LMFDB - Dirichlet character orbit 2382.bi

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2382, base_ring=CyclotomicField(396)) M = H._module chi = DirichletCharacter(H, M([198,1])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(5, 2382)) 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("2382.5"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$2382$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$1191$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$396$	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:	no, induced from 1191.bi	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	yes
Parity:	even	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);

Related number fields

Field of values:	$\Q(\zeta_{396})$	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 396 polynomial (not computed)	comment:Fixed field sage:chi.fixed_field()

First 31 of 120 characters in Galois orbit

Character	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$
$\chi_{2382}(5,\cdot)$	$1$	$1$	$e\left(\frac{199}{396}\right)$	$e\left(\frac{329}{396}\right)$	$e\left(\frac{169}{198}\right)$	$e\left(\frac{101}{396}\right)$	$e\left(\frac{73}{132}\right)$	$e\left(\frac{32}{99}\right)$	$e\left(\frac{2}{99}\right)$	$e\left(\frac{1}{198}\right)$	$e\left(\frac{193}{198}\right)$	$e\left(\frac{9}{11}\right)$
$\chi_{2382}(59,\cdot)$	$1$	$1$	$e\left(\frac{49}{396}\right)$	$e\left(\frac{83}{396}\right)$	$e\left(\frac{163}{198}\right)$	$e\left(\frac{395}{396}\right)$	$e\left(\frac{79}{132}\right)$	$e\left(\frac{83}{99}\right)$	$e\left(\frac{98}{99}\right)$	$e\left(\frac{49}{198}\right)$	$e\left(\frac{151}{198}\right)$	$e\left(\frac{1}{11}\right)$
$\chi_{2382}(77,\cdot)$	$1$	$1$	$e\left(\frac{271}{396}\right)$	$e\left(\frac{257}{396}\right)$	$e\left(\frac{61}{198}\right)$	$e\left(\frac{245}{396}\right)$	$e\left(\frac{49}{132}\right)$	$e\left(\frac{59}{99}\right)$	$e\left(\frac{47}{99}\right)$	$e\left(\frac{73}{198}\right)$	$e\left(\frac{31}{198}\right)$	$e\left(\frac{8}{11}\right)$
$\chi_{2382}(89,\cdot)$	$1$	$1$	$e\left(\frac{163}{396}\right)$	$e\left(\frac{365}{396}\right)$	$e\left(\frac{25}{198}\right)$	$e\left(\frac{29}{396}\right)$	$e\left(\frac{85}{132}\right)$	$e\left(\frac{68}{99}\right)$	$e\left(\frac{29}{99}\right)$	$e\left(\frac{163}{198}\right)$	$e\left(\frac{175}{198}\right)$	$e\left(\frac{4}{11}\right)$
$\chi_{2382}(101,\cdot)$	$1$	$1$	$e\left(\frac{41}{396}\right)$	$e\left(\frac{223}{396}\right)$	$e\left(\frac{197}{198}\right)$	$e\left(\frac{379}{396}\right)$	$e\left(\frac{23}{132}\right)$	$e\left(\frac{25}{99}\right)$	$e\left(\frac{82}{99}\right)$	$e\left(\frac{41}{198}\right)$	$e\left(\frac{191}{198}\right)$	$e\left(\frac{6}{11}\right)$
$\chi_{2382}(143,\cdot)$	$1$	$1$	$e\left(\frac{43}{396}\right)$	$e\left(\frac{89}{396}\right)$	$e\left(\frac{139}{198}\right)$	$e\left(\frac{185}{396}\right)$	$e\left(\frac{37}{132}\right)$	$e\left(\frac{89}{99}\right)$	$e\left(\frac{86}{99}\right)$	$e\left(\frac{43}{198}\right)$	$e\left(\frac{181}{198}\right)$	$e\left(\frac{2}{11}\right)$
