LMFDB - Dirichlet character orbit 799.q

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(799, base_ring=CyclotomicField(184)) M = H._module chi = DirichletCharacter(H, M([69,84])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(15, 799)) 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("799.15"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$799$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$799$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$184$	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:	$\Q(\zeta_{184})$	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 184 polynomial (not computed)	comment:Fixed field sage:chi.fixed_field()

First 31 of 88 characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{799}(15,\cdot)$	$-1$	$1$	$e\left(\frac{43}{92}\right)$	$e\left(\frac{93}{184}\right)$	$e\left(\frac{43}{46}\right)$	$e\left(\frac{61}{184}\right)$	$e\left(\frac{179}{184}\right)$	$e\left(\frac{135}{184}\right)$	$e\left(\frac{37}{92}\right)$	$e\left(\frac{1}{92}\right)$	$e\left(\frac{147}{184}\right)$	$e\left(\frac{151}{184}\right)$
$\chi_{799}(19,\cdot)$	$-1$	$1$	$e\left(\frac{79}{92}\right)$	$e\left(\frac{81}{184}\right)$	$e\left(\frac{33}{46}\right)$	$e\left(\frac{65}{184}\right)$	$e\left(\frac{55}{184}\right)$	$e\left(\frac{171}{184}\right)$	$e\left(\frac{53}{92}\right)$	$e\left(\frac{81}{92}\right)$	$e\left(\frac{39}{184}\right)$	$e\left(\frac{179}{184}\right)$
$\chi_{799}(26,\cdot)$	$-1$	$1$	$e\left(\frac{9}{92}\right)$	$e\left(\frac{135}{184}\right)$	$e\left(\frac{9}{46}\right)$	$e\left(\frac{47}{184}\right)$	$e\left(\frac{153}{184}\right)$	$e\left(\frac{101}{184}\right)$	$e\left(\frac{27}{92}\right)$	$e\left(\frac{43}{92}\right)$	$e\left(\frac{65}{184}\right)$	$e\left(\frac{53}{184}\right)$
$\chi_{799}(43,\cdot)$	$-1$	$1$	$e\left(\frac{77}{92}\right)$	$e\left(\frac{143}{184}\right)$	$e\left(\frac{31}{46}\right)$	$e\left(\frac{167}{184}\right)$	$e\left(\frac{113}{184}\right)$	$e\left(\frac{77}{184}\right)$	$e\left(\frac{47}{92}\right)$	$e\left(\frac{51}{92}\right)$	$e\left(\frac{137}{184}\right)$	$e\left(\frac{157}{184}\right)$
$\chi_{799}(60,\cdot)$	$-1$	$1$	$e\left(\frac{5}{92}\right)$	$e\left(\frac{167}{184}\right)$	$e\left(\frac{5}{46}\right)$	$e\left(\frac{159}{184}\right)$	$e\left(\frac{177}{184}\right)$	$e\left(\frac{5}{184}\right)$	$e\left(\frac{15}{92}\right)$	$e\left(\frac{75}{92}\right)$	$e\left(\frac{169}{184}\right)$	$e\left(\frac{101}{184}\right)$
$\chi_{799}(66,\cdot)$	$-1$	$1$	$e\left(\frac{79}{92}\right)$	$e\left(\frac{173}{184}\right)$	$e\left(\frac{33}{46}\right)$	$e\left(\frac{157}{184}\right)$	$e\left(\frac{147}{184}\right)$	$e\left(\frac{79}{184}\right)$	$e\left(\frac{53}{92}\right)$	$e\left(\frac{81}{92}\right)$	$e\left(\frac{131}{184}\right)$	$e\left(\frac{87}{184}\right)$
$\chi_{799}(70,\cdot)$	$-1$	$1$	$e\left(\frac{19}{92}\right)$	$e\left(\frac{9}{184}\right)$	$e\left(\frac{19}{46}\right)$	$e\left(\frac{89}{184}\right)$	$e\left(\frac{47}{184}\right)$	$e\left(\frac{19}{184}\right)$	$e\left(\frac{57}{92}\right)$	$e\left(\frac{9}{92}\right)$	$e\left(\frac{127}{184}\right)$	$e\left(\frac{163}{184}\right)$
