Properties

Label 1078.bf
Modulus $1078$
Conductor $539$
Order $210$
Real no
Primitive no
Minimal yes
Parity even

Related objects

Learn more

Show commands: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(1078, base_ring=CyclotomicField(210))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([125,189]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(17,1078))
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(1078\)
Conductor: \(539\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(210\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 539.bf
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Related number fields

Field of values: $\Q(\zeta_{105})$
Fixed field: Number field defined by a degree 210 polynomial (not computed)

First 31 of 48 characters in Galois orbit

Character \(-1\) \(1\) \(3\) \(5\) \(9\) \(13\) \(15\) \(17\) \(19\) \(23\) \(25\) \(27\)
\(\chi_{1078}(17,\cdot)\) \(1\) \(1\) \(e\left(\frac{167}{210}\right)\) \(e\left(\frac{181}{210}\right)\) \(e\left(\frac{62}{105}\right)\) \(e\left(\frac{19}{35}\right)\) \(e\left(\frac{23}{35}\right)\) \(e\left(\frac{103}{105}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{76}{105}\right)\) \(e\left(\frac{27}{70}\right)\)
\(\chi_{1078}(61,\cdot)\) \(1\) \(1\) \(e\left(\frac{97}{210}\right)\) \(e\left(\frac{41}{210}\right)\) \(e\left(\frac{97}{105}\right)\) \(e\left(\frac{19}{35}\right)\) \(e\left(\frac{23}{35}\right)\) \(e\left(\frac{68}{105}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{41}{105}\right)\) \(e\left(\frac{27}{70}\right)\)
\(\chi_{1078}(73,\cdot)\) \(1\) \(1\) \(e\left(\frac{101}{210}\right)\) \(e\left(\frac{73}{210}\right)\) \(e\left(\frac{101}{105}\right)\) \(e\left(\frac{27}{35}\right)\) \(e\left(\frac{29}{35}\right)\) \(e\left(\frac{34}{105}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{73}{105}\right)\) \(e\left(\frac{31}{70}\right)\)
\(\chi_{1078}(101,\cdot)\) \(1\) \(1\) \(e\left(\frac{173}{210}\right)\) \(e\left(\frac{19}{210}\right)\) \(e\left(\frac{68}{105}\right)\) \(e\left(\frac{31}{35}\right)\) \(e\left(\frac{32}{35}\right)\) \(e\left(\frac{52}{105}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{19}{105}\right)\) \(e\left(\frac{33}{70}\right)\)
\(\chi_{1078}(145,\cdot)\) \(1\) \(1\) \(e\left(\frac{193}{210}\right)\) \(e\left(\frac{179}{210}\right)\) \(e\left(\frac{88}{105}\right)\) \(e\left(\frac{1}{35}\right)\) \(e\left(\frac{27}{35}\right)\) \(e\left(\frac{92}{105}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{74}{105}\right)\) \(e\left(\frac{53}{70}\right)\)
\(\chi_{1078}(171,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{210}\right)\) \(e\left(\frac{31}{210}\right)\) \(e\left(\frac{17}{105}\right)\) \(e\left(\frac{34}{35}\right)\) \(e\left(\frac{8}{35}\right)\) \(e\left(\frac{13}{105}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{31}{105}\right)\) \(e\left(\frac{17}{70}\right)\)
\(\chi_{1078}(173,\cdot)\) \(1\) \(1\) \(e\left(\frac{169}{210}\right)\) \(e\left(\frac{197}{210}\right)\) \(e\left(\frac{64}{105}\right)\) \(e\left(\frac{23}{35}\right)\) \(e\left(\frac{26}{35}\right)\) \(e\left(\frac{86}{105}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{92}{105}\right)\) \(e\left(\frac{29}{70}\right)\)
\(\chi_{1078}(255,\cdot)\) \(1\) \(1\) \(e\left(\frac{23}{210}\right)\) \(e\left(\frac{79}{210}\right)\) \(e\left(\frac{23}{105}\right)\) \(e\left(\frac{11}{35}\right)\) \(e\left(\frac{17}{35}\right)\) \(e\left(\frac{67}{105}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{79}{105}\right)\) \(e\left(\frac{23}{70}\right)\)
\(\chi_{1078}(271,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{210}\right)\) \(e\left(\frac{113}{210}\right)\) \(e\left(\frac{1}{105}\right)\) \(e\left(\frac{2}{35}\right)\) \(e\left(\frac{19}{35}\right)\) \(e\left(\frac{44}{105}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{8}{105}\right)\) \(e\left(\frac{1}{70}\right)\)
