LMFDB - Dirichlet character orbit 3762.ec

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3762, base_ring=CyclotomicField(90)) M = H._module chi = DirichletCharacter(H, M([0,72,10])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(289,3762)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$3762$
Conductor:	$209$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$45$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 209.u	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:	45.45.43679806300610465846484971330073185012597520004657724600953543350870941304329239684756561.1

Characters in Galois orbit

Character	$-1$	$1$	$5$	$7$	$13$	$17$	$23$	$25$	$29$	$31$	$35$	$37$
$\chi_{3762}(289,\cdot)$	$1$	$1$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{3762}(631,\cdot)$	$1$	$1$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{3762}(757,\cdot)$	$1$	$1$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{3762}(883,\cdot)$	$1$	$1$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{3762}(955,\cdot)$	$1$	$1$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{3762}(973,\cdot)$	$1$	$1$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{3762}(1081,\cdot)$	$1$	$1$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{3762}(1225,\cdot)$	$1$	$1$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{3762}(1279,\cdot)$	$1$	$1$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{3762}(1423,\cdot)$	$1$	$1$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{3762}(1567,\cdot)$	$1$	$1$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{3762}(1621,\cdot)$	$1$	$1$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{3762}(1765,\cdot)$	$1$	$1$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{3762}(1963,\cdot)$	$1$	$1$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{3762}(2341,\cdot)$	$1$	$1$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{3762}(2467,\cdot)$	$1$	$1$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{3762}(2665,\cdot)$	$1$	$1$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{3762}(2809,\cdot)$	$1$	$1$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{3762}(2935,\cdot)$	$1$	$1$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{3762}(3007,\cdot)$	$1$	$1$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{3762}(3133,\cdot)$	$1$	$1$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{3762}(3151,\cdot)$	$1$	$1$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{3762}(3331,\cdot)$	$1$	$1$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{3762}(3349,\cdot)$	$1$	$1$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{4}{5}\right)$

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	\(-1\)	\(1\)	\(5\)	\(7\)	\(13\)	\(17\)	\(23\)	\(25\)	\(29\)	\(31\)	\(35\)	\(37\)
\(\chi_{3762}(289,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{3762}(631,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{3762}(757,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{3762}(883,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{3762}(955,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{3762}(973,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{3762}(1081,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{3762}(1225,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{3762}(1279,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{3762}(1423,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{3762}(1567,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{3762}(1621,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{3762}(1765,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{3762}(1963,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{3762}(2341,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{3762}(2467,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{3762}(2665,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{3762}(2809,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{3762}(2935,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{3762}(3007,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{3762}(3133,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{3762}(3151,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{3762}(3331,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{3762}(3349,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{4}{5}\right)\)

Introduction

L-functions

Modular forms

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	3762.ec
Modulus	$3762$
Conductor	$209$
Order	$45$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(3762\)
Conductor:	\(209\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(45\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 209.u	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)