LMFDB - Dirichlet character orbit 925.ch

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(925, base_ring=CyclotomicField(180)) M = H._module chi = DirichletCharacter(H, M([63,130])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(3,925)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$925$
Conductor:	$925$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$180$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)

Related number fields

Field of values:	$\Q(\zeta_{180})$
Fixed field:	Number field defined by a degree 180 polynomial (not computed)

First 31 of 48 characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$6$	$7$	$8$	$9$	$11$	$12$	$13$
$\chi_{925}(3,\cdot)$	$-1$	$1$	$e\left(\frac{13}{180}\right)$	$e\left(\frac{41}{180}\right)$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{67}{180}\right)$	$e\left(\frac{107}{180}\right)$
$\chi_{925}(28,\cdot)$	$-1$	$1$	$e\left(\frac{53}{180}\right)$	$e\left(\frac{1}{180}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{1}{90}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{107}{180}\right)$	$e\left(\frac{7}{180}\right)$
$\chi_{925}(58,\cdot)$	$-1$	$1$	$e\left(\frac{137}{180}\right)$	$e\left(\frac{169}{180}\right)$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{79}{90}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{83}{180}\right)$	$e\left(\frac{103}{180}\right)$
$\chi_{925}(62,\cdot)$	$-1$	$1$	$e\left(\frac{131}{180}\right)$	$e\left(\frac{67}{180}\right)$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{149}{180}\right)$	$e\left(\frac{109}{180}\right)$
$\chi_{925}(67,\cdot)$	$-1$	$1$	$e\left(\frac{7}{180}\right)$	$e\left(\frac{119}{180}\right)$	$e\left(\frac{7}{90}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{29}{90}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{133}{180}\right)$	$e\left(\frac{113}{180}\right)$
$\chi_{925}(77,\cdot)$	$-1$	$1$	$e\left(\frac{139}{180}\right)$	$e\left(\frac{23}{180}\right)$	$e\left(\frac{49}{90}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{121}{180}\right)$	$e\left(\frac{161}{180}\right)$
$\chi_{925}(78,\cdot)$	$-1$	$1$	$e\left(\frac{73}{180}\right)$	$e\left(\frac{161}{180}\right)$	$e\left(\frac{73}{90}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{71}{90}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{127}{180}\right)$	$e\left(\frac{47}{180}\right)$
$\chi_{925}(102,\cdot)$	$-1$	$1$	$e\left(\frac{179}{180}\right)$	$e\left(\frac{163}{180}\right)$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{73}{90}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{161}{180}\right)$	$e\left(\frac{61}{180}\right)$
$\chi_{925}(152,\cdot)$	$-1$	$1$	$e\left(\frac{19}{180}\right)$	$e\left(\frac{143}{180}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{1}{180}\right)$	$e\left(\frac{101}{180}\right)$
$\chi_{925}(173,\cdot)$	$-1$	$1$	$e\left(\frac{149}{180}\right)$	$e\left(\frac{13}{180}\right)$	$e\left(\frac{59}{90}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{131}{180}\right)$	$e\left(\frac{91}{180}\right)$
$\chi_{925}(178,\cdot)$	$-1$	$1$	$e\left(\frac{133}{180}\right)$	$e\left(\frac{101}{180}\right)$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{7}{180}\right)$	$e\left(\frac{167}{180}\right)$
$\chi_{925}(188,\cdot)$	$-1$	$1$	$e\left(\frac{121}{180}\right)$	$e\left(\frac{77}{180}\right)$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{77}{90}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{139}{180}\right)$	$e\left(\frac{179}{180}\right)$
$\chi_{925}(213,\cdot)$	$-1$	$1$	$e\left(\frac{161}{180}\right)$	$e\left(\frac{37}{180}\right)$	$e\left(\frac{71}{90}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{179}{180}\right)$	$e\left(\frac{79}{180}\right)$
$\chi_{925}(247,\cdot)$	$-1$	$1$	$e\left(\frac{23}{180}\right)$	$e\left(\frac{31}{180}\right)$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{77}{180}\right)$	$e\left(\frac{37}{180}\right)$
