LMFDB - Group of Dirichlet characters of modulus 1925

Show commands: PariGP / SageMath

sage: H = DirichletGroup(1925)

pari: g = idealstar(,1925,2)

Character group

sage: G.order() pari: g.no
Order	=	1200
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{10}\times C_{60}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{1925}(1002,\cdot)$, $\chi_{1925}(276,\cdot)$, $\chi_{1925}(1751,\cdot)$

First 32 of 1200 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	$-1$	$1$	$2$	$3$	$4$	$6$	$8$	$9$	$12$	$13$	$16$	$17$
$\chi_{1925}(1,\cdot)$	1925.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1925}(2,\cdot)$	1925.gc	60	yes	$1$	$1$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{53}{60}\right)$
$\chi_{1925}(3,\cdot)$	1925.fo	60	yes	$1$	$1$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{29}{30}\right)$	$-1$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{1925}(4,\cdot)$	1925.ef	30	yes	$1$	$1$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{23}{30}\right)$
$\chi_{1925}(6,\cdot)$	1925.bu	10	yes	$1$	$1$	$e\left(\frac{3}{10}\right)$	$-1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{9}{10}\right)$	$1$	$e\left(\frac{1}{10}\right)$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{1925}(8,\cdot)$	1925.dr	20	no	$1$	$1$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{13}{20}\right)$
$\chi_{1925}(9,\cdot)$	1925.ek	30	yes	$1$	$1$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{14}{15}\right)$	$1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{1925}(12,\cdot)$	1925.fz	60	no	$1$	$1$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{41}{60}\right)$
$\chi_{1925}(13,\cdot)$	1925.dx	20	yes	$-1$	$1$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{10}\right)$	$1$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{1}{5}\right)$	$-i$
$\chi_{1925}(16,\cdot)$	1925.cy	15	yes	$1$	$1$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{8}{15}\right)$
$\chi_{1925}(17,\cdot)$	1925.fw	60	yes	$-1$	$1$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{41}{60}\right)$	$-i$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{43}{60}\right)$
$\chi_{1925}(18,\cdot)$	1925.gd	60	no	$1$	$1$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{43}{60}\right)$
$\chi_{1925}(19,\cdot)$	1925.fg	30	yes	$1$	$1$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{7}{30}\right)$
$\chi_{1925}(23,\cdot)$	1925.fu	60	no	$-1$	$1$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{29}{60}\right)$
$\chi_{1925}(24,\cdot)$	1925.fe	30	no	$1$	$1$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{17}{30}\right)$
$\chi_{1925}(26,\cdot)$	1925.fd	30	no	$-1$	$1$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{19}{30}\right)$
$\chi_{1925}(27,\cdot)$	1925.df	20	yes	$1$	$1$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{9}{10}\right)$	$-1$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{4}{5}\right)$	$-i$
$\chi_{1925}(29,\cdot)$	1925.bo	10	no	$-1$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{1925}(31,\cdot)$	1925.dz	30	yes	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{10}\right)$	$1$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{23}{30}\right)$
$\chi_{1925}(32,\cdot)$	1925.cq	12	no	$1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$i$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{12}\right)$	$i$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{1925}(34,\cdot)$	1925.bx	10	no	$-1$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{1925}(36,\cdot)$	1925.r	5	no	$1$	$1$	$e\left(\frac{3}{5}\right)$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{4}{5}\right)$	$1$	$e\left(\frac{1}{5}\right)$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{1925}(37,\cdot)$	1925.fx	60	yes	$-1$	$1$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{43}{60}\right)$	$-i$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{59}{60}\right)$
$\chi_{1925}(38,\cdot)$	1925.gb	60	yes	$1$	$1$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{7}{60}\right)$
$\chi_{1925}(39,\cdot)$	1925.ew	30	yes	$-1$	$1$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{1}{15}\right)$	$-1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{1925}(41,\cdot)$	1925.bc	10	yes	$1$	$1$	$-1$	$e\left(\frac{3}{10}\right)$	$1$	$e\left(\frac{4}{5}\right)$	$-1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{5}\right)$	$1$	$e\left(\frac{4}{5}\right)$
$\chi_{1925}(43,\cdot)$	1925.k	4	no	$1$	$1$	$i$	$i$	$-1$	$-1$	$-i$	$-1$	$-i$	$-i$	$1$	$i$
$\chi_{1925}(46,\cdot)$	1925.eb	30	yes	$-1$	$1$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{15}\right)$	$-1$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{11}{30}\right)$
$\chi_{1925}(47,\cdot)$	1925.fo	60	yes	$1$	$1$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{19}{30}\right)$	$-1$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{12}\right)$
$\chi_{1925}(48,\cdot)$	1925.dd	20	yes	$1$	$1$	$-i$	$e\left(\frac{19}{20}\right)$	$-1$	$e\left(\frac{7}{10}\right)$	$i$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{3}{20}\right)$	$1$	$e\left(\frac{9}{20}\right)$
$\chi_{1925}(51,\cdot)$	1925.eo	30	no	$-1$	$1$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{19}{30}\right)$
$\chi_{1925}(52,\cdot)$	1925.fw	60	yes	$-1$	$1$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{17}{60}\right)$	$-i$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{31}{60}\right)$

