Properties

Label 1225.bj
Modulus $1225$
Conductor $1225$
Order $70$
Real no
Primitive yes
Minimal yes
Parity even

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(1225, base_ring=CyclotomicField(70))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([7,30]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(29,1225))
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(1225\)
Conductor: \(1225\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(70\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: yes
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: $\Q(\zeta_{35})$
Fixed field: Number field defined by a degree 70 polynomial

Characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(3\) \(4\) \(6\) \(8\) \(9\) \(11\) \(12\) \(13\) \(16\)
\(\chi_{1225}(29,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{70}\right)\) \(e\left(\frac{9}{70}\right)\) \(e\left(\frac{17}{35}\right)\) \(e\left(\frac{13}{35}\right)\) \(e\left(\frac{51}{70}\right)\) \(e\left(\frac{9}{35}\right)\) \(e\left(\frac{26}{35}\right)\) \(e\left(\frac{43}{70}\right)\) \(e\left(\frac{3}{70}\right)\) \(e\left(\frac{34}{35}\right)\)
\(\chi_{1225}(64,\cdot)\) \(1\) \(1\) \(e\left(\frac{61}{70}\right)\) \(e\left(\frac{57}{70}\right)\) \(e\left(\frac{26}{35}\right)\) \(e\left(\frac{24}{35}\right)\) \(e\left(\frac{43}{70}\right)\) \(e\left(\frac{22}{35}\right)\) \(e\left(\frac{13}{35}\right)\) \(e\left(\frac{39}{70}\right)\) \(e\left(\frac{19}{70}\right)\) \(e\left(\frac{17}{35}\right)\)
\(\chi_{1225}(134,\cdot)\) \(1\) \(1\) \(e\left(\frac{9}{70}\right)\) \(e\left(\frac{13}{70}\right)\) \(e\left(\frac{9}{35}\right)\) \(e\left(\frac{11}{35}\right)\) \(e\left(\frac{27}{70}\right)\) \(e\left(\frac{13}{35}\right)\) \(e\left(\frac{22}{35}\right)\) \(e\left(\frac{31}{70}\right)\) \(e\left(\frac{51}{70}\right)\) \(e\left(\frac{18}{35}\right)\)
\(\chi_{1225}(169,\cdot)\) \(1\) \(1\) \(e\left(\frac{53}{70}\right)\) \(e\left(\frac{61}{70}\right)\) \(e\left(\frac{18}{35}\right)\) \(e\left(\frac{22}{35}\right)\) \(e\left(\frac{19}{70}\right)\) \(e\left(\frac{26}{35}\right)\) \(e\left(\frac{9}{35}\right)\) \(e\left(\frac{27}{70}\right)\) \(e\left(\frac{67}{70}\right)\) \(e\left(\frac{1}{35}\right)\)
\(\chi_{1225}(204,\cdot)\) \(1\) \(1\) \(e\left(\frac{27}{70}\right)\) \(e\left(\frac{39}{70}\right)\) \(e\left(\frac{27}{35}\right)\) \(e\left(\frac{33}{35}\right)\) \(e\left(\frac{11}{70}\right)\) \(e\left(\frac{4}{35}\right)\) \(e\left(\frac{31}{35}\right)\) \(e\left(\frac{23}{70}\right)\) \(e\left(\frac{13}{70}\right)\) \(e\left(\frac{19}{35}\right)\)
\(\chi_{1225}(239,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{70}\right)\) \(e\left(\frac{17}{70}\right)\) \(e\left(\frac{1}{35}\right)\) \(e\left(\frac{9}{35}\right)\) \(e\left(\frac{3}{70}\right)\) \(e\left(\frac{17}{35}\right)\) \(e\left(\frac{18}{35}\right)\) \(e\left(\frac{19}{70}\right)\) \(e\left(\frac{29}{70}\right)\) \(e\left(\frac{2}{35}\right)\)
\(\chi_{1225}(309,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{70}\right)\) \(e\left(\frac{43}{70}\right)\) \(e\left(\frac{19}{35}\right)\) \(e\left(\frac{31}{35}\right)\) \(e\left(\frac{57}{70}\right)\) \(e\left(\frac{8}{35}\right)\) \(e\left(\frac{27}{35}\right)\) \(e\left(\frac{11}{70}\right)\) \(e\left(\frac{61}{70}\right)\) \(e\left(\frac{3}{35}\right)\)
