LMFDB - Dirichlet character orbit 767.w

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(767, base_ring=CyclotomicField(348)) M = H._module chi = DirichletCharacter(H, M([319,108])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(7, 767)) 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("767.7"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$767$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$767$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$348$	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:	yes	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:	$\Q(\zeta_{348})$	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 348 polynomial (not computed)	comment:Fixed field sage:chi.fixed_field()

First 31 of 112 characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{767}(7,\cdot)$	$-1$	$1$	$e\left(\frac{79}{348}\right)$	$e\left(\frac{16}{87}\right)$	$e\left(\frac{79}{174}\right)$	$e\left(\frac{13}{116}\right)$	$e\left(\frac{143}{348}\right)$	$e\left(\frac{233}{348}\right)$	$e\left(\frac{79}{116}\right)$	$e\left(\frac{32}{87}\right)$	$e\left(\frac{59}{174}\right)$	$e\left(\frac{61}{348}\right)$
$\chi_{767}(15,\cdot)$	$-1$	$1$	$e\left(\frac{17}{348}\right)$	$e\left(\frac{53}{87}\right)$	$e\left(\frac{17}{174}\right)$	$e\left(\frac{63}{116}\right)$	$e\left(\frac{229}{348}\right)$	$e\left(\frac{103}{348}\right)$	$e\left(\frac{17}{116}\right)$	$e\left(\frac{19}{87}\right)$	$e\left(\frac{103}{174}\right)$	$e\left(\frac{251}{348}\right)$
$\chi_{767}(19,\cdot)$	$-1$	$1$	$e\left(\frac{25}{348}\right)$	$e\left(\frac{37}{87}\right)$	$e\left(\frac{25}{174}\right)$	$e\left(\frac{79}{116}\right)$	$e\left(\frac{173}{348}\right)$	$e\left(\frac{131}{348}\right)$	$e\left(\frac{25}{116}\right)$	$e\left(\frac{74}{87}\right)$	$e\left(\frac{131}{174}\right)$	$e\left(\frac{103}{348}\right)$
$\chi_{767}(20,\cdot)$	$-1$	$1$	$e\left(\frac{19}{348}\right)$	$e\left(\frac{49}{87}\right)$	$e\left(\frac{19}{174}\right)$	$e\left(\frac{9}{116}\right)$	$e\left(\frac{215}{348}\right)$	$e\left(\frac{197}{348}\right)$	$e\left(\frac{19}{116}\right)$	$e\left(\frac{11}{87}\right)$	$e\left(\frac{23}{174}\right)$	$e\left(\frac{301}{348}\right)$
$\chi_{767}(28,\cdot)$	$-1$	$1$	$e\left(\frac{149}{348}\right)$	$e\left(\frac{50}{87}\right)$	$e\left(\frac{149}{174}\right)$	$e\left(\frac{95}{116}\right)$	$e\left(\frac{1}{348}\right)$	$e\left(\frac{43}{348}\right)$	$e\left(\frac{33}{116}\right)$	$e\left(\frac{13}{87}\right)$	$e\left(\frac{43}{174}\right)$	$e\left(\frac{71}{348}\right)$
$\chi_{767}(41,\cdot)$	$-1$	$1$	$e\left(\frac{113}{348}\right)$	$e\left(\frac{35}{87}\right)$	$e\left(\frac{113}{174}\right)$	$e\left(\frac{23}{116}\right)$	$e\left(\frac{253}{348}\right)$	$e\left(\frac{91}{348}\right)$	$e\left(\frac{113}{116}\right)$	$e\left(\frac{70}{87}\right)$	$e\left(\frac{91}{174}\right)$	$e\left(\frac{215}{348}\right)$
