LMFDB - Dirichlet character orbit 669.p

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(669, base_ring=CyclotomicField(222)) M = H._module chi = DirichletCharacter(H, M([111,89])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(5,669)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$669$
Conductor:	$669$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$222$	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:	$\Q(\zeta_{111})$
Fixed field:	Number field defined by a degree 222 polynomial (not computed)

First 31 of 72 characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$13$	$14$	$16$
$\chi_{669}(5,\cdot)$	$1$	$1$	$e\left(\frac{49}{74}\right)$	$e\left(\frac{12}{37}\right)$	$e\left(\frac{20}{111}\right)$	$e\left(\frac{7}{37}\right)$	$e\left(\frac{73}{74}\right)$	$e\left(\frac{187}{222}\right)$	$e\left(\frac{44}{111}\right)$	$e\left(\frac{69}{74}\right)$	$e\left(\frac{63}{74}\right)$	$e\left(\frac{24}{37}\right)$
$\chi_{669}(11,\cdot)$	$1$	$1$	$e\left(\frac{19}{74}\right)$	$e\left(\frac{19}{37}\right)$	$e\left(\frac{44}{111}\right)$	$e\left(\frac{8}{37}\right)$	$e\left(\frac{57}{74}\right)$	$e\left(\frac{145}{222}\right)$	$e\left(\frac{8}{111}\right)$	$e\left(\frac{63}{74}\right)$	$e\left(\frac{35}{74}\right)$	$e\left(\frac{1}{37}\right)$
$\chi_{669}(20,\cdot)$	$1$	$1$	$e\left(\frac{41}{74}\right)$	$e\left(\frac{4}{37}\right)$	$e\left(\frac{56}{111}\right)$	$e\left(\frac{27}{37}\right)$	$e\left(\frac{49}{74}\right)$	$e\left(\frac{13}{222}\right)$	$e\left(\frac{101}{111}\right)$	$e\left(\frac{23}{74}\right)$	$e\left(\frac{21}{74}\right)$	$e\left(\frac{8}{37}\right)$
$\chi_{669}(23,\cdot)$	$1$	$1$	$e\left(\frac{49}{74}\right)$	$e\left(\frac{12}{37}\right)$	$e\left(\frac{94}{111}\right)$	$e\left(\frac{7}{37}\right)$	$e\left(\frac{73}{74}\right)$	$e\left(\frac{113}{222}\right)$	$e\left(\frac{7}{111}\right)$	$e\left(\frac{69}{74}\right)$	$e\left(\frac{63}{74}\right)$	$e\left(\frac{24}{37}\right)$
$\chi_{669}(35,\cdot)$	$1$	$1$	$e\left(\frac{69}{74}\right)$	$e\left(\frac{32}{37}\right)$	$e\left(\frac{41}{111}\right)$	$e\left(\frac{31}{37}\right)$	$e\left(\frac{59}{74}\right)$	$e\left(\frac{67}{222}\right)$	$e\left(\frac{68}{111}\right)$	$e\left(\frac{73}{74}\right)$	$e\left(\frac{57}{74}\right)$	$e\left(\frac{27}{37}\right)$
$\chi_{669}(44,\cdot)$	$1$	$1$	$e\left(\frac{11}{74}\right)$	$e\left(\frac{11}{37}\right)$	$e\left(\frac{80}{111}\right)$	$e\left(\frac{28}{37}\right)$	$e\left(\frac{33}{74}\right)$	$e\left(\frac{193}{222}\right)$	$e\left(\frac{65}{111}\right)$	$e\left(\frac{17}{74}\right)$	$e\left(\frac{67}{74}\right)$	$e\left(\frac{22}{37}\right)$
$\chi_{669}(71,\cdot)$	$1$	$1$	$e\left(\frac{59}{74}\right)$	$e\left(\frac{22}{37}\right)$	$e\left(\frac{49}{111}\right)$	$e\left(\frac{19}{37}\right)$	$e\left(\frac{29}{74}\right)$	$e\left(\frac{53}{222}\right)$	$e\left(\frac{19}{111}\right)$	$e\left(\frac{71}{74}\right)$	$e\left(\frac{23}{74}\right)$	$e\left(\frac{7}{37}\right)$