\(\chi_{1225}(379,\cdot)\) \(1\) \(1\) \(e\left(\frac{37}{70}\right)\) \(e\left(\frac{69}{70}\right)\) \(e\left(\frac{2}{35}\right)\) \(e\left(\frac{18}{35}\right)\) \(e\left(\frac{41}{70}\right)\) \(e\left(\frac{34}{35}\right)\) \(e\left(\frac{1}{35}\right)\) \(e\left(\frac{3}{70}\right)\) \(e\left(\frac{23}{70}\right)\) \(e\left(\frac{4}{35}\right)\)
\(\chi_{1225}(414,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{70}\right)\) \(e\left(\frac{47}{70}\right)\) \(e\left(\frac{11}{35}\right)\) \(e\left(\frac{29}{35}\right)\) \(e\left(\frac{33}{70}\right)\) \(e\left(\frac{12}{35}\right)\) \(e\left(\frac{23}{35}\right)\) \(e\left(\frac{69}{70}\right)\) \(e\left(\frac{39}{70}\right)\) \(e\left(\frac{22}{35}\right)\)
\(\chi_{1225}(484,\cdot)\) \(1\) \(1\) \(e\left(\frac{29}{70}\right)\) \(e\left(\frac{3}{70}\right)\) \(e\left(\frac{29}{35}\right)\) \(e\left(\frac{16}{35}\right)\) \(e\left(\frac{17}{70}\right)\) \(e\left(\frac{3}{35}\right)\) \(e\left(\frac{32}{35}\right)\) \(e\left(\frac{61}{70}\right)\) \(e\left(\frac{1}{70}\right)\) \(e\left(\frac{23}{35}\right)\)
\(\chi_{1225}(519,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{70}\right)\) \(e\left(\frac{51}{70}\right)\) \(e\left(\frac{3}{35}\right)\) \(e\left(\frac{27}{35}\right)\) \(e\left(\frac{9}{70}\right)\) \(e\left(\frac{16}{35}\right)\) \(e\left(\frac{19}{35}\right)\) \(e\left(\frac{57}{70}\right)\) \(e\left(\frac{17}{70}\right)\) \(e\left(\frac{6}{35}\right)\)
\(\chi_{1225}(554,\cdot)\) \(1\) \(1\) \(e\left(\frac{47}{70}\right)\) \(e\left(\frac{29}{70}\right)\) \(e\left(\frac{12}{35}\right)\) \(e\left(\frac{3}{35}\right)\) \(e\left(\frac{1}{70}\right)\) \(e\left(\frac{29}{35}\right)\) \(e\left(\frac{6}{35}\right)\) \(e\left(\frac{53}{70}\right)\) \(e\left(\frac{33}{70}\right)\) \(e\left(\frac{24}{35}\right)\)
\(\chi_{1225}(659,\cdot)\) \(1\) \(1\) \(e\left(\frac{39}{70}\right)\) \(e\left(\frac{33}{70}\right)\) \(e\left(\frac{4}{35}\right)\) \(e\left(\frac{1}{35}\right)\) \(e\left(\frac{47}{70}\right)\) \(e\left(\frac{33}{35}\right)\) \(e\left(\frac{2}{35}\right)\) \(e\left(\frac{41}{70}\right)\) \(e\left(\frac{11}{70}\right)\) \(e\left(\frac{8}{35}\right)\)
\(\chi_{1225}(694,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{70}\right)\) \(e\left(\frac{11}{70}\right)\) \(e\left(\frac{13}{35}\right)\) \(e\left(\frac{12}{35}\right)\) \(e\left(\frac{39}{70}\right)\) \(e\left(\frac{11}{35}\right)\) \(e\left(\frac{24}{35}\right)\) \(e\left(\frac{37}{70}\right)\) \(e\left(\frac{27}{70}\right)\) \(e\left(\frac{26}{35}\right)\)
\(\chi_{1225}(729,\cdot)\) \(1\) \(1\) \(e\left(\frac{57}{70}\right)\) \(e\left(\frac{59}{70}\right)\) \(e\left(\frac{22}{35}\right)\) \(e\left(\frac{23}{35}\right)\) \(e\left(\frac{31}{70}\right)\) \(e\left(\frac{24}{35}\right)\) \(e\left(\frac{11}{35}\right)\) \(e\left(\frac{33}{70}\right)\) \(e\left(\frac{43}{70}\right)\) \(e\left(\frac{9}{35}\right)\)
