LMFDB - Dirichlet character orbit 2700.cn

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2700, base_ring=CyclotomicField(90)) M = H._module chi = DirichletCharacter(H, M([45,25,63])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(59,2700)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$2700$
Conductor:	$2700$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$90$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	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	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{2700}(59,\cdot)$	$1$	$1$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{59}{90}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{47}{90}\right)$
$\chi_{2700}(119,\cdot)$	$1$	$1$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{79}{90}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{79}{90}\right)$
$\chi_{2700}(239,\cdot)$	$1$	$1$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{53}{90}\right)$
$\chi_{2700}(419,\cdot)$	$1$	$1$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{59}{90}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{71}{90}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{59}{90}\right)$
$\chi_{2700}(479,\cdot)$	$1$	$1$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{1}{90}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{79}{90}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{7}{90}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{1}{90}\right)$
$\chi_{2700}(659,\cdot)$	$1$	$1$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{7}{90}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{49}{90}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{7}{90}\right)$
$\chi_{2700}(779,\cdot)$	$1$	$1$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{71}{90}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{29}{90}\right)$	$e\left(\frac{73}{90}\right)$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{71}{90}\right)$
$\chi_{2700}(839,\cdot)$	$1$	$1$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{59}{90}\right)$	$e\left(\frac{1}{90}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{13}{90}\right)$
$\chi_{2700}(959,\cdot)$	$1$	$1$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{77}{90}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{77}{90}\right)$
$\chi_{2700}(1019,\cdot)$	$1$	$1$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{19}{90}\right)$
$\chi_{2700}(1139,\cdot)$	$1$	$1$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{77}{90}\right)$	$e\left(\frac{79}{90}\right)$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{83}{90}\right)$
$\chi_{2700}(1319,\cdot)$	$1$	$1$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{89}{90}\right)$
$\chi_{2700}(1379,\cdot)$	$1$	$1$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{31}{90}\right)$
$\chi_{2700}(1559,\cdot)$	$1$	$1$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{71}{90}\right)$	$e\left(\frac{79}{90}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{37}{90}\right)$
$\chi_{2700}(1679,\cdot)$	$1$	$1$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{59}{90}\right)$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{77}{90}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{11}{90}\right)$
$\chi_{2700}(1739,\cdot)$	$1$	$1$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{29}{90}\right)$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{43}{90}\right)$
$\chi_{2700}(1859,\cdot)$	$1$	$1$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{1}{90}\right)$	$e\left(\frac{29}{90}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{17}{90}\right)$
$\chi_{2700}(1919,\cdot)$	$1$	$1$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{49}{90}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{1}{90}\right)$	$e\left(\frac{77}{90}\right)$	$e\left(\frac{73}{90}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{49}{90}\right)$
$\chi_{2700}(2039,\cdot)$	$1$	$1$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{49}{90}\right)$	$e\left(\frac{71}{90}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{23}{90}\right)$
$\chi_{2700}(2219,\cdot)$	$1$	$1$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{29}{90}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{7}{90}\right)$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{29}{90}\right)$
$\chi_{2700}(2279,\cdot)$	$1$	$1$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{49}{90}\right)$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{61}{90}\right)$
$\chi_{2700}(2459,\cdot)$	$1$	$1$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{73}{90}\right)$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{67}{90}\right)$
$\chi_{2700}(2579,\cdot)$	$1$	$1$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{41}{90}\right)$
$\chi_{2700}(2639,\cdot)$	$1$	$1$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{73}{90}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{7}{90}\right)$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{73}{90}\right)$