$\chi_{669}(77,\cdot)$	$1$	$1$	$e\left(\frac{39}{74}\right)$	$e\left(\frac{2}{37}\right)$	$e\left(\frac{65}{111}\right)$	$e\left(\frac{32}{37}\right)$	$e\left(\frac{43}{74}\right)$	$e\left(\frac{25}{222}\right)$	$e\left(\frac{32}{111}\right)$	$e\left(\frac{67}{74}\right)$	$e\left(\frac{29}{74}\right)$	$e\left(\frac{4}{37}\right)$
$\chi_{669}(80,\cdot)$	$1$	$1$	$e\left(\frac{33}{74}\right)$	$e\left(\frac{33}{37}\right)$	$e\left(\frac{92}{111}\right)$	$e\left(\frac{10}{37}\right)$	$e\left(\frac{25}{74}\right)$	$e\left(\frac{61}{222}\right)$	$e\left(\frac{47}{111}\right)$	$e\left(\frac{51}{74}\right)$	$e\left(\frac{53}{74}\right)$	$e\left(\frac{29}{37}\right)$
$\chi_{669}(92,\cdot)$	$1$	$1$	$e\left(\frac{41}{74}\right)$	$e\left(\frac{4}{37}\right)$	$e\left(\frac{19}{111}\right)$	$e\left(\frac{27}{37}\right)$	$e\left(\frac{49}{74}\right)$	$e\left(\frac{161}{222}\right)$	$e\left(\frac{64}{111}\right)$	$e\left(\frac{23}{74}\right)$	$e\left(\frac{21}{74}\right)$	$e\left(\frac{8}{37}\right)$
$\chi_{669}(107,\cdot)$	$1$	$1$	$e\left(\frac{13}{74}\right)$	$e\left(\frac{13}{37}\right)$	$e\left(\frac{71}{111}\right)$	$e\left(\frac{23}{37}\right)$	$e\left(\frac{39}{74}\right)$	$e\left(\frac{181}{222}\right)$	$e\left(\frac{23}{111}\right)$	$e\left(\frac{47}{74}\right)$	$e\left(\frac{59}{74}\right)$	$e\left(\frac{26}{37}\right)$
$\chi_{669}(113,\cdot)$	$1$	$1$	$e\left(\frac{27}{74}\right)$	$e\left(\frac{27}{37}\right)$	$e\left(\frac{82}{111}\right)$	$e\left(\frac{25}{37}\right)$	$e\left(\frac{7}{74}\right)$	$e\left(\frac{23}{222}\right)$	$e\left(\frac{25}{111}\right)$	$e\left(\frac{35}{74}\right)$	$e\left(\frac{3}{74}\right)$	$e\left(\frac{17}{37}\right)$
$\chi_{669}(122,\cdot)$	$1$	$1$	$e\left(\frac{47}{74}\right)$	$e\left(\frac{10}{37}\right)$	$e\left(\frac{103}{111}\right)$	$e\left(\frac{12}{37}\right)$	$e\left(\frac{67}{74}\right)$	$e\left(\frac{125}{222}\right)$	$e\left(\frac{49}{111}\right)$	$e\left(\frac{39}{74}\right)$	$e\left(\frac{71}{74}\right)$	$e\left(\frac{20}{37}\right)$
$\chi_{669}(134,\cdot)$	$1$	$1$	$e\left(\frac{25}{74}\right)$	$e\left(\frac{25}{37}\right)$	$e\left(\frac{91}{111}\right)$	$e\left(\frac{30}{37}\right)$	$e\left(\frac{1}{74}\right)$	$e\left(\frac{35}{222}\right)$	$e\left(\frac{67}{111}\right)$	$e\left(\frac{5}{74}\right)$	$e\left(\frac{11}{74}\right)$	$e\left(\frac{13}{37}\right)$
$\chi_{669}(137,\cdot)$	$1$	$1$	$e\left(\frac{9}{74}\right)$	$e\left(\frac{9}{37}\right)$	$e\left(\frac{52}{111}\right)$	$e\left(\frac{33}{37}\right)$	$e\left(\frac{27}{74}\right)$	$e\left(\frac{131}{222}\right)$	$e\left(\frac{70}{111}\right)$	$e\left(\frac{61}{74}\right)$	$e\left(\frac{1}{74}\right)$	$e\left(\frac{18}{37}\right)$
