LMFDB - Dirichlet character orbit 5400.fi

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(5400, base_ring=CyclotomicField(180)) M = H._module chi = DirichletCharacter(H, M([0,0,40,153])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(97, 5400)) 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("5400.97"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$5400$	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:	$180$	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.bj	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	yes
Parity:	odd	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(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	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{5400}(97,\cdot)$	$-1$	$1$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{167}{180}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{143}{180}\right)$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{8}{45}\right)$
$\chi_{5400}(313,\cdot)$	$-1$	$1$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{149}{180}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{161}{180}\right)$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{26}{45}\right)$
$\chi_{5400}(337,\cdot)$	$-1$	$1$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{19}{180}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{151}{180}\right)$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{16}{45}\right)$
$\chi_{5400}(553,\cdot)$	$-1$	$1$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{37}{180}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{133}{180}\right)$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{43}{45}\right)$
$\chi_{5400}(673,\cdot)$	$-1$	$1$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{161}{180}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{29}{180}\right)$	$e\left(\frac{59}{90}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{29}{45}\right)$
$\chi_{5400}(697,\cdot)$	$-1$	$1$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{67}{180}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{163}{180}\right)$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{28}{45}\right)$
$\chi_{5400}(817,\cdot)$	$-1$	$1$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{83}{180}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{167}{180}\right)$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{32}{45}\right)$
$\chi_{5400}(913,\cdot)$	$-1$	$1$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{49}{180}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{1}{180}\right)$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{1}{45}\right)$
$\chi_{5400}(1033,\cdot)$	$-1$	$1$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{173}{180}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{77}{180}\right)$	$e\left(\frac{17}{90}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{32}{45}\right)$
$\chi_{5400}(1177,\cdot)$	$-1$	$1$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{131}{180}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{179}{180}\right)$	$e\left(\frac{29}{90}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{44}{45}\right)$
$\chi_{5400}(1273,\cdot)$	$-1$	$1$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{61}{180}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{49}{180}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{4}{45}\right)$
$\chi_{5400}(1417,\cdot)$	$-1$	$1$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{163}{180}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{7}{180}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{7}{45}\right)$
$\chi_{5400}(1537,\cdot)$	$-1$	$1$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{179}{180}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{11}{180}\right)$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{11}{45}\right)$
$\chi_{5400}(1633,\cdot)$	$-1$	$1$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{73}{180}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{97}{180}\right)$	$e\left(\frac{67}{90}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{7}{45}\right)$
$\chi_{5400}(1753,\cdot)$	$-1$	$1$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{17}{180}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{173}{180}\right)$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{38}{45}\right)$
$\chi_{5400}(1777,\cdot)$	$-1$	$1$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{31}{180}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{19}{180}\right)$	$e\left(\frac{79}{90}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{19}{45}\right)$
$\chi_{5400}(1897,\cdot)$	$-1$	$1$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{47}{180}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{23}{180}\right)$	$e\left(\frac{53}{90}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{23}{45}\right)$
$\chi_{5400}(2113,\cdot)$	$-1$	$1$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{29}{180}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{41}{180}\right)$	$e\left(\frac{71}{90}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{41}{45}\right)$
$\chi_{5400}(2137,\cdot)$	$-1$	$1$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{79}{180}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{31}{180}\right)$	$e\left(\frac{1}{90}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{31}{45}\right)$
$\chi_{5400}(2353,\cdot)$	$-1$	$1$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{97}{180}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{13}{180}\right)$	$e\left(\frac{73}{90}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{13}{45}\right)$
$\chi_{5400}(2473,\cdot)$	$-1$	$1$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{41}{180}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{89}{180}\right)$	$e\left(\frac{29}{90}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{44}{45}\right)$
$\chi_{5400}(2497,\cdot)$	$-1$	$1$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{127}{180}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{43}{180}\right)$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{43}{45}\right)$
$\chi_{5400}(2617,\cdot)$	$-1$	$1$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{143}{180}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{47}{180}\right)$	$e\left(\frac{77}{90}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{2}{45}\right)$
$\chi_{5400}(2713,\cdot)$	$-1$	$1$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{109}{180}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{61}{180}\right)$	$e\left(\frac{31}{90}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{16}{45}\right)$
$\chi_{5400}(2833,\cdot)$	$-1$	$1$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{53}{180}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{137}{180}\right)$	$e\left(\frac{77}{90}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{2}{45}\right)$
$\chi_{5400}(2977,\cdot)$	$-1$	$1$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{11}{180}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{59}{180}\right)$	$e\left(\frac{89}{90}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{14}{45}\right)$
$\chi_{5400}(3073,\cdot)$	$-1$	$1$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{121}{180}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{109}{180}\right)$	$e\left(\frac{79}{90}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{19}{45}\right)$
$\chi_{5400}(3217,\cdot)$	$-1$	$1$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{43}{180}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{67}{180}\right)$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{22}{45}\right)$
$\chi_{5400}(3337,\cdot)$	$-1$	$1$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{59}{180}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{71}{180}\right)$	$e\left(\frac{11}{90}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{26}{45}\right)$
$\chi_{5400}(3433,\cdot)$	$-1$	$1$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{133}{180}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{157}{180}\right)$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{22}{45}\right)$
$\chi_{5400}(3553,\cdot)$	$-1$	$1$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{77}{180}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{53}{180}\right)$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{8}{45}\right)$

