LMFDB - Dirichlet character orbit 669.m

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(669, base_ring=CyclotomicField(222)) M = H._module chi = DirichletCharacter(H, M([0,172])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(19,669)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$669$
Conductor:	$223$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$111$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 223.g	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:	$\Q(\zeta_{111})$
Fixed field:	Number field defined by a degree 111 polynomial (not computed)

First 31 of 72 characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$13$	$14$	$16$
$\chi_{669}(19,\cdot)$	$1$	$1$	$e\left(\frac{17}{37}\right)$	$e\left(\frac{34}{37}\right)$	$e\left(\frac{106}{111}\right)$	$e\left(\frac{26}{37}\right)$	$e\left(\frac{14}{37}\right)$	$e\left(\frac{46}{111}\right)$	$e\left(\frac{100}{111}\right)$	$e\left(\frac{33}{37}\right)$	$e\left(\frac{6}{37}\right)$	$e\left(\frac{31}{37}\right)$
$\chi_{669}(25,\cdot)$	$1$	$1$	$e\left(\frac{12}{37}\right)$	$e\left(\frac{24}{37}\right)$	$e\left(\frac{40}{111}\right)$	$e\left(\frac{14}{37}\right)$	$e\left(\frac{36}{37}\right)$	$e\left(\frac{76}{111}\right)$	$e\left(\frac{88}{111}\right)$	$e\left(\frac{32}{37}\right)$	$e\left(\frac{26}{37}\right)$	$e\left(\frac{11}{37}\right)$
$\chi_{669}(31,\cdot)$	$1$	$1$	$e\left(\frac{18}{37}\right)$	$e\left(\frac{36}{37}\right)$	$e\left(\frac{97}{111}\right)$	$e\left(\frac{21}{37}\right)$	$e\left(\frac{17}{37}\right)$	$e\left(\frac{40}{111}\right)$	$e\left(\frac{58}{111}\right)$	$e\left(\frac{11}{37}\right)$	$e\left(\frac{2}{37}\right)$	$e\left(\frac{35}{37}\right)$
$\chi_{669}(37,\cdot)$	$1$	$1$	$e\left(\frac{9}{37}\right)$	$e\left(\frac{18}{37}\right)$	$e\left(\frac{104}{111}\right)$	$e\left(\frac{29}{37}\right)$	$e\left(\frac{27}{37}\right)$	$e\left(\frac{20}{111}\right)$	$e\left(\frac{29}{111}\right)$	$e\left(\frac{24}{37}\right)$	$e\left(\frac{1}{37}\right)$	$e\left(\frac{36}{37}\right)$
$\chi_{669}(43,\cdot)$	$1$	$1$	$e\left(\frac{25}{37}\right)$	$e\left(\frac{13}{37}\right)$	$e\left(\frac{34}{111}\right)$	$e\left(\frac{23}{37}\right)$	$e\left(\frac{1}{37}\right)$	$e\left(\frac{109}{111}\right)$	$e\left(\frac{97}{111}\right)$	$e\left(\frac{5}{37}\right)$	$e\left(\frac{11}{37}\right)$	$e\left(\frac{26}{37}\right)$
$\chi_{669}(55,\cdot)$	$1$	$1$	$e\left(\frac{34}{37}\right)$	$e\left(\frac{31}{37}\right)$	$e\left(\frac{64}{111}\right)$	$e\left(\frac{15}{37}\right)$	$e\left(\frac{28}{37}\right)$	$e\left(\frac{55}{111}\right)$	$e\left(\frac{52}{111}\right)$	$e\left(\frac{29}{37}\right)$	$e\left(\frac{12}{37}\right)$	$e\left(\frac{25}{37}\right)$
$\chi_{669}(58,\cdot)$	$1$	$1$	$e\left(\frac{27}{37}\right)$	$e\left(\frac{17}{37}\right)$	$e\left(\frac{53}{111}\right)$	$e\left(\frac{13}{37}\right)$	$e\left(\frac{7}{37}\right)$	$e\left(\frac{23}{111}\right)$	$e\left(\frac{50}{111}\right)$	$e\left(\frac{35}{37}\right)$	$e\left(\frac{3}{37}\right)$	$e\left(\frac{34}{37}\right)$