$\chi_{669}(140,\cdot)$	$1$	$1$	$e\left(\frac{61}{74}\right)$	$e\left(\frac{24}{37}\right)$	$e\left(\frac{77}{111}\right)$	$e\left(\frac{14}{37}\right)$	$e\left(\frac{35}{74}\right)$	$e\left(\frac{115}{222}\right)$	$e\left(\frac{14}{111}\right)$	$e\left(\frac{27}{74}\right)$	$e\left(\frac{15}{74}\right)$	$e\left(\frac{11}{37}\right)$
$\chi_{669}(149,\cdot)$	$1$	$1$	$e\left(\frac{51}{74}\right)$	$e\left(\frac{14}{37}\right)$	$e\left(\frac{11}{111}\right)$	$e\left(\frac{2}{37}\right)$	$e\left(\frac{5}{74}\right)$	$e\left(\frac{175}{222}\right)$	$e\left(\frac{2}{111}\right)$	$e\left(\frac{25}{74}\right)$	$e\left(\frac{55}{74}\right)$	$e\left(\frac{28}{37}\right)$
$\chi_{669}(158,\cdot)$	$1$	$1$	$e\left(\frac{63}{74}\right)$	$e\left(\frac{26}{37}\right)$	$e\left(\frac{68}{111}\right)$	$e\left(\frac{9}{37}\right)$	$e\left(\frac{41}{74}\right)$	$e\left(\frac{103}{222}\right)$	$e\left(\frac{83}{111}\right)$	$e\left(\frac{57}{74}\right)$	$e\left(\frac{7}{74}\right)$	$e\left(\frac{15}{37}\right)$
$\chi_{669}(161,\cdot)$	$1$	$1$	$e\left(\frac{69}{74}\right)$	$e\left(\frac{32}{37}\right)$	$e\left(\frac{4}{111}\right)$	$e\left(\frac{31}{37}\right)$	$e\left(\frac{59}{74}\right)$	$e\left(\frac{215}{222}\right)$	$e\left(\frac{31}{111}\right)$	$e\left(\frac{73}{74}\right)$	$e\left(\frac{57}{74}\right)$	$e\left(\frac{27}{37}\right)$
$\chi_{669}(170,\cdot)$	$1$	$1$	$e\left(\frac{27}{74}\right)$	$e\left(\frac{27}{37}\right)$	$e\left(\frac{8}{111}\right)$	$e\left(\frac{25}{37}\right)$	$e\left(\frac{7}{74}\right)$	$e\left(\frac{97}{222}\right)$	$e\left(\frac{62}{111}\right)$	$e\left(\frac{35}{74}\right)$	$e\left(\frac{3}{74}\right)$	$e\left(\frac{17}{37}\right)$
$\chi_{669}(173,\cdot)$	$1$	$1$	$e\left(\frac{57}{74}\right)$	$e\left(\frac{20}{37}\right)$	$e\left(\frac{58}{111}\right)$	$e\left(\frac{24}{37}\right)$	$e\left(\frac{23}{74}\right)$	$e\left(\frac{65}{222}\right)$	$e\left(\frac{61}{111}\right)$	$e\left(\frac{41}{74}\right)$	$e\left(\frac{31}{74}\right)$	$e\left(\frac{3}{37}\right)$
$\chi_{669}(176,\cdot)$	$1$	$1$	$e\left(\frac{3}{74}\right)$	$e\left(\frac{3}{37}\right)$	$e\left(\frac{5}{111}\right)$	$e\left(\frac{11}{37}\right)$	$e\left(\frac{9}{74}\right)$	$e\left(\frac{19}{222}\right)$	$e\left(\frac{11}{111}\right)$	$e\left(\frac{45}{74}\right)$	$e\left(\frac{25}{74}\right)$	$e\left(\frac{6}{37}\right)$
$\chi_{669}(185,\cdot)$	$1$	$1$	$e\left(\frac{67}{74}\right)$	$e\left(\frac{30}{37}\right)$	$e\left(\frac{13}{111}\right)$	$e\left(\frac{36}{37}\right)$	$e\left(\frac{53}{74}\right)$	$e\left(\frac{5}{222}\right)$	$e\left(\frac{73}{111}\right)$	$e\left(\frac{43}{74}\right)$	$e\left(\frac{65}{74}\right)$	$e\left(\frac{23}{37}\right)$
$\chi_{669}(194,\cdot)$	$1$	$1$	$e\left(\frac{21}{74}\right)$	$e\left(\frac{21}{37}\right)$	$e\left(\frac{35}{111}\right)$	$e\left(\frac{3}{37}\right)$	$e\left(\frac{63}{74}\right)$	$e\left(\frac{133}{222}\right)$	$e\left(\frac{77}{111}\right)$	$e\left(\frac{19}{74}\right)$	$e\left(\frac{27}{74}\right)$	$e\left(\frac{5}{37}\right)$
