LMFDB - Dirichlet character orbit 767.t

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(767, base_ring=CyclotomicField(174)) M = H._module chi = DirichletCharacter(H, M([58,33])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(42, 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("767.42"); 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:	$174$	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:	$\Q(\zeta_{87})$	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 174 polynomial (not computed)	comment:Fixed field sage:chi.fixed_field()

First 31 of 56 characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{767}(42,\cdot)$	$-1$	$1$	$e\left(\frac{91}{174}\right)$	$e\left(\frac{71}{87}\right)$	$e\left(\frac{4}{87}\right)$	$e\left(\frac{4}{29}\right)$	$e\left(\frac{59}{174}\right)$	$e\left(\frac{7}{87}\right)$	$e\left(\frac{33}{58}\right)$	$e\left(\frac{55}{87}\right)$	$e\left(\frac{115}{174}\right)$	$e\left(\frac{13}{174}\right)$
$\chi_{767}(55,\cdot)$	$-1$	$1$	$e\left(\frac{151}{174}\right)$	$e\left(\frac{5}{87}\right)$	$e\left(\frac{64}{87}\right)$	$e\left(\frac{6}{29}\right)$	$e\left(\frac{161}{174}\right)$	$e\left(\frac{25}{87}\right)$	$e\left(\frac{35}{58}\right)$	$e\left(\frac{10}{87}\right)$	$e\left(\frac{13}{174}\right)$	$e\left(\frac{121}{174}\right)$
$\chi_{767}(61,\cdot)$	$-1$	$1$	$e\left(\frac{119}{174}\right)$	$e\left(\frac{46}{87}\right)$	$e\left(\frac{32}{87}\right)$	$e\left(\frac{3}{29}\right)$	$e\left(\frac{37}{174}\right)$	$e\left(\frac{56}{87}\right)$	$e\left(\frac{3}{58}\right)$	$e\left(\frac{5}{87}\right)$	$e\left(\frac{137}{174}\right)$	$e\left(\frac{17}{174}\right)$
$\chi_{767}(113,\cdot)$	$-1$	$1$	$e\left(\frac{47}{174}\right)$	$e\left(\frac{73}{87}\right)$	$e\left(\frac{47}{87}\right)$	$e\left(\frac{18}{29}\right)$	$e\left(\frac{19}{174}\right)$	$e\left(\frac{17}{87}\right)$	$e\left(\frac{47}{58}\right)$	$e\left(\frac{59}{87}\right)$	$e\left(\frac{155}{174}\right)$	$e\left(\frac{131}{174}\right)$
$\chi_{767}(120,\cdot)$	$-1$	$1$	$e\left(\frac{61}{174}\right)$	$e\left(\frac{17}{87}\right)$	$e\left(\frac{61}{87}\right)$	$e\left(\frac{3}{29}\right)$	$e\left(\frac{95}{174}\right)$	$e\left(\frac{85}{87}\right)$	$e\left(\frac{3}{58}\right)$	$e\left(\frac{34}{87}\right)$	$e\left(\frac{79}{174}\right)$	$e\left(\frac{133}{174}\right)$
$\chi_{767}(126,\cdot)$	$-1$	$1$	$e\left(\frac{125}{174}\right)$	$e\left(\frac{22}{87}\right)$	$e\left(\frac{38}{87}\right)$	$e\left(\frac{9}{29}\right)$	$e\left(\frac{169}{174}\right)$	$e\left(\frac{23}{87}\right)$	$e\left(\frac{9}{58}\right)$	$e\left(\frac{44}{87}\right)$	$e\left(\frac{5}{174}\right)$	$e\left(\frac{167}{174}\right)$
$\chi_{767}(152,\cdot)$	$-1$	$1$	$e\left(\frac{65}{174}\right)$	$e\left(\frac{1}{87}\right)$	$e\left(\frac{65}{87}\right)$	$e\left(\frac{7}{29}\right)$	$e\left(\frac{67}{174}\right)$	$e\left(\frac{5}{87}\right)$	$e\left(\frac{7}{58}\right)$	$e\left(\frac{2}{87}\right)$	$e\left(\frac{107}{174}\right)$	$e\left(\frac{59}{174}\right)$