$\chi_{669}(73,\cdot)$	$1$	$1$	$e\left(\frac{3}{37}\right)$	$e\left(\frac{6}{37}\right)$	$e\left(\frac{47}{111}\right)$	$e\left(\frac{22}{37}\right)$	$e\left(\frac{9}{37}\right)$	$e\left(\frac{56}{111}\right)$	$e\left(\frac{59}{111}\right)$	$e\left(\frac{8}{37}\right)$	$e\left(\frac{25}{37}\right)$	$e\left(\frac{12}{37}\right)$
$\chi_{669}(76,\cdot)$	$1$	$1$	$e\left(\frac{13}{37}\right)$	$e\left(\frac{26}{37}\right)$	$e\left(\frac{31}{111}\right)$	$e\left(\frac{9}{37}\right)$	$e\left(\frac{2}{37}\right)$	$e\left(\frac{70}{111}\right)$	$e\left(\frac{46}{111}\right)$	$e\left(\frac{10}{37}\right)$	$e\left(\frac{22}{37}\right)$	$e\left(\frac{15}{37}\right)$
$\chi_{669}(94,\cdot)$	$1$	$1$	$e\left(\frac{18}{37}\right)$	$e\left(\frac{36}{37}\right)$	$e\left(\frac{23}{111}\right)$	$e\left(\frac{21}{37}\right)$	$e\left(\frac{17}{37}\right)$	$e\left(\frac{77}{111}\right)$	$e\left(\frac{95}{111}\right)$	$e\left(\frac{11}{37}\right)$	$e\left(\frac{2}{37}\right)$	$e\left(\frac{35}{37}\right)$
$\chi_{669}(100,\cdot)$	$1$	$1$	$e\left(\frac{8}{37}\right)$	$e\left(\frac{16}{37}\right)$	$e\left(\frac{76}{111}\right)$	$e\left(\frac{34}{37}\right)$	$e\left(\frac{24}{37}\right)$	$e\left(\frac{100}{111}\right)$	$e\left(\frac{34}{111}\right)$	$e\left(\frac{9}{37}\right)$	$e\left(\frac{5}{37}\right)$	$e\left(\frac{32}{37}\right)$
$\chi_{669}(106,\cdot)$	$1$	$1$	$e\left(\frac{30}{37}\right)$	$e\left(\frac{23}{37}\right)$	$e\left(\frac{26}{111}\right)$	$e\left(\frac{35}{37}\right)$	$e\left(\frac{16}{37}\right)$	$e\left(\frac{5}{111}\right)$	$e\left(\frac{35}{111}\right)$	$e\left(\frac{6}{37}\right)$	$e\left(\frac{28}{37}\right)$	$e\left(\frac{9}{37}\right)$
$\chi_{669}(109,\cdot)$	$1$	$1$	$e\left(\frac{8}{37}\right)$	$e\left(\frac{16}{37}\right)$	$e\left(\frac{2}{111}\right)$	$e\left(\frac{34}{37}\right)$	$e\left(\frac{24}{37}\right)$	$e\left(\frac{26}{111}\right)$	$e\left(\frac{71}{111}\right)$	$e\left(\frac{9}{37}\right)$	$e\left(\frac{5}{37}\right)$	$e\left(\frac{32}{37}\right)$
$\chi_{669}(121,\cdot)$	$1$	$1$	$e\left(\frac{19}{37}\right)$	$e\left(\frac{1}{37}\right)$	$e\left(\frac{88}{111}\right)$	$e\left(\frac{16}{37}\right)$	$e\left(\frac{20}{37}\right)$	$e\left(\frac{34}{111}\right)$	$e\left(\frac{16}{111}\right)$	$e\left(\frac{26}{37}\right)$	$e\left(\frac{35}{37}\right)$	$e\left(\frac{2}{37}\right)$
$\chi_{669}(124,\cdot)$	$1$	$1$	$e\left(\frac{14}{37}\right)$	$e\left(\frac{28}{37}\right)$	$e\left(\frac{22}{111}\right)$	$e\left(\frac{4}{37}\right)$	$e\left(\frac{5}{37}\right)$	$e\left(\frac{64}{111}\right)$	$e\left(\frac{4}{111}\right)$	$e\left(\frac{25}{37}\right)$	$e\left(\frac{18}{37}\right)$	$e\left(\frac{19}{37}\right)$