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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	$1925$
Structure	\(C_{2}\times C_{10}\times C_{60}\)
Order	$1200$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(8\)	\(9\)	\(12\)	\(13\)	\(16\)	\(17\)
\(\chi_{1925}(1,\cdot)\)	1925.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1925}(2,\cdot)\)	1925.gc	60	yes	\(1\)	\(1\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{53}{60}\right)\)
\(\chi_{1925}(3,\cdot)\)	1925.fo	60	yes	\(1\)	\(1\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(-1\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{1925}(4,\cdot)\)	1925.ef	30	yes	\(1\)	\(1\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{23}{30}\right)\)
\(\chi_{1925}(6,\cdot)\)	1925.bu	10	yes	\(1\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(-1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{1925}(8,\cdot)\)	1925.dr	20	no	\(1\)	\(1\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{13}{20}\right)\)
\(\chi_{1925}(9,\cdot)\)	1925.ek	30	yes	\(1\)	\(1\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{1925}(12,\cdot)\)	1925.fz	60	no	\(1\)	\(1\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{41}{60}\right)\)
\(\chi_{1925}(13,\cdot)\)	1925.dx	20	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(1\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(-i\)
\(\chi_{1925}(16,\cdot)\)	1925.cy	15	yes	\(1\)	\(1\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)
\(\chi_{1925}(17,\cdot)\)	1925.fw	60	yes	\(-1\)	\(1\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(-i\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{43}{60}\right)\)
\(\chi_{1925}(18,\cdot)\)	1925.gd	60	no	\(1\)	\(1\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{43}{60}\right)\)
\(\chi_{1925}(19,\cdot)\)	1925.fg	30	yes	\(1\)	\(1\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{7}{30}\right)\)
\(\chi_{1925}(23,\cdot)\)	1925.fu	60	no	\(-1\)	\(1\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{29}{60}\right)\)
\(\chi_{1925}(24,\cdot)\)	1925.fe	30	no	\(1\)	\(1\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{17}{30}\right)\)
\(\chi_{1925}(26,\cdot)\)	1925.fd	30	no	\(-1\)	\(1\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{19}{30}\right)\)
\(\chi_{1925}(27,\cdot)\)	1925.df	20	yes	\(1\)	\(1\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(-1\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(-i\)
\(\chi_{1925}(29,\cdot)\)	1925.bo	10	no	\(-1\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{1925}(31,\cdot)\)	1925.dz	30	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(1\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{23}{30}\right)\)
\(\chi_{1925}(32,\cdot)\)	1925.cq	12	no	\(1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(i\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(i\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{1925}(34,\cdot)\)	1925.bx	10	no	\(-1\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{1925}(36,\cdot)\)	1925.r	5	no	\(1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{1925}(37,\cdot)\)	1925.fx	60	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(-i\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{59}{60}\right)\)
\(\chi_{1925}(38,\cdot)\)	1925.gb	60	yes	\(1\)	\(1\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{7}{60}\right)\)
\(\chi_{1925}(39,\cdot)\)	1925.ew	30	yes	\(-1\)	\(1\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(-1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{1925}(41,\cdot)\)	1925.bc	10	yes	\(1\)	\(1\)	\(-1\)	\(e\left(\frac{3}{10}\right)\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(-1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(1\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{1925}(43,\cdot)\)	1925.k	4	no	\(1\)	\(1\)	\(i\)	\(i\)	\(-1\)	\(-1\)	\(-i\)	\(-1\)	\(-i\)	\(-i\)	\(1\)	\(i\)
\(\chi_{1925}(46,\cdot)\)	1925.eb	30	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(-1\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{11}{30}\right)\)
\(\chi_{1925}(47,\cdot)\)	1925.fo	60	yes	\(1\)	\(1\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(-1\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{1925}(48,\cdot)\)	1925.dd	20	yes	\(1\)	\(1\)	\(-i\)	\(e\left(\frac{19}{20}\right)\)	\(-1\)	\(e\left(\frac{7}{10}\right)\)	\(i\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(1\)	\(e\left(\frac{9}{20}\right)\)
\(\chi_{1925}(51,\cdot)\)	1925.eo	30	no	\(-1\)	\(1\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{19}{30}\right)\)
\(\chi_{1925}(52,\cdot)\)	1925.fw	60	yes	\(-1\)	\(1\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(-i\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{31}{60}\right)\)

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L-functions

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.