$\chi_{767}(45,\cdot)$	$-1$	$1$	$e\left(\frac{85}{348}\right)$	$e\left(\frac{4}{87}\right)$	$e\left(\frac{85}{174}\right)$	$e\left(\frac{83}{116}\right)$	$e\left(\frac{101}{348}\right)$	$e\left(\frac{167}{348}\right)$	$e\left(\frac{85}{116}\right)$	$e\left(\frac{8}{87}\right)$	$e\left(\frac{167}{174}\right)$	$e\left(\frac{211}{348}\right)$
$\chi_{767}(46,\cdot)$	$-1$	$1$	$e\left(\frac{67}{348}\right)$	$e\left(\frac{40}{87}\right)$	$e\left(\frac{67}{174}\right)$	$e\left(\frac{105}{116}\right)$	$e\left(\frac{227}{348}\right)$	$e\left(\frac{17}{348}\right)$	$e\left(\frac{67}{116}\right)$	$e\left(\frac{80}{87}\right)$	$e\left(\frac{17}{174}\right)$	$e\left(\frac{109}{348}\right)$
$\chi_{767}(63,\cdot)$	$-1$	$1$	$e\left(\frac{215}{348}\right)$	$e\left(\frac{5}{87}\right)$	$e\left(\frac{41}{174}\right)$	$e\left(\frac{53}{116}\right)$	$e\left(\frac{235}{348}\right)$	$e\left(\frac{13}{348}\right)$	$e\left(\frac{99}{116}\right)$	$e\left(\frac{10}{87}\right)$	$e\left(\frac{13}{174}\right)$	$e\left(\frac{329}{348}\right)$
$\chi_{767}(71,\cdot)$	$-1$	$1$	$e\left(\frac{109}{348}\right)$	$e\left(\frac{43}{87}\right)$	$e\left(\frac{109}{174}\right)$	$e\left(\frac{15}{116}\right)$	$e\left(\frac{281}{348}\right)$	$e\left(\frac{251}{348}\right)$	$e\left(\frac{109}{116}\right)$	$e\left(\frac{86}{87}\right)$	$e\left(\frac{77}{174}\right)$	$e\left(\frac{115}{348}\right)$
$\chi_{767}(76,\cdot)$	$-1$	$1$	$e\left(\frac{95}{348}\right)$	$e\left(\frac{71}{87}\right)$	$e\left(\frac{95}{174}\right)$	$e\left(\frac{45}{116}\right)$	$e\left(\frac{31}{348}\right)$	$e\left(\frac{289}{348}\right)$	$e\left(\frac{95}{116}\right)$	$e\left(\frac{55}{87}\right)$	$e\left(\frac{115}{174}\right)$	$e\left(\frac{113}{348}\right)$
$\chi_{767}(80,\cdot)$	$-1$	$1$	$e\left(\frac{89}{348}\right)$	$e\left(\frac{83}{87}\right)$	$e\left(\frac{89}{174}\right)$	$e\left(\frac{91}{116}\right)$	$e\left(\frac{73}{348}\right)$	$e\left(\frac{7}{348}\right)$	$e\left(\frac{89}{116}\right)$	$e\left(\frac{79}{87}\right)$	$e\left(\frac{7}{174}\right)$	$e\left(\frac{311}{348}\right)$
$\chi_{767}(84,\cdot)$	$-1$	$1$	$e\left(\frac{217}{348}\right)$	$e\left(\frac{1}{87}\right)$	$e\left(\frac{43}{174}\right)$	$e\left(\frac{115}{116}\right)$	$e\left(\frac{221}{348}\right)$	$e\left(\frac{107}{348}\right)$	$e\left(\frac{101}{116}\right)$	$e\left(\frac{2}{87}\right)$	$e\left(\frac{107}{174}\right)$	$e\left(\frac{31}{348}\right)$
$\chi_{767}(85,\cdot)$	$-1$	$1$	$e\left(\frac{247}{348}\right)$	$e\left(\frac{28}{87}\right)$	$e\left(\frac{73}{174}\right)$	$e\left(\frac{1}{116}\right)$	$e\left(\frac{11}{348}\right)$	$e\left(\frac{125}{348}\right)$	$e\left(\frac{15}{116}\right)$	$e\left(\frac{56}{87}\right)$	$e\left(\frac{125}{174}\right)$	$e\left(\frac{85}{348}\right)$
$\chi_{767}(110,\cdot)$	$-1$	$1$	$e\left(\frac{337}{348}\right)$	$e\left(\frac{22}{87}\right)$	$e\left(\frac{163}{174}\right)$	$e\left(\frac{7}{116}\right)$	$e\left(\frac{77}{348}\right)$	$e\left(\frac{179}{348}\right)$	$e\left(\frac{105}{116}\right)$	$e\left(\frac{44}{87}\right)$	$e\left(\frac{5}{174}\right)$	$e\left(\frac{247}{348}\right)$
