LMFDB - Dirichlet character orbit 1900.ce

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1900, base_ring=CyclotomicField(90)) M = H._module chi = DirichletCharacter(H, M([0,72,10])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(61,1900)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$1900$
Conductor:	$475$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$45$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 475.bc	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 45 polynomial

Characters in Galois orbit

Character	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$21$	$23$	$27$	$29$
$\chi_{1900}(61,\cdot)$	$1$	$1$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{22}{45}\right)$
$\chi_{1900}(81,\cdot)$	$1$	$1$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{41}{45}\right)$
$\chi_{1900}(161,\cdot)$	$1$	$1$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{7}{45}\right)$
$\chi_{1900}(321,\cdot)$	$1$	$1$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{29}{45}\right)$
$\chi_{1900}(441,\cdot)$	$1$	$1$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{13}{45}\right)$
$\chi_{1900}(461,\cdot)$	$1$	$1$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{32}{45}\right)$
$\chi_{1900}(481,\cdot)$	$1$	$1$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{1}{45}\right)$
$\chi_{1900}(541,\cdot)$	$1$	$1$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{43}{45}\right)$
$\chi_{1900}(681,\cdot)$	$1$	$1$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{26}{45}\right)$
$\chi_{1900}(821,\cdot)$	$1$	$1$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{4}{45}\right)$
$\chi_{1900}(841,\cdot)$	$1$	$1$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{23}{45}\right)$
$\chi_{1900}(861,\cdot)$	$1$	$1$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{37}{45}\right)$
$\chi_{1900}(921,\cdot)$	$1$	$1$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{34}{45}\right)$
$\chi_{1900}(1061,\cdot)$	$1$	$1$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{17}{45}\right)$
$\chi_{1900}(1081,\cdot)$	$1$	$1$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{11}{45}\right)$
$\chi_{1900}(1221,\cdot)$	$1$	$1$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{14}{45}\right)$
$\chi_{1900}(1241,\cdot)$	$1$	$1$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{28}{45}\right)$
$\chi_{1900}(1441,\cdot)$	$1$	$1$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{8}{45}\right)$
$\chi_{1900}(1461,\cdot)$	$1$	$1$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{2}{45}\right)$
$\chi_{1900}(1581,\cdot)$	$1$	$1$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{31}{45}\right)$
$\chi_{1900}(1621,\cdot)$	$1$	$1$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{19}{45}\right)$
$\chi_{1900}(1681,\cdot)$	$1$	$1$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{16}{45}\right)$
$\chi_{1900}(1821,\cdot)$	$1$	$1$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{44}{45}\right)$
$\chi_{1900}(1841,\cdot)$	$1$	$1$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{38}{45}\right)$

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	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(17\)	\(21\)	\(23\)	\(27\)	\(29\)
\(\chi_{1900}(61,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{22}{45}\right)\)
\(\chi_{1900}(81,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{41}{45}\right)\)
\(\chi_{1900}(161,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{7}{45}\right)\)
\(\chi_{1900}(321,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{29}{45}\right)\)
\(\chi_{1900}(441,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{13}{45}\right)\)
\(\chi_{1900}(461,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{32}{45}\right)\)
\(\chi_{1900}(481,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{1}{45}\right)\)
\(\chi_{1900}(541,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{43}{45}\right)\)
\(\chi_{1900}(681,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{26}{45}\right)\)
\(\chi_{1900}(821,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{4}{45}\right)\)
\(\chi_{1900}(841,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{23}{45}\right)\)
\(\chi_{1900}(861,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{37}{45}\right)\)
\(\chi_{1900}(921,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{34}{45}\right)\)
\(\chi_{1900}(1061,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{17}{45}\right)\)
\(\chi_{1900}(1081,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{11}{45}\right)\)
\(\chi_{1900}(1221,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{14}{45}\right)\)
\(\chi_{1900}(1241,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{28}{45}\right)\)
\(\chi_{1900}(1441,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{8}{45}\right)\)
\(\chi_{1900}(1461,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{2}{45}\right)\)
\(\chi_{1900}(1581,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{31}{45}\right)\)
\(\chi_{1900}(1621,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{19}{45}\right)\)
\(\chi_{1900}(1681,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{16}{45}\right)\)
\(\chi_{1900}(1821,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{44}{45}\right)\)
\(\chi_{1900}(1841,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{38}{45}\right)\)

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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.

Label	1900.ce
Modulus	$1900$
Conductor	$475$
Order	$45$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(1900\)
Conductor:	\(475\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(45\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 475.bc	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)