\(\chi_{1078}(283,\cdot)\) \(1\) \(1\) \(e\left(\frac{179}{210}\right)\) \(e\left(\frac{67}{210}\right)\) \(e\left(\frac{74}{105}\right)\) \(e\left(\frac{8}{35}\right)\) \(e\left(\frac{6}{35}\right)\) \(e\left(\frac{1}{105}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{67}{105}\right)\) \(e\left(\frac{39}{70}\right)\)
\(\chi_{1078}(299,\cdot)\) \(1\) \(1\) \(e\left(\frac{103}{210}\right)\) \(e\left(\frac{89}{210}\right)\) \(e\left(\frac{103}{105}\right)\) \(e\left(\frac{31}{35}\right)\) \(e\left(\frac{32}{35}\right)\) \(e\left(\frac{17}{105}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{89}{105}\right)\) \(e\left(\frac{33}{70}\right)\)
\(\chi_{1078}(327,\cdot)\) \(1\) \(1\) \(e\left(\frac{79}{210}\right)\) \(e\left(\frac{107}{210}\right)\) \(e\left(\frac{79}{105}\right)\) \(e\left(\frac{18}{35}\right)\) \(e\left(\frac{31}{35}\right)\) \(e\left(\frac{11}{105}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{2}{105}\right)\) \(e\left(\frac{9}{70}\right)\)
\(\chi_{1078}(369,\cdot)\) \(1\) \(1\) \(e\left(\frac{127}{210}\right)\) \(e\left(\frac{71}{210}\right)\) \(e\left(\frac{22}{105}\right)\) \(e\left(\frac{9}{35}\right)\) \(e\left(\frac{33}{35}\right)\) \(e\left(\frac{23}{105}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{71}{105}\right)\) \(e\left(\frac{57}{70}\right)\)
\(\chi_{1078}(381,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{210}\right)\) \(e\left(\frac{193}{210}\right)\) \(e\left(\frac{11}{105}\right)\) \(e\left(\frac{22}{35}\right)\) \(e\left(\frac{34}{35}\right)\) \(e\left(\frac{64}{105}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{88}{105}\right)\) \(e\left(\frac{11}{70}\right)\)
\(\chi_{1078}(409,\cdot)\) \(1\) \(1\) \(e\left(\frac{83}{210}\right)\) \(e\left(\frac{139}{210}\right)\) \(e\left(\frac{83}{105}\right)\) \(e\left(\frac{26}{35}\right)\) \(e\left(\frac{2}{35}\right)\) \(e\left(\frac{82}{105}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{34}{105}\right)\) \(e\left(\frac{13}{70}\right)\)
\(\chi_{1078}(425,\cdot)\) \(1\) \(1\) \(e\left(\frac{121}{210}\right)\) \(e\left(\frac{23}{210}\right)\) \(e\left(\frac{16}{105}\right)\) \(e\left(\frac{32}{35}\right)\) \(e\left(\frac{24}{35}\right)\) \(e\left(\frac{74}{105}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{23}{105}\right)\) \(e\left(\frac{51}{70}\right)\)
\(\chi_{1078}(437,\cdot)\) \(1\) \(1\) \(e\left(\frac{29}{210}\right)\) \(e\left(\frac{127}{210}\right)\) \(e\left(\frac{29}{105}\right)\) \(e\left(\frac{23}{35}\right)\) \(e\left(\frac{26}{35}\right)\) \(e\left(\frac{16}{105}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{22}{105}\right)\) \(e\left(\frac{29}{70}\right)\)
\(\chi_{1078}(453,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{210}\right)\) \(e\left(\frac{209}{210}\right)\) \(e\left(\frac{13}{105}\right)\) \(e\left(\frac{26}{35}\right)\) \(e\left(\frac{2}{35}\right)\) \(e\left(\frac{47}{105}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{104}{105}\right)\) \(e\left(\frac{13}{70}\right)\)
\(\chi_{1078}(479,\cdot)\) \(1\) \(1\) \(e\left(\frac{137}{210}\right)\) \(e\left(\frac{151}{210}\right)\) \(e\left(\frac{32}{105}\right)\) \(e\left(\frac{29}{35}\right)\) \(e\left(\frac{13}{35}\right)\) \(e\left(\frac{43}{105}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{46}{105}\right)\) \(e\left(\frac{67}{70}\right)\)
\(\chi_{1078}(481,\cdot)\) \(1\) \(1\) \(e\left(\frac{199}{210}\right)\) \(e\left(\frac{17}{210}\right)\) \(e\left(\frac{94}{105}\right)\) \(e\left(\frac{13}{35}\right)\) \(e\left(\frac{1}{35}\right)\) \(e\left(\frac{41}{105}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{17}{105}\right)\) \(e\left(\frac{59}{70}\right)\)
