LMFDB - Dirichlet character orbit 2988.bb

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2988, base_ring=CyclotomicField(246)) M = H._module chi = DirichletCharacter(H, M([0,41,36])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(29, 2988)) 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("2988.29"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$2988$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$747$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$246$	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 747.n	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:	$\Q(\zeta_{123})$
Fixed field:	Number field defined by a degree 246 polynomial (not computed)

First 31 of 80 characters in Galois orbit

Character	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$
$\chi_{2988}(29,\cdot)$	$-1$	$1$	$e\left(\frac{193}{246}\right)$	$e\left(\frac{103}{123}\right)$	$e\left(\frac{167}{246}\right)$	$e\left(\frac{74}{123}\right)$	$e\left(\frac{57}{82}\right)$	$e\left(\frac{36}{41}\right)$	$e\left(\frac{151}{246}\right)$	$e\left(\frac{70}{123}\right)$	$e\left(\frac{227}{246}\right)$	$e\left(\frac{110}{123}\right)$
$\chi_{2988}(41,\cdot)$	$-1$	$1$	$e\left(\frac{83}{246}\right)$	$e\left(\frac{29}{123}\right)$	$e\left(\frac{133}{246}\right)$	$e\left(\frac{28}{123}\right)$	$e\left(\frac{67}{82}\right)$	$e\left(\frac{38}{41}\right)$	$e\left(\frac{107}{246}\right)$	$e\left(\frac{83}{123}\right)$	$e\left(\frac{169}{246}\right)$	$e\left(\frac{25}{123}\right)$
$\chi_{2988}(65,\cdot)$	$-1$	$1$	$e\left(\frac{19}{246}\right)$	$e\left(\frac{100}{123}\right)$	$e\left(\frac{149}{246}\right)$	$e\left(\frac{122}{123}\right)$	$e\left(\frac{43}{82}\right)$	$e\left(\frac{25}{41}\right)$	$e\left(\frac{229}{246}\right)$	$e\left(\frac{19}{123}\right)$	$e\left(\frac{95}{246}\right)$	$e\left(\frac{65}{123}\right)$
$\chi_{2988}(77,\cdot)$	$-1$	$1$	$e\left(\frac{173}{246}\right)$	$e\left(\frac{56}{123}\right)$	$e\left(\frac{49}{246}\right)$	$e\left(\frac{88}{123}\right)$	$e\left(\frac{29}{82}\right)$	$e\left(\frac{14}{41}\right)$	$e\left(\frac{143}{246}\right)$	$e\left(\frac{50}{123}\right)$	$e\left(\frac{127}{246}\right)$	$e\left(\frac{61}{123}\right)$
$\chi_{2988}(113,\cdot)$	$-1$	$1$	$e\left(\frac{23}{246}\right)$	$e\left(\frac{11}{123}\right)$	$e\left(\frac{25}{246}\right)$	$e\left(\frac{70}{123}\right)$	$e\left(\frac{65}{82}\right)$	$e\left(\frac{13}{41}\right)$	$e\left(\frac{83}{246}\right)$	$e\left(\frac{23}{123}\right)$	$e\left(\frac{115}{246}\right)$	$e\left(\frac{1}{123}\right)$
$\chi_{2988}(173,\cdot)$	$-1$	$1$	$e\left(\frac{115}{246}\right)$	$e\left(\frac{55}{123}\right)$	$e\left(\frac{125}{246}\right)$	$e\left(\frac{104}{123}\right)$	$e\left(\frac{79}{82}\right)$	$e\left(\frac{24}{41}\right)$	$e\left(\frac{169}{246}\right)$	$e\left(\frac{115}{123}\right)$	$e\left(\frac{83}{246}\right)$	$e\left(\frac{5}{123}\right)$
