LMFDB - Dirichlet character orbit 106069.kg

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(106069, base_ring=CyclotomicField(1452)) M = H._module chi = DirichletCharacter(H, M([121,1438])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(587, 106069)) 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("106069.587"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$106069$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$106069$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$1452$	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:	even	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);

Related number fields

Field of values:	$\Q(\zeta_{1452})$
Fixed field:	Number field defined by a degree 1452 polynomial (not computed)

First 31 of 440 characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{106069}(587,\cdot)$	$1$	$1$	$e\left(\frac{159}{242}\right)$	$e\left(\frac{487}{726}\right)$	$e\left(\frac{38}{121}\right)$	$e\left(\frac{13}{132}\right)$	$e\left(\frac{119}{363}\right)$	$e\left(\frac{315}{484}\right)$	$e\left(\frac{235}{242}\right)$	$e\left(\frac{124}{363}\right)$	$e\left(\frac{1097}{1452}\right)$	$e\left(\frac{1}{132}\right)$
$\chi_{106069}(1071,\cdot)$	$1$	$1$	$e\left(\frac{25}{242}\right)$	$e\left(\frac{521}{726}\right)$	$e\left(\frac{25}{121}\right)$	$e\left(\frac{131}{132}\right)$	$e\left(\frac{298}{363}\right)$	$e\left(\frac{13}{484}\right)$	$e\left(\frac{75}{242}\right)$	$e\left(\frac{158}{363}\right)$	$e\left(\frac{139}{1452}\right)$	$e\left(\frac{71}{132}\right)$
$\chi_{106069}(1098,\cdot)$	$1$	$1$	$e\left(\frac{47}{242}\right)$	$e\left(\frac{631}{726}\right)$	$e\left(\frac{47}{121}\right)$	$e\left(\frac{109}{132}\right)$	$e\left(\frac{23}{363}\right)$	$e\left(\frac{431}{484}\right)$	$e\left(\frac{141}{242}\right)$	$e\left(\frac{268}{363}\right)$	$e\left(\frac{29}{1452}\right)$	$e\left(\frac{49}{132}\right)$
$\chi_{106069}(1311,\cdot)$	$1$	$1$	$e\left(\frac{203}{242}\right)$	$e\left(\frac{223}{726}\right)$	$e\left(\frac{82}{121}\right)$	$e\left(\frac{79}{132}\right)$	$e\left(\frac{53}{363}\right)$	$e\left(\frac{425}{484}\right)$	$e\left(\frac{125}{242}\right)$	$e\left(\frac{223}{363}\right)$	$e\left(\frac{635}{1452}\right)$	$e\left(\frac{67}{132}\right)$
$\chi_{106069}(1968,\cdot)$	$1$	$1$	$e\left(\frac{221}{242}\right)$	$e\left(\frac{511}{726}\right)$	$e\left(\frac{100}{121}\right)$	$e\left(\frac{7}{132}\right)$	$e\left(\frac{224}{363}\right)$	$e\left(\frac{173}{484}\right)$	$e\left(\frac{179}{242}\right)$	$e\left(\frac{148}{363}\right)$	$e\left(\frac{1403}{1452}\right)$	$e\left(\frac{31}{132}\right)$
$\chi_{106069}(1974,\cdot)$	$1$	$1$	$e\left(\frac{105}{242}\right)$	$e\left(\frac{349}{726}\right)$	$e\left(\frac{105}{121}\right)$	$e\left(\frac{97}{132}\right)$	$e\left(\frac{332}{363}\right)$	$e\left(\frac{103}{484}\right)$	$e\left(\frac{73}{242}\right)$	$e\left(\frac{349}{363}\right)$	$e\left(\frac{245}{1452}\right)$	$e\left(\frac{109}{132}\right)$
