LMFDB - Dirichlet character orbit 2700.cl

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2700, base_ring=CyclotomicField(90)) M = H._module chi = DirichletCharacter(H, M([0,80,81])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(169, 2700)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2700.169"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$2700$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$675$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$90$	comment:Order sage:chi.multiplicative_order() gp:charorder(g,chi) magma:Order(chi);
Real:	no	comment:Whether the character is real sage:chi.multiplicative_order() <= 2 gp:charorder(g,chi) <= 2 magma:Order(chi) le 2;
Primitive:	no, induced from 675.bg	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	yes
Parity:	even	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);

Related number fields

Field of values:	$\Q(\zeta_{45})$	comment:Field of values of chi sage:CyclotomicField(chi.multiplicative_order()) gp:nfinit(polcyclo(charorder(g,chi))) magma:CyclotomicField(Order(chi));
Fixed field:	Number field defined by a degree 90 polynomial	comment:Fixed field sage:chi.fixed_field()

Characters in Galois orbit

Character	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{2700}(169,\cdot)$	$1$	$1$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{32}{45}\right)$
$\chi_{2700}(229,\cdot)$	$1$	$1$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{43}{45}\right)$
$\chi_{2700}(409,\cdot)$	$1$	$1$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{31}{45}\right)$
$\chi_{2700}(529,\cdot)$	$1$	$1$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{49}{90}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{8}{45}\right)$
$\chi_{2700}(589,\cdot)$	$1$	$1$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{77}{90}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{19}{45}\right)$
$\chi_{2700}(709,\cdot)$	$1$	$1$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{41}{45}\right)$
$\chi_{2700}(769,\cdot)$	$1$	$1$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{59}{90}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{71}{90}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{7}{45}\right)$
$\chi_{2700}(889,\cdot)$	$1$	$1$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{29}{45}\right)$
$\chi_{2700}(1069,\cdot)$	$1$	$1$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{79}{90}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{17}{45}\right)$
$\chi_{2700}(1129,\cdot)$	$1$	$1$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{59}{90}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{28}{45}\right)$
$\chi_{2700}(1309,\cdot)$	$1$	$1$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{77}{90}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{16}{45}\right)$
$\chi_{2700}(1429,\cdot)$	$1$	$1$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{38}{45}\right)$
$\chi_{2700}(1489,\cdot)$	$1$	$1$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{4}{45}\right)$
$\chi_{2700}(1609,\cdot)$	$1$	$1$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{7}{90}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{26}{45}\right)$
$\chi_{2700}(1669,\cdot)$	$1$	$1$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{29}{90}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{37}{45}\right)$
$\chi_{2700}(1789,\cdot)$	$1$	$1$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{73}{90}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{7}{90}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{14}{45}\right)$
$\chi_{2700}(1969,\cdot)$	$1$	$1$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{49}{90}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{1}{90}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{2}{45}\right)$
$\chi_{2700}(2029,\cdot)$	$1$	$1$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{71}{90}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{29}{90}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{13}{45}\right)$
$\chi_{2700}(2209,\cdot)$	$1$	$1$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{1}{45}\right)$
$\chi_{2700}(2329,\cdot)$	$1$	$1$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{1}{90}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{79}{90}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{23}{45}\right)$
$\chi_{2700}(2389,\cdot)$	$1$	$1$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{34}{45}\right)$
$\chi_{2700}(2509,\cdot)$	$1$	$1$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{73}{90}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{11}{45}\right)$
$\chi_{2700}(2569,\cdot)$	$1$	$1$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{22}{45}\right)$
$\chi_{2700}(2689,\cdot)$	$1$	$1$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{44}{45}\right)$

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	\(-1\)	\(1\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)
\(\chi_{2700}(169,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{61}{90}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{32}{45}\right)\)
\(\chi_{2700}(229,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{41}{90}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{89}{90}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{43}{45}\right)\)
\(\chi_{2700}(409,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{17}{90}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{83}{90}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{31}{45}\right)\)
\(\chi_{2700}(529,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{61}{90}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{49}{90}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{8}{45}\right)\)
\(\chi_{2700}(589,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{83}{90}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{77}{90}\right)\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{19}{45}\right)\)
\(\chi_{2700}(709,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{37}{90}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{43}{90}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{41}{45}\right)\)
\(\chi_{2700}(769,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{59}{90}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{71}{90}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{7}{45}\right)\)
\(\chi_{2700}(889,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{13}{90}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{37}{90}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{29}{45}\right)\)
\(\chi_{2700}(1069,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{79}{90}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{31}{90}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{17}{45}\right)\)
\(\chi_{2700}(1129,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{11}{90}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{59}{90}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{28}{45}\right)\)
\(\chi_{2700}(1309,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{77}{90}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{16}{45}\right)\)
\(\chi_{2700}(1429,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{31}{90}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{38}{45}\right)\)
\(\chi_{2700}(1489,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{47}{90}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{4}{45}\right)\)
\(\chi_{2700}(1609,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{7}{90}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{13}{90}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{26}{45}\right)\)
\(\chi_{2700}(1669,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{29}{90}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{41}{90}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{37}{45}\right)\)
\(\chi_{2700}(1789,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{73}{90}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{7}{90}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{14}{45}\right)\)
\(\chi_{2700}(1969,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{49}{90}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{1}{90}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{2}{45}\right)\)
\(\chi_{2700}(2029,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{71}{90}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{29}{90}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{13}{45}\right)\)
\(\chi_{2700}(2209,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{47}{90}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{23}{90}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{1}{45}\right)\)
\(\chi_{2700}(2329,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{1}{90}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{79}{90}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{23}{45}\right)\)
\(\chi_{2700}(2389,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{23}{90}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{17}{90}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{34}{45}\right)\)
\(\chi_{2700}(2509,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{67}{90}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{73}{90}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{11}{45}\right)\)
\(\chi_{2700}(2569,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{89}{90}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{11}{90}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{22}{45}\right)\)
\(\chi_{2700}(2689,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{43}{90}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{67}{90}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{44}{45}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

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	2700.cl
Modulus	$2700$
Conductor	$675$
Order	$90$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(2700\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(675\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(90\)	comment:Order sage:chi.multiplicative_order() gp:charorder(g,chi) magma:Order(chi);
Real:	no	comment:Whether the character is real sage:chi.multiplicative_order() <= 2 gp:charorder(g,chi) <= 2 magma:Order(chi) le 2;
Primitive:	no, induced from 675.bg	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	yes
Parity:	even	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);