$\chi_{925}(252,\cdot)$	$-1$	$1$	$e\left(\frac{79}{180}\right)$	$e\left(\frac{83}{180}\right)$	$e\left(\frac{79}{90}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{61}{180}\right)$	$e\left(\frac{41}{180}\right)$
$\chi_{925}(262,\cdot)$	$-1$	$1$	$e\left(\frac{31}{180}\right)$	$e\left(\frac{167}{180}\right)$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{77}{90}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{49}{180}\right)$	$e\left(\frac{89}{180}\right)$
$\chi_{925}(263,\cdot)$	$-1$	$1$	$e\left(\frac{1}{180}\right)$	$e\left(\frac{17}{180}\right)$	$e\left(\frac{1}{90}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{19}{180}\right)$	$e\left(\frac{119}{180}\right)$
$\chi_{925}(287,\cdot)$	$-1$	$1$	$e\left(\frac{71}{180}\right)$	$e\left(\frac{127}{180}\right)$	$e\left(\frac{71}{90}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{89}{180}\right)$	$e\left(\frac{169}{180}\right)$
$\chi_{925}(317,\cdot)$	$-1$	$1$	$e\left(\frac{47}{180}\right)$	$e\left(\frac{79}{180}\right)$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{79}{90}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{173}{180}\right)$	$e\left(\frac{13}{180}\right)$
$\chi_{925}(337,\cdot)$	$-1$	$1$	$e\left(\frac{91}{180}\right)$	$e\left(\frac{107}{180}\right)$	$e\left(\frac{1}{90}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{109}{180}\right)$	$e\left(\frac{29}{180}\right)$
$\chi_{925}(358,\cdot)$	$-1$	$1$	$e\left(\frac{77}{180}\right)$	$e\left(\frac{49}{180}\right)$	$e\left(\frac{77}{90}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{49}{90}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{23}{180}\right)$	$e\left(\frac{163}{180}\right)$
$\chi_{925}(363,\cdot)$	$-1$	$1$	$e\left(\frac{61}{180}\right)$	$e\left(\frac{137}{180}\right)$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{79}{180}\right)$	$e\left(\frac{59}{180}\right)$
$\chi_{925}(373,\cdot)$	$-1$	$1$	$e\left(\frac{49}{180}\right)$	$e\left(\frac{113}{180}\right)$	$e\left(\frac{49}{90}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{31}{180}\right)$	$e\left(\frac{71}{180}\right)$
$\chi_{925}(398,\cdot)$	$-1$	$1$	$e\left(\frac{89}{180}\right)$	$e\left(\frac{73}{180}\right)$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{73}{90}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{71}{180}\right)$	$e\left(\frac{151}{180}\right)$
$\chi_{925}(428,\cdot)$	$-1$	$1$	$e\left(\frac{173}{180}\right)$	$e\left(\frac{61}{180}\right)$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{47}{180}\right)$	$e\left(\frac{67}{180}\right)$
$\chi_{925}(437,\cdot)$	$-1$	$1$	$e\left(\frac{151}{180}\right)$	$e\left(\frac{47}{180}\right)$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{169}{180}\right)$	$e\left(\frac{149}{180}\right)$
$\chi_{925}(447,\cdot)$	$-1$	$1$	$e\left(\frac{103}{180}\right)$	$e\left(\frac{131}{180}\right)$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{157}{180}\right)$	$e\left(\frac{17}{180}\right)$
$\chi_{925}(448,\cdot)$	$-1$	$1$	$e\left(\frac{109}{180}\right)$	$e\left(\frac{53}{180}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{91}{180}\right)$	$e\left(\frac{11}{180}\right)$
$\chi_{925}(472,\cdot)$	$-1$	$1$	$e\left(\frac{143}{180}\right)$	$e\left(\frac{91}{180}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{1}{90}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{17}{180}\right)$	$e\left(\frac{97}{180}\right)$
$\chi_{925}(502,\cdot)$	$-1$	$1$	$e\left(\frac{119}{180}\right)$	$e\left(\frac{43}{180}\right)$	$e\left(\frac{29}{90}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{101}{180}\right)$	$e\left(\frac{121}{180}\right)$
$\chi_{925}(522,\cdot)$	$-1$	$1$	$e\left(\frac{163}{180}\right)$	$e\left(\frac{71}{180}\right)$	$e\left(\frac{73}{90}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{71}{90}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{37}{180}\right)$	$e\left(\frac{137}{180}\right)$