$\chi_{106069}(2041,\cdot)$	$1$	$1$	$e\left(\frac{93}{242}\right)$	$e\left(\frac{157}{726}\right)$	$e\left(\frac{93}{121}\right)$	$e\left(\frac{79}{132}\right)$	$e\left(\frac{218}{363}\right)$	$e\left(\frac{29}{484}\right)$	$e\left(\frac{37}{242}\right)$	$e\left(\frac{157}{363}\right)$	$e\left(\frac{1427}{1452}\right)$	$e\left(\frac{67}{132}\right)$
$\chi_{106069}(2923,\cdot)$	$1$	$1$	$e\left(\frac{179}{242}\right)$	$e\left(\frac{565}{726}\right)$	$e\left(\frac{58}{121}\right)$	$e\left(\frac{109}{132}\right)$	$e\left(\frac{188}{363}\right)$	$e\left(\frac{35}{484}\right)$	$e\left(\frac{53}{242}\right)$	$e\left(\frac{202}{363}\right)$	$e\left(\frac{821}{1452}\right)$	$e\left(\frac{49}{132}\right)$
$\chi_{106069}(2990,\cdot)$	$1$	$1$	$e\left(\frac{195}{242}\right)$	$e\left(\frac{337}{726}\right)$	$e\left(\frac{74}{121}\right)$	$e\left(\frac{67}{132}\right)$	$e\left(\frac{98}{363}\right)$	$e\left(\frac{53}{484}\right)$	$e\left(\frac{101}{242}\right)$	$e\left(\frac{337}{363}\right)$	$e\left(\frac{455}{1452}\right)$	$e\left(\frac{127}{132}\right)$
$\chi_{106069}(3115,\cdot)$	$1$	$1$	$e\left(\frac{27}{242}\right)$	$e\left(\frac{311}{726}\right)$	$e\left(\frac{27}{121}\right)$	$e\left(\frac{35}{132}\right)$	$e\left(\frac{196}{363}\right)$	$e\left(\frac{469}{484}\right)$	$e\left(\frac{81}{242}\right)$	$e\left(\frac{311}{363}\right)$	$e\left(\frac{547}{1452}\right)$	$e\left(\frac{23}{132}\right)$
$\chi_{106069}(3236,\cdot)$	$1$	$1$	$e\left(\frac{53}{242}\right)$	$e\left(\frac{485}{726}\right)$	$e\left(\frac{53}{121}\right)$	$e\left(\frac{41}{132}\right)$	$e\left(\frac{322}{363}\right)$	$e\left(\frac{347}{484}\right)$	$e\left(\frac{159}{242}\right)$	$e\left(\frac{122}{363}\right)$	$e\left(\frac{769}{1452}\right)$	$e\left(\frac{125}{132}\right)$
$\chi_{106069}(3355,\cdot)$	$1$	$1$	$e\left(\frac{97}{242}\right)$	$e\left(\frac{463}{726}\right)$	$e\left(\frac{97}{121}\right)$	$e\left(\frac{19}{132}\right)$	$e\left(\frac{14}{363}\right)$	$e\left(\frac{457}{484}\right)$	$e\left(\frac{49}{242}\right)$	$e\left(\frac{100}{363}\right)$	$e\left(\frac{791}{1452}\right)$	$e\left(\frac{103}{132}\right)$
$\chi_{106069}(3647,\cdot)$	$1$	$1$	$e\left(\frac{3}{242}\right)$	$e\left(\frac{169}{726}\right)$	$e\left(\frac{3}{121}\right)$	$e\left(\frac{43}{132}\right)$	$e\left(\frac{89}{363}\right)$	$e\left(\frac{321}{484}\right)$	$e\left(\frac{9}{242}\right)$	$e\left(\frac{169}{363}\right)$	$e\left(\frac{491}{1452}\right)$	$e\left(\frac{115}{132}\right)$
$\chi_{106069}(3966,\cdot)$	$1$	$1$	$e\left(\frac{117}{242}\right)$	$e\left(\frac{299}{726}\right)$	$e\left(\frac{117}{121}\right)$	$e\left(\frac{5}{132}\right)$	$e\left(\frac{325}{363}\right)$	$e\left(\frac{419}{484}\right)$	$e\left(\frac{109}{242}\right)$	$e\left(\frac{299}{363}\right)$	$e\left(\frac{757}{1452}\right)$	$e\left(\frac{41}{132}\right)$
$\chi_{106069}(3991,\cdot)$	$1$	$1$	$e\left(\frac{155}{242}\right)$	$e\left(\frac{665}{726}\right)$	$e\left(\frac{34}{121}\right)$	$e\left(\frac{95}{132}\right)$	$e\left(\frac{202}{363}\right)$	$e\left(\frac{129}{484}\right)$	$e\left(\frac{223}{242}\right)$	$e\left(\frac{302}{363}\right)$	$e\left(\frac{523}{1452}\right)$	$e\left(\frac{119}{132}\right)$