$\chi_{767}(123,\cdot)$	$-1$	$1$	$e\left(\frac{181}{348}\right)$	$e\left(\frac{73}{87}\right)$	$e\left(\frac{7}{174}\right)$	$e\left(\frac{43}{116}\right)$	$e\left(\frac{125}{348}\right)$	$e\left(\frac{155}{348}\right)$	$e\left(\frac{65}{116}\right)$	$e\left(\frac{59}{87}\right)$	$e\left(\frac{155}{174}\right)$	$e\left(\frac{175}{348}\right)$
$\chi_{767}(137,\cdot)$	$-1$	$1$	$e\left(\frac{199}{348}\right)$	$e\left(\frac{37}{87}\right)$	$e\left(\frac{25}{174}\right)$	$e\left(\frac{21}{116}\right)$	$e\left(\frac{347}{348}\right)$	$e\left(\frac{305}{348}\right)$	$e\left(\frac{83}{116}\right)$	$e\left(\frac{74}{87}\right)$	$e\left(\frac{131}{174}\right)$	$e\left(\frac{277}{348}\right)$
$\chi_{767}(145,\cdot)$	$-1$	$1$	$e\left(\frac{233}{348}\right)$	$e\left(\frac{56}{87}\right)$	$e\left(\frac{59}{174}\right)$	$e\left(\frac{31}{116}\right)$	$e\left(\frac{109}{348}\right)$	$e\left(\frac{163}{348}\right)$	$e\left(\frac{1}{116}\right)$	$e\left(\frac{25}{87}\right)$	$e\left(\frac{163}{174}\right)$	$e\left(\frac{83}{348}\right)$
$\chi_{767}(154,\cdot)$	$-1$	$1$	$e\left(\frac{119}{348}\right)$	$e\left(\frac{23}{87}\right)$	$e\left(\frac{119}{174}\right)$	$e\left(\frac{93}{116}\right)$	$e\left(\frac{211}{348}\right)$	$e\left(\frac{25}{348}\right)$	$e\left(\frac{3}{116}\right)$	$e\left(\frac{46}{87}\right)$	$e\left(\frac{25}{174}\right)$	$e\left(\frac{17}{348}\right)$
$\chi_{767}(163,\cdot)$	$-1$	$1$	$e\left(\frac{259}{348}\right)$	$e\left(\frac{4}{87}\right)$	$e\left(\frac{85}{174}\right)$	$e\left(\frac{25}{116}\right)$	$e\left(\frac{275}{348}\right)$	$e\left(\frac{341}{348}\right)$	$e\left(\frac{27}{116}\right)$	$e\left(\frac{8}{87}\right)$	$e\left(\frac{167}{174}\right)$	$e\left(\frac{37}{348}\right)$
$\chi_{767}(167,\cdot)$	$-1$	$1$	$e\left(\frac{71}{348}\right)$	$e\left(\frac{32}{87}\right)$	$e\left(\frac{71}{174}\right)$	$e\left(\frac{113}{116}\right)$	$e\left(\frac{199}{348}\right)$	$e\left(\frac{205}{348}\right)$	$e\left(\frac{71}{116}\right)$	$e\left(\frac{64}{87}\right)$	$e\left(\frac{31}{174}\right)$	$e\left(\frac{209}{348}\right)$
$\chi_{767}(171,\cdot)$	$-1$	$1$	$e\left(\frac{161}{348}\right)$	$e\left(\frac{26}{87}\right)$	$e\left(\frac{161}{174}\right)$	$e\left(\frac{3}{116}\right)$	$e\left(\frac{265}{348}\right)$	$e\left(\frac{259}{348}\right)$	$e\left(\frac{45}{116}\right)$	$e\left(\frac{52}{87}\right)$	$e\left(\frac{85}{174}\right)$	$e\left(\frac{23}{348}\right)$
$\chi_{767}(175,\cdot)$	$-1$	$1$	$e\left(\frac{325}{348}\right)$	$e\left(\frac{46}{87}\right)$	$e\left(\frac{151}{174}\right)$	$e\left(\frac{99}{116}\right)$	$e\left(\frac{161}{348}\right)$	$e\left(\frac{311}{348}\right)$	$e\left(\frac{93}{116}\right)$	$e\left(\frac{5}{87}\right)$	$e\left(\frac{137}{174}\right)$	$e\left(\frac{295}{348}\right)$
$\chi_{767}(180,\cdot)$	$-1$	$1$	$e\left(\frac{155}{348}\right)$	$e\left(\frac{38}{87}\right)$	$e\left(\frac{155}{174}\right)$	$e\left(\frac{49}{116}\right)$	$e\left(\frac{307}{348}\right)$	$e\left(\frac{325}{348}\right)$	$e\left(\frac{39}{116}\right)$	$e\left(\frac{76}{87}\right)$	$e\left(\frac{151}{174}\right)$	$e\left(\frac{221}{348}\right)$