\(\chi_{1078}(523,\cdot)\) \(1\) \(1\) \(e\left(\frac{37}{210}\right)\) \(e\left(\frac{191}{210}\right)\) \(e\left(\frac{37}{105}\right)\) \(e\left(\frac{4}{35}\right)\) \(e\left(\frac{3}{35}\right)\) \(e\left(\frac{53}{105}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{86}{105}\right)\) \(e\left(\frac{37}{70}\right)\)
\(\chi_{1078}(535,\cdot)\) \(1\) \(1\) \(e\left(\frac{71}{210}\right)\) \(e\left(\frac{43}{210}\right)\) \(e\left(\frac{71}{105}\right)\) \(e\left(\frac{2}{35}\right)\) \(e\left(\frac{19}{35}\right)\) \(e\left(\frac{79}{105}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{43}{105}\right)\) \(e\left(\frac{1}{70}\right)\)
\(\chi_{1078}(563,\cdot)\) \(1\) \(1\) \(e\left(\frac{143}{210}\right)\) \(e\left(\frac{199}{210}\right)\) \(e\left(\frac{38}{105}\right)\) \(e\left(\frac{6}{35}\right)\) \(e\left(\frac{22}{35}\right)\) \(e\left(\frac{97}{105}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{94}{105}\right)\) \(e\left(\frac{3}{70}\right)\)
\(\chi_{1078}(579,\cdot)\) \(1\) \(1\) \(e\left(\frac{31}{210}\right)\) \(e\left(\frac{143}{210}\right)\) \(e\left(\frac{31}{105}\right)\) \(e\left(\frac{27}{35}\right)\) \(e\left(\frac{29}{35}\right)\) \(e\left(\frac{104}{105}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{38}{105}\right)\) \(e\left(\frac{31}{70}\right)\)
\(\chi_{1078}(591,\cdot)\) \(1\) \(1\) \(e\left(\frac{89}{210}\right)\) \(e\left(\frac{187}{210}\right)\) \(e\left(\frac{89}{105}\right)\) \(e\left(\frac{3}{35}\right)\) \(e\left(\frac{11}{35}\right)\) \(e\left(\frac{31}{105}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{82}{105}\right)\) \(e\left(\frac{19}{70}\right)\)
\(\chi_{1078}(633,\cdot)\) \(1\) \(1\) \(e\left(\frac{197}{210}\right)\) \(e\left(\frac{1}{210}\right)\) \(e\left(\frac{92}{105}\right)\) \(e\left(\frac{9}{35}\right)\) \(e\left(\frac{33}{35}\right)\) \(e\left(\frac{58}{105}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{1}{105}\right)\) \(e\left(\frac{57}{70}\right)\)
\(\chi_{1078}(635,\cdot)\) \(1\) \(1\) \(e\left(\frac{109}{210}\right)\) \(e\left(\frac{137}{210}\right)\) \(e\left(\frac{4}{105}\right)\) \(e\left(\frac{8}{35}\right)\) \(e\left(\frac{6}{35}\right)\) \(e\left(\frac{71}{105}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{32}{105}\right)\) \(e\left(\frac{39}{70}\right)\)
\(\chi_{1078}(677,\cdot)\) \(1\) \(1\) \(e\left(\frac{157}{210}\right)\) \(e\left(\frac{101}{210}\right)\) \(e\left(\frac{52}{105}\right)\) \(e\left(\frac{34}{35}\right)\) \(e\left(\frac{8}{35}\right)\) \(e\left(\frac{83}{105}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{101}{105}\right)\) \(e\left(\frac{17}{70}\right)\)
\(\chi_{1078}(689,\cdot)\) \(1\) \(1\) \(e\left(\frac{131}{210}\right)\) \(e\left(\frac{103}{210}\right)\) \(e\left(\frac{26}{105}\right)\) \(e\left(\frac{17}{35}\right)\) \(e\left(\frac{4}{35}\right)\) \(e\left(\frac{94}{105}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{103}{105}\right)\) \(e\left(\frac{61}{70}\right)\)
\(\chi_{1078}(733,\cdot)\) \(1\) \(1\) \(e\left(\frac{151}{210}\right)\) \(e\left(\frac{53}{210}\right)\) \(e\left(\frac{46}{105}\right)\) \(e\left(\frac{22}{35}\right)\) \(e\left(\frac{34}{35}\right)\) \(e\left(\frac{29}{105}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{53}{105}\right)\) \(e\left(\frac{11}{70}\right)\)
\(\chi_{1078}(745,\cdot)\) \(1\) \(1\) \(e\left(\frac{149}{210}\right)\) \(e\left(\frac{37}{210}\right)\) \(e\left(\frac{44}{105}\right)\) \(e\left(\frac{18}{35}\right)\) \(e\left(\frac{31}{35}\right)\) \(e\left(\frac{46}{105}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{37}{105}\right)\) \(e\left(\frac{9}{70}\right)\)