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	\(-1\)	\(1\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)
\(\chi_{5400}(97,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{167}{180}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{143}{180}\right)\)	\(e\left(\frac{83}{90}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{8}{45}\right)\)
\(\chi_{5400}(313,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{149}{180}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{161}{180}\right)\)	\(e\left(\frac{11}{90}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{26}{45}\right)\)
\(\chi_{5400}(337,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{19}{180}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{151}{180}\right)\)	\(e\left(\frac{31}{90}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{16}{45}\right)\)
\(\chi_{5400}(553,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{37}{180}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{133}{180}\right)\)	\(e\left(\frac{13}{90}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{43}{45}\right)\)
\(\chi_{5400}(673,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{161}{180}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{29}{180}\right)\)	\(e\left(\frac{59}{90}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{29}{45}\right)\)
\(\chi_{5400}(697,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{67}{180}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{163}{180}\right)\)	\(e\left(\frac{43}{90}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{28}{45}\right)\)
\(\chi_{5400}(817,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{83}{180}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{167}{180}\right)\)	\(e\left(\frac{17}{90}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{32}{45}\right)\)
\(\chi_{5400}(913,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{49}{180}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{1}{180}\right)\)	\(e\left(\frac{61}{90}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{1}{45}\right)\)
\(\chi_{5400}(1033,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{173}{180}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{77}{180}\right)\)	\(e\left(\frac{17}{90}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{32}{45}\right)\)
\(\chi_{5400}(1177,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{131}{180}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{179}{180}\right)\)	\(e\left(\frac{29}{90}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{44}{45}\right)\)
\(\chi_{5400}(1273,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{61}{180}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{49}{180}\right)\)	\(e\left(\frac{19}{90}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{4}{45}\right)\)
\(\chi_{5400}(1417,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{163}{180}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{7}{180}\right)\)	\(e\left(\frac{67}{90}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{7}{45}\right)\)
\(\chi_{5400}(1537,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{179}{180}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{11}{180}\right)\)	\(e\left(\frac{41}{90}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{11}{45}\right)\)
\(\chi_{5400}(1633,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{73}{180}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{97}{180}\right)\)	\(e\left(\frac{67}{90}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{7}{45}\right)\)
\(\chi_{5400}(1753,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{17}{180}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{173}{180}\right)\)	\(e\left(\frac{23}{90}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{38}{45}\right)\)
\(\chi_{5400}(1777,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{31}{180}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{19}{180}\right)\)	\(e\left(\frac{79}{90}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{19}{45}\right)\)
\(\chi_{5400}(1897,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{47}{180}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{23}{180}\right)\)	\(e\left(\frac{53}{90}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{23}{45}\right)\)
\(\chi_{5400}(2113,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{29}{180}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{41}{180}\right)\)	\(e\left(\frac{71}{90}\right)\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{41}{45}\right)\)
\(\chi_{5400}(2137,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{79}{180}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{31}{180}\right)\)	\(e\left(\frac{1}{90}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{31}{45}\right)\)
\(\chi_{5400}(2353,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{97}{180}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{13}{180}\right)\)	\(e\left(\frac{73}{90}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{13}{45}\right)\)
\(\chi_{5400}(2473,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{41}{180}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{89}{180}\right)\)	\(e\left(\frac{29}{90}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{44}{45}\right)\)
\(\chi_{5400}(2497,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{127}{180}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{43}{180}\right)\)	\(e\left(\frac{13}{90}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{43}{45}\right)\)
\(\chi_{5400}(2617,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{143}{180}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{47}{180}\right)\)	\(e\left(\frac{77}{90}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{2}{45}\right)\)
\(\chi_{5400}(2713,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{109}{180}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{61}{180}\right)\)	\(e\left(\frac{31}{90}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{16}{45}\right)\)
\(\chi_{5400}(2833,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{53}{180}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{137}{180}\right)\)	\(e\left(\frac{77}{90}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{2}{45}\right)\)
\(\chi_{5400}(2977,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{11}{180}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{59}{180}\right)\)	\(e\left(\frac{89}{90}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{14}{45}\right)\)
\(\chi_{5400}(3073,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{121}{180}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{109}{180}\right)\)	\(e\left(\frac{79}{90}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{19}{45}\right)\)
\(\chi_{5400}(3217,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{43}{180}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{67}{180}\right)\)	\(e\left(\frac{37}{90}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{22}{45}\right)\)
\(\chi_{5400}(3337,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{59}{180}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{71}{180}\right)\)	\(e\left(\frac{11}{90}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{26}{45}\right)\)
\(\chi_{5400}(3433,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{133}{180}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{157}{180}\right)\)	\(e\left(\frac{37}{90}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{22}{45}\right)\)
\(\chi_{5400}(3553,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{77}{180}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{53}{180}\right)\)	\(e\left(\frac{83}{90}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{8}{45}\right)\)

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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	5400.fi
Modulus	$5400$
Conductor	$675$
Order	$180$
Real	no
Primitive	no
Minimal	yes
Parity	odd

Modulus:	\(5400\)	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:	\(180\)	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.bj	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	yes
Parity:	odd	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);