$\chi_{2988}(293,\cdot)$	$-1$	$1$	$e\left(\frac{179}{246}\right)$	$e\left(\frac{107}{123}\right)$	$e\left(\frac{109}{246}\right)$	$e\left(\frac{10}{123}\right)$	$e\left(\frac{21}{82}\right)$	$e\left(\frac{37}{41}\right)$	$e\left(\frac{47}{246}\right)$	$e\left(\frac{56}{123}\right)$	$e\left(\frac{157}{246}\right)$	$e\left(\frac{88}{123}\right)$
$\chi_{2988}(317,\cdot)$	$-1$	$1$	$e\left(\frac{229}{246}\right)$	$e\left(\frac{40}{123}\right)$	$e\left(\frac{35}{246}\right)$	$e\left(\frac{98}{123}\right)$	$e\left(\frac{9}{82}\right)$	$e\left(\frac{10}{41}\right)$	$e\left(\frac{67}{246}\right)$	$e\left(\frac{106}{123}\right)$	$e\left(\frac{161}{246}\right)$	$e\left(\frac{26}{123}\right)$
$\chi_{2988}(353,\cdot)$	$-1$	$1$	$e\left(\frac{43}{246}\right)$	$e\left(\frac{58}{123}\right)$	$e\left(\frac{143}{246}\right)$	$e\left(\frac{56}{123}\right)$	$e\left(\frac{11}{82}\right)$	$e\left(\frac{35}{41}\right)$	$e\left(\frac{91}{246}\right)$	$e\left(\frac{43}{123}\right)$	$e\left(\frac{215}{246}\right)$	$e\left(\frac{50}{123}\right)$
$\chi_{2988}(365,\cdot)$	$-1$	$1$	$e\left(\frac{191}{246}\right)$	$e\left(\frac{86}{123}\right)$	$e\left(\frac{229}{246}\right)$	$e\left(\frac{100}{123}\right)$	$e\left(\frac{5}{82}\right)$	$e\left(\frac{1}{41}\right)$	$e\left(\frac{101}{246}\right)$	$e\left(\frac{68}{123}\right)$	$e\left(\frac{217}{246}\right)$	$e\left(\frac{19}{123}\right)$
$\chi_{2988}(401,\cdot)$	$-1$	$1$	$e\left(\frac{155}{246}\right)$	$e\left(\frac{26}{123}\right)$	$e\left(\frac{115}{246}\right)$	$e\left(\frac{76}{123}\right)$	$e\left(\frac{53}{82}\right)$	$e\left(\frac{27}{41}\right)$	$e\left(\frac{185}{246}\right)$	$e\left(\frac{32}{123}\right)$	$e\left(\frac{37}{246}\right)$	$e\left(\frac{103}{123}\right)$
$\chi_{2988}(425,\cdot)$	$-1$	$1$	$e\left(\frac{13}{246}\right)$	$e\left(\frac{49}{123}\right)$	$e\left(\frac{89}{246}\right)$	$e\left(\frac{77}{123}\right)$	$e\left(\frac{51}{82}\right)$	$e\left(\frac{2}{41}\right)$	$e\left(\frac{79}{246}\right)$	$e\left(\frac{13}{123}\right)$	$e\left(\frac{65}{246}\right)$	$e\left(\frac{38}{123}\right)$
$\chi_{2988}(509,\cdot)$	$-1$	$1$	$e\left(\frac{17}{246}\right)$	$e\left(\frac{83}{123}\right)$	$e\left(\frac{211}{246}\right)$	$e\left(\frac{25}{123}\right)$	$e\left(\frac{73}{82}\right)$	$e\left(\frac{31}{41}\right)$	$e\left(\frac{179}{246}\right)$	$e\left(\frac{17}{123}\right)$	$e\left(\frac{85}{246}\right)$	$e\left(\frac{97}{123}\right)$
$\chi_{2988}(617,\cdot)$	$-1$	$1$	$e\left(\frac{59}{246}\right)$	$e\left(\frac{71}{123}\right)$	$e\left(\frac{139}{246}\right)$	$e\left(\frac{94}{123}\right)$	$e\left(\frac{17}{82}\right)$	$e\left(\frac{28}{41}\right)$	$e\left(\frac{245}{246}\right)$	$e\left(\frac{59}{123}\right)$	$e\left(\frac{49}{246}\right)$	$e\left(\frac{40}{123}\right)$
$\chi_{2988}(689,\cdot)$	$-1$	$1$	$e\left(\frac{233}{246}\right)$	$e\left(\frac{74}{123}\right)$	$e\left(\frac{157}{246}\right)$	$e\left(\frac{46}{123}\right)$	$e\left(\frac{31}{82}\right)$	$e\left(\frac{39}{41}\right)$	$e\left(\frac{167}{246}\right)$	$e\left(\frac{110}{123}\right)$	$e\left(\frac{181}{246}\right)$	$e\left(\frac{85}{123}\right)$