$\chi_{106069}(4185,\cdot)$	$1$	$1$	$e\left(\frac{179}{242}\right)$	$e\left(\frac{323}{726}\right)$	$e\left(\frac{58}{121}\right)$	$e\left(\frac{65}{132}\right)$	$e\left(\frac{67}{363}\right)$	$e\left(\frac{35}{484}\right)$	$e\left(\frac{53}{242}\right)$	$e\left(\frac{323}{363}\right)$	$e\left(\frac{337}{1452}\right)$	$e\left(\frac{5}{132}\right)$
$\chi_{106069}(4356,\cdot)$	$1$	$1$	$e\left(\frac{95}{242}\right)$	$e\left(\frac{431}{726}\right)$	$e\left(\frac{95}{121}\right)$	$e\left(\frac{71}{132}\right)$	$e\left(\frac{358}{363}\right)$	$e\left(\frac{1}{484}\right)$	$e\left(\frac{43}{242}\right)$	$e\left(\frac{68}{363}\right)$	$e\left(\frac{1351}{1452}\right)$	$e\left(\frac{107}{132}\right)$
$\chi_{106069}(4429,\cdot)$	$1$	$1$	$e\left(\frac{65}{242}\right)$	$e\left(\frac{677}{726}\right)$	$e\left(\frac{65}{121}\right)$	$e\left(\frac{59}{132}\right)$	$e\left(\frac{73}{363}\right)$	$e\left(\frac{421}{484}\right)$	$e\left(\frac{195}{242}\right)$	$e\left(\frac{314}{363}\right)$	$e\left(\frac{1039}{1452}\right)$	$e\left(\frac{35}{132}\right)$
$\chi_{106069}(4596,\cdot)$	$1$	$1$	$e\left(\frac{237}{242}\right)$	$e\left(\frac{283}{726}\right)$	$e\left(\frac{116}{121}\right)$	$e\left(\frac{31}{132}\right)$	$e\left(\frac{134}{363}\right)$	$e\left(\frac{433}{484}\right)$	$e\left(\frac{227}{242}\right)$	$e\left(\frac{283}{363}\right)$	$e\left(\frac{311}{1452}\right)$	$e\left(\frac{43}{132}\right)$
$\chi_{106069}(5186,\cdot)$	$1$	$1$	$e\left(\frac{95}{242}\right)$	$e\left(\frac{673}{726}\right)$	$e\left(\frac{95}{121}\right)$	$e\left(\frac{49}{132}\right)$	$e\left(\frac{116}{363}\right)$	$e\left(\frac{243}{484}\right)$	$e\left(\frac{43}{242}\right)$	$e\left(\frac{310}{363}\right)$	$e\left(\frac{1109}{1452}\right)$	$e\left(\frac{85}{132}\right)$
$\chi_{106069}(5451,\cdot)$	$1$	$1$	$e\left(\frac{109}{242}\right)$	$e\left(\frac{413}{726}\right)$	$e\left(\frac{109}{121}\right)$	$e\left(\frac{59}{132}\right)$	$e\left(\frac{7}{363}\right)$	$e\left(\frac{289}{484}\right)$	$e\left(\frac{85}{242}\right)$	$e\left(\frac{50}{363}\right)$	$e\left(\frac{1303}{1452}\right)$	$e\left(\frac{35}{132}\right)$
$\chi_{106069}(5791,\cdot)$	$1$	$1$	$e\left(\frac{235}{242}\right)$	$e\left(\frac{251}{726}\right)$	$e\left(\frac{114}{121}\right)$	$e\left(\frac{17}{132}\right)$	$e\left(\frac{115}{363}\right)$	$e\left(\frac{219}{484}\right)$	$e\left(\frac{221}{242}\right)$	$e\left(\frac{251}{363}\right)$	$e\left(\frac{145}{1452}\right)$	$e\left(\frac{113}{132}\right)$
$\chi_{106069}(5816,\cdot)$	$1$	$1$	$e\left(\frac{81}{242}\right)$	$e\left(\frac{449}{726}\right)$	$e\left(\frac{81}{121}\right)$	$e\left(\frac{83}{132}\right)$	$e\left(\frac{346}{363}\right)$	$e\left(\frac{197}{484}\right)$	$e\left(\frac{1}{242}\right)$	$e\left(\frac{86}{363}\right)$	$e\left(\frac{1399}{1452}\right)$	$e\left(\frac{47}{132}\right)$
$\chi_{106069}(6035,\cdot)$	$1$	$1$	$e\left(\frac{105}{242}\right)$	$e\left(\frac{107}{726}\right)$	$e\left(\frac{105}{121}\right)$	$e\left(\frac{119}{132}\right)$	$e\left(\frac{211}{363}\right)$	$e\left(\frac{345}{484}\right)$	$e\left(\frac{73}{242}\right)$	$e\left(\frac{107}{363}\right)$	$e\left(\frac{487}{1452}\right)$	$e\left(\frac{131}{132}\right)$