$\chi_{669}(127,\cdot)$	$1$	$1$	$e\left(\frac{20}{37}\right)$	$e\left(\frac{3}{37}\right)$	$e\left(\frac{79}{111}\right)$	$e\left(\frac{11}{37}\right)$	$e\left(\frac{23}{37}\right)$	$e\left(\frac{28}{111}\right)$	$e\left(\frac{85}{111}\right)$	$e\left(\frac{4}{37}\right)$	$e\left(\frac{31}{37}\right)$	$e\left(\frac{6}{37}\right)$
$\chi_{669}(130,\cdot)$	$1$	$1$	$e\left(\frac{11}{37}\right)$	$e\left(\frac{22}{37}\right)$	$e\left(\frac{86}{111}\right)$	$e\left(\frac{19}{37}\right)$	$e\left(\frac{33}{37}\right)$	$e\left(\frac{8}{111}\right)$	$e\left(\frac{56}{111}\right)$	$e\left(\frac{17}{37}\right)$	$e\left(\frac{30}{37}\right)$	$e\left(\frac{7}{37}\right)$
$\chi_{669}(133,\cdot)$	$1$	$1$	$e\left(\frac{27}{37}\right)$	$e\left(\frac{17}{37}\right)$	$e\left(\frac{16}{111}\right)$	$e\left(\frac{13}{37}\right)$	$e\left(\frac{7}{37}\right)$	$e\left(\frac{97}{111}\right)$	$e\left(\frac{13}{111}\right)$	$e\left(\frac{35}{37}\right)$	$e\left(\frac{3}{37}\right)$	$e\left(\frac{34}{37}\right)$
$\chi_{669}(139,\cdot)$	$1$	$1$	$e\left(\frac{36}{37}\right)$	$e\left(\frac{35}{37}\right)$	$e\left(\frac{46}{111}\right)$	$e\left(\frac{5}{37}\right)$	$e\left(\frac{34}{37}\right)$	$e\left(\frac{43}{111}\right)$	$e\left(\frac{79}{111}\right)$	$e\left(\frac{22}{37}\right)$	$e\left(\frac{4}{37}\right)$	$e\left(\frac{33}{37}\right)$
$\chi_{669}(148,\cdot)$	$1$	$1$	$e\left(\frac{5}{37}\right)$	$e\left(\frac{10}{37}\right)$	$e\left(\frac{29}{111}\right)$	$e\left(\frac{12}{37}\right)$	$e\left(\frac{15}{37}\right)$	$e\left(\frac{44}{111}\right)$	$e\left(\frac{86}{111}\right)$	$e\left(\frac{1}{37}\right)$	$e\left(\frac{17}{37}\right)$	$e\left(\frac{20}{37}\right)$
$\chi_{669}(166,\cdot)$	$1$	$1$	$e\left(\frac{10}{37}\right)$	$e\left(\frac{20}{37}\right)$	$e\left(\frac{95}{111}\right)$	$e\left(\frac{24}{37}\right)$	$e\left(\frac{30}{37}\right)$	$e\left(\frac{14}{111}\right)$	$e\left(\frac{98}{111}\right)$	$e\left(\frac{2}{37}\right)$	$e\left(\frac{34}{37}\right)$	$e\left(\frac{3}{37}\right)$
$\chi_{669}(172,\cdot)$	$1$	$1$	$e\left(\frac{21}{37}\right)$	$e\left(\frac{5}{37}\right)$	$e\left(\frac{70}{111}\right)$	$e\left(\frac{6}{37}\right)$	$e\left(\frac{26}{37}\right)$	$e\left(\frac{22}{111}\right)$	$e\left(\frac{43}{111}\right)$	$e\left(\frac{19}{37}\right)$	$e\left(\frac{27}{37}\right)$	$e\left(\frac{10}{37}\right)$
$\chi_{669}(175,\cdot)$	$1$	$1$	$e\left(\frac{22}{37}\right)$	$e\left(\frac{7}{37}\right)$	$e\left(\frac{61}{111}\right)$	$e\left(\frac{1}{37}\right)$	$e\left(\frac{29}{37}\right)$	$e\left(\frac{16}{111}\right)$	$e\left(\frac{1}{111}\right)$	$e\left(\frac{34}{37}\right)$	$e\left(\frac{23}{37}\right)$	$e\left(\frac{14}{37}\right)$
$\chi_{669}(178,\cdot)$	$1$	$1$	$e\left(\frac{29}{37}\right)$	$e\left(\frac{21}{37}\right)$	$e\left(\frac{109}{111}\right)$	$e\left(\frac{3}{37}\right)$	$e\left(\frac{13}{37}\right)$	$e\left(\frac{85}{111}\right)$	$e\left(\frac{40}{111}\right)$	$e\left(\frac{28}{37}\right)$	$e\left(\frac{32}{37}\right)$	$e\left(\frac{5}{37}\right)$