$\chi_{2988}(713,\cdot)$	$-1$	$1$	$e\left(\frac{25}{246}\right)$	$e\left(\frac{28}{123}\right)$	$e\left(\frac{209}{246}\right)$	$e\left(\frac{44}{123}\right)$	$e\left(\frac{35}{82}\right)$	$e\left(\frac{7}{41}\right)$	$e\left(\frac{133}{246}\right)$	$e\left(\frac{25}{123}\right)$	$e\left(\frac{125}{246}\right)$	$e\left(\frac{92}{123}\right)$
$\chi_{2988}(725,\cdot)$	$-1$	$1$	$e\left(\frac{221}{246}\right)$	$e\left(\frac{95}{123}\right)$	$e\left(\frac{37}{246}\right)$	$e\left(\frac{79}{123}\right)$	$e\left(\frac{47}{82}\right)$	$e\left(\frac{34}{41}\right)$	$e\left(\frac{113}{246}\right)$	$e\left(\frac{98}{123}\right)$	$e\left(\frac{121}{246}\right)$	$e\left(\frac{31}{123}\right)$
$\chi_{2988}(785,\cdot)$	$-1$	$1$	$e\left(\frac{157}{246}\right)$	$e\left(\frac{43}{123}\right)$	$e\left(\frac{53}{246}\right)$	$e\left(\frac{50}{123}\right)$	$e\left(\frac{23}{82}\right)$	$e\left(\frac{21}{41}\right)$	$e\left(\frac{235}{246}\right)$	$e\left(\frac{34}{123}\right)$	$e\left(\frac{47}{246}\right)$	$e\left(\frac{71}{123}\right)$
$\chi_{2988}(833,\cdot)$	$-1$	$1$	$e\left(\frac{215}{246}\right)$	$e\left(\frac{44}{123}\right)$	$e\left(\frac{223}{246}\right)$	$e\left(\frac{34}{123}\right)$	$e\left(\frac{55}{82}\right)$	$e\left(\frac{11}{41}\right)$	$e\left(\frac{209}{246}\right)$	$e\left(\frac{92}{123}\right)$	$e\left(\frac{91}{246}\right)$	$e\left(\frac{4}{123}\right)$
$\chi_{2988}(857,\cdot)$	$-1$	$1$	$e\left(\frac{235}{246}\right)$	$e\left(\frac{91}{123}\right)$	$e\left(\frac{95}{246}\right)$	$e\left(\frac{20}{123}\right)$	$e\left(\frac{1}{82}\right)$	$e\left(\frac{33}{41}\right)$	$e\left(\frac{217}{246}\right)$	$e\left(\frac{112}{123}\right)$	$e\left(\frac{191}{246}\right)$	$e\left(\frac{53}{123}\right)$
$\chi_{2988}(893,\cdot)$	$-1$	$1$	$e\left(\frac{217}{246}\right)$	$e\left(\frac{61}{123}\right)$	$e\left(\frac{161}{246}\right)$	$e\left(\frac{8}{123}\right)$	$e\left(\frac{25}{82}\right)$	$e\left(\frac{5}{41}\right)$	$e\left(\frac{13}{246}\right)$	$e\left(\frac{94}{123}\right)$	$e\left(\frac{101}{246}\right)$	$e\left(\frac{95}{123}\right)$
$\chi_{2988}(905,\cdot)$	$-1$	$1$	$e\left(\frac{161}{246}\right)$	$e\left(\frac{77}{123}\right)$	$e\left(\frac{175}{246}\right)$	$e\left(\frac{121}{123}\right)$	$e\left(\frac{45}{82}\right)$	$e\left(\frac{9}{41}\right)$	$e\left(\frac{89}{246}\right)$	$e\left(\frac{38}{123}\right)$	$e\left(\frac{67}{246}\right)$	$e\left(\frac{7}{123}\right)$
$\chi_{2988}(929,\cdot)$	$-1$	$1$	$e\left(\frac{37}{246}\right)$	$e\left(\frac{7}{123}\right)$	$e\left(\frac{83}{246}\right)$	$e\left(\frac{11}{123}\right)$	$e\left(\frac{19}{82}\right)$	$e\left(\frac{12}{41}\right)$	$e\left(\frac{187}{246}\right)$	$e\left(\frac{37}{123}\right)$	$e\left(\frac{185}{246}\right)$	$e\left(\frac{23}{123}\right)$
$\chi_{2988}(941,\cdot)$	$-1$	$1$	$e\left(\frac{113}{246}\right)$	$e\left(\frac{38}{123}\right)$	$e\left(\frac{187}{246}\right)$	$e\left(\frac{7}{123}\right)$	$e\left(\frac{27}{82}\right)$	$e\left(\frac{30}{41}\right)$	$e\left(\frac{119}{246}\right)$	$e\left(\frac{113}{123}\right)$	$e\left(\frac{73}{246}\right)$	$e\left(\frac{37}{123}\right)$