$\chi_{669}(233,\cdot)$	$1$	$1$	$e\left(\frac{45}{74}\right)$	$e\left(\frac{8}{37}\right)$	$e\left(\frac{38}{111}\right)$	$e\left(\frac{17}{37}\right)$	$e\left(\frac{61}{74}\right)$	$e\left(\frac{211}{222}\right)$	$e\left(\frac{17}{111}\right)$	$e\left(\frac{9}{74}\right)$	$e\left(\frac{5}{74}\right)$	$e\left(\frac{16}{37}\right)$
$\chi_{669}(245,\cdot)$	$1$	$1$	$e\left(\frac{15}{74}\right)$	$e\left(\frac{15}{37}\right)$	$e\left(\frac{62}{111}\right)$	$e\left(\frac{18}{37}\right)$	$e\left(\frac{45}{74}\right)$	$e\left(\frac{169}{222}\right)$	$e\left(\frac{92}{111}\right)$	$e\left(\frac{3}{74}\right)$	$e\left(\frac{51}{74}\right)$	$e\left(\frac{30}{37}\right)$
$\chi_{669}(269,\cdot)$	$1$	$1$	$e\left(\frac{45}{74}\right)$	$e\left(\frac{8}{37}\right)$	$e\left(\frac{1}{111}\right)$	$e\left(\frac{17}{37}\right)$	$e\left(\frac{61}{74}\right)$	$e\left(\frac{137}{222}\right)$	$e\left(\frac{91}{111}\right)$	$e\left(\frac{9}{74}\right)$	$e\left(\frac{5}{74}\right)$	$e\left(\frac{16}{37}\right)$
$\chi_{669}(284,\cdot)$	$1$	$1$	$e\left(\frac{51}{74}\right)$	$e\left(\frac{14}{37}\right)$	$e\left(\frac{85}{111}\right)$	$e\left(\frac{2}{37}\right)$	$e\left(\frac{5}{74}\right)$	$e\left(\frac{101}{222}\right)$	$e\left(\frac{76}{111}\right)$	$e\left(\frac{25}{74}\right)$	$e\left(\frac{55}{74}\right)$	$e\left(\frac{28}{37}\right)$
$\chi_{669}(290,\cdot)$	$1$	$1$	$e\left(\frac{29}{74}\right)$	$e\left(\frac{29}{37}\right)$	$e\left(\frac{73}{111}\right)$	$e\left(\frac{20}{37}\right)$	$e\left(\frac{13}{74}\right)$	$e\left(\frac{11}{222}\right)$	$e\left(\frac{94}{111}\right)$	$e\left(\frac{65}{74}\right)$	$e\left(\frac{69}{74}\right)$	$e\left(\frac{21}{37}\right)$
$\chi_{669}(293,\cdot)$	$1$	$1$	$e\left(\frac{65}{74}\right)$	$e\left(\frac{28}{37}\right)$	$e\left(\frac{59}{111}\right)$	$e\left(\frac{4}{37}\right)$	$e\left(\frac{47}{74}\right)$	$e\left(\frac{91}{222}\right)$	$e\left(\frac{41}{111}\right)$	$e\left(\frac{13}{74}\right)$	$e\left(\frac{73}{74}\right)$	$e\left(\frac{19}{37}\right)$
$\chi_{669}(302,\cdot)$	$1$	$1$	$e\left(\frac{67}{74}\right)$	$e\left(\frac{30}{37}\right)$	$e\left(\frac{50}{111}\right)$	$e\left(\frac{36}{37}\right)$	$e\left(\frac{53}{74}\right)$	$e\left(\frac{79}{222}\right)$	$e\left(\frac{110}{111}\right)$	$e\left(\frac{43}{74}\right)$	$e\left(\frac{65}{74}\right)$	$e\left(\frac{23}{37}\right)$

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	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(13\)	\(14\)	\(16\)
\(\chi_{669}(5,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{74}\right)\)	\(e\left(\frac{12}{37}\right)\)	\(e\left(\frac{20}{111}\right)\)	\(e\left(\frac{7}{37}\right)\)	\(e\left(\frac{73}{74}\right)\)	\(e\left(\frac{187}{222}\right)\)	\(e\left(\frac{44}{111}\right)\)	\(e\left(\frac{69}{74}\right)\)	\(e\left(\frac{63}{74}\right)\)	\(e\left(\frac{24}{37}\right)\)
