LMFDB - Dirichlet character orbit 17550.ie

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(17550, base_ring=CyclotomicField(90)) M = H._module chi = DirichletCharacter(H, M([10,18,60])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(841, 17550)) 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("17550.841"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$17550$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$8775$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$45$	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 8775.ie	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 45 polynomial	comment:Fixed field sage:chi.fixed_field()

Characters in Galois orbit

Character	$-1$	$1$	$7$	$11$	$17$	$19$	$23$	$29$	$31$	$37$	$41$	$43$
$\chi_{17550}(841,\cdot)$	$1$	$1$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{7}{9}\right)$
$\chi_{17550}(1771,\cdot)$	$1$	$1$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{5}{9}\right)$
$\chi_{17550}(2011,\cdot)$	$1$	$1$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{1}{9}\right)$
$\chi_{17550}(2941,\cdot)$	$1$	$1$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{8}{9}\right)$
$\chi_{17550}(3181,\cdot)$	$1$	$1$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{4}{9}\right)$
$\chi_{17550}(4111,\cdot)$	$1$	$1$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{2}{9}\right)$
$\chi_{17550}(5281,\cdot)$	$1$	$1$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{5}{9}\right)$
$\chi_{17550}(5521,\cdot)$	$1$	$1$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{1}{9}\right)$
$\chi_{17550}(6691,\cdot)$	$1$	$1$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{4}{9}\right)$
$\chi_{17550}(7621,\cdot)$	$1$	$1$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{2}{9}\right)$
$\chi_{17550}(7861,\cdot)$	$1$	$1$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{7}{9}\right)$
$\chi_{17550}(8791,\cdot)$	$1$	$1$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{5}{9}\right)$
$\chi_{17550}(9031,\cdot)$	$1$	$1$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{1}{9}\right)$
$\chi_{17550}(9961,\cdot)$	$1$	$1$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{8}{9}\right)$
$\chi_{17550}(11131,\cdot)$	$1$	$1$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{2}{9}\right)$
$\chi_{17550}(11371,\cdot)$	$1$	$1$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{44}{45}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{7}{9}\right)$
$\chi_{17550}(12541,\cdot)$	$1$	$1$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{1}{9}\right)$
$\chi_{17550}(13471,\cdot)$	$1$	$1$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{41}{45}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{8}{45}\right)$	$e\left(\frac{8}{9}\right)$
$\chi_{17550}(13711,\cdot)$	$1$	$1$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{2}{45}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{4}{9}\right)$
$\chi_{17550}(14641,\cdot)$	$1$	$1$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{28}{45}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{11}{45}\right)$	$e\left(\frac{2}{9}\right)$
$\chi_{17550}(14881,\cdot)$	$1$	$1$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{19}{45}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{7}{9}\right)$
$\chi_{17550}(15811,\cdot)$	$1$	$1$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{45}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{26}{45}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{5}{9}\right)$
$\chi_{17550}(16981,\cdot)$	$1$	$1$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{31}{45}\right)$	$e\left(\frac{14}{45}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{8}{9}\right)$
$\chi_{17550}(17221,\cdot)$	$1$	$1$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{17}{45}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{16}{45}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{13}{45}\right)$	$e\left(\frac{4}{9}\right)$

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	\(-1\)	\(1\)	\(7\)	\(11\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)
\(\chi_{17550}(841,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{7}{9}\right)\)
\(\chi_{17550}(1771,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{5}{9}\right)\)
\(\chi_{17550}(2011,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{1}{9}\right)\)
\(\chi_{17550}(2941,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{8}{9}\right)\)
\(\chi_{17550}(3181,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{4}{9}\right)\)
\(\chi_{17550}(4111,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{2}{9}\right)\)
\(\chi_{17550}(5281,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{5}{9}\right)\)
\(\chi_{17550}(5521,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{1}{9}\right)\)
\(\chi_{17550}(6691,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{4}{9}\right)\)
\(\chi_{17550}(7621,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{2}{9}\right)\)
\(\chi_{17550}(7861,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{7}{9}\right)\)
\(\chi_{17550}(8791,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{5}{9}\right)\)
\(\chi_{17550}(9031,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{1}{9}\right)\)
\(\chi_{17550}(9961,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{8}{9}\right)\)
\(\chi_{17550}(11131,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{2}{9}\right)\)
\(\chi_{17550}(11371,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{32}{45}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{44}{45}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{7}{9}\right)\)
\(\chi_{17550}(12541,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{34}{45}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{22}{45}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{1}{9}\right)\)
\(\chi_{17550}(13471,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{41}{45}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{8}{45}\right)\)	\(e\left(\frac{8}{9}\right)\)
\(\chi_{17550}(13711,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{2}{45}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{4}{9}\right)\)
\(\chi_{17550}(14641,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{4}{45}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{28}{45}\right)\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{11}{45}\right)\)	\(e\left(\frac{2}{9}\right)\)
\(\chi_{17550}(14881,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{23}{45}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{19}{45}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{7}{9}\right)\)
\(\chi_{17550}(15811,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{1}{45}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{26}{45}\right)\)	\(e\left(\frac{7}{45}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{5}{9}\right)\)
\(\chi_{17550}(16981,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{43}{45}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{38}{45}\right)\)	\(e\left(\frac{31}{45}\right)\)	\(e\left(\frac{14}{45}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{8}{9}\right)\)
\(\chi_{17550}(17221,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{17}{45}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{37}{45}\right)\)	\(e\left(\frac{29}{45}\right)\)	\(e\left(\frac{16}{45}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{13}{45}\right)\)	\(e\left(\frac{4}{9}\right)\)

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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	17550.ie
Modulus	$17550$
Conductor	$8775$
Order	$45$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(17550\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(8775\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(45\)	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 8775.ie	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);