$\chi_{669}(181,\cdot)$	$1$	$1$	$e\left(\frac{1}{37}\right)$	$e\left(\frac{2}{37}\right)$	$e\left(\frac{28}{111}\right)$	$e\left(\frac{32}{37}\right)$	$e\left(\frac{3}{37}\right)$	$e\left(\frac{31}{111}\right)$	$e\left(\frac{106}{111}\right)$	$e\left(\frac{15}{37}\right)$	$e\left(\frac{33}{37}\right)$	$e\left(\frac{4}{37}\right)$
$\chi_{669}(199,\cdot)$	$1$	$1$	$e\left(\frac{24}{37}\right)$	$e\left(\frac{11}{37}\right)$	$e\left(\frac{43}{111}\right)$	$e\left(\frac{28}{37}\right)$	$e\left(\frac{35}{37}\right)$	$e\left(\frac{4}{111}\right)$	$e\left(\frac{28}{111}\right)$	$e\left(\frac{27}{37}\right)$	$e\left(\frac{15}{37}\right)$	$e\left(\frac{22}{37}\right)$
$\chi_{669}(202,\cdot)$	$1$	$1$	$e\left(\frac{3}{37}\right)$	$e\left(\frac{6}{37}\right)$	$e\left(\frac{10}{111}\right)$	$e\left(\frac{22}{37}\right)$	$e\left(\frac{9}{37}\right)$	$e\left(\frac{19}{111}\right)$	$e\left(\frac{22}{111}\right)$	$e\left(\frac{8}{37}\right)$	$e\left(\frac{25}{37}\right)$	$e\left(\frac{12}{37}\right)$
$\chi_{669}(211,\cdot)$	$1$	$1$	$e\left(\frac{26}{37}\right)$	$e\left(\frac{15}{37}\right)$	$e\left(\frac{25}{111}\right)$	$e\left(\frac{18}{37}\right)$	$e\left(\frac{4}{37}\right)$	$e\left(\frac{103}{111}\right)$	$e\left(\frac{55}{111}\right)$	$e\left(\frac{20}{37}\right)$	$e\left(\frac{7}{37}\right)$	$e\left(\frac{30}{37}\right)$
$\chi_{669}(217,\cdot)$	$1$	$1$	$e\left(\frac{28}{37}\right)$	$e\left(\frac{19}{37}\right)$	$e\left(\frac{7}{111}\right)$	$e\left(\frac{8}{37}\right)$	$e\left(\frac{10}{37}\right)$	$e\left(\frac{91}{111}\right)$	$e\left(\frac{82}{111}\right)$	$e\left(\frac{13}{37}\right)$	$e\left(\frac{36}{37}\right)$	$e\left(\frac{1}{37}\right)$
$\chi_{669}(220,\cdot)$	$1$	$1$	$e\left(\frac{30}{37}\right)$	$e\left(\frac{23}{37}\right)$	$e\left(\frac{100}{111}\right)$	$e\left(\frac{35}{37}\right)$	$e\left(\frac{16}{37}\right)$	$e\left(\frac{79}{111}\right)$	$e\left(\frac{109}{111}\right)$	$e\left(\frac{6}{37}\right)$	$e\left(\frac{28}{37}\right)$	$e\left(\frac{9}{37}\right)$
$\chi_{669}(232,\cdot)$	$1$	$1$	$e\left(\frac{23}{37}\right)$	$e\left(\frac{9}{37}\right)$	$e\left(\frac{89}{111}\right)$	$e\left(\frac{33}{37}\right)$	$e\left(\frac{32}{37}\right)$	$e\left(\frac{47}{111}\right)$	$e\left(\frac{107}{111}\right)$	$e\left(\frac{12}{37}\right)$	$e\left(\frac{19}{37}\right)$	$e\left(\frac{18}{37}\right)$

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	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(13\)	\(14\)	\(16\)
\(\chi_{669}(19,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{37}\right)\)	\(e\left(\frac{34}{37}\right)\)	\(e\left(\frac{106}{111}\right)\)	\(e\left(\frac{26}{37}\right)\)	\(e\left(\frac{14}{37}\right)\)	\(e\left(\frac{46}{111}\right)\)	\(e\left(\frac{100}{111}\right)\)	\(e\left(\frac{33}{37}\right)\)	\(e\left(\frac{6}{37}\right)\)	\(e\left(\frac{31}{37}\right)\)