$\chi_{767}(184,\cdot)$	$-1$	$1$	$e\left(\frac{137}{348}\right)$	$e\left(\frac{74}{87}\right)$	$e\left(\frac{137}{174}\right)$	$e\left(\frac{71}{116}\right)$	$e\left(\frac{85}{348}\right)$	$e\left(\frac{175}{348}\right)$	$e\left(\frac{21}{116}\right)$	$e\left(\frac{61}{87}\right)$	$e\left(\frac{1}{174}\right)$	$e\left(\frac{119}{348}\right)$
$\chi_{767}(189,\cdot)$	$-1$	$1$	$e\left(\frac{283}{348}\right)$	$e\left(\frac{43}{87}\right)$	$e\left(\frac{109}{174}\right)$	$e\left(\frac{73}{116}\right)$	$e\left(\frac{107}{348}\right)$	$e\left(\frac{77}{348}\right)$	$e\left(\frac{51}{116}\right)$	$e\left(\frac{86}{87}\right)$	$e\left(\frac{77}{174}\right)$	$e\left(\frac{289}{348}\right)$
$\chi_{767}(193,\cdot)$	$-1$	$1$	$e\left(\frac{227}{348}\right)$	$e\left(\frac{68}{87}\right)$	$e\left(\frac{53}{174}\right)$	$e\left(\frac{77}{116}\right)$	$e\left(\frac{151}{348}\right)$	$e\left(\frac{229}{348}\right)$	$e\left(\frac{111}{116}\right)$	$e\left(\frac{49}{87}\right)$	$e\left(\frac{55}{174}\right)$	$e\left(\frac{281}{348}\right)$
$\chi_{767}(197,\cdot)$	$-1$	$1$	$e\left(\frac{77}{348}\right)$	$e\left(\frac{20}{87}\right)$	$e\left(\frac{77}{174}\right)$	$e\left(\frac{67}{116}\right)$	$e\left(\frac{157}{348}\right)$	$e\left(\frac{139}{348}\right)$	$e\left(\frac{77}{116}\right)$	$e\left(\frac{40}{87}\right)$	$e\left(\frac{139}{174}\right)$	$e\left(\frac{11}{348}\right)$
$\chi_{767}(202,\cdot)$	$-1$	$1$	$e\left(\frac{43}{348}\right)$	$e\left(\frac{1}{87}\right)$	$e\left(\frac{43}{174}\right)$	$e\left(\frac{57}{116}\right)$	$e\left(\frac{47}{348}\right)$	$e\left(\frac{281}{348}\right)$	$e\left(\frac{43}{116}\right)$	$e\left(\frac{2}{87}\right)$	$e\left(\frac{107}{174}\right)$	$e\left(\frac{205}{348}\right)$
$\chi_{767}(206,\cdot)$	$-1$	$1$	$e\left(\frac{23}{348}\right)$	$e\left(\frac{41}{87}\right)$	$e\left(\frac{23}{174}\right)$	$e\left(\frac{17}{116}\right)$	$e\left(\frac{187}{348}\right)$	$e\left(\frac{37}{348}\right)$	$e\left(\frac{23}{116}\right)$	$e\left(\frac{82}{87}\right)$	$e\left(\frac{37}{174}\right)$	$e\left(\frac{53}{348}\right)$
$\chi_{767}(223,\cdot)$	$-1$	$1$	$e\left(\frac{125}{348}\right)$	$e\left(\frac{11}{87}\right)$	$e\left(\frac{125}{174}\right)$	$e\left(\frac{47}{116}\right)$	$e\left(\frac{169}{348}\right)$	$e\left(\frac{307}{348}\right)$	$e\left(\frac{9}{116}\right)$	$e\left(\frac{22}{87}\right)$	$e\left(\frac{133}{174}\right)$	$e\left(\frac{167}{348}\right)$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{767}(7,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{79}{348}\right)\)	\(e\left(\frac{16}{87}\right)\)	\(e\left(\frac{79}{174}\right)\)	\(e\left(\frac{13}{116}\right)\)	\(e\left(\frac{143}{348}\right)\)	\(e\left(\frac{233}{348}\right)\)	\(e\left(\frac{79}{116}\right)\)	\(e\left(\frac{32}{87}\right)\)	\(e\left(\frac{59}{174}\right)\)	\(e\left(\frac{61}{348}\right)\)