$\chi_{2988}(977,\cdot)$	$-1$	$1$	$e\left(\frac{35}{246}\right)$	$e\left(\frac{113}{123}\right)$	$e\left(\frac{145}{246}\right)$	$e\left(\frac{37}{123}\right)$	$e\left(\frac{49}{82}\right)$	$e\left(\frac{18}{41}\right)$	$e\left(\frac{137}{246}\right)$	$e\left(\frac{35}{123}\right)$	$e\left(\frac{175}{246}\right)$	$e\left(\frac{55}{123}\right)$
$\chi_{2988}(1013,\cdot)$	$-1$	$1$	$e\left(\frac{149}{246}\right)$	$e\left(\frac{98}{123}\right)$	$e\left(\frac{55}{246}\right)$	$e\left(\frac{31}{123}\right)$	$e\left(\frac{61}{82}\right)$	$e\left(\frac{4}{41}\right)$	$e\left(\frac{35}{246}\right)$	$e\left(\frac{26}{123}\right)$	$e\left(\frac{7}{246}\right)$	$e\left(\frac{76}{123}\right)$
$\chi_{2988}(1037,\cdot)$	$-1$	$1$	$e\left(\frac{1}{246}\right)$	$e\left(\frac{70}{123}\right)$	$e\left(\frac{215}{246}\right)$	$e\left(\frac{110}{123}\right)$	$e\left(\frac{67}{82}\right)$	$e\left(\frac{38}{41}\right)$	$e\left(\frac{25}{246}\right)$	$e\left(\frac{1}{123}\right)$	$e\left(\frac{5}{246}\right)$	$e\left(\frac{107}{123}\right)$
$\chi_{2988}(1073,\cdot)$	$-1$	$1$	$e\left(\frac{91}{246}\right)$	$e\left(\frac{97}{123}\right)$	$e\left(\frac{131}{246}\right)$	$e\left(\frac{47}{123}\right)$	$e\left(\frac{29}{82}\right)$	$e\left(\frac{14}{41}\right)$	$e\left(\frac{61}{246}\right)$	$e\left(\frac{91}{123}\right)$	$e\left(\frac{209}{246}\right)$	$e\left(\frac{20}{123}\right)$
$\chi_{2988}(1109,\cdot)$	$-1$	$1$	$e\left(\frac{187}{246}\right)$	$e\left(\frac{52}{123}\right)$	$e\left(\frac{107}{246}\right)$	$e\left(\frac{29}{123}\right)$	$e\left(\frac{65}{82}\right)$	$e\left(\frac{13}{41}\right)$	$e\left(\frac{1}{246}\right)$	$e\left(\frac{64}{123}\right)$	$e\left(\frac{197}{246}\right)$	$e\left(\frac{83}{123}\right)$
$\chi_{2988}(1157,\cdot)$	$-1$	$1$	$e\left(\frac{137}{246}\right)$	$e\left(\frac{119}{123}\right)$	$e\left(\frac{181}{246}\right)$	$e\left(\frac{64}{123}\right)$	$e\left(\frac{77}{82}\right)$	$e\left(\frac{40}{41}\right)$	$e\left(\frac{227}{246}\right)$	$e\left(\frac{14}{123}\right)$	$e\left(\frac{193}{246}\right)$	$e\left(\frac{22}{123}\right)$
$\chi_{2988}(1193,\cdot)$	$-1$	$1$	$e\left(\frac{167}{246}\right)$	$e\left(\frac{5}{123}\right)$	$e\left(\frac{235}{246}\right)$	$e\left(\frac{43}{123}\right)$	$e\left(\frac{37}{82}\right)$	$e\left(\frac{32}{41}\right)$	$e\left(\frac{239}{246}\right)$	$e\left(\frac{44}{123}\right)$	$e\left(\frac{97}{246}\right)$	$e\left(\frac{34}{123}\right)$

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	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)
\(\chi_{2988}(29,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{193}{246}\right)\)	\(e\left(\frac{103}{123}\right)\)	\(e\left(\frac{167}{246}\right)\)	\(e\left(\frac{74}{123}\right)\)	\(e\left(\frac{57}{82}\right)\)	\(e\left(\frac{36}{41}\right)\)	\(e\left(\frac{151}{246}\right)\)	\(e\left(\frac{70}{123}\right)\)	\(e\left(\frac{227}{246}\right)\)	\(e\left(\frac{110}{123}\right)\)