\(\chi_{669}(25,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{12}{37}\right)\)	\(e\left(\frac{24}{37}\right)\)	\(e\left(\frac{40}{111}\right)\)	\(e\left(\frac{14}{37}\right)\)	\(e\left(\frac{36}{37}\right)\)	\(e\left(\frac{76}{111}\right)\)	\(e\left(\frac{88}{111}\right)\)	\(e\left(\frac{32}{37}\right)\)	\(e\left(\frac{26}{37}\right)\)	\(e\left(\frac{11}{37}\right)\)
\(\chi_{669}(31,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{18}{37}\right)\)	\(e\left(\frac{36}{37}\right)\)	\(e\left(\frac{97}{111}\right)\)	\(e\left(\frac{21}{37}\right)\)	\(e\left(\frac{17}{37}\right)\)	\(e\left(\frac{40}{111}\right)\)	\(e\left(\frac{58}{111}\right)\)	\(e\left(\frac{11}{37}\right)\)	\(e\left(\frac{2}{37}\right)\)	\(e\left(\frac{35}{37}\right)\)
\(\chi_{669}(37,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{37}\right)\)	\(e\left(\frac{18}{37}\right)\)	\(e\left(\frac{104}{111}\right)\)	\(e\left(\frac{29}{37}\right)\)	\(e\left(\frac{27}{37}\right)\)	\(e\left(\frac{20}{111}\right)\)	\(e\left(\frac{29}{111}\right)\)	\(e\left(\frac{24}{37}\right)\)	\(e\left(\frac{1}{37}\right)\)	\(e\left(\frac{36}{37}\right)\)
\(\chi_{669}(43,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{37}\right)\)	\(e\left(\frac{13}{37}\right)\)	\(e\left(\frac{34}{111}\right)\)	\(e\left(\frac{23}{37}\right)\)	\(e\left(\frac{1}{37}\right)\)	\(e\left(\frac{109}{111}\right)\)	\(e\left(\frac{97}{111}\right)\)	\(e\left(\frac{5}{37}\right)\)	\(e\left(\frac{11}{37}\right)\)	\(e\left(\frac{26}{37}\right)\)
\(\chi_{669}(55,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{34}{37}\right)\)	\(e\left(\frac{31}{37}\right)\)	\(e\left(\frac{64}{111}\right)\)	\(e\left(\frac{15}{37}\right)\)	\(e\left(\frac{28}{37}\right)\)	\(e\left(\frac{55}{111}\right)\)	\(e\left(\frac{52}{111}\right)\)	\(e\left(\frac{29}{37}\right)\)	\(e\left(\frac{12}{37}\right)\)	\(e\left(\frac{25}{37}\right)\)
\(\chi_{669}(58,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{37}\right)\)	\(e\left(\frac{17}{37}\right)\)	\(e\left(\frac{53}{111}\right)\)	\(e\left(\frac{13}{37}\right)\)	\(e\left(\frac{7}{37}\right)\)	\(e\left(\frac{23}{111}\right)\)	\(e\left(\frac{50}{111}\right)\)	\(e\left(\frac{35}{37}\right)\)	\(e\left(\frac{3}{37}\right)\)	\(e\left(\frac{34}{37}\right)\)
\(\chi_{669}(73,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{37}\right)\)	\(e\left(\frac{6}{37}\right)\)	\(e\left(\frac{47}{111}\right)\)	\(e\left(\frac{22}{37}\right)\)	\(e\left(\frac{9}{37}\right)\)	\(e\left(\frac{56}{111}\right)\)	\(e\left(\frac{59}{111}\right)\)	\(e\left(\frac{8}{37}\right)\)	\(e\left(\frac{25}{37}\right)\)	\(e\left(\frac{12}{37}\right)\)
\(\chi_{669}(76,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{37}\right)\)	\(e\left(\frac{26}{37}\right)\)	\(e\left(\frac{31}{111}\right)\)	\(e\left(\frac{9}{37}\right)\)	\(e\left(\frac{2}{37}\right)\)	\(e\left(\frac{70}{111}\right)\)	\(e\left(\frac{46}{111}\right)\)	\(e\left(\frac{10}{37}\right)\)	\(e\left(\frac{22}{37}\right)\)	\(e\left(\frac{15}{37}\right)\)