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	\(-1\)	\(1\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)
\(\chi_{2700}(59,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{47}{90}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{23}{90}\right)\)	\(e\left(\frac{61}{90}\right)\)	\(e\left(\frac{59}{90}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{47}{90}\right)\)
\(\chi_{2700}(119,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{79}{90}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{31}{90}\right)\)	\(e\left(\frac{47}{90}\right)\)	\(e\left(\frac{13}{90}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{79}{90}\right)\)
\(\chi_{2700}(239,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{47}{90}\right)\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{11}{90}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{53}{90}\right)\)
\(\chi_{2700}(419,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{59}{90}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{71}{90}\right)\)	\(e\left(\frac{67}{90}\right)\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{59}{90}\right)\)
\(\chi_{2700}(479,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{1}{90}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{79}{90}\right)\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{7}{90}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{1}{90}\right)\)
\(\chi_{2700}(659,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{7}{90}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{13}{90}\right)\)	\(e\left(\frac{11}{90}\right)\)	\(e\left(\frac{49}{90}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{7}{90}\right)\)
\(\chi_{2700}(779,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{71}{90}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{29}{90}\right)\)	\(e\left(\frac{73}{90}\right)\)	\(e\left(\frac{47}{90}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{71}{90}\right)\)
\(\chi_{2700}(839,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{13}{90}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{37}{90}\right)\)	\(e\left(\frac{59}{90}\right)\)	\(e\left(\frac{1}{90}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{13}{90}\right)\)
\(\chi_{2700}(959,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{77}{90}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{31}{90}\right)\)	\(e\left(\frac{89}{90}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{77}{90}\right)\)
\(\chi_{2700}(1019,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{61}{90}\right)\)	\(e\left(\frac{17}{90}\right)\)	\(e\left(\frac{43}{90}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{19}{90}\right)\)
\(\chi_{2700}(1139,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{83}{90}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{77}{90}\right)\)	\(e\left(\frac{79}{90}\right)\)	\(e\left(\frac{41}{90}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{83}{90}\right)\)
\(\chi_{2700}(1319,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{89}{90}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{11}{90}\right)\)	\(e\left(\frac{37}{90}\right)\)	\(e\left(\frac{83}{90}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{89}{90}\right)\)
\(\chi_{2700}(1379,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{31}{90}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{23}{90}\right)\)	\(e\left(\frac{37}{90}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{31}{90}\right)\)
\(\chi_{2700}(1559,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{37}{90}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{43}{90}\right)\)	\(e\left(\frac{71}{90}\right)\)	\(e\left(\frac{79}{90}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{37}{90}\right)\)
\(\chi_{2700}(1679,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{11}{90}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{59}{90}\right)\)	\(e\left(\frac{43}{90}\right)\)	\(e\left(\frac{77}{90}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{11}{90}\right)\)
\(\chi_{2700}(1739,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{43}{90}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{67}{90}\right)\)	\(e\left(\frac{29}{90}\right)\)	\(e\left(\frac{31}{90}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{43}{90}\right)\)
\(\chi_{2700}(1859,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{17}{90}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{83}{90}\right)\)	\(e\left(\frac{1}{90}\right)\)	\(e\left(\frac{29}{90}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{17}{90}\right)\)
\(\chi_{2700}(1919,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{49}{90}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{1}{90}\right)\)	\(e\left(\frac{77}{90}\right)\)	\(e\left(\frac{73}{90}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{49}{90}\right)\)
\(\chi_{2700}(2039,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{23}{90}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{17}{90}\right)\)	\(e\left(\frac{49}{90}\right)\)	\(e\left(\frac{71}{90}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{23}{90}\right)\)
\(\chi_{2700}(2219,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{29}{90}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{41}{90}\right)\)	\(e\left(\frac{7}{90}\right)\)	\(e\left(\frac{23}{90}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{29}{90}\right)\)
\(\chi_{2700}(2279,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{61}{90}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{49}{90}\right)\)	\(e\left(\frac{83}{90}\right)\)	\(e\left(\frac{67}{90}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{61}{90}\right)\)
\(\chi_{2700}(2459,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{67}{90}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{73}{90}\right)\)	\(e\left(\frac{41}{90}\right)\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{67}{90}\right)\)
\(\chi_{2700}(2579,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{41}{90}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{89}{90}\right)\)	\(e\left(\frac{13}{90}\right)\)	\(e\left(\frac{17}{90}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{41}{90}\right)\)
\(\chi_{2700}(2639,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{73}{90}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{7}{90}\right)\)	\(e\left(\frac{89}{90}\right)\)	\(e\left(\frac{61}{90}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{73}{90}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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

Modulus:	\(2700\)
Conductor:	\(2700\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(90\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)