$\chi_{106069}(6208,\cdot)$	$1$	$1$	$e\left(\frac{183}{242}\right)$	$e\left(\frac{145}{726}\right)$	$e\left(\frac{62}{121}\right)$	$e\left(\frac{49}{132}\right)$	$e\left(\frac{347}{363}\right)$	$e\left(\frac{463}{484}\right)$	$e\left(\frac{65}{242}\right)$	$e\left(\frac{145}{363}\right)$	$e\left(\frac{185}{1452}\right)$	$e\left(\frac{85}{132}\right)$
$\chi_{106069}(6302,\cdot)$	$1$	$1$	$e\left(\frac{205}{242}\right)$	$e\left(\frac{497}{726}\right)$	$e\left(\frac{84}{121}\right)$	$e\left(\frac{5}{132}\right)$	$e\left(\frac{193}{363}\right)$	$e\left(\frac{155}{484}\right)$	$e\left(\frac{131}{242}\right)$	$e\left(\frac{134}{363}\right)$	$e\left(\frac{1285}{1452}\right)$	$e\left(\frac{41}{132}\right)$
$\chi_{106069}(6938,\cdot)$	$1$	$1$	$e\left(\frac{89}{242}\right)$	$e\left(\frac{577}{726}\right)$	$e\left(\frac{89}{121}\right)$	$e\left(\frac{73}{132}\right)$	$e\left(\frac{59}{363}\right)$	$e\left(\frac{327}{484}\right)$	$e\left(\frac{25}{242}\right)$	$e\left(\frac{214}{363}\right)$	$e\left(\frac{1337}{1452}\right)$	$e\left(\frac{97}{132}\right)$
$\chi_{106069}(7057,\cdot)$	$1$	$1$	$e\left(\frac{197}{242}\right)$	$e\left(\frac{611}{726}\right)$	$e\left(\frac{76}{121}\right)$	$e\left(\frac{59}{132}\right)$	$e\left(\frac{238}{363}\right)$	$e\left(\frac{25}{484}\right)$	$e\left(\frac{107}{242}\right)$	$e\left(\frac{248}{363}\right)$	$e\left(\frac{379}{1452}\right)$	$e\left(\frac{35}{132}\right)$
$\chi_{106069}(7084,\cdot)$	$1$	$1$	$e\left(\frac{5}{242}\right)$	$e\left(\frac{685}{726}\right)$	$e\left(\frac{5}{121}\right)$	$e\left(\frac{13}{132}\right)$	$e\left(\frac{350}{363}\right)$	$e\left(\frac{51}{484}\right)$	$e\left(\frac{15}{242}\right)$	$e\left(\frac{322}{363}\right)$	$e\left(\frac{173}{1452}\right)$	$e\left(\frac{1}{132}\right)$
$\chi_{106069}(7589,\cdot)$	$1$	$1$	$e\left(\frac{219}{242}\right)$	$e\left(\frac{721}{726}\right)$	$e\left(\frac{98}{121}\right)$	$e\left(\frac{103}{132}\right)$	$e\left(\frac{326}{363}\right)$	$e\left(\frac{201}{484}\right)$	$e\left(\frac{173}{242}\right)$	$e\left(\frac{358}{363}\right)$	$e\left(\frac{995}{1452}\right)$	$e\left(\frac{79}{132}\right)$
$\chi_{106069}(7689,\cdot)$	$1$	$1$	$e\left(\frac{31}{242}\right)$	$e\left(\frac{617}{726}\right)$	$e\left(\frac{31}{121}\right)$	$e\left(\frac{41}{132}\right)$	$e\left(\frac{355}{363}\right)$	$e\left(\frac{171}{484}\right)$	$e\left(\frac{93}{242}\right)$	$e\left(\frac{254}{363}\right)$	$e\left(\frac{637}{1452}\right)$	$e\left(\frac{125}{132}\right)$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{106069}(587,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{159}{242}\right)\)	\(e\left(\frac{487}{726}\right)\)	\(e\left(\frac{38}{121}\right)\)	\(e\left(\frac{13}{132}\right)\)	\(e\left(\frac{119}{363}\right)\)	\(e\left(\frac{315}{484}\right)\)	\(e\left(\frac{235}{242}\right)\)	\(e\left(\frac{124}{363}\right)\)	\(e\left(\frac{1097}{1452}\right)\)	\(e\left(\frac{1}{132}\right)\)