$\chi_{2382}(155,\cdot)$	$1$	$1$	$e\left(\frac{127}{396}\right)$	$e\left(\frac{5}{396}\right)$	$e\left(\frac{79}{198}\right)$	$e\left(\frac{353}{396}\right)$	$e\left(\frac{97}{132}\right)$	$e\left(\frac{5}{99}\right)$	$e\left(\frac{56}{99}\right)$	$e\left(\frac{127}{198}\right)$	$e\left(\frac{157}{198}\right)$	$e\left(\frac{10}{11}\right)$
$\chi_{2382}(161,\cdot)$	$1$	$1$	$e\left(\frac{337}{396}\right)$	$e\left(\frac{191}{396}\right)$	$e\left(\frac{127}{198}\right)$	$e\left(\frac{179}{396}\right)$	$e\left(\frac{115}{132}\right)$	$e\left(\frac{92}{99}\right)$	$e\left(\frac{80}{99}\right)$	$e\left(\frac{139}{198}\right)$	$e\left(\frac{97}{198}\right)$	$e\left(\frac{8}{11}\right)$
$\chi_{2382}(197,\cdot)$	$1$	$1$	$e\left(\frac{335}{396}\right)$	$e\left(\frac{325}{396}\right)$	$e\left(\frac{185}{198}\right)$	$e\left(\frac{373}{396}\right)$	$e\left(\frac{101}{132}\right)$	$e\left(\frac{28}{99}\right)$	$e\left(\frac{76}{99}\right)$	$e\left(\frac{137}{198}\right)$	$e\left(\frac{107}{198}\right)$	$e\left(\frac{1}{11}\right)$
$\chi_{2382}(215,\cdot)$	$1$	$1$	$e\left(\frac{277}{396}\right)$	$e\left(\frac{251}{396}\right)$	$e\left(\frac{85}{198}\right)$	$e\left(\frac{59}{396}\right)$	$e\left(\frac{91}{132}\right)$	$e\left(\frac{53}{99}\right)$	$e\left(\frac{59}{99}\right)$	$e\left(\frac{79}{198}\right)$	$e\left(\frac{1}{198}\right)$	$e\left(\frac{7}{11}\right)$
$\chi_{2382}(227,\cdot)$	$1$	$1$	$e\left(\frac{265}{396}\right)$	$e\left(\frac{263}{396}\right)$	$e\left(\frac{37}{198}\right)$	$e\left(\frac{35}{396}\right)$	$e\left(\frac{7}{132}\right)$	$e\left(\frac{65}{99}\right)$	$e\left(\frac{35}{99}\right)$	$e\left(\frac{67}{198}\right)$	$e\left(\frac{61}{198}\right)$	$e\left(\frac{9}{11}\right)$
$\chi_{2382}(233,\cdot)$	$1$	$1$	$e\left(\frac{343}{396}\right)$	$e\left(\frac{185}{396}\right)$	$e\left(\frac{151}{198}\right)$	$e\left(\frac{389}{396}\right)$	$e\left(\frac{25}{132}\right)$	$e\left(\frac{86}{99}\right)$	$e\left(\frac{92}{99}\right)$	$e\left(\frac{145}{198}\right)$	$e\left(\frac{67}{198}\right)$	$e\left(\frac{7}{11}\right)$
$\chi_{2382}(239,\cdot)$	$1$	$1$	$e\left(\frac{287}{396}\right)$	$e\left(\frac{373}{396}\right)$	$e\left(\frac{191}{198}\right)$	$e\left(\frac{277}{396}\right)$	$e\left(\frac{29}{132}\right)$	$e\left(\frac{76}{99}\right)$	$e\left(\frac{79}{99}\right)$	$e\left(\frac{89}{198}\right)$	$e\left(\frac{149}{198}\right)$	$e\left(\frac{9}{11}\right)$
$\chi_{2382}(245,\cdot)$	$1$	$1$	$e\left(\frac{65}{396}\right)$	$e\left(\frac{199}{396}\right)$	$e\left(\frac{95}{198}\right)$	$e\left(\frac{31}{396}\right)$	$e\left(\frac{59}{132}\right)$	$e\left(\frac{1}{99}\right)$	$e\left(\frac{31}{99}\right)$	$e\left(\frac{65}{198}\right)$	$e\left(\frac{71}{198}\right)$	$e\left(\frac{2}{11}\right)$
$\chi_{2382}(251,\cdot)$	$1$	$1$	$e\left(\frac{71}{396}\right)$	$e\left(\frac{193}{396}\right)$	$e\left(\frac{119}{198}\right)$	$e\left(\frac{241}{396}\right)$	$e\left(\frac{101}{132}\right)$	$e\left(\frac{94}{99}\right)$	$e\left(\frac{43}{99}\right)$	$e\left(\frac{71}{198}\right)$	$e\left(\frac{41}{198}\right)$	$e\left(\frac{1}{11}\right)$