$\chi_{767}(165,\cdot)$	$-1$	$1$	$e\left(\frac{11}{174}\right)$	$e\left(\frac{43}{87}\right)$	$e\left(\frac{11}{87}\right)$	$e\left(\frac{11}{29}\right)$	$e\left(\frac{97}{174}\right)$	$e\left(\frac{41}{87}\right)$	$e\left(\frac{11}{58}\right)$	$e\left(\frac{86}{87}\right)$	$e\left(\frac{77}{174}\right)$	$e\left(\frac{101}{174}\right)$
$\chi_{767}(172,\cdot)$	$-1$	$1$	$e\left(\frac{163}{174}\right)$	$e\left(\frac{44}{87}\right)$	$e\left(\frac{76}{87}\right)$	$e\left(\frac{18}{29}\right)$	$e\left(\frac{77}{174}\right)$	$e\left(\frac{46}{87}\right)$	$e\left(\frac{47}{58}\right)$	$e\left(\frac{1}{87}\right)$	$e\left(\frac{97}{174}\right)$	$e\left(\frac{73}{174}\right)$
$\chi_{767}(185,\cdot)$	$-1$	$1$	$e\left(\frac{67}{174}\right)$	$e\left(\frac{80}{87}\right)$	$e\left(\frac{67}{87}\right)$	$e\left(\frac{9}{29}\right)$	$e\left(\frac{53}{174}\right)$	$e\left(\frac{52}{87}\right)$	$e\left(\frac{9}{58}\right)$	$e\left(\frac{73}{87}\right)$	$e\left(\frac{121}{174}\right)$	$e\left(\frac{109}{174}\right)$
$\chi_{767}(191,\cdot)$	$-1$	$1$	$e\left(\frac{173}{174}\right)$	$e\left(\frac{4}{87}\right)$	$e\left(\frac{86}{87}\right)$	$e\left(\frac{28}{29}\right)$	$e\left(\frac{7}{174}\right)$	$e\left(\frac{20}{87}\right)$	$e\left(\frac{57}{58}\right)$	$e\left(\frac{8}{87}\right)$	$e\left(\frac{167}{174}\right)$	$e\left(\frac{149}{174}\right)$
$\chi_{767}(211,\cdot)$	$-1$	$1$	$e\left(\frac{7}{174}\right)$	$e\left(\frac{59}{87}\right)$	$e\left(\frac{7}{87}\right)$	$e\left(\frac{7}{29}\right)$	$e\left(\frac{125}{174}\right)$	$e\left(\frac{34}{87}\right)$	$e\left(\frac{7}{58}\right)$	$e\left(\frac{31}{87}\right)$	$e\left(\frac{49}{174}\right)$	$e\left(\frac{1}{174}\right)$
$\chi_{767}(217,\cdot)$	$-1$	$1$	$e\left(\frac{143}{174}\right)$	$e\left(\frac{37}{87}\right)$	$e\left(\frac{56}{87}\right)$	$e\left(\frac{27}{29}\right)$	$e\left(\frac{43}{174}\right)$	$e\left(\frac{11}{87}\right)$	$e\left(\frac{27}{58}\right)$	$e\left(\frac{74}{87}\right)$	$e\left(\frac{131}{174}\right)$	$e\left(\frac{95}{174}\right)$
$\chi_{767}(224,\cdot)$	$-1$	$1$	$e\left(\frac{127}{174}\right)$	$e\left(\frac{14}{87}\right)$	$e\left(\frac{40}{87}\right)$	$e\left(\frac{11}{29}\right)$	$e\left(\frac{155}{174}\right)$	$e\left(\frac{70}{87}\right)$	$e\left(\frac{11}{58}\right)$	$e\left(\frac{28}{87}\right)$	$e\left(\frac{19}{174}\right)$	$e\left(\frac{43}{174}\right)$
$\chi_{767}(250,\cdot)$	$-1$	$1$	$e\left(\frac{115}{174}\right)$	$e\left(\frac{62}{87}\right)$	$e\left(\frac{28}{87}\right)$	$e\left(\frac{28}{29}\right)$	$e\left(\frac{65}{174}\right)$	$e\left(\frac{49}{87}\right)$	$e\left(\frac{57}{58}\right)$	$e\left(\frac{37}{87}\right)$	$e\left(\frac{109}{174}\right)$	$e\left(\frac{91}{174}\right)$