$\chi_{799}(76,\cdot)$	$-1$	$1$	$e\left(\frac{41}{92}\right)$	$e\left(\frac{155}{184}\right)$	$e\left(\frac{41}{46}\right)$	$e\left(\frac{163}{184}\right)$	$e\left(\frac{53}{184}\right)$	$e\left(\frac{41}{184}\right)$	$e\left(\frac{31}{92}\right)$	$e\left(\frac{63}{92}\right)$	$e\left(\frac{61}{184}\right)$	$e\left(\frac{129}{184}\right)$
$\chi_{799}(77,\cdot)$	$-1$	$1$	$e\left(\frac{1}{92}\right)$	$e\left(\frac{15}{184}\right)$	$e\left(\frac{1}{46}\right)$	$e\left(\frac{87}{184}\right)$	$e\left(\frac{17}{184}\right)$	$e\left(\frac{93}{184}\right)$	$e\left(\frac{3}{92}\right)$	$e\left(\frac{15}{92}\right)$	$e\left(\frac{89}{184}\right)$	$e\left(\frac{149}{184}\right)$
$\chi_{799}(87,\cdot)$	$-1$	$1$	$e\left(\frac{71}{92}\right)$	$e\left(\frac{145}{184}\right)$	$e\left(\frac{25}{46}\right)$	$e\left(\frac{105}{184}\right)$	$e\left(\frac{103}{184}\right)$	$e\left(\frac{163}{184}\right)$	$e\left(\frac{29}{92}\right)$	$e\left(\frac{53}{92}\right)$	$e\left(\frac{63}{184}\right)$	$e\left(\frac{91}{184}\right)$
$\chi_{799}(104,\cdot)$	$-1$	$1$	$e\left(\frac{63}{92}\right)$	$e\left(\frac{25}{184}\right)$	$e\left(\frac{17}{46}\right)$	$e\left(\frac{145}{184}\right)$	$e\left(\frac{151}{184}\right)$	$e\left(\frac{155}{184}\right)$	$e\left(\frac{5}{92}\right)$	$e\left(\frac{25}{92}\right)$	$e\left(\frac{87}{184}\right)$	$e\left(\frac{3}{184}\right)$
$\chi_{799}(117,\cdot)$	$-1$	$1$	$e\left(\frac{19}{92}\right)$	$e\left(\frac{101}{184}\right)$	$e\left(\frac{19}{46}\right)$	$e\left(\frac{181}{184}\right)$	$e\left(\frac{139}{184}\right)$	$e\left(\frac{111}{184}\right)$	$e\left(\frac{57}{92}\right)$	$e\left(\frac{9}{92}\right)$	$e\left(\frac{35}{184}\right)$	$e\left(\frac{71}{184}\right)$
$\chi_{799}(127,\cdot)$	$-1$	$1$	$e\left(\frac{29}{92}\right)$	$e\left(\frac{67}{184}\right)$	$e\left(\frac{29}{46}\right)$	$e\left(\frac{131}{184}\right)$	$e\left(\frac{125}{184}\right)$	$e\left(\frac{121}{184}\right)$	$e\left(\frac{87}{92}\right)$	$e\left(\frac{67}{92}\right)$	$e\left(\frac{5}{184}\right)$	$e\left(\frac{89}{184}\right)$
$\chi_{799}(134,\cdot)$	$-1$	$1$	$e\left(\frac{71}{92}\right)$	$e\left(\frac{53}{184}\right)$	$e\left(\frac{25}{46}\right)$	$e\left(\frac{13}{184}\right)$	$e\left(\frac{11}{184}\right)$	$e\left(\frac{71}{184}\right)$	$e\left(\frac{29}{92}\right)$	$e\left(\frac{53}{92}\right)$	$e\left(\frac{155}{184}\right)$	$e\left(\frac{183}{184}\right)$
$\chi_{799}(138,\cdot)$	$-1$	$1$	$e\left(\frac{7}{92}\right)$	$e\left(\frac{105}{184}\right)$	$e\left(\frac{7}{46}\right)$	$e\left(\frac{57}{184}\right)$	$e\left(\frac{119}{184}\right)$	$e\left(\frac{99}{184}\right)$	$e\left(\frac{21}{92}\right)$	$e\left(\frac{13}{92}\right)$	$e\left(\frac{71}{184}\right)$	$e\left(\frac{123}{184}\right)$