$\chi_{2382}(263,\cdot)$	$1$	$1$	$e\left(\frac{215}{396}\right)$	$e\left(\frac{49}{396}\right)$	$e\left(\frac{101}{198}\right)$	$e\left(\frac{133}{396}\right)$	$e\left(\frac{53}{132}\right)$	$e\left(\frac{49}{99}\right)$	$e\left(\frac{34}{99}\right)$	$e\left(\frac{17}{198}\right)$	$e\left(\frac{113}{198}\right)$	$e\left(\frac{10}{11}\right)$
$\chi_{2382}(299,\cdot)$	$1$	$1$	$e\left(\frac{109}{396}\right)$	$e\left(\frac{23}{396}\right)$	$e\left(\frac{7}{198}\right)$	$e\left(\frac{119}{396}\right)$	$e\left(\frac{103}{132}\right)$	$e\left(\frac{23}{99}\right)$	$e\left(\frac{20}{99}\right)$	$e\left(\frac{109}{198}\right)$	$e\left(\frac{49}{198}\right)$	$e\left(\frac{2}{11}\right)$
$\chi_{2382}(317,\cdot)$	$1$	$1$	$e\left(\frac{181}{396}\right)$	$e\left(\frac{347}{396}\right)$	$e\left(\frac{97}{198}\right)$	$e\left(\frac{263}{396}\right)$	$e\left(\frac{79}{132}\right)$	$e\left(\frac{50}{99}\right)$	$e\left(\frac{65}{99}\right)$	$e\left(\frac{181}{198}\right)$	$e\left(\frac{85}{198}\right)$	$e\left(\frac{1}{11}\right)$
$\chi_{2382}(323,\cdot)$	$1$	$1$	$e\left(\frac{347}{396}\right)$	$e\left(\frac{313}{396}\right)$	$e\left(\frac{35}{198}\right)$	$e\left(\frac{1}{396}\right)$	$e\left(\frac{53}{132}\right)$	$e\left(\frac{16}{99}\right)$	$e\left(\frac{1}{99}\right)$	$e\left(\frac{149}{198}\right)$	$e\left(\frac{47}{198}\right)$	$e\left(\frac{10}{11}\right)$
$\chi_{2382}(347,\cdot)$	$1$	$1$	$e\left(\frac{245}{396}\right)$	$e\left(\frac{19}{396}\right)$	$e\left(\frac{23}{198}\right)$	$e\left(\frac{391}{396}\right)$	$e\left(\frac{131}{132}\right)$	$e\left(\frac{19}{99}\right)$	$e\left(\frac{94}{99}\right)$	$e\left(\frac{47}{198}\right)$	$e\left(\frac{161}{198}\right)$	$e\left(\frac{5}{11}\right)$
$\chi_{2382}(359,\cdot)$	$1$	$1$	$e\left(\frac{371}{396}\right)$	$e\left(\frac{289}{396}\right)$	$e\left(\frac{131}{198}\right)$	$e\left(\frac{49}{396}\right)$	$e\left(\frac{89}{132}\right)$	$e\left(\frac{91}{99}\right)$	$e\left(\frac{49}{99}\right)$	$e\left(\frac{173}{198}\right)$	$e\left(\frac{125}{198}\right)$	$e\left(\frac{6}{11}\right)$
$\chi_{2382}(377,\cdot)$	$1$	$1$	$e\left(\frac{91}{396}\right)$	$e\left(\frac{41}{396}\right)$	$e\left(\frac{133}{198}\right)$	$e\left(\frac{281}{396}\right)$	$e\left(\frac{109}{132}\right)$	$e\left(\frac{41}{99}\right)$	$e\left(\frac{83}{99}\right)$	$e\left(\frac{91}{198}\right)$	$e\left(\frac{139}{198}\right)$	$e\left(\frac{5}{11}\right)$
$\chi_{2382}(419,\cdot)$	$1$	$1$	$e\left(\frac{185}{396}\right)$	$e\left(\frac{79}{396}\right)$	$e\left(\frac{179}{198}\right)$	$e\left(\frac{271}{396}\right)$	$e\left(\frac{107}{132}\right)$	$e\left(\frac{79}{99}\right)$	$e\left(\frac{73}{99}\right)$	$e\left(\frac{185}{198}\right)$	$e\left(\frac{65}{198}\right)$	$e\left(\frac{4}{11}\right)$
$\chi_{2382}(425,\cdot)$	$1$	$1$	$e\left(\frac{221}{396}\right)$	$e\left(\frac{43}{396}\right)$	$e\left(\frac{125}{198}\right)$	$e\left(\frac{343}{396}\right)$	$e\left(\frac{95}{132}\right)$	$e\left(\frac{43}{99}\right)$	$e\left(\frac{46}{99}\right)$	$e\left(\frac{23}{198}\right)$	$e\left(\frac{83}{198}\right)$	$e\left(\frac{9}{11}\right)$
