LMFDB - Dirichlet character orbit 8925.jp

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8925, base_ring=CyclotomicField(80)) M = H._module chi = DirichletCharacter(H, M([40,8,0,65])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(29,8925)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$8925$
Conductor:	$1275$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$80$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 1275.cr	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:	$\Q(\zeta_{80})$
Fixed field:	Number field defined by a degree 80 polynomial

First 31 of 32 characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$8$	$11$	$13$	$16$	$19$	$22$	$23$	$26$
$\chi_{8925}(29,\cdot)$	$1$	$1$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{8925}(554,\cdot)$	$1$	$1$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{33}{80}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{33}{80}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{8925}(1184,\cdot)$	$1$	$1$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{7}{80}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{8925}(1289,\cdot)$	$1$	$1$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{19}{80}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{19}{80}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{8925}(1604,\cdot)$	$1$	$1$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{53}{80}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{31}{80}\right)$	$e\left(\frac{53}{80}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{8925}(1814,\cdot)$	$1$	$1$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{8925}(2234,\cdot)$	$1$	$1$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{27}{80}\right)$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{8925}(2339,\cdot)$	$1$	$1$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{49}{80}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{3}{80}\right)$	$e\left(\frac{49}{80}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{8925}(2759,\cdot)$	$1$	$1$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{8925}(2969,\cdot)$	$1$	$1$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{8925}(3284,\cdot)$	$1$	$1$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{11}{80}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{17}{80}\right)$	$e\left(\frac{11}{80}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{8925}(3389,\cdot)$	$1$	$1$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{8925}(4019,\cdot)$	$1$	$1$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{57}{80}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{57}{80}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{8925}(4544,\cdot)$	$1$	$1$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{7}{80}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{7}{80}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{8925}(4754,\cdot)$	$1$	$1$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{8925}(4859,\cdot)$	$1$	$1$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{57}{80}\right)$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{8925}(5069,\cdot)$	$1$	$1$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{27}{80}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{49}{80}\right)$	$e\left(\frac{27}{80}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{8925}(5384,\cdot)$	$1$	$1$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{31}{80}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{31}{80}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{8925}(5804,\cdot)$	$1$	$1$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{11}{80}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{8925}(5909,\cdot)$	$1$	$1$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{67}{80}\right)$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{8925}(6329,\cdot)$	$1$	$1$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{21}{80}\right)$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{8925}(6539,\cdot)$	$1$	$1$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{8925}(6644,\cdot)$	$1$	$1$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{67}{80}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{67}{80}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{8925}(6854,\cdot)$	$1$	$1$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{8925}(6959,\cdot)$	$1$	$1$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{21}{80}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{21}{80}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{8925}(7169,\cdot)$	$1$	$1$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{8925}(7589,\cdot)$	$1$	$1$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{8925}(7694,\cdot)$	$1$	$1$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{17}{80}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{19}{80}\right)$	$e\left(\frac{17}{80}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{8925}(8114,\cdot)$	$1$	$1$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{53}{80}\right)$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{8925}(8429,\cdot)$	$1$	$1$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{3}{80}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{3}{80}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{8925}(8639,\cdot)$	$1$	$1$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{33}{80}\right)$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{5}{8}\right)$

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	\(-1\)	\(1\)	\(2\)	\(4\)	\(8\)	\(11\)	\(13\)	\(16\)	\(19\)	\(22\)	\(23\)	\(26\)
\(\chi_{8925}(29,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{63}{80}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{63}{80}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{8925}(554,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{33}{80}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{33}{80}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{8925}(1184,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{7}{80}\right)\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{8925}(1289,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{19}{80}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{19}{80}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{8925}(1604,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{53}{80}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{31}{80}\right)\)	\(e\left(\frac{53}{80}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{8925}(1814,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{79}{80}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{79}{80}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{8925}(2234,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{27}{80}\right)\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{8925}(2339,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{49}{80}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{3}{80}\right)\)	\(e\left(\frac{49}{80}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{8925}(2759,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{71}{80}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{71}{80}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{8925}(2969,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{77}{80}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{39}{80}\right)\)	\(e\left(\frac{77}{80}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{8925}(3284,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{11}{80}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{17}{80}\right)\)	\(e\left(\frac{11}{80}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{8925}(3389,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{63}{80}\right)\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{8925}(4019,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{57}{80}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{57}{80}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{8925}(4544,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{7}{80}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{7}{80}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{8925}(4754,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{71}{80}\right)\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{8925}(4859,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{57}{80}\right)\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{8925}(5069,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{27}{80}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{49}{80}\right)\)	\(e\left(\frac{27}{80}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{8925}(5384,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{31}{80}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{77}{80}\right)\)	\(e\left(\frac{31}{80}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{8925}(5804,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{11}{80}\right)\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{8925}(5909,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{1}{80}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{67}{80}\right)\)	\(e\left(\frac{1}{80}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{8925}(6329,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{21}{80}\right)\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{8925}(6539,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{29}{80}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{29}{80}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{8925}(6644,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{67}{80}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{67}{80}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{8925}(6854,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{1}{80}\right)\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{8925}(6959,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{21}{80}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{47}{80}\right)\)	\(e\left(\frac{21}{80}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{8925}(7169,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{47}{80}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{29}{80}\right)\)	\(e\left(\frac{47}{80}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{8925}(7589,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{8925}(7694,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{17}{80}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{19}{80}\right)\)	\(e\left(\frac{17}{80}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{8925}(8114,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{39}{80}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{53}{80}\right)\)	\(e\left(\frac{39}{80}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{8925}(8429,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{3}{80}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{3}{80}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{8925}(8639,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{33}{80}\right)\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{5}{8}\right)\)

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First 31 of 32 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.jp
Modulus	$8925$
Conductor	$1275$
Order	$80$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(8925\)
Conductor:	\(1275\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(80\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 1275.cr	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)