$\chi_{799}(151,\cdot)$	$-1$	$1$	$e\left(\frac{63}{92}\right)$	$e\left(\frac{117}{184}\right)$	$e\left(\frac{17}{46}\right)$	$e\left(\frac{53}{184}\right)$	$e\left(\frac{59}{184}\right)$	$e\left(\frac{63}{184}\right)$	$e\left(\frac{5}{92}\right)$	$e\left(\frac{25}{92}\right)$	$e\left(\frac{179}{184}\right)$	$e\left(\frac{95}{184}\right)$
$\chi_{799}(161,\cdot)$	$-1$	$1$	$e\left(\frac{21}{92}\right)$	$e\left(\frac{131}{184}\right)$	$e\left(\frac{21}{46}\right)$	$e\left(\frac{171}{184}\right)$	$e\left(\frac{173}{184}\right)$	$e\left(\frac{113}{184}\right)$	$e\left(\frac{63}{92}\right)$	$e\left(\frac{39}{92}\right)$	$e\left(\frac{29}{184}\right)$	$e\left(\frac{1}{184}\right)$
$\chi_{799}(172,\cdot)$	$-1$	$1$	$e\left(\frac{39}{92}\right)$	$e\left(\frac{33}{184}\right)$	$e\left(\frac{39}{46}\right)$	$e\left(\frac{81}{184}\right)$	$e\left(\frac{111}{184}\right)$	$e\left(\frac{131}{184}\right)$	$e\left(\frac{25}{92}\right)$	$e\left(\frac{33}{92}\right)$	$e\left(\frac{159}{184}\right)$	$e\left(\frac{107}{184}\right)$
$\chi_{799}(179,\cdot)$	$-1$	$1$	$e\left(\frac{37}{92}\right)$	$e\left(\frac{95}{184}\right)$	$e\left(\frac{37}{46}\right)$	$e\left(\frac{183}{184}\right)$	$e\left(\frac{169}{184}\right)$	$e\left(\frac{37}{184}\right)$	$e\left(\frac{19}{92}\right)$	$e\left(\frac{3}{92}\right)$	$e\left(\frac{73}{184}\right)$	$e\left(\frac{85}{184}\right)$
$\chi_{799}(185,\cdot)$	$-1$	$1$	$e\left(\frac{7}{92}\right)$	$e\left(\frac{13}{184}\right)$	$e\left(\frac{7}{46}\right)$	$e\left(\frac{149}{184}\right)$	$e\left(\frac{27}{184}\right)$	$e\left(\frac{7}{184}\right)$	$e\left(\frac{21}{92}\right)$	$e\left(\frac{13}{92}\right)$	$e\left(\frac{163}{184}\right)$	$e\left(\frac{31}{184}\right)$
$\chi_{799}(219,\cdot)$	$-1$	$1$	$e\left(\frac{39}{92}\right)$	$e\left(\frac{125}{184}\right)$	$e\left(\frac{39}{46}\right)$	$e\left(\frac{173}{184}\right)$	$e\left(\frac{19}{184}\right)$	$e\left(\frac{39}{184}\right)$	$e\left(\frac{25}{92}\right)$	$e\left(\frac{33}{92}\right)$	$e\left(\frac{67}{184}\right)$	$e\left(\frac{15}{184}\right)$
$\chi_{799}(223,\cdot)$	$-1$	$1$	$e\left(\frac{15}{92}\right)$	$e\left(\frac{41}{184}\right)$	$e\left(\frac{15}{46}\right)$	$e\left(\frac{17}{184}\right)$	$e\left(\frac{71}{184}\right)$	$e\left(\frac{107}{184}\right)$	$e\left(\frac{45}{92}\right)$	$e\left(\frac{41}{92}\right)$	$e\left(\frac{47}{184}\right)$	$e\left(\frac{27}{184}\right)$
$\chi_{799}(229,\cdot)$	$-1$	$1$	$e\left(\frac{57}{92}\right)$	$e\left(\frac{27}{184}\right)$	$e\left(\frac{11}{46}\right)$	$e\left(\frac{83}{184}\right)$	$e\left(\frac{141}{184}\right)$	$e\left(\frac{57}{184}\right)$	$e\left(\frac{79}{92}\right)$	$e\left(\frac{27}{92}\right)$	$e\left(\frac{13}{184}\right)$	$e\left(\frac{121}{184}\right)$
$\chi_{799}(240,\cdot)$	$-1$	$1$	$e\left(\frac{59}{92}\right)$	$e\left(\frac{57}{184}\right)$	$e\left(\frac{13}{46}\right)$	$e\left(\frac{73}{184}\right)$	$e\left(\frac{175}{184}\right)$	$e\left(\frac{59}{184}\right)$	$e\left(\frac{85}{92}\right)$	$e\left(\frac{57}{92}\right)$	$e\left(\frac{7}{184}\right)$	$e\left(\frac{51}{184}\right)$