$\chi_{767}(269,\cdot)$	$-1$	$1$	$e\left(\frac{167}{174}\right)$	$e\left(\frac{28}{87}\right)$	$e\left(\frac{80}{87}\right)$	$e\left(\frac{22}{29}\right)$	$e\left(\frac{49}{174}\right)$	$e\left(\frac{53}{87}\right)$	$e\left(\frac{51}{58}\right)$	$e\left(\frac{56}{87}\right)$	$e\left(\frac{125}{174}\right)$	$e\left(\frac{173}{174}\right)$
$\chi_{767}(276,\cdot)$	$-1$	$1$	$e\left(\frac{85}{174}\right)$	$e\left(\frac{8}{87}\right)$	$e\left(\frac{85}{87}\right)$	$e\left(\frac{27}{29}\right)$	$e\left(\frac{101}{174}\right)$	$e\left(\frac{40}{87}\right)$	$e\left(\frac{27}{58}\right)$	$e\left(\frac{16}{87}\right)$	$e\left(\frac{73}{174}\right)$	$e\left(\frac{37}{174}\right)$
$\chi_{767}(308,\cdot)$	$-1$	$1$	$e\left(\frac{77}{174}\right)$	$e\left(\frac{40}{87}\right)$	$e\left(\frac{77}{87}\right)$	$e\left(\frac{19}{29}\right)$	$e\left(\frac{157}{174}\right)$	$e\left(\frac{26}{87}\right)$	$e\left(\frac{19}{58}\right)$	$e\left(\frac{80}{87}\right)$	$e\left(\frac{17}{174}\right)$	$e\left(\frac{11}{174}\right)$
$\chi_{767}(328,\cdot)$	$-1$	$1$	$e\left(\frac{109}{174}\right)$	$e\left(\frac{86}{87}\right)$	$e\left(\frac{22}{87}\right)$	$e\left(\frac{22}{29}\right)$	$e\left(\frac{107}{174}\right)$	$e\left(\frac{82}{87}\right)$	$e\left(\frac{51}{58}\right)$	$e\left(\frac{85}{87}\right)$	$e\left(\frac{67}{174}\right)$	$e\left(\frac{115}{174}\right)$
$\chi_{767}(334,\cdot)$	$-1$	$1$	$e\left(\frac{53}{174}\right)$	$e\left(\frac{49}{87}\right)$	$e\left(\frac{53}{87}\right)$	$e\left(\frac{24}{29}\right)$	$e\left(\frac{151}{174}\right)$	$e\left(\frac{71}{87}\right)$	$e\left(\frac{53}{58}\right)$	$e\left(\frac{11}{87}\right)$	$e\left(\frac{23}{174}\right)$	$e\left(\frac{107}{174}\right)$
$\chi_{767}(347,\cdot)$	$-1$	$1$	$e\left(\frac{83}{174}\right)$	$e\left(\frac{16}{87}\right)$	$e\left(\frac{83}{87}\right)$	$e\left(\frac{25}{29}\right)$	$e\left(\frac{115}{174}\right)$	$e\left(\frac{80}{87}\right)$	$e\left(\frac{25}{58}\right)$	$e\left(\frac{32}{87}\right)$	$e\left(\frac{59}{174}\right)$	$e\left(\frac{161}{174}\right)$
$\chi_{767}(360,\cdot)$	$-1$	$1$	$e\left(\frac{95}{174}\right)$	$e\left(\frac{55}{87}\right)$	$e\left(\frac{8}{87}\right)$	$e\left(\frac{8}{29}\right)$	$e\left(\frac{31}{174}\right)$	$e\left(\frac{14}{87}\right)$	$e\left(\frac{37}{58}\right)$	$e\left(\frac{23}{87}\right)$	$e\left(\frac{143}{174}\right)$	$e\left(\frac{113}{174}\right)$
$\chi_{767}(367,\cdot)$	$-1$	$1$	$e\left(\frac{19}{174}\right)$	$e\left(\frac{11}{87}\right)$	$e\left(\frac{19}{87}\right)$	$e\left(\frac{19}{29}\right)$	$e\left(\frac{41}{174}\right)$	$e\left(\frac{55}{87}\right)$	$e\left(\frac{19}{58}\right)$	$e\left(\frac{22}{87}\right)$	$e\left(\frac{133}{174}\right)$	$e\left(\frac{127}{174}\right)$
$\chi_{767}(386,\cdot)$	$-1$	$1$	$e\left(\frac{131}{174}\right)$	$e\left(\frac{85}{87}\right)$	$e\left(\frac{44}{87}\right)$	$e\left(\frac{15}{29}\right)$	$e\left(\frac{127}{174}\right)$	$e\left(\frac{77}{87}\right)$	$e\left(\frac{15}{58}\right)$	$e\left(\frac{83}{87}\right)$	$e\left(\frac{47}{174}\right)$	$e\left(\frac{143}{174}\right)$