\(\chi_{767}(15,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{17}{348}\right)\)	\(e\left(\frac{53}{87}\right)\)	\(e\left(\frac{17}{174}\right)\)	\(e\left(\frac{63}{116}\right)\)	\(e\left(\frac{229}{348}\right)\)	\(e\left(\frac{103}{348}\right)\)	\(e\left(\frac{17}{116}\right)\)	\(e\left(\frac{19}{87}\right)\)	\(e\left(\frac{103}{174}\right)\)	\(e\left(\frac{251}{348}\right)\)
\(\chi_{767}(19,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{25}{348}\right)\)	\(e\left(\frac{37}{87}\right)\)	\(e\left(\frac{25}{174}\right)\)	\(e\left(\frac{79}{116}\right)\)	\(e\left(\frac{173}{348}\right)\)	\(e\left(\frac{131}{348}\right)\)	\(e\left(\frac{25}{116}\right)\)	\(e\left(\frac{74}{87}\right)\)	\(e\left(\frac{131}{174}\right)\)	\(e\left(\frac{103}{348}\right)\)
\(\chi_{767}(20,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{19}{348}\right)\)	\(e\left(\frac{49}{87}\right)\)	\(e\left(\frac{19}{174}\right)\)	\(e\left(\frac{9}{116}\right)\)	\(e\left(\frac{215}{348}\right)\)	\(e\left(\frac{197}{348}\right)\)	\(e\left(\frac{19}{116}\right)\)	\(e\left(\frac{11}{87}\right)\)	\(e\left(\frac{23}{174}\right)\)	\(e\left(\frac{301}{348}\right)\)
\(\chi_{767}(28,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{149}{348}\right)\)	\(e\left(\frac{50}{87}\right)\)	\(e\left(\frac{149}{174}\right)\)	\(e\left(\frac{95}{116}\right)\)	\(e\left(\frac{1}{348}\right)\)	\(e\left(\frac{43}{348}\right)\)	\(e\left(\frac{33}{116}\right)\)	\(e\left(\frac{13}{87}\right)\)	\(e\left(\frac{43}{174}\right)\)	\(e\left(\frac{71}{348}\right)\)
\(\chi_{767}(41,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{113}{348}\right)\)	\(e\left(\frac{35}{87}\right)\)	\(e\left(\frac{113}{174}\right)\)	\(e\left(\frac{23}{116}\right)\)	\(e\left(\frac{253}{348}\right)\)	\(e\left(\frac{91}{348}\right)\)	\(e\left(\frac{113}{116}\right)\)	\(e\left(\frac{70}{87}\right)\)	\(e\left(\frac{91}{174}\right)\)	\(e\left(\frac{215}{348}\right)\)
\(\chi_{767}(45,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{85}{348}\right)\)	\(e\left(\frac{4}{87}\right)\)	\(e\left(\frac{85}{174}\right)\)	\(e\left(\frac{83}{116}\right)\)	\(e\left(\frac{101}{348}\right)\)	\(e\left(\frac{167}{348}\right)\)	\(e\left(\frac{85}{116}\right)\)	\(e\left(\frac{8}{87}\right)\)	\(e\left(\frac{167}{174}\right)\)	\(e\left(\frac{211}{348}\right)\)
\(\chi_{767}(46,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{67}{348}\right)\)	\(e\left(\frac{40}{87}\right)\)	\(e\left(\frac{67}{174}\right)\)	\(e\left(\frac{105}{116}\right)\)	\(e\left(\frac{227}{348}\right)\)	\(e\left(\frac{17}{348}\right)\)	\(e\left(\frac{67}{116}\right)\)	\(e\left(\frac{80}{87}\right)\)	\(e\left(\frac{17}{174}\right)\)	\(e\left(\frac{109}{348}\right)\)
\(\chi_{767}(63,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{215}{348}\right)\)	\(e\left(\frac{5}{87}\right)\)	\(e\left(\frac{41}{174}\right)\)	\(e\left(\frac{53}{116}\right)\)	\(e\left(\frac{235}{348}\right)\)	\(e\left(\frac{13}{348}\right)\)	\(e\left(\frac{99}{116}\right)\)	\(e\left(\frac{10}{87}\right)\)	\(e\left(\frac{13}{174}\right)\)	\(e\left(\frac{329}{348}\right)\)