\(\chi_{669}(94,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{18}{37}\right)\)	\(e\left(\frac{36}{37}\right)\)	\(e\left(\frac{23}{111}\right)\)	\(e\left(\frac{21}{37}\right)\)	\(e\left(\frac{17}{37}\right)\)	\(e\left(\frac{77}{111}\right)\)	\(e\left(\frac{95}{111}\right)\)	\(e\left(\frac{11}{37}\right)\)	\(e\left(\frac{2}{37}\right)\)	\(e\left(\frac{35}{37}\right)\)
\(\chi_{669}(100,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{37}\right)\)	\(e\left(\frac{16}{37}\right)\)	\(e\left(\frac{76}{111}\right)\)	\(e\left(\frac{34}{37}\right)\)	\(e\left(\frac{24}{37}\right)\)	\(e\left(\frac{100}{111}\right)\)	\(e\left(\frac{34}{111}\right)\)	\(e\left(\frac{9}{37}\right)\)	\(e\left(\frac{5}{37}\right)\)	\(e\left(\frac{32}{37}\right)\)
\(\chi_{669}(106,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{30}{37}\right)\)	\(e\left(\frac{23}{37}\right)\)	\(e\left(\frac{26}{111}\right)\)	\(e\left(\frac{35}{37}\right)\)	\(e\left(\frac{16}{37}\right)\)	\(e\left(\frac{5}{111}\right)\)	\(e\left(\frac{35}{111}\right)\)	\(e\left(\frac{6}{37}\right)\)	\(e\left(\frac{28}{37}\right)\)	\(e\left(\frac{9}{37}\right)\)
\(\chi_{669}(109,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{37}\right)\)	\(e\left(\frac{16}{37}\right)\)	\(e\left(\frac{2}{111}\right)\)	\(e\left(\frac{34}{37}\right)\)	\(e\left(\frac{24}{37}\right)\)	\(e\left(\frac{26}{111}\right)\)	\(e\left(\frac{71}{111}\right)\)	\(e\left(\frac{9}{37}\right)\)	\(e\left(\frac{5}{37}\right)\)	\(e\left(\frac{32}{37}\right)\)
\(\chi_{669}(121,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{37}\right)\)	\(e\left(\frac{1}{37}\right)\)	\(e\left(\frac{88}{111}\right)\)	\(e\left(\frac{16}{37}\right)\)	\(e\left(\frac{20}{37}\right)\)	\(e\left(\frac{34}{111}\right)\)	\(e\left(\frac{16}{111}\right)\)	\(e\left(\frac{26}{37}\right)\)	\(e\left(\frac{35}{37}\right)\)	\(e\left(\frac{2}{37}\right)\)
\(\chi_{669}(124,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{14}{37}\right)\)	\(e\left(\frac{28}{37}\right)\)	\(e\left(\frac{22}{111}\right)\)	\(e\left(\frac{4}{37}\right)\)	\(e\left(\frac{5}{37}\right)\)	\(e\left(\frac{64}{111}\right)\)	\(e\left(\frac{4}{111}\right)\)	\(e\left(\frac{25}{37}\right)\)	\(e\left(\frac{18}{37}\right)\)	\(e\left(\frac{19}{37}\right)\)
\(\chi_{669}(127,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{20}{37}\right)\)	\(e\left(\frac{3}{37}\right)\)	\(e\left(\frac{79}{111}\right)\)	\(e\left(\frac{11}{37}\right)\)	\(e\left(\frac{23}{37}\right)\)	\(e\left(\frac{28}{111}\right)\)	\(e\left(\frac{85}{111}\right)\)	\(e\left(\frac{4}{37}\right)\)	\(e\left(\frac{31}{37}\right)\)	\(e\left(\frac{6}{37}\right)\)
\(\chi_{669}(130,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{37}\right)\)	\(e\left(\frac{22}{37}\right)\)	\(e\left(\frac{86}{111}\right)\)	\(e\left(\frac{19}{37}\right)\)	\(e\left(\frac{33}{37}\right)\)	\(e\left(\frac{8}{111}\right)\)	\(e\left(\frac{56}{111}\right)\)	\(e\left(\frac{17}{37}\right)\)	\(e\left(\frac{30}{37}\right)\)	\(e\left(\frac{7}{37}\right)\)