\(\chi_{106069}(1071,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{242}\right)\)	\(e\left(\frac{521}{726}\right)\)	\(e\left(\frac{25}{121}\right)\)	\(e\left(\frac{131}{132}\right)\)	\(e\left(\frac{298}{363}\right)\)	\(e\left(\frac{13}{484}\right)\)	\(e\left(\frac{75}{242}\right)\)	\(e\left(\frac{158}{363}\right)\)	\(e\left(\frac{139}{1452}\right)\)	\(e\left(\frac{71}{132}\right)\)
\(\chi_{106069}(1098,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{242}\right)\)	\(e\left(\frac{631}{726}\right)\)	\(e\left(\frac{47}{121}\right)\)	\(e\left(\frac{109}{132}\right)\)	\(e\left(\frac{23}{363}\right)\)	\(e\left(\frac{431}{484}\right)\)	\(e\left(\frac{141}{242}\right)\)	\(e\left(\frac{268}{363}\right)\)	\(e\left(\frac{29}{1452}\right)\)	\(e\left(\frac{49}{132}\right)\)
\(\chi_{106069}(1311,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{203}{242}\right)\)	\(e\left(\frac{223}{726}\right)\)	\(e\left(\frac{82}{121}\right)\)	\(e\left(\frac{79}{132}\right)\)	\(e\left(\frac{53}{363}\right)\)	\(e\left(\frac{425}{484}\right)\)	\(e\left(\frac{125}{242}\right)\)	\(e\left(\frac{223}{363}\right)\)	\(e\left(\frac{635}{1452}\right)\)	\(e\left(\frac{67}{132}\right)\)
\(\chi_{106069}(1968,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{221}{242}\right)\)	\(e\left(\frac{511}{726}\right)\)	\(e\left(\frac{100}{121}\right)\)	\(e\left(\frac{7}{132}\right)\)	\(e\left(\frac{224}{363}\right)\)	\(e\left(\frac{173}{484}\right)\)	\(e\left(\frac{179}{242}\right)\)	\(e\left(\frac{148}{363}\right)\)	\(e\left(\frac{1403}{1452}\right)\)	\(e\left(\frac{31}{132}\right)\)
\(\chi_{106069}(1974,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{105}{242}\right)\)	\(e\left(\frac{349}{726}\right)\)	\(e\left(\frac{105}{121}\right)\)	\(e\left(\frac{97}{132}\right)\)	\(e\left(\frac{332}{363}\right)\)	\(e\left(\frac{103}{484}\right)\)	\(e\left(\frac{73}{242}\right)\)	\(e\left(\frac{349}{363}\right)\)	\(e\left(\frac{245}{1452}\right)\)	\(e\left(\frac{109}{132}\right)\)
\(\chi_{106069}(2041,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{93}{242}\right)\)	\(e\left(\frac{157}{726}\right)\)	\(e\left(\frac{93}{121}\right)\)	\(e\left(\frac{79}{132}\right)\)	\(e\left(\frac{218}{363}\right)\)	\(e\left(\frac{29}{484}\right)\)	\(e\left(\frac{37}{242}\right)\)	\(e\left(\frac{157}{363}\right)\)	\(e\left(\frac{1427}{1452}\right)\)	\(e\left(\frac{67}{132}\right)\)
\(\chi_{106069}(2923,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{179}{242}\right)\)	\(e\left(\frac{565}{726}\right)\)	\(e\left(\frac{58}{121}\right)\)	\(e\left(\frac{109}{132}\right)\)	\(e\left(\frac{188}{363}\right)\)	\(e\left(\frac{35}{484}\right)\)	\(e\left(\frac{53}{242}\right)\)	\(e\left(\frac{202}{363}\right)\)	\(e\left(\frac{821}{1452}\right)\)	\(e\left(\frac{49}{132}\right)\)
\(\chi_{106069}(2990,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{195}{242}\right)\)	\(e\left(\frac{337}{726}\right)\)	\(e\left(\frac{74}{121}\right)\)	\(e\left(\frac{67}{132}\right)\)	\(e\left(\frac{98}{363}\right)\)	\(e\left(\frac{53}{484}\right)\)	\(e\left(\frac{101}{242}\right)\)	\(e\left(\frac{337}{363}\right)\)	\(e\left(\frac{455}{1452}\right)\)	\(e\left(\frac{127}{132}\right)\)