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

Character	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(7\)	\(8\)	\(9\)	\(11\)	\(12\)	\(13\)
\(\chi_{925}(3,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{13}{180}\right)\)	\(e\left(\frac{41}{180}\right)\)	\(e\left(\frac{13}{90}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{41}{90}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{67}{180}\right)\)	\(e\left(\frac{107}{180}\right)\)
\(\chi_{925}(28,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{53}{180}\right)\)	\(e\left(\frac{1}{180}\right)\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{1}{90}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{107}{180}\right)\)	\(e\left(\frac{7}{180}\right)\)
\(\chi_{925}(58,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{137}{180}\right)\)	\(e\left(\frac{169}{180}\right)\)	\(e\left(\frac{47}{90}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{79}{90}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{83}{180}\right)\)	\(e\left(\frac{103}{180}\right)\)
\(\chi_{925}(62,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{131}{180}\right)\)	\(e\left(\frac{67}{180}\right)\)	\(e\left(\frac{41}{90}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{67}{90}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{149}{180}\right)\)	\(e\left(\frac{109}{180}\right)\)
\(\chi_{925}(67,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{7}{180}\right)\)	\(e\left(\frac{119}{180}\right)\)	\(e\left(\frac{7}{90}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{29}{90}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{133}{180}\right)\)	\(e\left(\frac{113}{180}\right)\)
\(\chi_{925}(77,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{139}{180}\right)\)	\(e\left(\frac{23}{180}\right)\)	\(e\left(\frac{49}{90}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{23}{90}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{121}{180}\right)\)	\(e\left(\frac{161}{180}\right)\)
\(\chi_{925}(78,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{73}{180}\right)\)	\(e\left(\frac{161}{180}\right)\)	\(e\left(\frac{73}{90}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{71}{90}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{127}{180}\right)\)	\(e\left(\frac{47}{180}\right)\)
\(\chi_{925}(102,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{179}{180}\right)\)	\(e\left(\frac{163}{180}\right)\)	\(e\left(\frac{89}{90}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{73}{90}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{161}{180}\right)\)	\(e\left(\frac{61}{180}\right)\)
\(\chi_{925}(152,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{19}{180}\right)\)	\(e\left(\frac{143}{180}\right)\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{1}{180}\right)\)	\(e\left(\frac{101}{180}\right)\)
\(\chi_{925}(173,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{149}{180}\right)\)	\(e\left(\frac{13}{180}\right)\)	\(e\left(\frac{59}{90}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{13}{90}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{131}{180}\right)\)	\(e\left(\frac{91}{180}\right)\)
\(\chi_{925}(178,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{133}{180}\right)\)	\(e\left(\frac{101}{180}\right)\)	\(e\left(\frac{43}{90}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{11}{90}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{7}{180}\right)\)	\(e\left(\frac{167}{180}\right)\)
\(\chi_{925}(188,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{121}{180}\right)\)	\(e\left(\frac{77}{180}\right)\)	\(e\left(\frac{31}{90}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{77}{90}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{139}{180}\right)\)	\(e\left(\frac{179}{180}\right)\)
\(\chi_{925}(213,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{161}{180}\right)\)	\(e\left(\frac{37}{180}\right)\)	\(e\left(\frac{71}{90}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{37}{90}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{179}{180}\right)\)	\(e\left(\frac{79}{180}\right)\)
\(\chi_{925}(247,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{23}{180}\right)\)	\(e\left(\frac{31}{180}\right)\)	\(e\left(\frac{23}{90}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{31}{90}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{77}{180}\right)\)	\(e\left(\frac{37}{180}\right)\)
\(\chi_{925}(252,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{79}{180}\right)\)	\(e\left(\frac{83}{180}\right)\)	\(e\left(\frac{79}{90}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{83}{90}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{61}{180}\right)\)	\(e\left(\frac{41}{180}\right)\)
\(\chi_{925}(262,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{31}{180}\right)\)	\(e\left(\frac{167}{180}\right)\)	\(e\left(\frac{31}{90}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{77}{90}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{49}{180}\right)\)	\(e\left(\frac{89}{180}\right)\)