\(\chi_{669}(133,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{37}\right)\)	\(e\left(\frac{17}{37}\right)\)	\(e\left(\frac{16}{111}\right)\)	\(e\left(\frac{13}{37}\right)\)	\(e\left(\frac{7}{37}\right)\)	\(e\left(\frac{97}{111}\right)\)	\(e\left(\frac{13}{111}\right)\)	\(e\left(\frac{35}{37}\right)\)	\(e\left(\frac{3}{37}\right)\)	\(e\left(\frac{34}{37}\right)\)
\(\chi_{669}(139,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{36}{37}\right)\)	\(e\left(\frac{35}{37}\right)\)	\(e\left(\frac{46}{111}\right)\)	\(e\left(\frac{5}{37}\right)\)	\(e\left(\frac{34}{37}\right)\)	\(e\left(\frac{43}{111}\right)\)	\(e\left(\frac{79}{111}\right)\)	\(e\left(\frac{22}{37}\right)\)	\(e\left(\frac{4}{37}\right)\)	\(e\left(\frac{33}{37}\right)\)
\(\chi_{669}(148,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{37}\right)\)	\(e\left(\frac{10}{37}\right)\)	\(e\left(\frac{29}{111}\right)\)	\(e\left(\frac{12}{37}\right)\)	\(e\left(\frac{15}{37}\right)\)	\(e\left(\frac{44}{111}\right)\)	\(e\left(\frac{86}{111}\right)\)	\(e\left(\frac{1}{37}\right)\)	\(e\left(\frac{17}{37}\right)\)	\(e\left(\frac{20}{37}\right)\)
\(\chi_{669}(166,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{10}{37}\right)\)	\(e\left(\frac{20}{37}\right)\)	\(e\left(\frac{95}{111}\right)\)	\(e\left(\frac{24}{37}\right)\)	\(e\left(\frac{30}{37}\right)\)	\(e\left(\frac{14}{111}\right)\)	\(e\left(\frac{98}{111}\right)\)	\(e\left(\frac{2}{37}\right)\)	\(e\left(\frac{34}{37}\right)\)	\(e\left(\frac{3}{37}\right)\)
\(\chi_{669}(172,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{21}{37}\right)\)	\(e\left(\frac{5}{37}\right)\)	\(e\left(\frac{70}{111}\right)\)	\(e\left(\frac{6}{37}\right)\)	\(e\left(\frac{26}{37}\right)\)	\(e\left(\frac{22}{111}\right)\)	\(e\left(\frac{43}{111}\right)\)	\(e\left(\frac{19}{37}\right)\)	\(e\left(\frac{27}{37}\right)\)	\(e\left(\frac{10}{37}\right)\)
\(\chi_{669}(175,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{22}{37}\right)\)	\(e\left(\frac{7}{37}\right)\)	\(e\left(\frac{61}{111}\right)\)	\(e\left(\frac{1}{37}\right)\)	\(e\left(\frac{29}{37}\right)\)	\(e\left(\frac{16}{111}\right)\)	\(e\left(\frac{1}{111}\right)\)	\(e\left(\frac{34}{37}\right)\)	\(e\left(\frac{23}{37}\right)\)	\(e\left(\frac{14}{37}\right)\)
\(\chi_{669}(178,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{37}\right)\)	\(e\left(\frac{21}{37}\right)\)	\(e\left(\frac{109}{111}\right)\)	\(e\left(\frac{3}{37}\right)\)	\(e\left(\frac{13}{37}\right)\)	\(e\left(\frac{85}{111}\right)\)	\(e\left(\frac{40}{111}\right)\)	\(e\left(\frac{28}{37}\right)\)	\(e\left(\frac{32}{37}\right)\)	\(e\left(\frac{5}{37}\right)\)