$\chi_{799}(246,\cdot)$	$-1$	$1$	$e\left(\frac{45}{92}\right)$	$e\left(\frac{123}{184}\right)$	$e\left(\frac{45}{46}\right)$	$e\left(\frac{51}{184}\right)$	$e\left(\frac{29}{184}\right)$	$e\left(\frac{137}{184}\right)$	$e\left(\frac{43}{92}\right)$	$e\left(\frac{31}{92}\right)$	$e\left(\frac{141}{184}\right)$	$e\left(\frac{81}{184}\right)$
$\chi_{799}(257,\cdot)$	$-1$	$1$	$e\left(\frac{3}{92}\right)$	$e\left(\frac{137}{184}\right)$	$e\left(\frac{3}{46}\right)$	$e\left(\frac{169}{184}\right)$	$e\left(\frac{143}{184}\right)$	$e\left(\frac{3}{184}\right)$	$e\left(\frac{9}{92}\right)$	$e\left(\frac{45}{92}\right)$	$e\left(\frac{175}{184}\right)$	$e\left(\frac{171}{184}\right)$
$\chi_{799}(264,\cdot)$	$-1$	$1$	$e\left(\frac{41}{92}\right)$	$e\left(\frac{63}{184}\right)$	$e\left(\frac{41}{46}\right)$	$e\left(\frac{71}{184}\right)$	$e\left(\frac{145}{184}\right)$	$e\left(\frac{133}{184}\right)$	$e\left(\frac{31}{92}\right)$	$e\left(\frac{63}{92}\right)$	$e\left(\frac{153}{184}\right)$	$e\left(\frac{37}{184}\right)$
$\chi_{799}(270,\cdot)$	$-1$	$1$	$e\left(\frac{15}{92}\right)$	$e\left(\frac{133}{184}\right)$	$e\left(\frac{15}{46}\right)$	$e\left(\frac{109}{184}\right)$	$e\left(\frac{163}{184}\right)$	$e\left(\frac{15}{184}\right)$	$e\left(\frac{45}{92}\right)$	$e\left(\frac{41}{92}\right)$	$e\left(\frac{139}{184}\right)$	$e\left(\frac{119}{184}\right)$
$\chi_{799}(274,\cdot)$	$-1$	$1$	$e\left(\frac{35}{92}\right)$	$e\left(\frac{65}{184}\right)$	$e\left(\frac{35}{46}\right)$	$e\left(\frac{9}{184}\right)$	$e\left(\frac{135}{184}\right)$	$e\left(\frac{35}{184}\right)$	$e\left(\frac{13}{92}\right)$	$e\left(\frac{65}{92}\right)$	$e\left(\frac{79}{184}\right)$	$e\left(\frac{155}{184}\right)$
$\chi_{799}(280,\cdot)$	$-1$	$1$	$e\left(\frac{73}{92}\right)$	$e\left(\frac{83}{184}\right)$	$e\left(\frac{27}{46}\right)$	$e\left(\frac{3}{184}\right)$	$e\left(\frac{45}{184}\right)$	$e\left(\frac{73}{184}\right)$	$e\left(\frac{35}{92}\right)$	$e\left(\frac{83}{92}\right)$	$e\left(\frac{149}{184}\right)$	$e\left(\frac{113}{184}\right)$
$\chi_{799}(287,\cdot)$	$-1$	$1$	$e\left(\frac{59}{92}\right)$	$e\left(\frac{149}{184}\right)$	$e\left(\frac{13}{46}\right)$	$e\left(\frac{165}{184}\right)$	$e\left(\frac{83}{184}\right)$	$e\left(\frac{151}{184}\right)$	$e\left(\frac{85}{92}\right)$	$e\left(\frac{57}{92}\right)$	$e\left(\frac{99}{184}\right)$	$e\left(\frac{143}{184}\right)$

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$ over number fields
Genus 2 curves
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Character	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{799}(15,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{43}{92}\right)\)	\(e\left(\frac{93}{184}\right)\)	\(e\left(\frac{43}{46}\right)\)	\(e\left(\frac{61}{184}\right)\)	\(e\left(\frac{179}{184}\right)\)	\(e\left(\frac{135}{184}\right)\)	\(e\left(\frac{37}{92}\right)\)	\(e\left(\frac{1}{92}\right)\)	\(e\left(\frac{147}{184}\right)\)	\(e\left(\frac{151}{184}\right)\)