\(\chi_{106069}(3115,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{242}\right)\)	\(e\left(\frac{311}{726}\right)\)	\(e\left(\frac{27}{121}\right)\)	\(e\left(\frac{35}{132}\right)\)	\(e\left(\frac{196}{363}\right)\)	\(e\left(\frac{469}{484}\right)\)	\(e\left(\frac{81}{242}\right)\)	\(e\left(\frac{311}{363}\right)\)	\(e\left(\frac{547}{1452}\right)\)	\(e\left(\frac{23}{132}\right)\)
\(\chi_{106069}(3236,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{242}\right)\)	\(e\left(\frac{485}{726}\right)\)	\(e\left(\frac{53}{121}\right)\)	\(e\left(\frac{41}{132}\right)\)	\(e\left(\frac{322}{363}\right)\)	\(e\left(\frac{347}{484}\right)\)	\(e\left(\frac{159}{242}\right)\)	\(e\left(\frac{122}{363}\right)\)	\(e\left(\frac{769}{1452}\right)\)	\(e\left(\frac{125}{132}\right)\)
\(\chi_{106069}(3355,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{97}{242}\right)\)	\(e\left(\frac{463}{726}\right)\)	\(e\left(\frac{97}{121}\right)\)	\(e\left(\frac{19}{132}\right)\)	\(e\left(\frac{14}{363}\right)\)	\(e\left(\frac{457}{484}\right)\)	\(e\left(\frac{49}{242}\right)\)	\(e\left(\frac{100}{363}\right)\)	\(e\left(\frac{791}{1452}\right)\)	\(e\left(\frac{103}{132}\right)\)
\(\chi_{106069}(3647,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{242}\right)\)	\(e\left(\frac{169}{726}\right)\)	\(e\left(\frac{3}{121}\right)\)	\(e\left(\frac{43}{132}\right)\)	\(e\left(\frac{89}{363}\right)\)	\(e\left(\frac{321}{484}\right)\)	\(e\left(\frac{9}{242}\right)\)	\(e\left(\frac{169}{363}\right)\)	\(e\left(\frac{491}{1452}\right)\)	\(e\left(\frac{115}{132}\right)\)
\(\chi_{106069}(3966,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{117}{242}\right)\)	\(e\left(\frac{299}{726}\right)\)	\(e\left(\frac{117}{121}\right)\)	\(e\left(\frac{5}{132}\right)\)	\(e\left(\frac{325}{363}\right)\)	\(e\left(\frac{419}{484}\right)\)	\(e\left(\frac{109}{242}\right)\)	\(e\left(\frac{299}{363}\right)\)	\(e\left(\frac{757}{1452}\right)\)	\(e\left(\frac{41}{132}\right)\)
\(\chi_{106069}(3991,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{155}{242}\right)\)	\(e\left(\frac{665}{726}\right)\)	\(e\left(\frac{34}{121}\right)\)	\(e\left(\frac{95}{132}\right)\)	\(e\left(\frac{202}{363}\right)\)	\(e\left(\frac{129}{484}\right)\)	\(e\left(\frac{223}{242}\right)\)	\(e\left(\frac{302}{363}\right)\)	\(e\left(\frac{523}{1452}\right)\)	\(e\left(\frac{119}{132}\right)\)
\(\chi_{106069}(4185,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{179}{242}\right)\)	\(e\left(\frac{323}{726}\right)\)	\(e\left(\frac{58}{121}\right)\)	\(e\left(\frac{65}{132}\right)\)	\(e\left(\frac{67}{363}\right)\)	\(e\left(\frac{35}{484}\right)\)	\(e\left(\frac{53}{242}\right)\)	\(e\left(\frac{323}{363}\right)\)	\(e\left(\frac{337}{1452}\right)\)	\(e\left(\frac{5}{132}\right)\)
\(\chi_{106069}(4356,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{95}{242}\right)\)	\(e\left(\frac{431}{726}\right)\)	\(e\left(\frac{95}{121}\right)\)	\(e\left(\frac{71}{132}\right)\)	\(e\left(\frac{358}{363}\right)\)	\(e\left(\frac{1}{484}\right)\)	\(e\left(\frac{43}{242}\right)\)	\(e\left(\frac{68}{363}\right)\)	\(e\left(\frac{1351}{1452}\right)\)	\(e\left(\frac{107}{132}\right)\)