\(\chi_{2988}(41,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{83}{246}\right)\)	\(e\left(\frac{29}{123}\right)\)	\(e\left(\frac{133}{246}\right)\)	\(e\left(\frac{28}{123}\right)\)	\(e\left(\frac{67}{82}\right)\)	\(e\left(\frac{38}{41}\right)\)	\(e\left(\frac{107}{246}\right)\)	\(e\left(\frac{83}{123}\right)\)	\(e\left(\frac{169}{246}\right)\)	\(e\left(\frac{25}{123}\right)\)
\(\chi_{2988}(65,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{19}{246}\right)\)	\(e\left(\frac{100}{123}\right)\)	\(e\left(\frac{149}{246}\right)\)	\(e\left(\frac{122}{123}\right)\)	\(e\left(\frac{43}{82}\right)\)	\(e\left(\frac{25}{41}\right)\)	\(e\left(\frac{229}{246}\right)\)	\(e\left(\frac{19}{123}\right)\)	\(e\left(\frac{95}{246}\right)\)	\(e\left(\frac{65}{123}\right)\)
\(\chi_{2988}(77,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{173}{246}\right)\)	\(e\left(\frac{56}{123}\right)\)	\(e\left(\frac{49}{246}\right)\)	\(e\left(\frac{88}{123}\right)\)	\(e\left(\frac{29}{82}\right)\)	\(e\left(\frac{14}{41}\right)\)	\(e\left(\frac{143}{246}\right)\)	\(e\left(\frac{50}{123}\right)\)	\(e\left(\frac{127}{246}\right)\)	\(e\left(\frac{61}{123}\right)\)
\(\chi_{2988}(113,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{23}{246}\right)\)	\(e\left(\frac{11}{123}\right)\)	\(e\left(\frac{25}{246}\right)\)	\(e\left(\frac{70}{123}\right)\)	\(e\left(\frac{65}{82}\right)\)	\(e\left(\frac{13}{41}\right)\)	\(e\left(\frac{83}{246}\right)\)	\(e\left(\frac{23}{123}\right)\)	\(e\left(\frac{115}{246}\right)\)	\(e\left(\frac{1}{123}\right)\)
\(\chi_{2988}(173,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{115}{246}\right)\)	\(e\left(\frac{55}{123}\right)\)	\(e\left(\frac{125}{246}\right)\)	\(e\left(\frac{104}{123}\right)\)	\(e\left(\frac{79}{82}\right)\)	\(e\left(\frac{24}{41}\right)\)	\(e\left(\frac{169}{246}\right)\)	\(e\left(\frac{115}{123}\right)\)	\(e\left(\frac{83}{246}\right)\)	\(e\left(\frac{5}{123}\right)\)
\(\chi_{2988}(293,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{179}{246}\right)\)	\(e\left(\frac{107}{123}\right)\)	\(e\left(\frac{109}{246}\right)\)	\(e\left(\frac{10}{123}\right)\)	\(e\left(\frac{21}{82}\right)\)	\(e\left(\frac{37}{41}\right)\)	\(e\left(\frac{47}{246}\right)\)	\(e\left(\frac{56}{123}\right)\)	\(e\left(\frac{157}{246}\right)\)	\(e\left(\frac{88}{123}\right)\)
\(\chi_{2988}(317,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{229}{246}\right)\)	\(e\left(\frac{40}{123}\right)\)	\(e\left(\frac{35}{246}\right)\)	\(e\left(\frac{98}{123}\right)\)	\(e\left(\frac{9}{82}\right)\)	\(e\left(\frac{10}{41}\right)\)	\(e\left(\frac{67}{246}\right)\)	\(e\left(\frac{106}{123}\right)\)	\(e\left(\frac{161}{246}\right)\)	\(e\left(\frac{26}{123}\right)\)
\(\chi_{2988}(353,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{43}{246}\right)\)	\(e\left(\frac{58}{123}\right)\)	\(e\left(\frac{143}{246}\right)\)	\(e\left(\frac{56}{123}\right)\)	\(e\left(\frac{11}{82}\right)\)	\(e\left(\frac{35}{41}\right)\)	\(e\left(\frac{91}{246}\right)\)	\(e\left(\frac{43}{123}\right)\)	\(e\left(\frac{215}{246}\right)\)	\(e\left(\frac{50}{123}\right)\)