\(\chi_{799}(19,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{79}{92}\right)\)	\(e\left(\frac{81}{184}\right)\)	\(e\left(\frac{33}{46}\right)\)	\(e\left(\frac{65}{184}\right)\)	\(e\left(\frac{55}{184}\right)\)	\(e\left(\frac{171}{184}\right)\)	\(e\left(\frac{53}{92}\right)\)	\(e\left(\frac{81}{92}\right)\)	\(e\left(\frac{39}{184}\right)\)	\(e\left(\frac{179}{184}\right)\)
\(\chi_{799}(26,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{9}{92}\right)\)	\(e\left(\frac{135}{184}\right)\)	\(e\left(\frac{9}{46}\right)\)	\(e\left(\frac{47}{184}\right)\)	\(e\left(\frac{153}{184}\right)\)	\(e\left(\frac{101}{184}\right)\)	\(e\left(\frac{27}{92}\right)\)	\(e\left(\frac{43}{92}\right)\)	\(e\left(\frac{65}{184}\right)\)	\(e\left(\frac{53}{184}\right)\)
\(\chi_{799}(43,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{77}{92}\right)\)	\(e\left(\frac{143}{184}\right)\)	\(e\left(\frac{31}{46}\right)\)	\(e\left(\frac{167}{184}\right)\)	\(e\left(\frac{113}{184}\right)\)	\(e\left(\frac{77}{184}\right)\)	\(e\left(\frac{47}{92}\right)\)	\(e\left(\frac{51}{92}\right)\)	\(e\left(\frac{137}{184}\right)\)	\(e\left(\frac{157}{184}\right)\)
\(\chi_{799}(60,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{5}{92}\right)\)	\(e\left(\frac{167}{184}\right)\)	\(e\left(\frac{5}{46}\right)\)	\(e\left(\frac{159}{184}\right)\)	\(e\left(\frac{177}{184}\right)\)	\(e\left(\frac{5}{184}\right)\)	\(e\left(\frac{15}{92}\right)\)	\(e\left(\frac{75}{92}\right)\)	\(e\left(\frac{169}{184}\right)\)	\(e\left(\frac{101}{184}\right)\)
\(\chi_{799}(66,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{79}{92}\right)\)	\(e\left(\frac{173}{184}\right)\)	\(e\left(\frac{33}{46}\right)\)	\(e\left(\frac{157}{184}\right)\)	\(e\left(\frac{147}{184}\right)\)	\(e\left(\frac{79}{184}\right)\)	\(e\left(\frac{53}{92}\right)\)	\(e\left(\frac{81}{92}\right)\)	\(e\left(\frac{131}{184}\right)\)	\(e\left(\frac{87}{184}\right)\)
\(\chi_{799}(70,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{19}{92}\right)\)	\(e\left(\frac{9}{184}\right)\)	\(e\left(\frac{19}{46}\right)\)	\(e\left(\frac{89}{184}\right)\)	\(e\left(\frac{47}{184}\right)\)	\(e\left(\frac{19}{184}\right)\)	\(e\left(\frac{57}{92}\right)\)	\(e\left(\frac{9}{92}\right)\)	\(e\left(\frac{127}{184}\right)\)	\(e\left(\frac{163}{184}\right)\)
\(\chi_{799}(76,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{41}{92}\right)\)	\(e\left(\frac{155}{184}\right)\)	\(e\left(\frac{41}{46}\right)\)	\(e\left(\frac{163}{184}\right)\)	\(e\left(\frac{53}{184}\right)\)	\(e\left(\frac{41}{184}\right)\)	\(e\left(\frac{31}{92}\right)\)	\(e\left(\frac{63}{92}\right)\)	\(e\left(\frac{61}{184}\right)\)	\(e\left(\frac{129}{184}\right)\)
\(\chi_{799}(77,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{92}\right)\)	\(e\left(\frac{15}{184}\right)\)	\(e\left(\frac{1}{46}\right)\)	\(e\left(\frac{87}{184}\right)\)	\(e\left(\frac{17}{184}\right)\)	\(e\left(\frac{93}{184}\right)\)	\(e\left(\frac{3}{92}\right)\)	\(e\left(\frac{15}{92}\right)\)	\(e\left(\frac{89}{184}\right)\)	\(e\left(\frac{149}{184}\right)\)