$\chi_{2382}(443,\cdot)$	$1$	$1$	$e\left(\frac{251}{396}\right)$	$e\left(\frac{13}{396}\right)$	$e\left(\frac{47}{198}\right)$	$e\left(\frac{205}{396}\right)$	$e\left(\frac{41}{132}\right)$	$e\left(\frac{13}{99}\right)$	$e\left(\frac{7}{99}\right)$	$e\left(\frac{53}{198}\right)$	$e\left(\frac{131}{198}\right)$	$e\left(\frac{4}{11}\right)$
$\chi_{2382}(449,\cdot)$	$1$	$1$	$e\left(\frac{389}{396}\right)$	$e\left(\frac{271}{396}\right)$	$e\left(\frac{5}{198}\right)$	$e\left(\frac{283}{396}\right)$	$e\left(\frac{83}{132}\right)$	$e\left(\frac{73}{99}\right)$	$e\left(\frac{85}{99}\right)$	$e\left(\frac{191}{198}\right)$	$e\left(\frac{35}{198}\right)$	$e\left(\frac{3}{11}\right)$
$\chi_{2382}(455,\cdot)$	$1$	$1$	$e\left(\frac{233}{396}\right)$	$e\left(\frac{31}{396}\right)$	$e\left(\frac{173}{198}\right)$	$e\left(\frac{367}{396}\right)$	$e\left(\frac{47}{132}\right)$	$e\left(\frac{31}{99}\right)$	$e\left(\frac{70}{99}\right)$	$e\left(\frac{35}{198}\right)$	$e\left(\frac{23}{198}\right)$	$e\left(\frac{7}{11}\right)$
$\chi_{2382}(491,\cdot)$	$1$	$1$	$e\left(\frac{25}{396}\right)$	$e\left(\frac{107}{396}\right)$	$e\left(\frac{67}{198}\right)$	$e\left(\frac{347}{396}\right)$	$e\left(\frac{43}{132}\right)$	$e\left(\frac{8}{99}\right)$	$e\left(\frac{50}{99}\right)$	$e\left(\frac{25}{198}\right)$	$e\left(\frac{73}{198}\right)$	$e\left(\frac{5}{11}\right)$
$\chi_{2382}(509,\cdot)$	$1$	$1$	$e\left(\frac{311}{396}\right)$	$e\left(\frac{349}{396}\right)$	$e\left(\frac{89}{198}\right)$	$e\left(\frac{325}{396}\right)$	$e\left(\frac{65}{132}\right)$	$e\left(\frac{52}{99}\right)$	$e\left(\frac{28}{99}\right)$	$e\left(\frac{113}{198}\right)$	$e\left(\frac{29}{198}\right)$	$e\left(\frac{5}{11}\right)$
$\chi_{2382}(605,\cdot)$	$1$	$1$	$e\left(\frac{83}{396}\right)$	$e\left(\frac{181}{396}\right)$	$e\left(\frac{167}{198}\right)$	$e\left(\frac{265}{396}\right)$	$e\left(\frac{53}{132}\right)$	$e\left(\frac{82}{99}\right)$	$e\left(\frac{67}{99}\right)$	$e\left(\frac{83}{198}\right)$	$e\left(\frac{179}{198}\right)$	$e\left(\frac{10}{11}\right)$
$\chi_{2382}(629,\cdot)$	$1$	$1$	$e\left(\frac{323}{396}\right)$	$e\left(\frac{337}{396}\right)$	$e\left(\frac{137}{198}\right)$	$e\left(\frac{349}{396}\right)$	$e\left(\frac{17}{132}\right)$	$e\left(\frac{40}{99}\right)$	$e\left(\frac{52}{99}\right)$	$e\left(\frac{125}{198}\right)$	$e\left(\frac{167}{198}\right)$	$e\left(\frac{3}{11}\right)$

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	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)
\(\chi_{2382}(5,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{199}{396}\right)\)	\(e\left(\frac{329}{396}\right)\)	\(e\left(\frac{169}{198}\right)\)	\(e\left(\frac{101}{396}\right)\)	\(e\left(\frac{73}{132}\right)\)	\(e\left(\frac{32}{99}\right)\)	\(e\left(\frac{2}{99}\right)\)	\(e\left(\frac{1}{198}\right)\)	\(e\left(\frac{193}{198}\right)\)	\(e\left(\frac{9}{11}\right)\)