\(\chi_{2988}(365,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{191}{246}\right)\)	\(e\left(\frac{86}{123}\right)\)	\(e\left(\frac{229}{246}\right)\)	\(e\left(\frac{100}{123}\right)\)	\(e\left(\frac{5}{82}\right)\)	\(e\left(\frac{1}{41}\right)\)	\(e\left(\frac{101}{246}\right)\)	\(e\left(\frac{68}{123}\right)\)	\(e\left(\frac{217}{246}\right)\)	\(e\left(\frac{19}{123}\right)\)
\(\chi_{2988}(401,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{155}{246}\right)\)	\(e\left(\frac{26}{123}\right)\)	\(e\left(\frac{115}{246}\right)\)	\(e\left(\frac{76}{123}\right)\)	\(e\left(\frac{53}{82}\right)\)	\(e\left(\frac{27}{41}\right)\)	\(e\left(\frac{185}{246}\right)\)	\(e\left(\frac{32}{123}\right)\)	\(e\left(\frac{37}{246}\right)\)	\(e\left(\frac{103}{123}\right)\)
\(\chi_{2988}(425,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{13}{246}\right)\)	\(e\left(\frac{49}{123}\right)\)	\(e\left(\frac{89}{246}\right)\)	\(e\left(\frac{77}{123}\right)\)	\(e\left(\frac{51}{82}\right)\)	\(e\left(\frac{2}{41}\right)\)	\(e\left(\frac{79}{246}\right)\)	\(e\left(\frac{13}{123}\right)\)	\(e\left(\frac{65}{246}\right)\)	\(e\left(\frac{38}{123}\right)\)
\(\chi_{2988}(509,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{17}{246}\right)\)	\(e\left(\frac{83}{123}\right)\)	\(e\left(\frac{211}{246}\right)\)	\(e\left(\frac{25}{123}\right)\)	\(e\left(\frac{73}{82}\right)\)	\(e\left(\frac{31}{41}\right)\)	\(e\left(\frac{179}{246}\right)\)	\(e\left(\frac{17}{123}\right)\)	\(e\left(\frac{85}{246}\right)\)	\(e\left(\frac{97}{123}\right)\)
\(\chi_{2988}(617,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{59}{246}\right)\)	\(e\left(\frac{71}{123}\right)\)	\(e\left(\frac{139}{246}\right)\)	\(e\left(\frac{94}{123}\right)\)	\(e\left(\frac{17}{82}\right)\)	\(e\left(\frac{28}{41}\right)\)	\(e\left(\frac{245}{246}\right)\)	\(e\left(\frac{59}{123}\right)\)	\(e\left(\frac{49}{246}\right)\)	\(e\left(\frac{40}{123}\right)\)
\(\chi_{2988}(689,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{233}{246}\right)\)	\(e\left(\frac{74}{123}\right)\)	\(e\left(\frac{157}{246}\right)\)	\(e\left(\frac{46}{123}\right)\)	\(e\left(\frac{31}{82}\right)\)	\(e\left(\frac{39}{41}\right)\)	\(e\left(\frac{167}{246}\right)\)	\(e\left(\frac{110}{123}\right)\)	\(e\left(\frac{181}{246}\right)\)	\(e\left(\frac{85}{123}\right)\)
\(\chi_{2988}(713,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{25}{246}\right)\)	\(e\left(\frac{28}{123}\right)\)	\(e\left(\frac{209}{246}\right)\)	\(e\left(\frac{44}{123}\right)\)	\(e\left(\frac{35}{82}\right)\)	\(e\left(\frac{7}{41}\right)\)	\(e\left(\frac{133}{246}\right)\)	\(e\left(\frac{25}{123}\right)\)	\(e\left(\frac{125}{246}\right)\)	\(e\left(\frac{92}{123}\right)\)
\(\chi_{2988}(725,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{221}{246}\right)\)	\(e\left(\frac{95}{123}\right)\)	\(e\left(\frac{37}{246}\right)\)	\(e\left(\frac{79}{123}\right)\)	\(e\left(\frac{47}{82}\right)\)	\(e\left(\frac{34}{41}\right)\)	\(e\left(\frac{113}{246}\right)\)	\(e\left(\frac{98}{123}\right)\)	\(e\left(\frac{121}{246}\right)\)	\(e\left(\frac{31}{123}\right)\)
