LMFDB - Dirichlet character orbit 3800.fd

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3800, base_ring=CyclotomicField(90)) M = H._module chi = DirichletCharacter(H, M([0,0,63,40])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(9,3800)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$3800$
Conductor:	$475$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$90$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 475.bg	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:	$\Q(\zeta_{45})$
Fixed field:	Number field defined by a degree 90 polynomial

Characters in Galois orbit

Character	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$21$	$23$	$27$	$29$
$\chi_{3800}(9,\cdot)$	$1$	$1$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{49}{90}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{43}{45}\right)$
$\chi_{3800}(169,\cdot)$	$1$	$1$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{79}{90}\right)$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{1}{90}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{11}{45}\right)$
$\chi_{3800}(289,\cdot)$	$1$	$1$	$e\left(\frac{49}{90}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{1}{90}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{22}{45}\right)$
$\chi_{3800}(329,\cdot)$	$1$	$1$	$e\left(\frac{73}{90}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{71}{90}\right)$	$e\left(\frac{7}{90}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{59}{90}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{19}{45}\right)$
$\chi_{3800}(529,\cdot)$	$1$	$1$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{90}\right)$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{49}{90}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{44}{45}\right)$
$\chi_{3800}(689,\cdot)$	$1$	$1$	$e\left(\frac{59}{90}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{71}{90}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{7}{90}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{32}{45}\right)$
$\chi_{3800}(769,\cdot)$	$1$	$1$	$e\left(\frac{7}{90}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{29}{90}\right)$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{71}{90}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{16}{45}\right)$
$\chi_{3800}(929,\cdot)$	$1$	$1$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{77}{90}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{29}{45}\right)$
$\chi_{3800}(1089,\cdot)$	$1$	$1$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{77}{90}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{37}{45}\right)$
$\chi_{3800}(1289,\cdot)$	$1$	$1$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{73}{90}\right)$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{17}{45}\right)$
$\chi_{3800}(1529,\cdot)$	$1$	$1$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{34}{45}\right)$
$\chi_{3800}(1689,\cdot)$	$1$	$1$	$e\left(\frac{29}{90}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{2}{45}\right)$
$\chi_{3800}(1809,\cdot)$	$1$	$1$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{77}{90}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{13}{45}\right)$
$\chi_{3800}(2209,\cdot)$	$1$	$1$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{23}{45}\right)$
$\chi_{3800}(2289,\cdot)$	$1$	$1$	$e\left(\frac{79}{90}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{7}{45}\right)$
$\chi_{3800}(2569,\cdot)$	$1$	$1$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{59}{90}\right)$	$e\left(\frac{73}{90}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{31}{45}\right)$
$\chi_{3800}(2609,\cdot)$	$1$	$1$	$e\left(\frac{1}{90}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{79}{90}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{28}{45}\right)$
$\chi_{3800}(2809,\cdot)$	$1$	$1$	$e\left(\frac{71}{90}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{29}{90}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{8}{45}\right)$
$\chi_{3800}(2969,\cdot)$	$1$	$1$	$e\left(\frac{77}{90}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{49}{90}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{41}{45}\right)$
$\chi_{3800}(3209,\cdot)$	$1$	$1$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{7}{90}\right)$	$e\left(\frac{59}{90}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{73}{90}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{38}{45}\right)$
$\chi_{3800}(3329,\cdot)$	$1$	$1$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{29}{90}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{4}{45}\right)$
$\chi_{3800}(3369,\cdot)$	$1$	$1$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{1}{45}\right)$
$\chi_{3800}(3569,\cdot)$	$1$	$1$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{26}{45}\right)$
$\chi_{3800}(3729,\cdot)$	$1$	$1$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{79}{90}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{14}{45}\right)$

