LMFDB - Dirichlet character orbit 2700.cr

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2700, base_ring=CyclotomicField(180)) M = H._module chi = DirichletCharacter(H, M([0,80,171])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(13,2700)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$2700$
Conductor:	$675$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$180$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 675.bj	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:	$\Q(\zeta_{180})$
Fixed field:	Number field defined by a degree 180 polynomial (not computed)

First 31 of 48 characters in Galois orbit

Character	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{2700}(13,\cdot)$	$-1$	$1$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{109}{180}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{61}{180}\right)$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{16}{45}\right)$
$\chi_{2700}(97,\cdot)$	$-1$	$1$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{167}{180}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{143}{180}\right)$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{8}{45}\right)$
$\chi_{2700}(133,\cdot)$	$-1$	$1$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{53}{180}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{137}{180}\right)$	$e\left(\frac{77}{90}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{2}{45}\right)$
$\chi_{2700}(277,\cdot)$	$-1$	$1$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{11}{180}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{59}{180}\right)$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{14}{45}\right)$
$\chi_{2700}(313,\cdot)$	$-1$	$1$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{149}{180}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{161}{180}\right)$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{26}{45}\right)$
$\chi_{2700}(337,\cdot)$	$-1$	$1$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{19}{180}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{151}{180}\right)$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{16}{45}\right)$
$\chi_{2700}(373,\cdot)$	$-1$	$1$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{121}{180}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{109}{180}\right)$	$e\left(\frac{79}{90}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{19}{45}\right)$
$\chi_{2700}(517,\cdot)$	$-1$	$1$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{43}{180}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{67}{180}\right)$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{22}{45}\right)$
$\chi_{2700}(553,\cdot)$	$-1$	$1$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{37}{180}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{133}{180}\right)$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{43}{45}\right)$
$\chi_{2700}(637,\cdot)$	$-1$	$1$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{59}{180}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{71}{180}\right)$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{26}{45}\right)$
$\chi_{2700}(673,\cdot)$	$-1$	$1$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{161}{180}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{29}{180}\right)$	$e\left(\frac{59}{90}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{29}{45}\right)$
$\chi_{2700}(697,\cdot)$	$-1$	$1$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{67}{180}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{163}{180}\right)$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{28}{45}\right)$
$\chi_{2700}(733,\cdot)$	$-1$	$1$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{133}{180}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{157}{180}\right)$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{22}{45}\right)$
$\chi_{2700}(817,\cdot)$	$-1$	$1$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{83}{180}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{167}{180}\right)$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{32}{45}\right)$
$\chi_{2700}(853,\cdot)$	$-1$	$1$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{77}{180}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{53}{180}\right)$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{8}{45}\right)$
$\chi_{2700}(877,\cdot)$	$-1$	$1$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{91}{180}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{79}{180}\right)$	$e\left(\frac{49}{90}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{34}{45}\right)$
$\chi_{2700}(913,\cdot)$	$-1$	$1$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{49}{180}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{1}{180}\right)$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{1}{45}\right)$
$\chi_{2700}(997,\cdot)$	$-1$	$1$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{107}{180}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{83}{180}\right)$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{38}{45}\right)$
$\chi_{2700}(1033,\cdot)$	$-1$	$1$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{173}{180}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{77}{180}\right)$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{32}{45}\right)$
$\chi_{2700}(1177,\cdot)$	$-1$	$1$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{131}{180}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{179}{180}\right)$	$e\left(\frac{29}{90}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{44}{45}\right)$
$\chi_{2700}(1213,\cdot)$	$-1$	$1$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{89}{180}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{101}{180}\right)$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{11}{45}\right)$
$\chi_{2700}(1237,\cdot)$	$-1$	$1$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{139}{180}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{91}{180}\right)$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{1}{45}\right)$
$\chi_{2700}(1273,\cdot)$	$-1$	$1$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{61}{180}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{49}{180}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{4}{45}\right)$
$\chi_{2700}(1417,\cdot)$	$-1$	$1$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{163}{180}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{7}{180}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{7}{45}\right)$
$\chi_{2700}(1453,\cdot)$	$-1$	$1$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{157}{180}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{73}{180}\right)$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{28}{45}\right)$
$\chi_{2700}(1537,\cdot)$	$-1$	$1$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{179}{180}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{11}{180}\right)$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{11}{45}\right)$
$\chi_{2700}(1573,\cdot)$	$-1$	$1$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{101}{180}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{149}{180}\right)$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{14}{45}\right)$
$\chi_{2700}(1597,\cdot)$	$-1$	$1$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{7}{180}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{103}{180}\right)$	$e\left(\frac{73}{90}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{13}{45}\right)$
$\chi_{2700}(1633,\cdot)$	$-1$	$1$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{73}{180}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{97}{180}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{7}{45}\right)$
$\chi_{2700}(1717,\cdot)$	$-1$	$1$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{23}{180}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{107}{180}\right)$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{17}{45}\right)$
$\chi_{2700}(1753,\cdot)$	$-1$	$1$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{17}{180}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{173}{180}\right)$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{38}{45}\right)$