\(\chi_{2382}(59,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{396}\right)\)	\(e\left(\frac{83}{396}\right)\)	\(e\left(\frac{163}{198}\right)\)	\(e\left(\frac{395}{396}\right)\)	\(e\left(\frac{79}{132}\right)\)	\(e\left(\frac{83}{99}\right)\)	\(e\left(\frac{98}{99}\right)\)	\(e\left(\frac{49}{198}\right)\)	\(e\left(\frac{151}{198}\right)\)	\(e\left(\frac{1}{11}\right)\)
\(\chi_{2382}(77,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{271}{396}\right)\)	\(e\left(\frac{257}{396}\right)\)	\(e\left(\frac{61}{198}\right)\)	\(e\left(\frac{245}{396}\right)\)	\(e\left(\frac{49}{132}\right)\)	\(e\left(\frac{59}{99}\right)\)	\(e\left(\frac{47}{99}\right)\)	\(e\left(\frac{73}{198}\right)\)	\(e\left(\frac{31}{198}\right)\)	\(e\left(\frac{8}{11}\right)\)
\(\chi_{2382}(89,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{163}{396}\right)\)	\(e\left(\frac{365}{396}\right)\)	\(e\left(\frac{25}{198}\right)\)	\(e\left(\frac{29}{396}\right)\)	\(e\left(\frac{85}{132}\right)\)	\(e\left(\frac{68}{99}\right)\)	\(e\left(\frac{29}{99}\right)\)	\(e\left(\frac{163}{198}\right)\)	\(e\left(\frac{175}{198}\right)\)	\(e\left(\frac{4}{11}\right)\)
\(\chi_{2382}(101,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{396}\right)\)	\(e\left(\frac{223}{396}\right)\)	\(e\left(\frac{197}{198}\right)\)	\(e\left(\frac{379}{396}\right)\)	\(e\left(\frac{23}{132}\right)\)	\(e\left(\frac{25}{99}\right)\)	\(e\left(\frac{82}{99}\right)\)	\(e\left(\frac{41}{198}\right)\)	\(e\left(\frac{191}{198}\right)\)	\(e\left(\frac{6}{11}\right)\)
\(\chi_{2382}(143,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{396}\right)\)	\(e\left(\frac{89}{396}\right)\)	\(e\left(\frac{139}{198}\right)\)	\(e\left(\frac{185}{396}\right)\)	\(e\left(\frac{37}{132}\right)\)	\(e\left(\frac{89}{99}\right)\)	\(e\left(\frac{86}{99}\right)\)	\(e\left(\frac{43}{198}\right)\)	\(e\left(\frac{181}{198}\right)\)	\(e\left(\frac{2}{11}\right)\)
\(\chi_{2382}(155,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{127}{396}\right)\)	\(e\left(\frac{5}{396}\right)\)	\(e\left(\frac{79}{198}\right)\)	\(e\left(\frac{353}{396}\right)\)	\(e\left(\frac{97}{132}\right)\)	\(e\left(\frac{5}{99}\right)\)	\(e\left(\frac{56}{99}\right)\)	\(e\left(\frac{127}{198}\right)\)	\(e\left(\frac{157}{198}\right)\)	\(e\left(\frac{10}{11}\right)\)
\(\chi_{2382}(161,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{337}{396}\right)\)	\(e\left(\frac{191}{396}\right)\)	\(e\left(\frac{127}{198}\right)\)	\(e\left(\frac{179}{396}\right)\)	\(e\left(\frac{115}{132}\right)\)	\(e\left(\frac{92}{99}\right)\)	\(e\left(\frac{80}{99}\right)\)	\(e\left(\frac{139}{198}\right)\)	\(e\left(\frac{97}{198}\right)\)	\(e\left(\frac{8}{11}\right)\)
\(\chi_{2382}(197,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{335}{396}\right)\)	\(e\left(\frac{325}{396}\right)\)	\(e\left(\frac{185}{198}\right)\)	\(e\left(\frac{373}{396}\right)\)	\(e\left(\frac{101}{132}\right)\)	\(e\left(\frac{28}{99}\right)\)	\(e\left(\frac{76}{99}\right)\)	\(e\left(\frac{137}{198}\right)\)	\(e\left(\frac{107}{198}\right)\)	\(e\left(\frac{1}{11}\right)\)