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	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(17\)	\(21\)	\(23\)	\(27\)	\(29\)
\(\chi_{3800}(9,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{90}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{47}{90}\right)\)	\(e\left(\frac{49}{90}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{43}{45}\right)\)
\(\chi_{3800}(169,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{90}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{79}{90}\right)\)	\(e\left(\frac{23}{90}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{1}{90}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{11}{45}\right)\)
\(\chi_{3800}(289,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{90}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{23}{90}\right)\)	\(e\left(\frac{1}{90}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{47}{90}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{22}{45}\right)\)
\(\chi_{3800}(329,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{73}{90}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{71}{90}\right)\)	\(e\left(\frac{7}{90}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{59}{90}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{19}{45}\right)\)
\(\chi_{3800}(529,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{90}\right)\)	\(e\left(\frac{47}{90}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{49}{90}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{44}{45}\right)\)
\(\chi_{3800}(689,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{90}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{13}{90}\right)\)	\(e\left(\frac{71}{90}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{7}{90}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{32}{45}\right)\)
\(\chi_{3800}(769,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{90}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{29}{90}\right)\)	\(e\left(\frac{13}{90}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{71}{90}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{16}{45}\right)\)
\(\chi_{3800}(929,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{83}{90}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{61}{90}\right)\)	\(e\left(\frac{77}{90}\right)\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{29}{45}\right)\)
\(\chi_{3800}(1089,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{61}{90}\right)\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{77}{90}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{37}{45}\right)\)
\(\chi_{3800}(1289,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{89}{90}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{73}{90}\right)\)	\(e\left(\frac{11}{90}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{67}{90}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{17}{45}\right)\)
\(\chi_{3800}(1529,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{90}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{11}{90}\right)\)	\(e\left(\frac{67}{90}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{89}{90}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{34}{45}\right)\)
\(\chi_{3800}(1689,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{90}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{43}{90}\right)\)	\(e\left(\frac{41}{90}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{37}{90}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{2}{45}\right)\)
\(\chi_{3800}(1809,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{90}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{77}{90}\right)\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{83}{90}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{13}{45}\right)\)
\(\chi_{3800}(2209,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{90}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{67}{90}\right)\)	\(e\left(\frac{89}{90}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{43}{90}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{23}{45}\right)\)
\(\chi_{3800}(2289,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{90}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{83}{90}\right)\)	\(e\left(\frac{31}{90}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{17}{90}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{7}{45}\right)\)
\(\chi_{3800}(2569,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{90}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{59}{90}\right)\)	\(e\left(\frac{73}{90}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{11}{90}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{31}{45}\right)\)
\(\chi_{3800}(2609,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{90}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{17}{90}\right)\)	\(e\left(\frac{79}{90}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{23}{90}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{28}{45}\right)\)
\(\chi_{3800}(2809,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{90}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{37}{90}\right)\)	\(e\left(\frac{29}{90}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{13}{90}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{8}{45}\right)\)
\(\chi_{3800}(2969,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{77}{90}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{49}{90}\right)\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{61}{90}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{41}{45}\right)\)
\(\chi_{3800}(3209,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{90}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{7}{90}\right)\)	\(e\left(\frac{59}{90}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{73}{90}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{38}{45}\right)\)
\(\chi_{3800}(3329,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{90}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{41}{90}\right)\)	\(e\left(\frac{37}{90}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{29}{90}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{4}{45}\right)\)
\(\chi_{3800}(3369,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{90}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{89}{90}\right)\)	\(e\left(\frac{43}{90}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{41}{90}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{1}{45}\right)\)
\(\chi_{3800}(3569,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{90}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{83}{90}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{31}{90}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{26}{45}\right)\)
\(\chi_{3800}(3729,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{90}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{31}{90}\right)\)	\(e\left(\frac{17}{90}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{79}{90}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{14}{45}\right)\)

Introduction

L-functions

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Varieties

Fields

Representations

Groups

Database

Properties

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Basic properties

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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	3800.fd
Modulus	$3800$
Conductor	$475$
Order	$90$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(3800\)
Conductor:	\(475\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(90\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 475.bg	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)