\(\chi_{799}(87,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{71}{92}\right)\)	\(e\left(\frac{145}{184}\right)\)	\(e\left(\frac{25}{46}\right)\)	\(e\left(\frac{105}{184}\right)\)	\(e\left(\frac{103}{184}\right)\)	\(e\left(\frac{163}{184}\right)\)	\(e\left(\frac{29}{92}\right)\)	\(e\left(\frac{53}{92}\right)\)	\(e\left(\frac{63}{184}\right)\)	\(e\left(\frac{91}{184}\right)\)
\(\chi_{799}(104,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{63}{92}\right)\)	\(e\left(\frac{25}{184}\right)\)	\(e\left(\frac{17}{46}\right)\)	\(e\left(\frac{145}{184}\right)\)	\(e\left(\frac{151}{184}\right)\)	\(e\left(\frac{155}{184}\right)\)	\(e\left(\frac{5}{92}\right)\)	\(e\left(\frac{25}{92}\right)\)	\(e\left(\frac{87}{184}\right)\)	\(e\left(\frac{3}{184}\right)\)
\(\chi_{799}(117,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{19}{92}\right)\)	\(e\left(\frac{101}{184}\right)\)	\(e\left(\frac{19}{46}\right)\)	\(e\left(\frac{181}{184}\right)\)	\(e\left(\frac{139}{184}\right)\)	\(e\left(\frac{111}{184}\right)\)	\(e\left(\frac{57}{92}\right)\)	\(e\left(\frac{9}{92}\right)\)	\(e\left(\frac{35}{184}\right)\)	\(e\left(\frac{71}{184}\right)\)
\(\chi_{799}(127,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{29}{92}\right)\)	\(e\left(\frac{67}{184}\right)\)	\(e\left(\frac{29}{46}\right)\)	\(e\left(\frac{131}{184}\right)\)	\(e\left(\frac{125}{184}\right)\)	\(e\left(\frac{121}{184}\right)\)	\(e\left(\frac{87}{92}\right)\)	\(e\left(\frac{67}{92}\right)\)	\(e\left(\frac{5}{184}\right)\)	\(e\left(\frac{89}{184}\right)\)
\(\chi_{799}(134,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{71}{92}\right)\)	\(e\left(\frac{53}{184}\right)\)	\(e\left(\frac{25}{46}\right)\)	\(e\left(\frac{13}{184}\right)\)	\(e\left(\frac{11}{184}\right)\)	\(e\left(\frac{71}{184}\right)\)	\(e\left(\frac{29}{92}\right)\)	\(e\left(\frac{53}{92}\right)\)	\(e\left(\frac{155}{184}\right)\)	\(e\left(\frac{183}{184}\right)\)
\(\chi_{799}(138,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{7}{92}\right)\)	\(e\left(\frac{105}{184}\right)\)	\(e\left(\frac{7}{46}\right)\)	\(e\left(\frac{57}{184}\right)\)	\(e\left(\frac{119}{184}\right)\)	\(e\left(\frac{99}{184}\right)\)	\(e\left(\frac{21}{92}\right)\)	\(e\left(\frac{13}{92}\right)\)	\(e\left(\frac{71}{184}\right)\)	\(e\left(\frac{123}{184}\right)\)
\(\chi_{799}(151,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{63}{92}\right)\)	\(e\left(\frac{117}{184}\right)\)	\(e\left(\frac{17}{46}\right)\)	\(e\left(\frac{53}{184}\right)\)	\(e\left(\frac{59}{184}\right)\)	\(e\left(\frac{63}{184}\right)\)	\(e\left(\frac{5}{92}\right)\)	\(e\left(\frac{25}{92}\right)\)	\(e\left(\frac{179}{184}\right)\)	\(e\left(\frac{95}{184}\right)\)
\(\chi_{799}(161,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{21}{92}\right)\)	\(e\left(\frac{131}{184}\right)\)	\(e\left(\frac{21}{46}\right)\)	\(e\left(\frac{171}{184}\right)\)	\(e\left(\frac{173}{184}\right)\)	\(e\left(\frac{113}{184}\right)\)	\(e\left(\frac{63}{92}\right)\)	\(e\left(\frac{39}{92}\right)\)	\(e\left(\frac{29}{184}\right)\)	\(e\left(\frac{1}{184}\right)\)