$\chi_{767}(393,\cdot)$	$-1$	$1$	$e\left(\frac{169}{174}\right)$	$e\left(\frac{20}{87}\right)$	$e\left(\frac{82}{87}\right)$	$e\left(\frac{24}{29}\right)$	$e\left(\frac{35}{174}\right)$	$e\left(\frac{13}{87}\right)$	$e\left(\frac{53}{58}\right)$	$e\left(\frac{40}{87}\right)$	$e\left(\frac{139}{174}\right)$	$e\left(\frac{49}{174}\right)$
$\chi_{767}(406,\cdot)$	$-1$	$1$	$e\left(\frac{25}{174}\right)$	$e\left(\frac{74}{87}\right)$	$e\left(\frac{25}{87}\right)$	$e\left(\frac{25}{29}\right)$	$e\left(\frac{173}{174}\right)$	$e\left(\frac{22}{87}\right)$	$e\left(\frac{25}{58}\right)$	$e\left(\frac{61}{87}\right)$	$e\left(\frac{1}{174}\right)$	$e\left(\frac{103}{174}\right)$
$\chi_{767}(419,\cdot)$	$-1$	$1$	$e\left(\frac{37}{174}\right)$	$e\left(\frac{26}{87}\right)$	$e\left(\frac{37}{87}\right)$	$e\left(\frac{8}{29}\right)$	$e\left(\frac{89}{174}\right)$	$e\left(\frac{43}{87}\right)$	$e\left(\frac{37}{58}\right)$	$e\left(\frac{52}{87}\right)$	$e\left(\frac{85}{174}\right)$	$e\left(\frac{55}{174}\right)$
$\chi_{767}(445,\cdot)$	$-1$	$1$	$e\left(\frac{73}{174}\right)$	$e\left(\frac{56}{87}\right)$	$e\left(\frac{73}{87}\right)$	$e\left(\frac{15}{29}\right)$	$e\left(\frac{11}{174}\right)$	$e\left(\frac{19}{87}\right)$	$e\left(\frac{15}{58}\right)$	$e\left(\frac{25}{87}\right)$	$e\left(\frac{163}{174}\right)$	$e\left(\frac{85}{174}\right)$
$\chi_{767}(451,\cdot)$	$-1$	$1$	$e\left(\frac{59}{174}\right)$	$e\left(\frac{25}{87}\right)$	$e\left(\frac{59}{87}\right)$	$e\left(\frac{1}{29}\right)$	$e\left(\frac{109}{174}\right)$	$e\left(\frac{38}{87}\right)$	$e\left(\frac{1}{58}\right)$	$e\left(\frac{50}{87}\right)$	$e\left(\frac{65}{174}\right)$	$e\left(\frac{83}{174}\right)$
$\chi_{767}(490,\cdot)$	$-1$	$1$	$e\left(\frac{71}{174}\right)$	$e\left(\frac{64}{87}\right)$	$e\left(\frac{71}{87}\right)$	$e\left(\frac{13}{29}\right)$	$e\left(\frac{25}{174}\right)$	$e\left(\frac{59}{87}\right)$	$e\left(\frac{13}{58}\right)$	$e\left(\frac{41}{87}\right)$	$e\left(\frac{149}{174}\right)$	$e\left(\frac{35}{174}\right)$
$\chi_{767}(503,\cdot)$	$-1$	$1$	$e\left(\frac{89}{174}\right)$	$e\left(\frac{79}{87}\right)$	$e\left(\frac{2}{87}\right)$	$e\left(\frac{2}{29}\right)$	$e\left(\frac{73}{174}\right)$	$e\left(\frac{47}{87}\right)$	$e\left(\frac{31}{58}\right)$	$e\left(\frac{71}{87}\right)$	$e\left(\frac{101}{174}\right)$	$e\left(\frac{137}{174}\right)$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{767}(42,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{91}{174}\right)\)	\(e\left(\frac{71}{87}\right)\)	\(e\left(\frac{4}{87}\right)\)	\(e\left(\frac{4}{29}\right)\)	\(e\left(\frac{59}{174}\right)\)	\(e\left(\frac{7}{87}\right)\)	\(e\left(\frac{33}{58}\right)\)	\(e\left(\frac{55}{87}\right)\)	\(e\left(\frac{115}{174}\right)\)	\(e\left(\frac{13}{174}\right)\)