\(\chi_{669}(11,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{74}\right)\)	\(e\left(\frac{19}{37}\right)\)	\(e\left(\frac{44}{111}\right)\)	\(e\left(\frac{8}{37}\right)\)	\(e\left(\frac{57}{74}\right)\)	\(e\left(\frac{145}{222}\right)\)	\(e\left(\frac{8}{111}\right)\)	\(e\left(\frac{63}{74}\right)\)	\(e\left(\frac{35}{74}\right)\)	\(e\left(\frac{1}{37}\right)\)
\(\chi_{669}(20,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{74}\right)\)	\(e\left(\frac{4}{37}\right)\)	\(e\left(\frac{56}{111}\right)\)	\(e\left(\frac{27}{37}\right)\)	\(e\left(\frac{49}{74}\right)\)	\(e\left(\frac{13}{222}\right)\)	\(e\left(\frac{101}{111}\right)\)	\(e\left(\frac{23}{74}\right)\)	\(e\left(\frac{21}{74}\right)\)	\(e\left(\frac{8}{37}\right)\)
\(\chi_{669}(23,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{74}\right)\)	\(e\left(\frac{12}{37}\right)\)	\(e\left(\frac{94}{111}\right)\)	\(e\left(\frac{7}{37}\right)\)	\(e\left(\frac{73}{74}\right)\)	\(e\left(\frac{113}{222}\right)\)	\(e\left(\frac{7}{111}\right)\)	\(e\left(\frac{69}{74}\right)\)	\(e\left(\frac{63}{74}\right)\)	\(e\left(\frac{24}{37}\right)\)
\(\chi_{669}(35,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{69}{74}\right)\)	\(e\left(\frac{32}{37}\right)\)	\(e\left(\frac{41}{111}\right)\)	\(e\left(\frac{31}{37}\right)\)	\(e\left(\frac{59}{74}\right)\)	\(e\left(\frac{67}{222}\right)\)	\(e\left(\frac{68}{111}\right)\)	\(e\left(\frac{73}{74}\right)\)	\(e\left(\frac{57}{74}\right)\)	\(e\left(\frac{27}{37}\right)\)
\(\chi_{669}(44,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{74}\right)\)	\(e\left(\frac{11}{37}\right)\)	\(e\left(\frac{80}{111}\right)\)	\(e\left(\frac{28}{37}\right)\)	\(e\left(\frac{33}{74}\right)\)	\(e\left(\frac{193}{222}\right)\)	\(e\left(\frac{65}{111}\right)\)	\(e\left(\frac{17}{74}\right)\)	\(e\left(\frac{67}{74}\right)\)	\(e\left(\frac{22}{37}\right)\)
\(\chi_{669}(71,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{74}\right)\)	\(e\left(\frac{22}{37}\right)\)	\(e\left(\frac{49}{111}\right)\)	\(e\left(\frac{19}{37}\right)\)	\(e\left(\frac{29}{74}\right)\)	\(e\left(\frac{53}{222}\right)\)	\(e\left(\frac{19}{111}\right)\)	\(e\left(\frac{71}{74}\right)\)	\(e\left(\frac{23}{74}\right)\)	\(e\left(\frac{7}{37}\right)\)
\(\chi_{669}(77,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{39}{74}\right)\)	\(e\left(\frac{2}{37}\right)\)	\(e\left(\frac{65}{111}\right)\)	\(e\left(\frac{32}{37}\right)\)	\(e\left(\frac{43}{74}\right)\)	\(e\left(\frac{25}{222}\right)\)	\(e\left(\frac{32}{111}\right)\)	\(e\left(\frac{67}{74}\right)\)	\(e\left(\frac{29}{74}\right)\)	\(e\left(\frac{4}{37}\right)\)
\(\chi_{669}(80,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{33}{74}\right)\)	\(e\left(\frac{33}{37}\right)\)	\(e\left(\frac{92}{111}\right)\)	\(e\left(\frac{10}{37}\right)\)	\(e\left(\frac{25}{74}\right)\)	\(e\left(\frac{61}{222}\right)\)	\(e\left(\frac{47}{111}\right)\)	\(e\left(\frac{51}{74}\right)\)	\(e\left(\frac{53}{74}\right)\)	\(e\left(\frac{29}{37}\right)\)