\(\chi_{2382}(215,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{277}{396}\right)\)	\(e\left(\frac{251}{396}\right)\)	\(e\left(\frac{85}{198}\right)\)	\(e\left(\frac{59}{396}\right)\)	\(e\left(\frac{91}{132}\right)\)	\(e\left(\frac{53}{99}\right)\)	\(e\left(\frac{59}{99}\right)\)	\(e\left(\frac{79}{198}\right)\)	\(e\left(\frac{1}{198}\right)\)	\(e\left(\frac{7}{11}\right)\)
\(\chi_{2382}(227,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{265}{396}\right)\)	\(e\left(\frac{263}{396}\right)\)	\(e\left(\frac{37}{198}\right)\)	\(e\left(\frac{35}{396}\right)\)	\(e\left(\frac{7}{132}\right)\)	\(e\left(\frac{65}{99}\right)\)	\(e\left(\frac{35}{99}\right)\)	\(e\left(\frac{67}{198}\right)\)	\(e\left(\frac{61}{198}\right)\)	\(e\left(\frac{9}{11}\right)\)
\(\chi_{2382}(233,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{343}{396}\right)\)	\(e\left(\frac{185}{396}\right)\)	\(e\left(\frac{151}{198}\right)\)	\(e\left(\frac{389}{396}\right)\)	\(e\left(\frac{25}{132}\right)\)	\(e\left(\frac{86}{99}\right)\)	\(e\left(\frac{92}{99}\right)\)	\(e\left(\frac{145}{198}\right)\)	\(e\left(\frac{67}{198}\right)\)	\(e\left(\frac{7}{11}\right)\)
\(\chi_{2382}(239,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{287}{396}\right)\)	\(e\left(\frac{373}{396}\right)\)	\(e\left(\frac{191}{198}\right)\)	\(e\left(\frac{277}{396}\right)\)	\(e\left(\frac{29}{132}\right)\)	\(e\left(\frac{76}{99}\right)\)	\(e\left(\frac{79}{99}\right)\)	\(e\left(\frac{89}{198}\right)\)	\(e\left(\frac{149}{198}\right)\)	\(e\left(\frac{9}{11}\right)\)
\(\chi_{2382}(245,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{65}{396}\right)\)	\(e\left(\frac{199}{396}\right)\)	\(e\left(\frac{95}{198}\right)\)	\(e\left(\frac{31}{396}\right)\)	\(e\left(\frac{59}{132}\right)\)	\(e\left(\frac{1}{99}\right)\)	\(e\left(\frac{31}{99}\right)\)	\(e\left(\frac{65}{198}\right)\)	\(e\left(\frac{71}{198}\right)\)	\(e\left(\frac{2}{11}\right)\)
\(\chi_{2382}(251,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{396}\right)\)	\(e\left(\frac{193}{396}\right)\)	\(e\left(\frac{119}{198}\right)\)	\(e\left(\frac{241}{396}\right)\)	\(e\left(\frac{101}{132}\right)\)	\(e\left(\frac{94}{99}\right)\)	\(e\left(\frac{43}{99}\right)\)	\(e\left(\frac{71}{198}\right)\)	\(e\left(\frac{41}{198}\right)\)	\(e\left(\frac{1}{11}\right)\)
\(\chi_{2382}(263,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{215}{396}\right)\)	\(e\left(\frac{49}{396}\right)\)	\(e\left(\frac{101}{198}\right)\)	\(e\left(\frac{133}{396}\right)\)	\(e\left(\frac{53}{132}\right)\)	\(e\left(\frac{49}{99}\right)\)	\(e\left(\frac{34}{99}\right)\)	\(e\left(\frac{17}{198}\right)\)	\(e\left(\frac{113}{198}\right)\)	\(e\left(\frac{10}{11}\right)\)
\(\chi_{2382}(299,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{109}{396}\right)\)	\(e\left(\frac{23}{396}\right)\)	\(e\left(\frac{7}{198}\right)\)	\(e\left(\frac{119}{396}\right)\)	\(e\left(\frac{103}{132}\right)\)	\(e\left(\frac{23}{99}\right)\)	\(e\left(\frac{20}{99}\right)\)	\(e\left(\frac{109}{198}\right)\)	\(e\left(\frac{49}{198}\right)\)	\(e\left(\frac{2}{11}\right)\)