\(\chi_{767}(55,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{151}{174}\right)\)	\(e\left(\frac{5}{87}\right)\)	\(e\left(\frac{64}{87}\right)\)	\(e\left(\frac{6}{29}\right)\)	\(e\left(\frac{161}{174}\right)\)	\(e\left(\frac{25}{87}\right)\)	\(e\left(\frac{35}{58}\right)\)	\(e\left(\frac{10}{87}\right)\)	\(e\left(\frac{13}{174}\right)\)	\(e\left(\frac{121}{174}\right)\)
\(\chi_{767}(61,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{119}{174}\right)\)	\(e\left(\frac{46}{87}\right)\)	\(e\left(\frac{32}{87}\right)\)	\(e\left(\frac{3}{29}\right)\)	\(e\left(\frac{37}{174}\right)\)	\(e\left(\frac{56}{87}\right)\)	\(e\left(\frac{3}{58}\right)\)	\(e\left(\frac{5}{87}\right)\)	\(e\left(\frac{137}{174}\right)\)	\(e\left(\frac{17}{174}\right)\)
\(\chi_{767}(113,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{47}{174}\right)\)	\(e\left(\frac{73}{87}\right)\)	\(e\left(\frac{47}{87}\right)\)	\(e\left(\frac{18}{29}\right)\)	\(e\left(\frac{19}{174}\right)\)	\(e\left(\frac{17}{87}\right)\)	\(e\left(\frac{47}{58}\right)\)	\(e\left(\frac{59}{87}\right)\)	\(e\left(\frac{155}{174}\right)\)	\(e\left(\frac{131}{174}\right)\)
\(\chi_{767}(120,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{61}{174}\right)\)	\(e\left(\frac{17}{87}\right)\)	\(e\left(\frac{61}{87}\right)\)	\(e\left(\frac{3}{29}\right)\)	\(e\left(\frac{95}{174}\right)\)	\(e\left(\frac{85}{87}\right)\)	\(e\left(\frac{3}{58}\right)\)	\(e\left(\frac{34}{87}\right)\)	\(e\left(\frac{79}{174}\right)\)	\(e\left(\frac{133}{174}\right)\)
\(\chi_{767}(126,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{125}{174}\right)\)	\(e\left(\frac{22}{87}\right)\)	\(e\left(\frac{38}{87}\right)\)	\(e\left(\frac{9}{29}\right)\)	\(e\left(\frac{169}{174}\right)\)	\(e\left(\frac{23}{87}\right)\)	\(e\left(\frac{9}{58}\right)\)	\(e\left(\frac{44}{87}\right)\)	\(e\left(\frac{5}{174}\right)\)	\(e\left(\frac{167}{174}\right)\)
\(\chi_{767}(152,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{65}{174}\right)\)	\(e\left(\frac{1}{87}\right)\)	\(e\left(\frac{65}{87}\right)\)	\(e\left(\frac{7}{29}\right)\)	\(e\left(\frac{67}{174}\right)\)	\(e\left(\frac{5}{87}\right)\)	\(e\left(\frac{7}{58}\right)\)	\(e\left(\frac{2}{87}\right)\)	\(e\left(\frac{107}{174}\right)\)	\(e\left(\frac{59}{174}\right)\)
\(\chi_{767}(165,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{11}{174}\right)\)	\(e\left(\frac{43}{87}\right)\)	\(e\left(\frac{11}{87}\right)\)	\(e\left(\frac{11}{29}\right)\)	\(e\left(\frac{97}{174}\right)\)	\(e\left(\frac{41}{87}\right)\)	\(e\left(\frac{11}{58}\right)\)	\(e\left(\frac{86}{87}\right)\)	\(e\left(\frac{77}{174}\right)\)	\(e\left(\frac{101}{174}\right)\)
\(\chi_{767}(172,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{163}{174}\right)\)	\(e\left(\frac{44}{87}\right)\)	\(e\left(\frac{76}{87}\right)\)	\(e\left(\frac{18}{29}\right)\)	\(e\left(\frac{77}{174}\right)\)	\(e\left(\frac{46}{87}\right)\)	\(e\left(\frac{47}{58}\right)\)	\(e\left(\frac{1}{87}\right)\)	\(e\left(\frac{97}{174}\right)\)	\(e\left(\frac{73}{174}\right)\)