\(\chi_{106069}(4429,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{65}{242}\right)\)	\(e\left(\frac{677}{726}\right)\)	\(e\left(\frac{65}{121}\right)\)	\(e\left(\frac{59}{132}\right)\)	\(e\left(\frac{73}{363}\right)\)	\(e\left(\frac{421}{484}\right)\)	\(e\left(\frac{195}{242}\right)\)	\(e\left(\frac{314}{363}\right)\)	\(e\left(\frac{1039}{1452}\right)\)	\(e\left(\frac{35}{132}\right)\)
\(\chi_{106069}(4596,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{237}{242}\right)\)	\(e\left(\frac{283}{726}\right)\)	\(e\left(\frac{116}{121}\right)\)	\(e\left(\frac{31}{132}\right)\)	\(e\left(\frac{134}{363}\right)\)	\(e\left(\frac{433}{484}\right)\)	\(e\left(\frac{227}{242}\right)\)	\(e\left(\frac{283}{363}\right)\)	\(e\left(\frac{311}{1452}\right)\)	\(e\left(\frac{43}{132}\right)\)
\(\chi_{106069}(5186,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{95}{242}\right)\)	\(e\left(\frac{673}{726}\right)\)	\(e\left(\frac{95}{121}\right)\)	\(e\left(\frac{49}{132}\right)\)	\(e\left(\frac{116}{363}\right)\)	\(e\left(\frac{243}{484}\right)\)	\(e\left(\frac{43}{242}\right)\)	\(e\left(\frac{310}{363}\right)\)	\(e\left(\frac{1109}{1452}\right)\)	\(e\left(\frac{85}{132}\right)\)
\(\chi_{106069}(5451,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{109}{242}\right)\)	\(e\left(\frac{413}{726}\right)\)	\(e\left(\frac{109}{121}\right)\)	\(e\left(\frac{59}{132}\right)\)	\(e\left(\frac{7}{363}\right)\)	\(e\left(\frac{289}{484}\right)\)	\(e\left(\frac{85}{242}\right)\)	\(e\left(\frac{50}{363}\right)\)	\(e\left(\frac{1303}{1452}\right)\)	\(e\left(\frac{35}{132}\right)\)
\(\chi_{106069}(5791,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{235}{242}\right)\)	\(e\left(\frac{251}{726}\right)\)	\(e\left(\frac{114}{121}\right)\)	\(e\left(\frac{17}{132}\right)\)	\(e\left(\frac{115}{363}\right)\)	\(e\left(\frac{219}{484}\right)\)	\(e\left(\frac{221}{242}\right)\)	\(e\left(\frac{251}{363}\right)\)	\(e\left(\frac{145}{1452}\right)\)	\(e\left(\frac{113}{132}\right)\)
\(\chi_{106069}(5816,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{81}{242}\right)\)	\(e\left(\frac{449}{726}\right)\)	\(e\left(\frac{81}{121}\right)\)	\(e\left(\frac{83}{132}\right)\)	\(e\left(\frac{346}{363}\right)\)	\(e\left(\frac{197}{484}\right)\)	\(e\left(\frac{1}{242}\right)\)	\(e\left(\frac{86}{363}\right)\)	\(e\left(\frac{1399}{1452}\right)\)	\(e\left(\frac{47}{132}\right)\)
\(\chi_{106069}(6035,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{105}{242}\right)\)	\(e\left(\frac{107}{726}\right)\)	\(e\left(\frac{105}{121}\right)\)	\(e\left(\frac{119}{132}\right)\)	\(e\left(\frac{211}{363}\right)\)	\(e\left(\frac{345}{484}\right)\)	\(e\left(\frac{73}{242}\right)\)	\(e\left(\frac{107}{363}\right)\)	\(e\left(\frac{487}{1452}\right)\)	\(e\left(\frac{131}{132}\right)\)
\(\chi_{106069}(6208,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{183}{242}\right)\)	\(e\left(\frac{145}{726}\right)\)	\(e\left(\frac{62}{121}\right)\)	\(e\left(\frac{49}{132}\right)\)	\(e\left(\frac{347}{363}\right)\)	\(e\left(\frac{463}{484}\right)\)	\(e\left(\frac{65}{242}\right)\)	\(e\left(\frac{145}{363}\right)\)	\(e\left(\frac{185}{1452}\right)\)	\(e\left(\frac{85}{132}\right)\)