\(\chi_{2382}(317,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{181}{396}\right)\)	\(e\left(\frac{347}{396}\right)\)	\(e\left(\frac{97}{198}\right)\)	\(e\left(\frac{263}{396}\right)\)	\(e\left(\frac{79}{132}\right)\)	\(e\left(\frac{50}{99}\right)\)	\(e\left(\frac{65}{99}\right)\)	\(e\left(\frac{181}{198}\right)\)	\(e\left(\frac{85}{198}\right)\)	\(e\left(\frac{1}{11}\right)\)
\(\chi_{2382}(323,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{347}{396}\right)\)	\(e\left(\frac{313}{396}\right)\)	\(e\left(\frac{35}{198}\right)\)	\(e\left(\frac{1}{396}\right)\)	\(e\left(\frac{53}{132}\right)\)	\(e\left(\frac{16}{99}\right)\)	\(e\left(\frac{1}{99}\right)\)	\(e\left(\frac{149}{198}\right)\)	\(e\left(\frac{47}{198}\right)\)	\(e\left(\frac{10}{11}\right)\)
\(\chi_{2382}(347,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{245}{396}\right)\)	\(e\left(\frac{19}{396}\right)\)	\(e\left(\frac{23}{198}\right)\)	\(e\left(\frac{391}{396}\right)\)	\(e\left(\frac{131}{132}\right)\)	\(e\left(\frac{19}{99}\right)\)	\(e\left(\frac{94}{99}\right)\)	\(e\left(\frac{47}{198}\right)\)	\(e\left(\frac{161}{198}\right)\)	\(e\left(\frac{5}{11}\right)\)
\(\chi_{2382}(359,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{371}{396}\right)\)	\(e\left(\frac{289}{396}\right)\)	\(e\left(\frac{131}{198}\right)\)	\(e\left(\frac{49}{396}\right)\)	\(e\left(\frac{89}{132}\right)\)	\(e\left(\frac{91}{99}\right)\)	\(e\left(\frac{49}{99}\right)\)	\(e\left(\frac{173}{198}\right)\)	\(e\left(\frac{125}{198}\right)\)	\(e\left(\frac{6}{11}\right)\)
\(\chi_{2382}(377,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{91}{396}\right)\)	\(e\left(\frac{41}{396}\right)\)	\(e\left(\frac{133}{198}\right)\)	\(e\left(\frac{281}{396}\right)\)	\(e\left(\frac{109}{132}\right)\)	\(e\left(\frac{41}{99}\right)\)	\(e\left(\frac{83}{99}\right)\)	\(e\left(\frac{91}{198}\right)\)	\(e\left(\frac{139}{198}\right)\)	\(e\left(\frac{5}{11}\right)\)
\(\chi_{2382}(419,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{185}{396}\right)\)	\(e\left(\frac{79}{396}\right)\)	\(e\left(\frac{179}{198}\right)\)	\(e\left(\frac{271}{396}\right)\)	\(e\left(\frac{107}{132}\right)\)	\(e\left(\frac{79}{99}\right)\)	\(e\left(\frac{73}{99}\right)\)	\(e\left(\frac{185}{198}\right)\)	\(e\left(\frac{65}{198}\right)\)	\(e\left(\frac{4}{11}\right)\)
\(\chi_{2382}(425,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{221}{396}\right)\)	\(e\left(\frac{43}{396}\right)\)	\(e\left(\frac{125}{198}\right)\)	\(e\left(\frac{343}{396}\right)\)	\(e\left(\frac{95}{132}\right)\)	\(e\left(\frac{43}{99}\right)\)	\(e\left(\frac{46}{99}\right)\)	\(e\left(\frac{23}{198}\right)\)	\(e\left(\frac{83}{198}\right)\)	\(e\left(\frac{9}{11}\right)\)
\(\chi_{2382}(443,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{251}{396}\right)\)	\(e\left(\frac{13}{396}\right)\)	\(e\left(\frac{47}{198}\right)\)	\(e\left(\frac{205}{396}\right)\)	\(e\left(\frac{41}{132}\right)\)	\(e\left(\frac{13}{99}\right)\)	\(e\left(\frac{7}{99}\right)\)	\(e\left(\frac{53}{198}\right)\)	\(e\left(\frac{131}{198}\right)\)	\(e\left(\frac{4}{11}\right)\)