\(\chi_{767}(185,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{67}{174}\right)\)	\(e\left(\frac{80}{87}\right)\)	\(e\left(\frac{67}{87}\right)\)	\(e\left(\frac{9}{29}\right)\)	\(e\left(\frac{53}{174}\right)\)	\(e\left(\frac{52}{87}\right)\)	\(e\left(\frac{9}{58}\right)\)	\(e\left(\frac{73}{87}\right)\)	\(e\left(\frac{121}{174}\right)\)	\(e\left(\frac{109}{174}\right)\)
\(\chi_{767}(191,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{173}{174}\right)\)	\(e\left(\frac{4}{87}\right)\)	\(e\left(\frac{86}{87}\right)\)	\(e\left(\frac{28}{29}\right)\)	\(e\left(\frac{7}{174}\right)\)	\(e\left(\frac{20}{87}\right)\)	\(e\left(\frac{57}{58}\right)\)	\(e\left(\frac{8}{87}\right)\)	\(e\left(\frac{167}{174}\right)\)	\(e\left(\frac{149}{174}\right)\)
\(\chi_{767}(211,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{7}{174}\right)\)	\(e\left(\frac{59}{87}\right)\)	\(e\left(\frac{7}{87}\right)\)	\(e\left(\frac{7}{29}\right)\)	\(e\left(\frac{125}{174}\right)\)	\(e\left(\frac{34}{87}\right)\)	\(e\left(\frac{7}{58}\right)\)	\(e\left(\frac{31}{87}\right)\)	\(e\left(\frac{49}{174}\right)\)	\(e\left(\frac{1}{174}\right)\)
\(\chi_{767}(217,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{143}{174}\right)\)	\(e\left(\frac{37}{87}\right)\)	\(e\left(\frac{56}{87}\right)\)	\(e\left(\frac{27}{29}\right)\)	\(e\left(\frac{43}{174}\right)\)	\(e\left(\frac{11}{87}\right)\)	\(e\left(\frac{27}{58}\right)\)	\(e\left(\frac{74}{87}\right)\)	\(e\left(\frac{131}{174}\right)\)	\(e\left(\frac{95}{174}\right)\)
\(\chi_{767}(224,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{127}{174}\right)\)	\(e\left(\frac{14}{87}\right)\)	\(e\left(\frac{40}{87}\right)\)	\(e\left(\frac{11}{29}\right)\)	\(e\left(\frac{155}{174}\right)\)	\(e\left(\frac{70}{87}\right)\)	\(e\left(\frac{11}{58}\right)\)	\(e\left(\frac{28}{87}\right)\)	\(e\left(\frac{19}{174}\right)\)	\(e\left(\frac{43}{174}\right)\)
\(\chi_{767}(250,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{115}{174}\right)\)	\(e\left(\frac{62}{87}\right)\)	\(e\left(\frac{28}{87}\right)\)	\(e\left(\frac{28}{29}\right)\)	\(e\left(\frac{65}{174}\right)\)	\(e\left(\frac{49}{87}\right)\)	\(e\left(\frac{57}{58}\right)\)	\(e\left(\frac{37}{87}\right)\)	\(e\left(\frac{109}{174}\right)\)	\(e\left(\frac{91}{174}\right)\)
\(\chi_{767}(269,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{167}{174}\right)\)	\(e\left(\frac{28}{87}\right)\)	\(e\left(\frac{80}{87}\right)\)	\(e\left(\frac{22}{29}\right)\)	\(e\left(\frac{49}{174}\right)\)	\(e\left(\frac{53}{87}\right)\)	\(e\left(\frac{51}{58}\right)\)	\(e\left(\frac{56}{87}\right)\)	\(e\left(\frac{125}{174}\right)\)	\(e\left(\frac{173}{174}\right)\)
\(\chi_{767}(276,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{85}{174}\right)\)	\(e\left(\frac{8}{87}\right)\)	\(e\left(\frac{85}{87}\right)\)	\(e\left(\frac{27}{29}\right)\)	\(e\left(\frac{101}{174}\right)\)	\(e\left(\frac{40}{87}\right)\)	\(e\left(\frac{27}{58}\right)\)	\(e\left(\frac{16}{87}\right)\)	\(e\left(\frac{73}{174}\right)\)	\(e\left(\frac{37}{174}\right)\)
