LMFDB - Dirichlet character orbit 8925.lb

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8925, base_ring=CyclotomicField(240)) M = H._module chi = DirichletCharacter(H, M([0,228,160,15])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(88,8925)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$8925$
Conductor:	$2975$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$240$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 2975.fn	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)

Related number fields

Field of values:	$\Q(\zeta_{240})$
Fixed field:	Number field defined by a degree 240 polynomial (not computed)

First 31 of 64 characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$8$	$11$	$13$	$16$	$19$	$22$	$23$	$26$
$\chi_{8925}(88,\cdot)$	$1$	$1$	$e\left(\frac{19}{120}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{73}{240}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{37}{120}\right)$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{173}{240}\right)$	$e\left(\frac{11}{24}\right)$
$\chi_{8925}(142,\cdot)$	$1$	$1$	$e\left(\frac{53}{120}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{71}{240}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{59}{120}\right)$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{211}{240}\right)$	$e\left(\frac{13}{24}\right)$
$\chi_{8925}(403,\cdot)$	$1$	$1$	$e\left(\frac{7}{120}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{229}{240}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{1}{120}\right)$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{89}{240}\right)$	$e\left(\frac{23}{24}\right)$
$\chi_{8925}(487,\cdot)$	$1$	$1$	$e\left(\frac{109}{120}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{223}{240}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{67}{120}\right)$	$e\left(\frac{67}{80}\right)$	$e\left(\frac{203}{240}\right)$	$e\left(\frac{5}{24}\right)$
$\chi_{8925}(583,\cdot)$	$1$	$1$	$e\left(\frac{23}{120}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{221}{240}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{89}{120}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{1}{240}\right)$	$e\left(\frac{7}{24}\right)$
$\chi_{8925}(772,\cdot)$	$1$	$1$	$e\left(\frac{17}{120}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{179}{240}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{71}{120}\right)$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{79}{240}\right)$	$e\left(\frac{1}{24}\right)$
$\chi_{8925}(877,\cdot)$	$1$	$1$	$e\left(\frac{41}{120}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{107}{240}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{23}{120}\right)$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{7}{240}\right)$	$e\left(\frac{1}{24}\right)$
$\chi_{8925}(898,\cdot)$	$1$	$1$	$e\left(\frac{11}{120}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{17}{240}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{53}{120}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{37}{240}\right)$	$e\left(\frac{19}{24}\right)$
$\chi_{8925}(1108,\cdot)$	$1$	$1$	$e\left(\frac{83}{120}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{41}{240}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{29}{120}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{61}{240}\right)$	$e\left(\frac{19}{24}\right)$
$\chi_{8925}(1348,\cdot)$	$1$	$1$	$e\left(\frac{31}{120}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{157}{240}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{73}{120}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{17}{240}\right)$	$e\left(\frac{23}{24}\right)$
$\chi_{8925}(1423,\cdot)$	$1$	$1$	$e\left(\frac{71}{120}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{197}{240}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{113}{120}\right)$	$e\left(\frac{33}{80}\right)$	$e\left(\frac{217}{240}\right)$	$e\left(\frac{7}{24}\right)$
$\chi_{8925}(1537,\cdot)$	$1$	$1$	$e\left(\frac{49}{120}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{163}{240}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{7}{120}\right)$	$e\left(\frac{7}{80}\right)$	$e\left(\frac{143}{240}\right)$	$e\left(\frac{17}{24}\right)$
$\chi_{8925}(1642,\cdot)$	$1$	$1$	$e\left(\frac{73}{120}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{91}{240}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{79}{120}\right)$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{71}{240}\right)$	$e\left(\frac{17}{24}\right)$
$\chi_{8925}(1663,\cdot)$	$1$	$1$	$e\left(\frac{19}{120}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{193}{240}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{37}{120}\right)$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{53}{240}\right)$	$e\left(\frac{11}{24}\right)$