\(\chi_{1225}(764,\cdot)\) \(1\) \(1\) \(e\left(\frac{31}{70}\right)\) \(e\left(\frac{37}{70}\right)\) \(e\left(\frac{31}{35}\right)\) \(e\left(\frac{34}{35}\right)\) \(e\left(\frac{23}{70}\right)\) \(e\left(\frac{2}{35}\right)\) \(e\left(\frac{33}{35}\right)\) \(e\left(\frac{29}{70}\right)\) \(e\left(\frac{59}{70}\right)\) \(e\left(\frac{27}{35}\right)\)
\(\chi_{1225}(869,\cdot)\) \(1\) \(1\) \(e\left(\frac{23}{70}\right)\) \(e\left(\frac{41}{70}\right)\) \(e\left(\frac{23}{35}\right)\) \(e\left(\frac{32}{35}\right)\) \(e\left(\frac{69}{70}\right)\) \(e\left(\frac{6}{35}\right)\) \(e\left(\frac{29}{35}\right)\) \(e\left(\frac{17}{70}\right)\) \(e\left(\frac{37}{70}\right)\) \(e\left(\frac{11}{35}\right)\)
\(\chi_{1225}(904,\cdot)\) \(1\) \(1\) \(e\left(\frac{67}{70}\right)\) \(e\left(\frac{19}{70}\right)\) \(e\left(\frac{32}{35}\right)\) \(e\left(\frac{8}{35}\right)\) \(e\left(\frac{61}{70}\right)\) \(e\left(\frac{19}{35}\right)\) \(e\left(\frac{16}{35}\right)\) \(e\left(\frac{13}{70}\right)\) \(e\left(\frac{53}{70}\right)\) \(e\left(\frac{29}{35}\right)\)
\(\chi_{1225}(939,\cdot)\) \(1\) \(1\) \(e\left(\frac{41}{70}\right)\) \(e\left(\frac{67}{70}\right)\) \(e\left(\frac{6}{35}\right)\) \(e\left(\frac{19}{35}\right)\) \(e\left(\frac{53}{70}\right)\) \(e\left(\frac{32}{35}\right)\) \(e\left(\frac{3}{35}\right)\) \(e\left(\frac{9}{70}\right)\) \(e\left(\frac{69}{70}\right)\) \(e\left(\frac{12}{35}\right)\)
\(\chi_{1225}(1009,\cdot)\) \(1\) \(1\) \(e\left(\frac{59}{70}\right)\) \(e\left(\frac{23}{70}\right)\) \(e\left(\frac{24}{35}\right)\) \(e\left(\frac{6}{35}\right)\) \(e\left(\frac{37}{70}\right)\) \(e\left(\frac{23}{35}\right)\) \(e\left(\frac{12}{35}\right)\) \(e\left(\frac{1}{70}\right)\) \(e\left(\frac{31}{70}\right)\) \(e\left(\frac{13}{35}\right)\)
\(\chi_{1225}(1044,\cdot)\) \(1\) \(1\) \(e\left(\frac{33}{70}\right)\) \(e\left(\frac{1}{70}\right)\) \(e\left(\frac{33}{35}\right)\) \(e\left(\frac{17}{35}\right)\) \(e\left(\frac{29}{70}\right)\) \(e\left(\frac{1}{35}\right)\) \(e\left(\frac{34}{35}\right)\) \(e\left(\frac{67}{70}\right)\) \(e\left(\frac{47}{70}\right)\) \(e\left(\frac{31}{35}\right)\)
\(\chi_{1225}(1114,\cdot)\) \(1\) \(1\) \(e\left(\frac{51}{70}\right)\) \(e\left(\frac{27}{70}\right)\) \(e\left(\frac{16}{35}\right)\) \(e\left(\frac{4}{35}\right)\) \(e\left(\frac{13}{70}\right)\) \(e\left(\frac{27}{35}\right)\) \(e\left(\frac{8}{35}\right)\) \(e\left(\frac{59}{70}\right)\) \(e\left(\frac{9}{70}\right)\) \(e\left(\frac{32}{35}\right)\)
\(\chi_{1225}(1184,\cdot)\) \(1\) \(1\) \(e\left(\frac{69}{70}\right)\) \(e\left(\frac{53}{70}\right)\) \(e\left(\frac{34}{35}\right)\) \(e\left(\frac{26}{35}\right)\) \(e\left(\frac{67}{70}\right)\) \(e\left(\frac{18}{35}\right)\) \(e\left(\frac{17}{35}\right)\) \(e\left(\frac{51}{70}\right)\) \(e\left(\frac{41}{70}\right)\) \(e\left(\frac{33}{35}\right)\)
\(\chi_{1225}(1219,\cdot)\) \(1\) \(1\) \(e\left(\frac{43}{70}\right)\) \(e\left(\frac{31}{70}\right)\) \(e\left(\frac{8}{35}\right)\) \(e\left(\frac{2}{35}\right)\) \(e\left(\frac{59}{70}\right)\) \(e\left(\frac{31}{35}\right)\) \(e\left(\frac{4}{35}\right)\) \(e\left(\frac{47}{70}\right)\) \(e\left(\frac{57}{70}\right)\) \(e\left(\frac{16}{35}\right)\)