\(\chi_{767}(71,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{109}{348}\right)\)	\(e\left(\frac{43}{87}\right)\)	\(e\left(\frac{109}{174}\right)\)	\(e\left(\frac{15}{116}\right)\)	\(e\left(\frac{281}{348}\right)\)	\(e\left(\frac{251}{348}\right)\)	\(e\left(\frac{109}{116}\right)\)	\(e\left(\frac{86}{87}\right)\)	\(e\left(\frac{77}{174}\right)\)	\(e\left(\frac{115}{348}\right)\)
\(\chi_{767}(76,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{95}{348}\right)\)	\(e\left(\frac{71}{87}\right)\)	\(e\left(\frac{95}{174}\right)\)	\(e\left(\frac{45}{116}\right)\)	\(e\left(\frac{31}{348}\right)\)	\(e\left(\frac{289}{348}\right)\)	\(e\left(\frac{95}{116}\right)\)	\(e\left(\frac{55}{87}\right)\)	\(e\left(\frac{115}{174}\right)\)	\(e\left(\frac{113}{348}\right)\)
\(\chi_{767}(80,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{89}{348}\right)\)	\(e\left(\frac{83}{87}\right)\)	\(e\left(\frac{89}{174}\right)\)	\(e\left(\frac{91}{116}\right)\)	\(e\left(\frac{73}{348}\right)\)	\(e\left(\frac{7}{348}\right)\)	\(e\left(\frac{89}{116}\right)\)	\(e\left(\frac{79}{87}\right)\)	\(e\left(\frac{7}{174}\right)\)	\(e\left(\frac{311}{348}\right)\)
\(\chi_{767}(84,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{217}{348}\right)\)	\(e\left(\frac{1}{87}\right)\)	\(e\left(\frac{43}{174}\right)\)	\(e\left(\frac{115}{116}\right)\)	\(e\left(\frac{221}{348}\right)\)	\(e\left(\frac{107}{348}\right)\)	\(e\left(\frac{101}{116}\right)\)	\(e\left(\frac{2}{87}\right)\)	\(e\left(\frac{107}{174}\right)\)	\(e\left(\frac{31}{348}\right)\)
\(\chi_{767}(85,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{247}{348}\right)\)	\(e\left(\frac{28}{87}\right)\)	\(e\left(\frac{73}{174}\right)\)	\(e\left(\frac{1}{116}\right)\)	\(e\left(\frac{11}{348}\right)\)	\(e\left(\frac{125}{348}\right)\)	\(e\left(\frac{15}{116}\right)\)	\(e\left(\frac{56}{87}\right)\)	\(e\left(\frac{125}{174}\right)\)	\(e\left(\frac{85}{348}\right)\)
\(\chi_{767}(110,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{337}{348}\right)\)	\(e\left(\frac{22}{87}\right)\)	\(e\left(\frac{163}{174}\right)\)	\(e\left(\frac{7}{116}\right)\)	\(e\left(\frac{77}{348}\right)\)	\(e\left(\frac{179}{348}\right)\)	\(e\left(\frac{105}{116}\right)\)	\(e\left(\frac{44}{87}\right)\)	\(e\left(\frac{5}{174}\right)\)	\(e\left(\frac{247}{348}\right)\)
\(\chi_{767}(123,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{181}{348}\right)\)	\(e\left(\frac{73}{87}\right)\)	\(e\left(\frac{7}{174}\right)\)	\(e\left(\frac{43}{116}\right)\)	\(e\left(\frac{125}{348}\right)\)	\(e\left(\frac{155}{348}\right)\)	\(e\left(\frac{65}{116}\right)\)	\(e\left(\frac{59}{87}\right)\)	\(e\left(\frac{155}{174}\right)\)	\(e\left(\frac{175}{348}\right)\)
\(\chi_{767}(137,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{199}{348}\right)\)	\(e\left(\frac{37}{87}\right)\)	\(e\left(\frac{25}{174}\right)\)	\(e\left(\frac{21}{116}\right)\)	\(e\left(\frac{347}{348}\right)\)	\(e\left(\frac{305}{348}\right)\)	\(e\left(\frac{83}{116}\right)\)	\(e\left(\frac{74}{87}\right)\)	\(e\left(\frac{131}{174}\right)\)	\(e\left(\frac{277}{348}\right)\)