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	\(-1\)	\(1\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)
\(\chi_{2700}(13,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{109}{180}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{61}{180}\right)\)	\(e\left(\frac{31}{90}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{16}{45}\right)\)
\(\chi_{2700}(97,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{167}{180}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{143}{180}\right)\)	\(e\left(\frac{83}{90}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{8}{45}\right)\)
\(\chi_{2700}(133,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{53}{180}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{137}{180}\right)\)	\(e\left(\frac{77}{90}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{2}{45}\right)\)
\(\chi_{2700}(277,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{11}{180}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{59}{180}\right)\)	\(e\left(\frac{89}{90}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{14}{45}\right)\)
\(\chi_{2700}(313,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{149}{180}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{161}{180}\right)\)	\(e\left(\frac{11}{90}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{26}{45}\right)\)
\(\chi_{2700}(337,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{19}{180}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{151}{180}\right)\)	\(e\left(\frac{31}{90}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{16}{45}\right)\)
\(\chi_{2700}(373,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{121}{180}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{109}{180}\right)\)	\(e\left(\frac{79}{90}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{19}{45}\right)\)
\(\chi_{2700}(517,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{43}{180}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{67}{180}\right)\)	\(e\left(\frac{37}{90}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{22}{45}\right)\)
\(\chi_{2700}(553,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{37}{180}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{133}{180}\right)\)	\(e\left(\frac{13}{90}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{43}{45}\right)\)
\(\chi_{2700}(637,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{59}{180}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{71}{180}\right)\)	\(e\left(\frac{11}{90}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{26}{45}\right)\)
\(\chi_{2700}(673,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{161}{180}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{29}{180}\right)\)	\(e\left(\frac{59}{90}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{29}{45}\right)\)
\(\chi_{2700}(697,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{67}{180}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{163}{180}\right)\)	\(e\left(\frac{43}{90}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{28}{45}\right)\)
\(\chi_{2700}(733,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{133}{180}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{157}{180}\right)\)	\(e\left(\frac{37}{90}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{22}{45}\right)\)
\(\chi_{2700}(817,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{83}{180}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{167}{180}\right)\)	\(e\left(\frac{17}{90}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{32}{45}\right)\)
\(\chi_{2700}(853,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{77}{180}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{53}{180}\right)\)	\(e\left(\frac{83}{90}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{8}{45}\right)\)
\(\chi_{2700}(877,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{91}{180}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{79}{180}\right)\)	\(e\left(\frac{49}{90}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{34}{45}\right)\)
\(\chi_{2700}(913,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{49}{180}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{1}{180}\right)\)	\(e\left(\frac{61}{90}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{1}{45}\right)\)
\(\chi_{2700}(997,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{107}{180}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{83}{180}\right)\)	\(e\left(\frac{23}{90}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{38}{45}\right)\)
\(\chi_{2700}(1033,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{173}{180}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{77}{180}\right)\)	\(e\left(\frac{17}{90}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{32}{45}\right)\)
\(\chi_{2700}(1177,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{131}{180}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{179}{180}\right)\)	\(e\left(\frac{29}{90}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{44}{45}\right)\)
\(\chi_{2700}(1213,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{89}{180}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{101}{180}\right)\)	\(e\left(\frac{41}{90}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{11}{45}\right)\)
\(\chi_{2700}(1237,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{139}{180}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{91}{180}\right)\)	\(e\left(\frac{61}{90}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{1}{45}\right)\)
\(\chi_{2700}(1273,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{61}{180}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{49}{180}\right)\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{4}{45}\right)\)
\(\chi_{2700}(1417,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{163}{180}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{7}{180}\right)\)	\(e\left(\frac{67}{90}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{7}{45}\right)\)
\(\chi_{2700}(1453,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{157}{180}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{73}{180}\right)\)	\(e\left(\frac{43}{90}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{28}{45}\right)\)
\(\chi_{2700}(1537,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{179}{180}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{11}{180}\right)\)	\(e\left(\frac{41}{90}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{11}{45}\right)\)
\(\chi_{2700}(1573,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{101}{180}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{149}{180}\right)\)	\(e\left(\frac{89}{90}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{14}{45}\right)\)
\(\chi_{2700}(1597,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{7}{180}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{103}{180}\right)\)	\(e\left(\frac{73}{90}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{13}{45}\right)\)
\(\chi_{2700}(1633,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{73}{180}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{97}{180}\right)\)	\(e\left(\frac{67}{90}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{7}{45}\right)\)
\(\chi_{2700}(1717,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{23}{180}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{107}{180}\right)\)	\(e\left(\frac{47}{90}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{17}{45}\right)\)
\(\chi_{2700}(1753,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{17}{180}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{173}{180}\right)\)	\(e\left(\frac{23}{90}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{38}{45}\right)\)

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First 31 of 48 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.cr
Modulus	$2700$
Conductor	$675$
Order	$180$
Real	no
Primitive	no
Minimal	yes
Parity	odd

Modulus:	\(2700\)
Conductor:	\(675\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(180\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 675.bj	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)