{47}{60}\right)\)
\(\chi_{925}(28,\cdot)\)	925.ch	180	yes	\(-1\)	\(1\)	\(e\left(\frac{53}{180}\right)\)	\(e\left(\frac{1}{180}\right)\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{1}{90}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{107}{180}\right)\)	\(e\left(\frac{7}{180}\right)\)
\(\chi_{925}(29,\cdot)\)	925.bx	60	yes	\(-1\)	\(1\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{19}{60}\right)\)
\(\chi_{925}(31,\cdot)\)	925.bh	20	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(1\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{20}\right)\)
\(\chi_{925}(32,\cdot)\)	925.bq	36	no	\(1\)	\(1\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(-i\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{5}{18}\right)\)
\(\chi_{925}(33,\cdot)\)	925.cc	180	yes	\(-1\)	\(1\)	\(e\left(\frac{127}{180}\right)\)	\(e\left(\frac{89}{180}\right)\)	\(e\left(\frac{37}{90}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{89}{90}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{163}{180}\right)\)	\(e\left(\frac{173}{180}\right)\)
\(\chi_{925}(34,\cdot)\)	925.bz	90	yes	\(1\)	\(1\)	\(e\left(\frac{83}{90}\right)\)	\(e\left(\frac{61}{90}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{47}{90}\right)\)	\(e\left(\frac{67}{90}\right)\)
\(\chi_{925}(36,\cdot)\)	925.r	10	yes	\(1\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{925}(38,\cdot)\)	925.bf	20	no	\(-1\)	\(1\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(-i\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)
\(\chi_{925}(39,\cdot)\)	925.cf	180	yes	\(-1\)	\(1\)	\(e\left(\frac{59}{180}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{59}{90}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{43}{90}\right)\)	\(e\left(\frac{1}{180}\right)\)
\(\chi_{925}(41,\cdot)\)	925.ca	90	yes	\(1\)	\(1\)	\(e\left(\frac{23}{90}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{37}{90}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Learn more

Character group

First 32 of 720 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.