Properties

Label 8470.da
Modulus $8470$
Conductor $4235$
Order $132$
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(8470, base_ring=CyclotomicField(132))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([99,88,114]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(263,8470))
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(8470\)
Conductor: \(4235\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(132\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 4235.db
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: $\Q(\zeta_{132})$
Fixed field: Number field defined by a degree 132 polynomial (not computed)

First 31 of 40 characters in Galois orbit

Character \(-1\) \(1\) \(3\) \(9\) \(13\) \(17\) \(19\) \(23\) \(27\) \(29\) \(31\) \(37\)
\(\chi_{8470}(263,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{97}{132}\right)\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{5}{132}\right)\) \(-i\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{47}{132}\right)\)
\(\chi_{8470}(373,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{44}\right)\) \(e\left(\frac{65}{132}\right)\) \(e\left(\frac{25}{33}\right)\) \(e\left(\frac{85}{132}\right)\) \(-i\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{7}{132}\right)\)
\(\chi_{8470}(417,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{3}{44}\right)\) \(e\left(\frac{127}{132}\right)\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{95}{132}\right)\) \(i\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{101}{132}\right)\)
\(\chi_{8470}(527,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{31}{44}\right)\) \(e\left(\frac{95}{132}\right)\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{43}{132}\right)\) \(i\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{61}{132}\right)\)
\(\chi_{8470}(1033,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{41}{44}\right)\) \(e\left(\frac{49}{132}\right)\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{125}{132}\right)\) \(-i\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{119}{132}\right)\)
\(\chi_{8470}(1143,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{17}{132}\right)\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{73}{132}\right)\) \(-i\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{79}{132}\right)\)
\(\chi_{8470}(1187,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{79}{132}\right)\) \(e\left(\frac{5}{33}\right)\) \(e\left(\frac{83}{132}\right)\) \(i\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{41}{132}\right)\)
\(\chi_{8470}(1297,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{47}{132}\right)\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{31}{132}\right)\) \(i\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{1}{132}\right)\)
\(\chi_{8470}(1803,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{1}{132}\right)\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{113}{132}\right)\) \(-i\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{59}{132}\right)\)
\(\chi_{8470}(1913,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{44}\right)\) \(e\left(\frac{101}{132}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{61}{132}\right)\) \(-i\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{19}{132}\right)\)
\(\chi_{8470}(1957,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{43}{44}\right)\) \(e\left(\frac{31}{132}\right)\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{71}{132}\right)\) \(i\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{113}{132}\right)\)
\(\chi_{8470}(2067,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{27}{44}\right)\) \(e\left(\frac{131}{132}\right)\) \(e\left(\frac{25}{33}\right)\) \(e\left(\frac{19}{132}\right)\) \(i\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{73}{132}\right)\)
\(\chi_{8470}(2573,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{85}{132}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{101}{132}\right)\) \(-i\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{131}{132}\right)\)
\(\chi_{8470}(2683,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{53}{132}\right)\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{49}{132}\right)\) \(-i\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{91}{132}\right)\)
\(\chi_{8470}(2727,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{115}{132}\right)\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{59}{132}\right)\) \(i\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{53}{132}\right)\)
\(\chi_{8470}(2837,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{3}{44}\right)\) \(e\left(\frac{83}{132}\right)\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{7}{132}\right)\) \(i\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{13}{132}\right)\)
\(\chi_{8470}(3343,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{37}{132}\right)\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{89}{132}\right)\) \(-i\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{71}{132}\right)\)
\(\chi_{8470}(3453,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{41}{44}\right)\) \(e\left(\frac{5}{132}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{37}{132}\right)\) \(-i\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{5}{33}\right)\) \(e\left(\frac{31}{132}\right)\)
\(\chi_{8470}(3497,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{39}{44}\right)\) \(e\left(\frac{67}{132}\right)\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{47}{132}\right)\) \(i\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{125}{132}\right)\)
\(\chi_{8470}(3607,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{35}{132}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{127}{132}\right)\) \(i\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{85}{132}\right)\)
\(\chi_{8470}(4223,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{89}{132}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{25}{132}\right)\) \(-i\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{103}{132}\right)\)
\(\chi_{8470}(4267,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{15}{44}\right)\) \(e\left(\frac{19}{132}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{35}{132}\right)\) \(i\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{65}{132}\right)\)
\(\chi_{8470}(4377,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{43}{44}\right)\) \(e\left(\frac{119}{132}\right)\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{115}{132}\right)\) \(i\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{25}{132}\right)\)
\(\chi_{8470}(4883,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{73}{132}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{65}{132}\right)\) \(-i\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{83}{132}\right)\)
\(\chi_{8470}(4993,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{41}{132}\right)\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{13}{132}\right)\) \(-i\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{43}{132}\right)\)
\(\chi_{8470}(5037,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{103}{132}\right)\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{23}{132}\right)\) \(i\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{5}{132}\right)\)
\(\chi_{8470}(5147,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{71}{132}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{103}{132}\right)\) \(i\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{5}{33}\right)\) \(e\left(\frac{97}{132}\right)\)
\(\chi_{8470}(5653,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{29}{44}\right)\) \(e\left(\frac{25}{132}\right)\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{53}{132}\right)\) \(-i\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{25}{33}\right)\) \(e\left(\frac{23}{132}\right)\)
\(\chi_{8470}(5763,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{125}{132}\right)\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{1}{132}\right)\) \(-i\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{115}{132}\right)\)
\(\chi_{8470}(5917,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{39}{44}\right)\) \(e\left(\frac{23}{132}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{91}{132}\right)\) \(i\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{37}{132}\right)\)
\(\chi_{8470}(6423,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{44}\right)\) \(e\left(\frac{109}{132}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{41}{132}\right)\) \(-i\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{95}{132}\right)\)