\(\chi_{2382}(449,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{389}{396}\right)\)	\(e\left(\frac{271}{396}\right)\)	\(e\left(\frac{5}{198}\right)\)	\(e\left(\frac{283}{396}\right)\)	\(e\left(\frac{83}{132}\right)\)	\(e\left(\frac{73}{99}\right)\)	\(e\left(\frac{85}{99}\right)\)	\(e\left(\frac{191}{198}\right)\)	\(e\left(\frac{35}{198}\right)\)	\(e\left(\frac{3}{11}\right)\)
\(\chi_{2382}(455,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{233}{396}\right)\)	\(e\left(\frac{31}{396}\right)\)	\(e\left(\frac{173}{198}\right)\)	\(e\left(\frac{367}{396}\right)\)	\(e\left(\frac{47}{132}\right)\)	\(e\left(\frac{31}{99}\right)\)	\(e\left(\frac{70}{99}\right)\)	\(e\left(\frac{35}{198}\right)\)	\(e\left(\frac{23}{198}\right)\)	\(e\left(\frac{7}{11}\right)\)
\(\chi_{2382}(491,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{396}\right)\)	\(e\left(\frac{107}{396}\right)\)	\(e\left(\frac{67}{198}\right)\)	\(e\left(\frac{347}{396}\right)\)	\(e\left(\frac{43}{132}\right)\)	\(e\left(\frac{8}{99}\right)\)	\(e\left(\frac{50}{99}\right)\)	\(e\left(\frac{25}{198}\right)\)	\(e\left(\frac{73}{198}\right)\)	\(e\left(\frac{5}{11}\right)\)
\(\chi_{2382}(509,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{311}{396}\right)\)	\(e\left(\frac{349}{396}\right)\)	\(e\left(\frac{89}{198}\right)\)	\(e\left(\frac{325}{396}\right)\)	\(e\left(\frac{65}{132}\right)\)	\(e\left(\frac{52}{99}\right)\)	\(e\left(\frac{28}{99}\right)\)	\(e\left(\frac{113}{198}\right)\)	\(e\left(\frac{29}{198}\right)\)	\(e\left(\frac{5}{11}\right)\)
\(\chi_{2382}(605,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{83}{396}\right)\)	\(e\left(\frac{181}{396}\right)\)	\(e\left(\frac{167}{198}\right)\)	\(e\left(\frac{265}{396}\right)\)	\(e\left(\frac{53}{132}\right)\)	\(e\left(\frac{82}{99}\right)\)	\(e\left(\frac{67}{99}\right)\)	\(e\left(\frac{83}{198}\right)\)	\(e\left(\frac{179}{198}\right)\)	\(e\left(\frac{10}{11}\right)\)
\(\chi_{2382}(629,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{323}{396}\right)\)	\(e\left(\frac{337}{396}\right)\)	\(e\left(\frac{137}{198}\right)\)	\(e\left(\frac{349}{396}\right)\)	\(e\left(\frac{17}{132}\right)\)	\(e\left(\frac{40}{99}\right)\)	\(e\left(\frac{52}{99}\right)\)	\(e\left(\frac{125}{198}\right)\)	\(e\left(\frac{167}{198}\right)\)	\(e\left(\frac{3}{11}\right)\)

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First 31 of 120 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	2382.bi
Modulus	$2382$
Conductor	$1191$
Order	$396$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(2382\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(1191\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(396\)	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:	no, induced from 1191.bi	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	yes
Parity:	even	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);