\(\chi_{669}(92,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{74}\right)\)	\(e\left(\frac{4}{37}\right)\)	\(e\left(\frac{19}{111}\right)\)	\(e\left(\frac{27}{37}\right)\)	\(e\left(\frac{49}{74}\right)\)	\(e\left(\frac{161}{222}\right)\)	\(e\left(\frac{64}{111}\right)\)	\(e\left(\frac{23}{74}\right)\)	\(e\left(\frac{21}{74}\right)\)	\(e\left(\frac{8}{37}\right)\)
\(\chi_{669}(107,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{74}\right)\)	\(e\left(\frac{13}{37}\right)\)	\(e\left(\frac{71}{111}\right)\)	\(e\left(\frac{23}{37}\right)\)	\(e\left(\frac{39}{74}\right)\)	\(e\left(\frac{181}{222}\right)\)	\(e\left(\frac{23}{111}\right)\)	\(e\left(\frac{47}{74}\right)\)	\(e\left(\frac{59}{74}\right)\)	\(e\left(\frac{26}{37}\right)\)
\(\chi_{669}(113,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{74}\right)\)	\(e\left(\frac{27}{37}\right)\)	\(e\left(\frac{82}{111}\right)\)	\(e\left(\frac{25}{37}\right)\)	\(e\left(\frac{7}{74}\right)\)	\(e\left(\frac{23}{222}\right)\)	\(e\left(\frac{25}{111}\right)\)	\(e\left(\frac{35}{74}\right)\)	\(e\left(\frac{3}{74}\right)\)	\(e\left(\frac{17}{37}\right)\)
\(\chi_{669}(122,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{74}\right)\)	\(e\left(\frac{10}{37}\right)\)	\(e\left(\frac{103}{111}\right)\)	\(e\left(\frac{12}{37}\right)\)	\(e\left(\frac{67}{74}\right)\)	\(e\left(\frac{125}{222}\right)\)	\(e\left(\frac{49}{111}\right)\)	\(e\left(\frac{39}{74}\right)\)	\(e\left(\frac{71}{74}\right)\)	\(e\left(\frac{20}{37}\right)\)
\(\chi_{669}(134,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{74}\right)\)	\(e\left(\frac{25}{37}\right)\)	\(e\left(\frac{91}{111}\right)\)	\(e\left(\frac{30}{37}\right)\)	\(e\left(\frac{1}{74}\right)\)	\(e\left(\frac{35}{222}\right)\)	\(e\left(\frac{67}{111}\right)\)	\(e\left(\frac{5}{74}\right)\)	\(e\left(\frac{11}{74}\right)\)	\(e\left(\frac{13}{37}\right)\)
\(\chi_{669}(137,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{74}\right)\)	\(e\left(\frac{9}{37}\right)\)	\(e\left(\frac{52}{111}\right)\)	\(e\left(\frac{33}{37}\right)\)	\(e\left(\frac{27}{74}\right)\)	\(e\left(\frac{131}{222}\right)\)	\(e\left(\frac{70}{111}\right)\)	\(e\left(\frac{61}{74}\right)\)	\(e\left(\frac{1}{74}\right)\)	\(e\left(\frac{18}{37}\right)\)
\(\chi_{669}(140,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{74}\right)\)	\(e\left(\frac{24}{37}\right)\)	\(e\left(\frac{77}{111}\right)\)	\(e\left(\frac{14}{37}\right)\)	\(e\left(\frac{35}{74}\right)\)	\(e\left(\frac{115}{222}\right)\)	\(e\left(\frac{14}{111}\right)\)	\(e\left(\frac{27}{74}\right)\)	\(e\left(\frac{15}{74}\right)\)	\(e\left(\frac{11}{37}\right)\)
\(\chi_{669}(149,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{51}{74}\right)\)	\(e\left(\frac{14}{37}\right)\)	\(e\left(\frac{11}{111}\right)\)	\(e\left(\frac{2}{37}\right)\)	\(e\left(\frac{5}{74}\right)\)	\(e\left(\frac{175}{222}\right)\)	\(e\left(\frac{2}{111}\right)\)	\(e\left(\frac{25}{74}\right)\)	\(e\left(\frac{55}{74}\right)\)	\(e\left(\frac{28}{37}\right)\)