$\chi_{8925}(1873,\cdot)$	$1$	$1$	$e\left(\frac{91}{120}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{217}{240}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{13}{120}\right)$	$e\left(\frac{53}{80}\right)$	$e\left(\frac{77}{240}\right)$	$e\left(\frac{11}{24}\right)$
$\chi_{8925}(1927,\cdot)$	$1$	$1$	$e\left(\frac{101}{120}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{167}{240}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{83}{120}\right)$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{67}{240}\right)$	$e\left(\frac{13}{24}\right)$
$\chi_{8925}(2188,\cdot)$	$1$	$1$	$e\left(\frac{79}{120}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{133}{240}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{97}{120}\right)$	$e\left(\frac{17}{80}\right)$	$e\left(\frac{233}{240}\right)$	$e\left(\frac{23}{24}\right)$
$\chi_{8925}(2272,\cdot)$	$1$	$1$	$e\left(\frac{37}{120}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{79}{240}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{91}{120}\right)$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{59}{240}\right)$	$e\left(\frac{5}{24}\right)$
$\chi_{8925}(2662,\cdot)$	$1$	$1$	$e\left(\frac{89}{120}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{203}{240}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{47}{120}\right)$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{103}{240}\right)$	$e\left(\frac{1}{24}\right)$
$\chi_{8925}(2683,\cdot)$	$1$	$1$	$e\left(\frac{83}{120}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{161}{240}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{29}{120}\right)$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{181}{240}\right)$	$e\left(\frac{19}{24}\right)$
$\chi_{8925}(2692,\cdot)$	$1$	$1$	$e\left(\frac{13}{120}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{151}{240}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{19}{120}\right)$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{131}{240}\right)$	$e\left(\frac{5}{24}\right)$
$\chi_{8925}(3133,\cdot)$	$1$	$1$	$e\left(\frac{103}{120}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{61}{240}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{49}{120}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{161}{240}\right)$	$e\left(\frac{23}{24}\right)$
$\chi_{8925}(3208,\cdot)$	$1$	$1$	$e\left(\frac{23}{120}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{101}{240}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{89}{120}\right)$	$e\left(\frac{49}{80}\right)$	$e\left(\frac{121}{240}\right)$	$e\left(\frac{7}{24}\right)$
$\chi_{8925}(3292,\cdot)$	$1$	$1$	$e\left(\frac{53}{120}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{191}{240}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{59}{120}\right)$	$e\left(\frac{19}{80}\right)$	$e\left(\frac{91}{240}\right)$	$e\left(\frac{13}{24}\right)$
$\chi_{8925}(3322,\cdot)$	$1$	$1$	$e\left(\frac{97}{120}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{19}{240}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{31}{120}\right)$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{239}{240}\right)$	$e\left(\frac{17}{24}\right)$
$\chi_{8925}(3427,\cdot)$	$1$	$1$	$e\left(\frac{1}{120}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{187}{240}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{103}{120}\right)$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{167}{240}\right)$	$e\left(\frac{17}{24}\right)$
$\chi_{8925}(3448,\cdot)$	$1$	$1$	$e\left(\frac{91}{120}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{97}{240}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{13}{120}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{197}{240}\right)$	$e\left(\frac{11}{24}\right)$
$\chi_{8925}(3658,\cdot)$	$1$	$1$	$e\left(\frac{43}{120}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{121}{240}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{109}{120}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{221}{240}\right)$	$e\left(\frac{11}{24}\right)$
$\chi_{8925}(3712,\cdot)$	$1$	$1$	$e\left(\frac{29}{120}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{23}{240}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{107}{120}\right)$	$e\left(\frac{27}{80}\right)$	$e\left(\frac{163}{240}\right)$	$e\left(\frac{13}{24}\right)$
$\chi_{8925}(3973,\cdot)$	$1$	$1$	$e\left(\frac{31}{120}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{37}{240}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{73}{120}\right)$	$e\left(\frac{33}{80}\right)$	$e\left(\frac{137}{240}\right)$	$e\left(\frac{23}{24}\right)$
$\chi_{8925}(4153,\cdot)$	$1$	$1$	$e\left(\frac{47}{120}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{29}{240}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{41}{120}\right)$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{49}{240}\right)$	$e\left(\frac{7}{24}\right)$