\(\chi_{767}(145,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{233}{348}\right)\)	\(e\left(\frac{56}{87}\right)\)	\(e\left(\frac{59}{174}\right)\)	\(e\left(\frac{31}{116}\right)\)	\(e\left(\frac{109}{348}\right)\)	\(e\left(\frac{163}{348}\right)\)	\(e\left(\frac{1}{116}\right)\)	\(e\left(\frac{25}{87}\right)\)	\(e\left(\frac{163}{174}\right)\)	\(e\left(\frac{83}{348}\right)\)
\(\chi_{767}(154,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{119}{348}\right)\)	\(e\left(\frac{23}{87}\right)\)	\(e\left(\frac{119}{174}\right)\)	\(e\left(\frac{93}{116}\right)\)	\(e\left(\frac{211}{348}\right)\)	\(e\left(\frac{25}{348}\right)\)	\(e\left(\frac{3}{116}\right)\)	\(e\left(\frac{46}{87}\right)\)	\(e\left(\frac{25}{174}\right)\)	\(e\left(\frac{17}{348}\right)\)
\(\chi_{767}(163,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{259}{348}\right)\)	\(e\left(\frac{4}{87}\right)\)	\(e\left(\frac{85}{174}\right)\)	\(e\left(\frac{25}{116}\right)\)	\(e\left(\frac{275}{348}\right)\)	\(e\left(\frac{341}{348}\right)\)	\(e\left(\frac{27}{116}\right)\)	\(e\left(\frac{8}{87}\right)\)	\(e\left(\frac{167}{174}\right)\)	\(e\left(\frac{37}{348}\right)\)
\(\chi_{767}(167,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{71}{348}\right)\)	\(e\left(\frac{32}{87}\right)\)	\(e\left(\frac{71}{174}\right)\)	\(e\left(\frac{113}{116}\right)\)	\(e\left(\frac{199}{348}\right)\)	\(e\left(\frac{205}{348}\right)\)	\(e\left(\frac{71}{116}\right)\)	\(e\left(\frac{64}{87}\right)\)	\(e\left(\frac{31}{174}\right)\)	\(e\left(\frac{209}{348}\right)\)
\(\chi_{767}(171,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{161}{348}\right)\)	\(e\left(\frac{26}{87}\right)\)	\(e\left(\frac{161}{174}\right)\)	\(e\left(\frac{3}{116}\right)\)	\(e\left(\frac{265}{348}\right)\)	\(e\left(\frac{259}{348}\right)\)	\(e\left(\frac{45}{116}\right)\)	\(e\left(\frac{52}{87}\right)\)	\(e\left(\frac{85}{174}\right)\)	\(e\left(\frac{23}{348}\right)\)
\(\chi_{767}(175,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{325}{348}\right)\)	\(e\left(\frac{46}{87}\right)\)	\(e\left(\frac{151}{174}\right)\)	\(e\left(\frac{99}{116}\right)\)	\(e\left(\frac{161}{348}\right)\)	\(e\left(\frac{311}{348}\right)\)	\(e\left(\frac{93}{116}\right)\)	\(e\left(\frac{5}{87}\right)\)	\(e\left(\frac{137}{174}\right)\)	\(e\left(\frac{295}{348}\right)\)
\(\chi_{767}(180,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{155}{348}\right)\)	\(e\left(\frac{38}{87}\right)\)	\(e\left(\frac{155}{174}\right)\)	\(e\left(\frac{49}{116}\right)\)	\(e\left(\frac{307}{348}\right)\)	\(e\left(\frac{325}{348}\right)\)	\(e\left(\frac{39}{116}\right)\)	\(e\left(\frac{76}{87}\right)\)	\(e\left(\frac{151}{174}\right)\)	\(e\left(\frac{221}{348}\right)\)