\(\chi_{2988}(785,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{157}{246}\right)\)	\(e\left(\frac{43}{123}\right)\)	\(e\left(\frac{53}{246}\right)\)	\(e\left(\frac{50}{123}\right)\)	\(e\left(\frac{23}{82}\right)\)	\(e\left(\frac{21}{41}\right)\)	\(e\left(\frac{235}{246}\right)\)	\(e\left(\frac{34}{123}\right)\)	\(e\left(\frac{47}{246}\right)\)	\(e\left(\frac{71}{123}\right)\)
\(\chi_{2988}(833,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{215}{246}\right)\)	\(e\left(\frac{44}{123}\right)\)	\(e\left(\frac{223}{246}\right)\)	\(e\left(\frac{34}{123}\right)\)	\(e\left(\frac{55}{82}\right)\)	\(e\left(\frac{11}{41}\right)\)	\(e\left(\frac{209}{246}\right)\)	\(e\left(\frac{92}{123}\right)\)	\(e\left(\frac{91}{246}\right)\)	\(e\left(\frac{4}{123}\right)\)
\(\chi_{2988}(857,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{235}{246}\right)\)	\(e\left(\frac{91}{123}\right)\)	\(e\left(\frac{95}{246}\right)\)	\(e\left(\frac{20}{123}\right)\)	\(e\left(\frac{1}{82}\right)\)	\(e\left(\frac{33}{41}\right)\)	\(e\left(\frac{217}{246}\right)\)	\(e\left(\frac{112}{123}\right)\)	\(e\left(\frac{191}{246}\right)\)	\(e\left(\frac{53}{123}\right)\)
\(\chi_{2988}(893,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{217}{246}\right)\)	\(e\left(\frac{61}{123}\right)\)	\(e\left(\frac{161}{246}\right)\)	\(e\left(\frac{8}{123}\right)\)	\(e\left(\frac{25}{82}\right)\)	\(e\left(\frac{5}{41}\right)\)	\(e\left(\frac{13}{246}\right)\)	\(e\left(\frac{94}{123}\right)\)	\(e\left(\frac{101}{246}\right)\)	\(e\left(\frac{95}{123}\right)\)
\(\chi_{2988}(905,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{161}{246}\right)\)	\(e\left(\frac{77}{123}\right)\)	\(e\left(\frac{175}{246}\right)\)	\(e\left(\frac{121}{123}\right)\)	\(e\left(\frac{45}{82}\right)\)	\(e\left(\frac{9}{41}\right)\)	\(e\left(\frac{89}{246}\right)\)	\(e\left(\frac{38}{123}\right)\)	\(e\left(\frac{67}{246}\right)\)	\(e\left(\frac{7}{123}\right)\)
\(\chi_{2988}(929,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{37}{246}\right)\)	\(e\left(\frac{7}{123}\right)\)	\(e\left(\frac{83}{246}\right)\)	\(e\left(\frac{11}{123}\right)\)	\(e\left(\frac{19}{82}\right)\)	\(e\left(\frac{12}{41}\right)\)	\(e\left(\frac{187}{246}\right)\)	\(e\left(\frac{37}{123}\right)\)	\(e\left(\frac{185}{246}\right)\)	\(e\left(\frac{23}{123}\right)\)
\(\chi_{2988}(941,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{113}{246}\right)\)	\(e\left(\frac{38}{123}\right)\)	\(e\left(\frac{187}{246}\right)\)	\(e\left(\frac{7}{123}\right)\)	\(e\left(\frac{27}{82}\right)\)	\(e\left(\frac{30}{41}\right)\)	\(e\left(\frac{119}{246}\right)\)	\(e\left(\frac{113}{123}\right)\)	\(e\left(\frac{73}{246}\right)\)	\(e\left(\frac{37}{123}\right)\)
\(\chi_{2988}(977,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{35}{246}\right)\)	\(e\left(\frac{113}{123}\right)\)	\(e\left(\frac{145}{246}\right)\)	\(e\left(\frac{37}{123}\right)\)	\(e\left(\frac{49}{82}\right)\)	\(e\left(\frac{18}{41}\right)\)	\(e\left(\frac{137}{246}\right)\)	\(e\left(\frac{35}{123}\right)\)	\(e\left(\frac{175}{246}\right)\)	\(e\left(\frac{55}{123}\right)\)