\(\chi_{799}(172,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{39}{92}\right)\)	\(e\left(\frac{33}{184}\right)\)	\(e\left(\frac{39}{46}\right)\)	\(e\left(\frac{81}{184}\right)\)	\(e\left(\frac{111}{184}\right)\)	\(e\left(\frac{131}{184}\right)\)	\(e\left(\frac{25}{92}\right)\)	\(e\left(\frac{33}{92}\right)\)	\(e\left(\frac{159}{184}\right)\)	\(e\left(\frac{107}{184}\right)\)
\(\chi_{799}(179,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{37}{92}\right)\)	\(e\left(\frac{95}{184}\right)\)	\(e\left(\frac{37}{46}\right)\)	\(e\left(\frac{183}{184}\right)\)	\(e\left(\frac{169}{184}\right)\)	\(e\left(\frac{37}{184}\right)\)	\(e\left(\frac{19}{92}\right)\)	\(e\left(\frac{3}{92}\right)\)	\(e\left(\frac{73}{184}\right)\)	\(e\left(\frac{85}{184}\right)\)
\(\chi_{799}(185,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{7}{92}\right)\)	\(e\left(\frac{13}{184}\right)\)	\(e\left(\frac{7}{46}\right)\)	\(e\left(\frac{149}{184}\right)\)	\(e\left(\frac{27}{184}\right)\)	\(e\left(\frac{7}{184}\right)\)	\(e\left(\frac{21}{92}\right)\)	\(e\left(\frac{13}{92}\right)\)	\(e\left(\frac{163}{184}\right)\)	\(e\left(\frac{31}{184}\right)\)
\(\chi_{799}(219,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{39}{92}\right)\)	\(e\left(\frac{125}{184}\right)\)	\(e\left(\frac{39}{46}\right)\)	\(e\left(\frac{173}{184}\right)\)	\(e\left(\frac{19}{184}\right)\)	\(e\left(\frac{39}{184}\right)\)	\(e\left(\frac{25}{92}\right)\)	\(e\left(\frac{33}{92}\right)\)	\(e\left(\frac{67}{184}\right)\)	\(e\left(\frac{15}{184}\right)\)
\(\chi_{799}(223,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{15}{92}\right)\)	\(e\left(\frac{41}{184}\right)\)	\(e\left(\frac{15}{46}\right)\)	\(e\left(\frac{17}{184}\right)\)	\(e\left(\frac{71}{184}\right)\)	\(e\left(\frac{107}{184}\right)\)	\(e\left(\frac{45}{92}\right)\)	\(e\left(\frac{41}{92}\right)\)	\(e\left(\frac{47}{184}\right)\)	\(e\left(\frac{27}{184}\right)\)
\(\chi_{799}(229,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{57}{92}\right)\)	\(e\left(\frac{27}{184}\right)\)	\(e\left(\frac{11}{46}\right)\)	\(e\left(\frac{83}{184}\right)\)	\(e\left(\frac{141}{184}\right)\)	\(e\left(\frac{57}{184}\right)\)	\(e\left(\frac{79}{92}\right)\)	\(e\left(\frac{27}{92}\right)\)	\(e\left(\frac{13}{184}\right)\)	\(e\left(\frac{121}{184}\right)\)
\(\chi_{799}(240,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{59}{92}\right)\)	\(e\left(\frac{57}{184}\right)\)	\(e\left(\frac{13}{46}\right)\)	\(e\left(\frac{73}{184}\right)\)	\(e\left(\frac{175}{184}\right)\)	\(e\left(\frac{59}{184}\right)\)	\(e\left(\frac{85}{92}\right)\)	\(e\left(\frac{57}{92}\right)\)	\(e\left(\frac{7}{184}\right)\)	\(e\left(\frac{51}{184}\right)\)