\(\chi_{669}(181,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{37}\right)\)	\(e\left(\frac{2}{37}\right)\)	\(e\left(\frac{28}{111}\right)\)	\(e\left(\frac{32}{37}\right)\)	\(e\left(\frac{3}{37}\right)\)	\(e\left(\frac{31}{111}\right)\)	\(e\left(\frac{106}{111}\right)\)	\(e\left(\frac{15}{37}\right)\)	\(e\left(\frac{33}{37}\right)\)	\(e\left(\frac{4}{37}\right)\)
\(\chi_{669}(199,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{24}{37}\right)\)	\(e\left(\frac{11}{37}\right)\)	\(e\left(\frac{43}{111}\right)\)	\(e\left(\frac{28}{37}\right)\)	\(e\left(\frac{35}{37}\right)\)	\(e\left(\frac{4}{111}\right)\)	\(e\left(\frac{28}{111}\right)\)	\(e\left(\frac{27}{37}\right)\)	\(e\left(\frac{15}{37}\right)\)	\(e\left(\frac{22}{37}\right)\)
\(\chi_{669}(202,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{37}\right)\)	\(e\left(\frac{6}{37}\right)\)	\(e\left(\frac{10}{111}\right)\)	\(e\left(\frac{22}{37}\right)\)	\(e\left(\frac{9}{37}\right)\)	\(e\left(\frac{19}{111}\right)\)	\(e\left(\frac{22}{111}\right)\)	\(e\left(\frac{8}{37}\right)\)	\(e\left(\frac{25}{37}\right)\)	\(e\left(\frac{12}{37}\right)\)
\(\chi_{669}(211,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{26}{37}\right)\)	\(e\left(\frac{15}{37}\right)\)	\(e\left(\frac{25}{111}\right)\)	\(e\left(\frac{18}{37}\right)\)	\(e\left(\frac{4}{37}\right)\)	\(e\left(\frac{103}{111}\right)\)	\(e\left(\frac{55}{111}\right)\)	\(e\left(\frac{20}{37}\right)\)	\(e\left(\frac{7}{37}\right)\)	\(e\left(\frac{30}{37}\right)\)
\(\chi_{669}(217,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{28}{37}\right)\)	\(e\left(\frac{19}{37}\right)\)	\(e\left(\frac{7}{111}\right)\)	\(e\left(\frac{8}{37}\right)\)	\(e\left(\frac{10}{37}\right)\)	\(e\left(\frac{91}{111}\right)\)	\(e\left(\frac{82}{111}\right)\)	\(e\left(\frac{13}{37}\right)\)	\(e\left(\frac{36}{37}\right)\)	\(e\left(\frac{1}{37}\right)\)
\(\chi_{669}(220,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{30}{37}\right)\)	\(e\left(\frac{23}{37}\right)\)	\(e\left(\frac{100}{111}\right)\)	\(e\left(\frac{35}{37}\right)\)	\(e\left(\frac{16}{37}\right)\)	\(e\left(\frac{79}{111}\right)\)	\(e\left(\frac{109}{111}\right)\)	\(e\left(\frac{6}{37}\right)\)	\(e\left(\frac{28}{37}\right)\)	\(e\left(\frac{9}{37}\right)\)
\(\chi_{669}(232,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{37}\right)\)	\(e\left(\frac{9}{37}\right)\)	\(e\left(\frac{89}{111}\right)\)	\(e\left(\frac{33}{37}\right)\)	\(e\left(\frac{32}{37}\right)\)	\(e\left(\frac{47}{111}\right)\)	\(e\left(\frac{107}{111}\right)\)	\(e\left(\frac{12}{37}\right)\)	\(e\left(\frac{19}{37}\right)\)	\(e\left(\frac{18}{37}\right)\)

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First 31 of 72 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	669.m
Modulus	$669$
Conductor	$223$
Order	$111$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(669\)
Conductor:	\(223\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(111\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 223.g	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)