\(\chi_{767}(308,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{77}{174}\right)\)	\(e\left(\frac{40}{87}\right)\)	\(e\left(\frac{77}{87}\right)\)	\(e\left(\frac{19}{29}\right)\)	\(e\left(\frac{157}{174}\right)\)	\(e\left(\frac{26}{87}\right)\)	\(e\left(\frac{19}{58}\right)\)	\(e\left(\frac{80}{87}\right)\)	\(e\left(\frac{17}{174}\right)\)	\(e\left(\frac{11}{174}\right)\)
\(\chi_{767}(328,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{109}{174}\right)\)	\(e\left(\frac{86}{87}\right)\)	\(e\left(\frac{22}{87}\right)\)	\(e\left(\frac{22}{29}\right)\)	\(e\left(\frac{107}{174}\right)\)	\(e\left(\frac{82}{87}\right)\)	\(e\left(\frac{51}{58}\right)\)	\(e\left(\frac{85}{87}\right)\)	\(e\left(\frac{67}{174}\right)\)	\(e\left(\frac{115}{174}\right)\)
\(\chi_{767}(334,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{53}{174}\right)\)	\(e\left(\frac{49}{87}\right)\)	\(e\left(\frac{53}{87}\right)\)	\(e\left(\frac{24}{29}\right)\)	\(e\left(\frac{151}{174}\right)\)	\(e\left(\frac{71}{87}\right)\)	\(e\left(\frac{53}{58}\right)\)	\(e\left(\frac{11}{87}\right)\)	\(e\left(\frac{23}{174}\right)\)	\(e\left(\frac{107}{174}\right)\)
\(\chi_{767}(347,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{83}{174}\right)\)	\(e\left(\frac{16}{87}\right)\)	\(e\left(\frac{83}{87}\right)\)	\(e\left(\frac{25}{29}\right)\)	\(e\left(\frac{115}{174}\right)\)	\(e\left(\frac{80}{87}\right)\)	\(e\left(\frac{25}{58}\right)\)	\(e\left(\frac{32}{87}\right)\)	\(e\left(\frac{59}{174}\right)\)	\(e\left(\frac{161}{174}\right)\)
\(\chi_{767}(360,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{95}{174}\right)\)	\(e\left(\frac{55}{87}\right)\)	\(e\left(\frac{8}{87}\right)\)	\(e\left(\frac{8}{29}\right)\)	\(e\left(\frac{31}{174}\right)\)	\(e\left(\frac{14}{87}\right)\)	\(e\left(\frac{37}{58}\right)\)	\(e\left(\frac{23}{87}\right)\)	\(e\left(\frac{143}{174}\right)\)	\(e\left(\frac{113}{174}\right)\)
\(\chi_{767}(367,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{19}{174}\right)\)	\(e\left(\frac{11}{87}\right)\)	\(e\left(\frac{19}{87}\right)\)	\(e\left(\frac{19}{29}\right)\)	\(e\left(\frac{41}{174}\right)\)	\(e\left(\frac{55}{87}\right)\)	\(e\left(\frac{19}{58}\right)\)	\(e\left(\frac{22}{87}\right)\)	\(e\left(\frac{133}{174}\right)\)	\(e\left(\frac{127}{174}\right)\)
\(\chi_{767}(386,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{131}{174}\right)\)	\(e\left(\frac{85}{87}\right)\)	\(e\left(\frac{44}{87}\right)\)	\(e\left(\frac{15}{29}\right)\)	\(e\left(\frac{127}{174}\right)\)	\(e\left(\frac{77}{87}\right)\)	\(e\left(\frac{15}{58}\right)\)	\(e\left(\frac{83}{87}\right)\)	\(e\left(\frac{47}{174}\right)\)	\(e\left(\frac{143}{174}\right)\)