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	\(-1\)	\(1\)	\(2\)	\(4\)	\(8\)	\(11\)	\(13\)	\(16\)	\(19\)	\(22\)	\(23\)	\(26\)
\(\chi_{8925}(88,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{120}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{73}{240}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{37}{120}\right)\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{173}{240}\right)\)	\(e\left(\frac{11}{24}\right)\)
\(\chi_{8925}(142,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{120}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{71}{240}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{59}{120}\right)\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{211}{240}\right)\)	\(e\left(\frac{13}{24}\right)\)
\(\chi_{8925}(403,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{120}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{229}{240}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{1}{120}\right)\)	\(e\left(\frac{1}{80}\right)\)	\(e\left(\frac{89}{240}\right)\)	\(e\left(\frac{23}{24}\right)\)
\(\chi_{8925}(487,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{109}{120}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{223}{240}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{67}{120}\right)\)	\(e\left(\frac{67}{80}\right)\)	\(e\left(\frac{203}{240}\right)\)	\(e\left(\frac{5}{24}\right)\)
\(\chi_{8925}(583,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{120}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{221}{240}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{89}{120}\right)\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{1}{240}\right)\)	\(e\left(\frac{7}{24}\right)\)
\(\chi_{8925}(772,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{120}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{179}{240}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{71}{120}\right)\)	\(e\left(\frac{71}{80}\right)\)	\(e\left(\frac{79}{240}\right)\)	\(e\left(\frac{1}{24}\right)\)
\(\chi_{8925}(877,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{120}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{107}{240}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{23}{120}\right)\)	\(e\left(\frac{63}{80}\right)\)	\(e\left(\frac{7}{240}\right)\)	\(e\left(\frac{1}{24}\right)\)
\(\chi_{8925}(898,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{120}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{17}{240}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{53}{120}\right)\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{37}{240}\right)\)	\(e\left(\frac{19}{24}\right)\)
\(\chi_{8925}(1108,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{83}{120}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{41}{240}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{29}{120}\right)\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{61}{240}\right)\)	\(e\left(\frac{19}{24}\right)\)
\(\chi_{8925}(1348,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{120}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{157}{240}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{73}{120}\right)\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{17}{240}\right)\)	\(e\left(\frac{23}{24}\right)\)
\(\chi_{8925}(1423,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{120}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{197}{240}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{113}{120}\right)\)	\(e\left(\frac{33}{80}\right)\)	\(e\left(\frac{217}{240}\right)\)	\(e\left(\frac{7}{24}\right)\)
\(\chi_{8925}(1537,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{120}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{163}{240}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{7}{120}\right)\)	\(e\left(\frac{7}{80}\right)\)	\(e\left(\frac{143}{240}\right)\)	\(e\left(\frac{17}{24}\right)\)
\(\chi_{8925}(1642,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{73}{120}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{91}{240}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{79}{120}\right)\)	\(e\left(\frac{79}{80}\right)\)	\(e\left(\frac{71}{240}\right)\)	\(e\left(\frac{17}{24}\right)\)
\(\chi_{8925}(1663,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{120}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{193}{240}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{37}{120}\right)\)	\(e\left(\frac{77}{80}\right)\)	\(e\left(\frac{53}{240}\right)\)	\(e\left(\frac{11}{24}\right)\)
\(\chi_{8925}(1873,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{91}{120}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{217}{240}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{13}{120}\right)\)	\(e\left(\frac{53}{80}\right)\)	\(e\left(\frac{77}{240}\right)\)	\(e\left(\frac{11}{24}\right)\)
\(\chi_{8925}(1927,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{101}{120}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{167}{240}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{83}{120}\right)\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{67}{240}\right)\)	\(e\left(\frac{13}{24}\right)\)
\(\chi_{8925}(2188,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{120}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{133}{240}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{97}{120}\right)\)	\(e\left(\frac{17}{80}\right)\)	\(e\left(\frac{233}{240}\right)\)	\(e\left(\frac{23}{24}\right)\)
\(\chi_{8925}(2272,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{120}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{79}{240}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{91}{120}\right)\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{59}{240}\right)\)	\(e\left(\frac{5}{24}\right)\)
\(\chi_{8925}(2662,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{89}{120}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{203}{240}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{47}{120}\right)\)	\(e\left(\frac{47}{80}\right)\)	\(e\left(\frac{103}{240}\right)\)	\(e\left(\frac{1}{24}\right)\)
\(\chi_{8925}(2683,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{83}{120}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{161}{240}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{29}{120}\right)\)	\(e\left(\frac{29}{80}\right)\)	\(e\left(\frac{181}{240}\right)\)	\(e\left(\frac{19}{24}\right)\)
\(\chi_{8925}(2692,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{120}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{151}{240}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{19}{120}\right)\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{131}{240}\right)\)	\(e\left(\frac{5}{24}\right)\)
\(\chi_{8925}(3133,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{103}{120}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{61}{240}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{49}{120}\right)\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{161}{240}\right)\)	\(e\left(\frac{23}{24}\right)\)
\(\chi_{8925}(3208,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{120}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{101}{240}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{89}{120}\right)\)	\(e\left(\frac{49}{80}\right)\)	\(e\left(\frac{121}{240}\right)\)	\(e\left(\frac{7}{24}\right)\)
\(\chi_{8925}(3292,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{120}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{191}{240}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{59}{120}\right)\)	\(e\left(\frac{19}{80}\right)\)	\(e\left(\frac{91}{240}\right)\)	\(e\left(\frac{13}{24}\right)\)
\(\chi_{8925}(3322,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{97}{120}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{19}{240}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{31}{120}\right)\)	\(e\left(\frac{71}{80}\right)\)	\(e\left(\frac{239}{240}\right)\)	\(e\left(\frac{17}{24}\right)\)
\(\chi_{8925}(3427,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{120}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{187}{240}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{103}{120}\right)\)	\(e\left(\frac{63}{80}\right)\)	\(e\left(\frac{167}{240}\right)\)	\(e\left(\frac{17}{24}\right)\)
\(\chi_{8925}(3448,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{91}{120}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{97}{240}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{13}{120}\right)\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{197}{240}\right)\)	\(e\left(\frac{11}{24}\right)\)
\(\chi_{8925}(3658,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{120}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{121}{240}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{109}{120}\right)\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{221}{240}\right)\)	\(e\left(\frac{11}{24}\right)\)
\(\chi_{8925}(3712,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{120}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{23}{240}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{107}{120}\right)\)	\(e\left(\frac{27}{80}\right)\)	\(e\left(\frac{163}{240}\right)\)	\(e\left(\frac{13}{24}\right)\)
\(\chi_{8925}(3973,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{120}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{37}{240}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{73}{120}\right)\)	\(e\left(\frac{33}{80}\right)\)	\(e\left(\frac{137}{240}\right)\)	\(e\left(\frac{23}{24}\right)\)
\(\chi_{8925}(4153,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{120}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{29}{240}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{41}{120}\right)\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{49}{240}\right)\)	\(e\left(\frac{7}{24}\right)\)

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First 31 of 64 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	8925.lb
Modulus	$8925$
Conductor	$2975$
Order	$240$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(8925\)
Conductor:	\(2975\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(240\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 2975.fn	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)