\(\chi_{767}(184,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{137}{348}\right)\)	\(e\left(\frac{74}{87}\right)\)	\(e\left(\frac{137}{174}\right)\)	\(e\left(\frac{71}{116}\right)\)	\(e\left(\frac{85}{348}\right)\)	\(e\left(\frac{175}{348}\right)\)	\(e\left(\frac{21}{116}\right)\)	\(e\left(\frac{61}{87}\right)\)	\(e\left(\frac{1}{174}\right)\)	\(e\left(\frac{119}{348}\right)\)
\(\chi_{767}(189,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{283}{348}\right)\)	\(e\left(\frac{43}{87}\right)\)	\(e\left(\frac{109}{174}\right)\)	\(e\left(\frac{73}{116}\right)\)	\(e\left(\frac{107}{348}\right)\)	\(e\left(\frac{77}{348}\right)\)	\(e\left(\frac{51}{116}\right)\)	\(e\left(\frac{86}{87}\right)\)	\(e\left(\frac{77}{174}\right)\)	\(e\left(\frac{289}{348}\right)\)
\(\chi_{767}(193,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{227}{348}\right)\)	\(e\left(\frac{68}{87}\right)\)	\(e\left(\frac{53}{174}\right)\)	\(e\left(\frac{77}{116}\right)\)	\(e\left(\frac{151}{348}\right)\)	\(e\left(\frac{229}{348}\right)\)	\(e\left(\frac{111}{116}\right)\)	\(e\left(\frac{49}{87}\right)\)	\(e\left(\frac{55}{174}\right)\)	\(e\left(\frac{281}{348}\right)\)
\(\chi_{767}(197,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{77}{348}\right)\)	\(e\left(\frac{20}{87}\right)\)	\(e\left(\frac{77}{174}\right)\)	\(e\left(\frac{67}{116}\right)\)	\(e\left(\frac{157}{348}\right)\)	\(e\left(\frac{139}{348}\right)\)	\(e\left(\frac{77}{116}\right)\)	\(e\left(\frac{40}{87}\right)\)	\(e\left(\frac{139}{174}\right)\)	\(e\left(\frac{11}{348}\right)\)
\(\chi_{767}(202,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{43}{348}\right)\)	\(e\left(\frac{1}{87}\right)\)	\(e\left(\frac{43}{174}\right)\)	\(e\left(\frac{57}{116}\right)\)	\(e\left(\frac{47}{348}\right)\)	\(e\left(\frac{281}{348}\right)\)	\(e\left(\frac{43}{116}\right)\)	\(e\left(\frac{2}{87}\right)\)	\(e\left(\frac{107}{174}\right)\)	\(e\left(\frac{205}{348}\right)\)
\(\chi_{767}(206,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{23}{348}\right)\)	\(e\left(\frac{41}{87}\right)\)	\(e\left(\frac{23}{174}\right)\)	\(e\left(\frac{17}{116}\right)\)	\(e\left(\frac{187}{348}\right)\)	\(e\left(\frac{37}{348}\right)\)	\(e\left(\frac{23}{116}\right)\)	\(e\left(\frac{82}{87}\right)\)	\(e\left(\frac{37}{174}\right)\)	\(e\left(\frac{53}{348}\right)\)
\(\chi_{767}(223,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{125}{348}\right)\)	\(e\left(\frac{11}{87}\right)\)	\(e\left(\frac{125}{174}\right)\)	\(e\left(\frac{47}{116}\right)\)	\(e\left(\frac{169}{348}\right)\)	\(e\left(\frac{307}{348}\right)\)	\(e\left(\frac{9}{116}\right)\)	\(e\left(\frac{22}{87}\right)\)	\(e\left(\frac{133}{174}\right)\)	\(e\left(\frac{167}{348}\right)\)

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First 31 of 112 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	767.w
Modulus	$767$
Conductor	$767$
Order	$348$
Real	no
Primitive	yes
Minimal	yes
Parity	odd

Modulus:	\(767\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(767\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(348\)	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:	yes	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);