\(\chi_{925}(263,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{180}\right)\)	\(e\left(\frac{17}{180}\right)\)	\(e\left(\frac{1}{90}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{17}{90}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{19}{180}\right)\)	\(e\left(\frac{119}{180}\right)\)
\(\chi_{925}(287,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{71}{180}\right)\)	\(e\left(\frac{127}{180}\right)\)	\(e\left(\frac{71}{90}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{37}{90}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{89}{180}\right)\)	\(e\left(\frac{169}{180}\right)\)
\(\chi_{925}(317,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{47}{180}\right)\)	\(e\left(\frac{79}{180}\right)\)	\(e\left(\frac{47}{90}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{79}{90}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{173}{180}\right)\)	\(e\left(\frac{13}{180}\right)\)
\(\chi_{925}(337,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{91}{180}\right)\)	\(e\left(\frac{107}{180}\right)\)	\(e\left(\frac{1}{90}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{17}{90}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{109}{180}\right)\)	\(e\left(\frac{29}{180}\right)\)
\(\chi_{925}(358,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{77}{180}\right)\)	\(e\left(\frac{49}{180}\right)\)	\(e\left(\frac{77}{90}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{49}{90}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{23}{180}\right)\)	\(e\left(\frac{163}{180}\right)\)
\(\chi_{925}(363,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{61}{180}\right)\)	\(e\left(\frac{137}{180}\right)\)	\(e\left(\frac{61}{90}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{47}{90}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{79}{180}\right)\)	\(e\left(\frac{59}{180}\right)\)
\(\chi_{925}(373,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{49}{180}\right)\)	\(e\left(\frac{113}{180}\right)\)	\(e\left(\frac{49}{90}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{23}{90}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{31}{180}\right)\)	\(e\left(\frac{71}{180}\right)\)
\(\chi_{925}(398,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{89}{180}\right)\)	\(e\left(\frac{73}{180}\right)\)	\(e\left(\frac{89}{90}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{73}{90}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{71}{180}\right)\)	\(e\left(\frac{151}{180}\right)\)
\(\chi_{925}(428,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{173}{180}\right)\)	\(e\left(\frac{61}{180}\right)\)	\(e\left(\frac{83}{90}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{61}{90}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{47}{180}\right)\)	\(e\left(\frac{67}{180}\right)\)
\(\chi_{925}(437,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{151}{180}\right)\)	\(e\left(\frac{47}{180}\right)\)	\(e\left(\frac{61}{90}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{47}{90}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{169}{180}\right)\)	\(e\left(\frac{149}{180}\right)\)
\(\chi_{925}(447,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{103}{180}\right)\)	\(e\left(\frac{131}{180}\right)\)	\(e\left(\frac{13}{90}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{41}{90}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{157}{180}\right)\)	\(e\left(\frac{17}{180}\right)\)
\(\chi_{925}(448,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{109}{180}\right)\)	\(e\left(\frac{53}{180}\right)\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{91}{180}\right)\)	\(e\left(\frac{11}{180}\right)\)
\(\chi_{925}(472,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{143}{180}\right)\)	\(e\left(\frac{91}{180}\right)\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{1}{90}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{17}{180}\right)\)	\(e\left(\frac{97}{180}\right)\)
\(\chi_{925}(502,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{119}{180}\right)\)	\(e\left(\frac{43}{180}\right)\)	\(e\left(\frac{29}{90}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{43}{90}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{101}{180}\right)\)	\(e\left(\frac{121}{180}\right)\)
\(\chi_{925}(522,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{163}{180}\right)\)	\(e\left(\frac{71}{180}\right)\)	\(e\left(\frac{73}{90}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{71}{90}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{37}{180}\right)\)	\(e\left(\frac{137}{180}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Basic properties

Related number fields

First 31 of 48 characters in Galois orbit

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

Label	925.ch
Modulus	$925$
Conductor	$925$
Order	$180$
Real	no
Primitive	yes
Minimal	yes
Parity	odd

Modulus:	\(925\)
Conductor:	\(925\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(180\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)