\(\chi_{106069}(6302,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{205}{242}\right)\)	\(e\left(\frac{497}{726}\right)\)	\(e\left(\frac{84}{121}\right)\)	\(e\left(\frac{5}{132}\right)\)	\(e\left(\frac{193}{363}\right)\)	\(e\left(\frac{155}{484}\right)\)	\(e\left(\frac{131}{242}\right)\)	\(e\left(\frac{134}{363}\right)\)	\(e\left(\frac{1285}{1452}\right)\)	\(e\left(\frac{41}{132}\right)\)
\(\chi_{106069}(6938,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{89}{242}\right)\)	\(e\left(\frac{577}{726}\right)\)	\(e\left(\frac{89}{121}\right)\)	\(e\left(\frac{73}{132}\right)\)	\(e\left(\frac{59}{363}\right)\)	\(e\left(\frac{327}{484}\right)\)	\(e\left(\frac{25}{242}\right)\)	\(e\left(\frac{214}{363}\right)\)	\(e\left(\frac{1337}{1452}\right)\)	\(e\left(\frac{97}{132}\right)\)
\(\chi_{106069}(7057,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{197}{242}\right)\)	\(e\left(\frac{611}{726}\right)\)	\(e\left(\frac{76}{121}\right)\)	\(e\left(\frac{59}{132}\right)\)	\(e\left(\frac{238}{363}\right)\)	\(e\left(\frac{25}{484}\right)\)	\(e\left(\frac{107}{242}\right)\)	\(e\left(\frac{248}{363}\right)\)	\(e\left(\frac{379}{1452}\right)\)	\(e\left(\frac{35}{132}\right)\)
\(\chi_{106069}(7084,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{242}\right)\)	\(e\left(\frac{685}{726}\right)\)	\(e\left(\frac{5}{121}\right)\)	\(e\left(\frac{13}{132}\right)\)	\(e\left(\frac{350}{363}\right)\)	\(e\left(\frac{51}{484}\right)\)	\(e\left(\frac{15}{242}\right)\)	\(e\left(\frac{322}{363}\right)\)	\(e\left(\frac{173}{1452}\right)\)	\(e\left(\frac{1}{132}\right)\)
\(\chi_{106069}(7589,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{219}{242}\right)\)	\(e\left(\frac{721}{726}\right)\)	\(e\left(\frac{98}{121}\right)\)	\(e\left(\frac{103}{132}\right)\)	\(e\left(\frac{326}{363}\right)\)	\(e\left(\frac{201}{484}\right)\)	\(e\left(\frac{173}{242}\right)\)	\(e\left(\frac{358}{363}\right)\)	\(e\left(\frac{995}{1452}\right)\)	\(e\left(\frac{79}{132}\right)\)
\(\chi_{106069}(7689,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{242}\right)\)	\(e\left(\frac{617}{726}\right)\)	\(e\left(\frac{31}{121}\right)\)	\(e\left(\frac{41}{132}\right)\)	\(e\left(\frac{355}{363}\right)\)	\(e\left(\frac{171}{484}\right)\)	\(e\left(\frac{93}{242}\right)\)	\(e\left(\frac{254}{363}\right)\)	\(e\left(\frac{637}{1452}\right)\)	\(e\left(\frac{125}{132}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Basic properties

Related number fields

First 31 of 440 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	106069.kg
Modulus	$106069$
Conductor	$106069$
Order	$1452$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(106069\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(106069\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(1452\)	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:	even	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);