\(\chi_{767}(393,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{169}{174}\right)\)	\(e\left(\frac{20}{87}\right)\)	\(e\left(\frac{82}{87}\right)\)	\(e\left(\frac{24}{29}\right)\)	\(e\left(\frac{35}{174}\right)\)	\(e\left(\frac{13}{87}\right)\)	\(e\left(\frac{53}{58}\right)\)	\(e\left(\frac{40}{87}\right)\)	\(e\left(\frac{139}{174}\right)\)	\(e\left(\frac{49}{174}\right)\)
\(\chi_{767}(406,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{25}{174}\right)\)	\(e\left(\frac{74}{87}\right)\)	\(e\left(\frac{25}{87}\right)\)	\(e\left(\frac{25}{29}\right)\)	\(e\left(\frac{173}{174}\right)\)	\(e\left(\frac{22}{87}\right)\)	\(e\left(\frac{25}{58}\right)\)	\(e\left(\frac{61}{87}\right)\)	\(e\left(\frac{1}{174}\right)\)	\(e\left(\frac{103}{174}\right)\)
\(\chi_{767}(419,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{37}{174}\right)\)	\(e\left(\frac{26}{87}\right)\)	\(e\left(\frac{37}{87}\right)\)	\(e\left(\frac{8}{29}\right)\)	\(e\left(\frac{89}{174}\right)\)	\(e\left(\frac{43}{87}\right)\)	\(e\left(\frac{37}{58}\right)\)	\(e\left(\frac{52}{87}\right)\)	\(e\left(\frac{85}{174}\right)\)	\(e\left(\frac{55}{174}\right)\)
\(\chi_{767}(445,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{73}{174}\right)\)	\(e\left(\frac{56}{87}\right)\)	\(e\left(\frac{73}{87}\right)\)	\(e\left(\frac{15}{29}\right)\)	\(e\left(\frac{11}{174}\right)\)	\(e\left(\frac{19}{87}\right)\)	\(e\left(\frac{15}{58}\right)\)	\(e\left(\frac{25}{87}\right)\)	\(e\left(\frac{163}{174}\right)\)	\(e\left(\frac{85}{174}\right)\)
\(\chi_{767}(451,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{59}{174}\right)\)	\(e\left(\frac{25}{87}\right)\)	\(e\left(\frac{59}{87}\right)\)	\(e\left(\frac{1}{29}\right)\)	\(e\left(\frac{109}{174}\right)\)	\(e\left(\frac{38}{87}\right)\)	\(e\left(\frac{1}{58}\right)\)	\(e\left(\frac{50}{87}\right)\)	\(e\left(\frac{65}{174}\right)\)	\(e\left(\frac{83}{174}\right)\)
\(\chi_{767}(490,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{71}{174}\right)\)	\(e\left(\frac{64}{87}\right)\)	\(e\left(\frac{71}{87}\right)\)	\(e\left(\frac{13}{29}\right)\)	\(e\left(\frac{25}{174}\right)\)	\(e\left(\frac{59}{87}\right)\)	\(e\left(\frac{13}{58}\right)\)	\(e\left(\frac{41}{87}\right)\)	\(e\left(\frac{149}{174}\right)\)	\(e\left(\frac{35}{174}\right)\)
\(\chi_{767}(503,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{89}{174}\right)\)	\(e\left(\frac{79}{87}\right)\)	\(e\left(\frac{2}{87}\right)\)	\(e\left(\frac{2}{29}\right)\)	\(e\left(\frac{73}{174}\right)\)	\(e\left(\frac{47}{87}\right)\)	\(e\left(\frac{31}{58}\right)\)	\(e\left(\frac{71}{87}\right)\)	\(e\left(\frac{101}{174}\right)\)	\(e\left(\frac{137}{174}\right)\)

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First 31 of 56 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.t
Modulus	$767$
Conductor	$767$
Order	$174$
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:	\(174\)	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);