\(\chi_{799}(246,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{45}{92}\right)\)	\(e\left(\frac{123}{184}\right)\)	\(e\left(\frac{45}{46}\right)\)	\(e\left(\frac{51}{184}\right)\)	\(e\left(\frac{29}{184}\right)\)	\(e\left(\frac{137}{184}\right)\)	\(e\left(\frac{43}{92}\right)\)	\(e\left(\frac{31}{92}\right)\)	\(e\left(\frac{141}{184}\right)\)	\(e\left(\frac{81}{184}\right)\)
\(\chi_{799}(257,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{3}{92}\right)\)	\(e\left(\frac{137}{184}\right)\)	\(e\left(\frac{3}{46}\right)\)	\(e\left(\frac{169}{184}\right)\)	\(e\left(\frac{143}{184}\right)\)	\(e\left(\frac{3}{184}\right)\)	\(e\left(\frac{9}{92}\right)\)	\(e\left(\frac{45}{92}\right)\)	\(e\left(\frac{175}{184}\right)\)	\(e\left(\frac{171}{184}\right)\)
\(\chi_{799}(264,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{41}{92}\right)\)	\(e\left(\frac{63}{184}\right)\)	\(e\left(\frac{41}{46}\right)\)	\(e\left(\frac{71}{184}\right)\)	\(e\left(\frac{145}{184}\right)\)	\(e\left(\frac{133}{184}\right)\)	\(e\left(\frac{31}{92}\right)\)	\(e\left(\frac{63}{92}\right)\)	\(e\left(\frac{153}{184}\right)\)	\(e\left(\frac{37}{184}\right)\)
\(\chi_{799}(270,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{15}{92}\right)\)	\(e\left(\frac{133}{184}\right)\)	\(e\left(\frac{15}{46}\right)\)	\(e\left(\frac{109}{184}\right)\)	\(e\left(\frac{163}{184}\right)\)	\(e\left(\frac{15}{184}\right)\)	\(e\left(\frac{45}{92}\right)\)	\(e\left(\frac{41}{92}\right)\)	\(e\left(\frac{139}{184}\right)\)	\(e\left(\frac{119}{184}\right)\)
\(\chi_{799}(274,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{35}{92}\right)\)	\(e\left(\frac{65}{184}\right)\)	\(e\left(\frac{35}{46}\right)\)	\(e\left(\frac{9}{184}\right)\)	\(e\left(\frac{135}{184}\right)\)	\(e\left(\frac{35}{184}\right)\)	\(e\left(\frac{13}{92}\right)\)	\(e\left(\frac{65}{92}\right)\)	\(e\left(\frac{79}{184}\right)\)	\(e\left(\frac{155}{184}\right)\)
\(\chi_{799}(280,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{73}{92}\right)\)	\(e\left(\frac{83}{184}\right)\)	\(e\left(\frac{27}{46}\right)\)	\(e\left(\frac{3}{184}\right)\)	\(e\left(\frac{45}{184}\right)\)	\(e\left(\frac{73}{184}\right)\)	\(e\left(\frac{35}{92}\right)\)	\(e\left(\frac{83}{92}\right)\)	\(e\left(\frac{149}{184}\right)\)	\(e\left(\frac{113}{184}\right)\)
\(\chi_{799}(287,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{59}{92}\right)\)	\(e\left(\frac{149}{184}\right)\)	\(e\left(\frac{13}{46}\right)\)	\(e\left(\frac{165}{184}\right)\)	\(e\left(\frac{83}{184}\right)\)	\(e\left(\frac{151}{184}\right)\)	\(e\left(\frac{85}{92}\right)\)	\(e\left(\frac{57}{92}\right)\)	\(e\left(\frac{99}{184}\right)\)	\(e\left(\frac{143}{184}\right)\)

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First 31 of 88 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	799.q
Modulus	$799$
Conductor	$799$
Order	$184$
Real	no
Primitive	yes
Minimal	yes
Parity	odd

Modulus:	\(799\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(799\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(184\)	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);