\(\chi_{669}(158,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{63}{74}\right)\)	\(e\left(\frac{26}{37}\right)\)	\(e\left(\frac{68}{111}\right)\)	\(e\left(\frac{9}{37}\right)\)	\(e\left(\frac{41}{74}\right)\)	\(e\left(\frac{103}{222}\right)\)	\(e\left(\frac{83}{111}\right)\)	\(e\left(\frac{57}{74}\right)\)	\(e\left(\frac{7}{74}\right)\)	\(e\left(\frac{15}{37}\right)\)
\(\chi_{669}(161,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{69}{74}\right)\)	\(e\left(\frac{32}{37}\right)\)	\(e\left(\frac{4}{111}\right)\)	\(e\left(\frac{31}{37}\right)\)	\(e\left(\frac{59}{74}\right)\)	\(e\left(\frac{215}{222}\right)\)	\(e\left(\frac{31}{111}\right)\)	\(e\left(\frac{73}{74}\right)\)	\(e\left(\frac{57}{74}\right)\)	\(e\left(\frac{27}{37}\right)\)
\(\chi_{669}(170,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{74}\right)\)	\(e\left(\frac{27}{37}\right)\)	\(e\left(\frac{8}{111}\right)\)	\(e\left(\frac{25}{37}\right)\)	\(e\left(\frac{7}{74}\right)\)	\(e\left(\frac{97}{222}\right)\)	\(e\left(\frac{62}{111}\right)\)	\(e\left(\frac{35}{74}\right)\)	\(e\left(\frac{3}{74}\right)\)	\(e\left(\frac{17}{37}\right)\)
\(\chi_{669}(173,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{57}{74}\right)\)	\(e\left(\frac{20}{37}\right)\)	\(e\left(\frac{58}{111}\right)\)	\(e\left(\frac{24}{37}\right)\)	\(e\left(\frac{23}{74}\right)\)	\(e\left(\frac{65}{222}\right)\)	\(e\left(\frac{61}{111}\right)\)	\(e\left(\frac{41}{74}\right)\)	\(e\left(\frac{31}{74}\right)\)	\(e\left(\frac{3}{37}\right)\)
\(\chi_{669}(176,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{74}\right)\)	\(e\left(\frac{3}{37}\right)\)	\(e\left(\frac{5}{111}\right)\)	\(e\left(\frac{11}{37}\right)\)	\(e\left(\frac{9}{74}\right)\)	\(e\left(\frac{19}{222}\right)\)	\(e\left(\frac{11}{111}\right)\)	\(e\left(\frac{45}{74}\right)\)	\(e\left(\frac{25}{74}\right)\)	\(e\left(\frac{6}{37}\right)\)
\(\chi_{669}(185,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{74}\right)\)	\(e\left(\frac{30}{37}\right)\)	\(e\left(\frac{13}{111}\right)\)	\(e\left(\frac{36}{37}\right)\)	\(e\left(\frac{53}{74}\right)\)	\(e\left(\frac{5}{222}\right)\)	\(e\left(\frac{73}{111}\right)\)	\(e\left(\frac{43}{74}\right)\)	\(e\left(\frac{65}{74}\right)\)	\(e\left(\frac{23}{37}\right)\)
\(\chi_{669}(194,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{21}{74}\right)\)	\(e\left(\frac{21}{37}\right)\)	\(e\left(\frac{35}{111}\right)\)	\(e\left(\frac{3}{37}\right)\)	\(e\left(\frac{63}{74}\right)\)	\(e\left(\frac{133}{222}\right)\)	\(e\left(\frac{77}{111}\right)\)	\(e\left(\frac{19}{74}\right)\)	\(e\left(\frac{27}{74}\right)\)	\(e\left(\frac{5}{37}\right)\)