\(\chi_{2988}(1013,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{149}{246}\right)\)	\(e\left(\frac{98}{123}\right)\)	\(e\left(\frac{55}{246}\right)\)	\(e\left(\frac{31}{123}\right)\)	\(e\left(\frac{61}{82}\right)\)	\(e\left(\frac{4}{41}\right)\)	\(e\left(\frac{35}{246}\right)\)	\(e\left(\frac{26}{123}\right)\)	\(e\left(\frac{7}{246}\right)\)	\(e\left(\frac{76}{123}\right)\)
\(\chi_{2988}(1037,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{246}\right)\)	\(e\left(\frac{70}{123}\right)\)	\(e\left(\frac{215}{246}\right)\)	\(e\left(\frac{110}{123}\right)\)	\(e\left(\frac{67}{82}\right)\)	\(e\left(\frac{38}{41}\right)\)	\(e\left(\frac{25}{246}\right)\)	\(e\left(\frac{1}{123}\right)\)	\(e\left(\frac{5}{246}\right)\)	\(e\left(\frac{107}{123}\right)\)
\(\chi_{2988}(1073,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{91}{246}\right)\)	\(e\left(\frac{97}{123}\right)\)	\(e\left(\frac{131}{246}\right)\)	\(e\left(\frac{47}{123}\right)\)	\(e\left(\frac{29}{82}\right)\)	\(e\left(\frac{14}{41}\right)\)	\(e\left(\frac{61}{246}\right)\)	\(e\left(\frac{91}{123}\right)\)	\(e\left(\frac{209}{246}\right)\)	\(e\left(\frac{20}{123}\right)\)
\(\chi_{2988}(1109,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{187}{246}\right)\)	\(e\left(\frac{52}{123}\right)\)	\(e\left(\frac{107}{246}\right)\)	\(e\left(\frac{29}{123}\right)\)	\(e\left(\frac{65}{82}\right)\)	\(e\left(\frac{13}{41}\right)\)	\(e\left(\frac{1}{246}\right)\)	\(e\left(\frac{64}{123}\right)\)	\(e\left(\frac{197}{246}\right)\)	\(e\left(\frac{83}{123}\right)\)
\(\chi_{2988}(1157,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{137}{246}\right)\)	\(e\left(\frac{119}{123}\right)\)	\(e\left(\frac{181}{246}\right)\)	\(e\left(\frac{64}{123}\right)\)	\(e\left(\frac{77}{82}\right)\)	\(e\left(\frac{40}{41}\right)\)	\(e\left(\frac{227}{246}\right)\)	\(e\left(\frac{14}{123}\right)\)	\(e\left(\frac{193}{246}\right)\)	\(e\left(\frac{22}{123}\right)\)
\(\chi_{2988}(1193,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{167}{246}\right)\)	\(e\left(\frac{5}{123}\right)\)	\(e\left(\frac{235}{246}\right)\)	\(e\left(\frac{43}{123}\right)\)	\(e\left(\frac{37}{82}\right)\)	\(e\left(\frac{32}{41}\right)\)	\(e\left(\frac{239}{246}\right)\)	\(e\left(\frac{44}{123}\right)\)	\(e\left(\frac{97}{246}\right)\)	\(e\left(\frac{34}{123}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Basic properties

Related number fields

First 31 of 80 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	2988.bb
Modulus	$2988$
Conductor	$747$
Order	$246$
Real	no
Primitive	no
Minimal	yes
Parity	odd

Modulus:	\(2988\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(747\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(246\)	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 747.n	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);