LMFDB - Dirichlet character orbit 1225.bm

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1225, base_ring=CyclotomicField(84)) M = H._module chi = DirichletCharacter(H, M([21,8])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(32,1225)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$1225$
Conductor:	$245$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$84$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 245.w	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)

Related number fields

Field of values:	$\Q(\zeta_{84})$
Fixed field:	Number field defined by a degree 84 polynomial

Characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$6$	$8$	$9$	$11$	$12$	$13$	$16$
$\chi_{1225}(32,\cdot)$	$-1$	$1$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{71}{84}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{19}{21}\right)$
$\chi_{1225}(93,\cdot)$	$-1$	$1$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{71}{84}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{17}{21}\right)$
$\chi_{1225}(107,\cdot)$	$-1$	$1$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{67}{84}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{20}{21}\right)$
$\chi_{1225}(193,\cdot)$	$-1$	$1$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{10}{21}\right)$
$\chi_{1225}(207,\cdot)$	$-1$	$1$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{1}{21}\right)$
$\chi_{1225}(268,\cdot)$	$-1$	$1$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{59}{84}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{2}{21}\right)$
$\chi_{1225}(282,\cdot)$	$-1$	$1$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{53}{84}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{5}{21}\right)$
$\chi_{1225}(368,\cdot)$	$-1$	$1$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{53}{84}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{13}{21}\right)$
$\chi_{1225}(382,\cdot)$	$-1$	$1$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{4}{21}\right)$
$\chi_{1225}(443,\cdot)$	$-1$	$1$	$e\left(\frac{71}{84}\right)$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{8}{21}\right)$
$\chi_{1225}(457,\cdot)$	$-1$	$1$	$e\left(\frac{53}{84}\right)$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{11}{21}\right)$
$\chi_{1225}(543,\cdot)$	$-1$	$1$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{16}{21}\right)$
$\chi_{1225}(632,\cdot)$	$-1$	$1$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{17}{21}\right)$
$\chi_{1225}(718,\cdot)$	$-1$	$1$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{67}{84}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{19}{21}\right)$
$\chi_{1225}(732,\cdot)$	$-1$	$1$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{10}{21}\right)$
$\chi_{1225}(793,\cdot)$	$-1$	$1$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{25}{84}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{23}{84}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{20}{21}\right)$
$\chi_{1225}(807,\cdot)$	$-1$	$1$	$e\left(\frac{65}{84}\right)$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{2}{21}\right)$
$\chi_{1225}(893,\cdot)$	$-1$	$1$	$e\left(\frac{43}{84}\right)$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{19}{84}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{1}{21}\right)$
$\chi_{1225}(907,\cdot)$	$-1$	$1$	$e\left(\frac{13}{84}\right)$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{13}{21}\right)$
$\chi_{1225}(968,\cdot)$	$-1$	$1$	$e\left(\frac{47}{84}\right)$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{5}{21}\right)$
$\chi_{1225}(982,\cdot)$	$-1$	$1$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{8}{21}\right)$
$\chi_{1225}(1068,\cdot)$	$-1$	$1$	$e\left(\frac{67}{84}\right)$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{4}{21}\right)$
$\chi_{1225}(1082,\cdot)$	$-1$	$1$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{73}{84}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{16}{21}\right)$
$\chi_{1225}(1143,\cdot)$	$-1$	$1$	$e\left(\frac{11}{84}\right)$	$e\left(\frac{61}{84}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{11}{21}\right)$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(8\)	\(9\)	\(11\)	\(12\)	\(13\)	\(16\)
\(\chi_{1225}(32,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{71}{84}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{19}{21}\right)\)
\(\chi_{1225}(93,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{71}{84}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{17}{21}\right)\)
\(\chi_{1225}(107,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{67}{84}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{20}{21}\right)\)
\(\chi_{1225}(193,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{43}{84}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{10}{21}\right)\)
\(\chi_{1225}(207,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{1}{21}\right)\)
\(\chi_{1225}(268,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{59}{84}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{2}{21}\right)\)
\(\chi_{1225}(282,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{43}{84}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{53}{84}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{5}{21}\right)\)
\(\chi_{1225}(368,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{55}{84}\right)\)	\(e\left(\frac{53}{84}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{13}{21}\right)\)
\(\chi_{1225}(382,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{47}{84}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{4}{21}\right)\)
\(\chi_{1225}(443,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{71}{84}\right)\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{47}{84}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{8}{21}\right)\)
\(\chi_{1225}(457,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{53}{84}\right)\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{11}{21}\right)\)
\(\chi_{1225}(543,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{16}{21}\right)\)
\(\chi_{1225}(632,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{17}{84}\right)\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{29}{84}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{17}{21}\right)\)
\(\chi_{1225}(718,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{29}{84}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{67}{84}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{19}{21}\right)\)
\(\chi_{1225}(732,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{10}{21}\right)\)
\(\chi_{1225}(793,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{25}{84}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{23}{84}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{20}{21}\right)\)
\(\chi_{1225}(807,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{65}{84}\right)\)	\(e\left(\frac{55}{84}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{17}{84}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{2}{21}\right)\)
\(\chi_{1225}(893,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{43}{84}\right)\)	\(e\left(\frac{17}{84}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{19}{84}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{1}{21}\right)\)
\(\chi_{1225}(907,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{13}{84}\right)\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{13}{21}\right)\)
\(\chi_{1225}(968,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{47}{84}\right)\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{5}{21}\right)\)
\(\chi_{1225}(982,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{29}{84}\right)\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{8}{21}\right)\)
\(\chi_{1225}(1068,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{67}{84}\right)\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{55}{84}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{4}{21}\right)\)
\(\chi_{1225}(1082,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{73}{84}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{16}{21}\right)\)
\(\chi_{1225}(1143,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{11}{84}\right)\)	\(e\left(\frac{61}{84}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{11}{21}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Basic properties

Related number fields

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	1225.bm
Modulus	$1225$
Conductor	$245$
Order	$84$
Real	no
Primitive	no
Minimal	yes
Parity	odd

Modulus:	\(1225\)
Conductor:	\(245\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(84\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 245.w	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)