\(\chi_{669}(233,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{45}{74}\right)\)	\(e\left(\frac{8}{37}\right)\)	\(e\left(\frac{38}{111}\right)\)	\(e\left(\frac{17}{37}\right)\)	\(e\left(\frac{61}{74}\right)\)	\(e\left(\frac{211}{222}\right)\)	\(e\left(\frac{17}{111}\right)\)	\(e\left(\frac{9}{74}\right)\)	\(e\left(\frac{5}{74}\right)\)	\(e\left(\frac{16}{37}\right)\)
\(\chi_{669}(245,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{15}{74}\right)\)	\(e\left(\frac{15}{37}\right)\)	\(e\left(\frac{62}{111}\right)\)	\(e\left(\frac{18}{37}\right)\)	\(e\left(\frac{45}{74}\right)\)	\(e\left(\frac{169}{222}\right)\)	\(e\left(\frac{92}{111}\right)\)	\(e\left(\frac{3}{74}\right)\)	\(e\left(\frac{51}{74}\right)\)	\(e\left(\frac{30}{37}\right)\)
\(\chi_{669}(269,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{45}{74}\right)\)	\(e\left(\frac{8}{37}\right)\)	\(e\left(\frac{1}{111}\right)\)	\(e\left(\frac{17}{37}\right)\)	\(e\left(\frac{61}{74}\right)\)	\(e\left(\frac{137}{222}\right)\)	\(e\left(\frac{91}{111}\right)\)	\(e\left(\frac{9}{74}\right)\)	\(e\left(\frac{5}{74}\right)\)	\(e\left(\frac{16}{37}\right)\)
\(\chi_{669}(284,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{51}{74}\right)\)	\(e\left(\frac{14}{37}\right)\)	\(e\left(\frac{85}{111}\right)\)	\(e\left(\frac{2}{37}\right)\)	\(e\left(\frac{5}{74}\right)\)	\(e\left(\frac{101}{222}\right)\)	\(e\left(\frac{76}{111}\right)\)	\(e\left(\frac{25}{74}\right)\)	\(e\left(\frac{55}{74}\right)\)	\(e\left(\frac{28}{37}\right)\)
\(\chi_{669}(290,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{74}\right)\)	\(e\left(\frac{29}{37}\right)\)	\(e\left(\frac{73}{111}\right)\)	\(e\left(\frac{20}{37}\right)\)	\(e\left(\frac{13}{74}\right)\)	\(e\left(\frac{11}{222}\right)\)	\(e\left(\frac{94}{111}\right)\)	\(e\left(\frac{65}{74}\right)\)	\(e\left(\frac{69}{74}\right)\)	\(e\left(\frac{21}{37}\right)\)
\(\chi_{669}(293,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{65}{74}\right)\)	\(e\left(\frac{28}{37}\right)\)	\(e\left(\frac{59}{111}\right)\)	\(e\left(\frac{4}{37}\right)\)	\(e\left(\frac{47}{74}\right)\)	\(e\left(\frac{91}{222}\right)\)	\(e\left(\frac{41}{111}\right)\)	\(e\left(\frac{13}{74}\right)\)	\(e\left(\frac{73}{74}\right)\)	\(e\left(\frac{19}{37}\right)\)
\(\chi_{669}(302,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{74}\right)\)	\(e\left(\frac{30}{37}\right)\)	\(e\left(\frac{50}{111}\right)\)	\(e\left(\frac{36}{37}\right)\)	\(e\left(\frac{53}{74}\right)\)	\(e\left(\frac{79}{222}\right)\)	\(e\left(\frac{110}{111}\right)\)	\(e\left(\frac{43}{74}\right)\)	\(e\left(\frac{65}{74}\right)\)	\(e\left(\frac{23}{37}\right)\)

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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.p
Modulus	$669$
Conductor	$669$
Order	$222$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(669\)
Conductor:	\(669\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(222\)	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)