Properties

Label 1375.cp
Modulus $1375$
Conductor $1375$
Order $100$
Real no
Primitive yes
Minimal yes
Parity odd

Related objects

Learn more

Show commands: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(1375, base_ring=CyclotomicField(100))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([93,60]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(42,1375))
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(1375\)
Conductor: \(1375\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(100\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: yes
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: odd
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Related number fields

Field of values: $\Q(\zeta_{100})$
Fixed field: Number field defined by a degree 100 polynomial

First 31 of 40 characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(3\) \(4\) \(6\) \(7\) \(8\) \(9\) \(12\) \(13\) \(14\)
\(\chi_{1375}(42,\cdot)\) \(-1\) \(1\) \(e\left(\frac{53}{100}\right)\) \(e\left(\frac{31}{100}\right)\) \(e\left(\frac{3}{50}\right)\) \(e\left(\frac{21}{25}\right)\) \(i\) \(e\left(\frac{59}{100}\right)\) \(e\left(\frac{31}{50}\right)\) \(e\left(\frac{37}{100}\right)\) \(e\left(\frac{87}{100}\right)\) \(e\left(\frac{39}{50}\right)\)
\(\chi_{1375}(48,\cdot)\) \(-1\) \(1\) \(e\left(\frac{31}{100}\right)\) \(e\left(\frac{37}{100}\right)\) \(e\left(\frac{31}{50}\right)\) \(e\left(\frac{17}{25}\right)\) \(-i\) \(e\left(\frac{93}{100}\right)\) \(e\left(\frac{37}{50}\right)\) \(e\left(\frac{99}{100}\right)\) \(e\left(\frac{49}{100}\right)\) \(e\left(\frac{3}{50}\right)\)
\(\chi_{1375}(108,\cdot)\) \(-1\) \(1\) \(e\left(\frac{83}{100}\right)\) \(e\left(\frac{41}{100}\right)\) \(e\left(\frac{33}{50}\right)\) \(e\left(\frac{6}{25}\right)\) \(-i\) \(e\left(\frac{49}{100}\right)\) \(e\left(\frac{41}{50}\right)\) \(e\left(\frac{7}{100}\right)\) \(e\left(\frac{57}{100}\right)\) \(e\left(\frac{29}{50}\right)\)
\(\chi_{1375}(113,\cdot)\) \(-1\) \(1\) \(e\left(\frac{39}{100}\right)\) \(e\left(\frac{53}{100}\right)\) \(e\left(\frac{39}{50}\right)\) \(e\left(\frac{23}{25}\right)\) \(-i\) \(e\left(\frac{17}{100}\right)\) \(e\left(\frac{3}{50}\right)\) \(e\left(\frac{31}{100}\right)\) \(e\left(\frac{81}{100}\right)\) \(e\left(\frac{7}{50}\right)\)
\(\chi_{1375}(202,\cdot)\) \(-1\) \(1\) \(e\left(\frac{81}{100}\right)\) \(e\left(\frac{87}{100}\right)\) \(e\left(\frac{31}{50}\right)\) \(e\left(\frac{17}{25}\right)\) \(i\) \(e\left(\frac{43}{100}\right)\) \(e\left(\frac{37}{50}\right)\) \(e\left(\frac{49}{100}\right)\) \(e\left(\frac{99}{100}\right)\) \(e\left(\frac{3}{50}\right)\)
\(\chi_{1375}(203,\cdot)\) \(-1\) \(1\) \(e\left(\frac{87}{100}\right)\) \(e\left(\frac{49}{100}\right)\) \(e\left(\frac{37}{50}\right)\) \(e\left(\frac{9}{25}\right)\) \(-i\) \(e\left(\frac{61}{100}\right)\) \(e\left(\frac{49}{50}\right)\) \(e\left(\frac{23}{100}\right)\) \(e\left(\frac{73}{100}\right)\) \(e\left(\frac{31}{50}\right)\)
\(\chi_{1375}(212,\cdot)\) \(-1\) \(1\) \(e\left(\frac{49}{100}\right)\) \(e\left(\frac{23}{100}\right)\) \(e\left(\frac{49}{50}\right)\) \(e\left(\frac{18}{25}\right)\) \(i\) \(e\left(\frac{47}{100}\right)\) \(e\left(\frac{23}{50}\right)\) \(e\left(\frac{21}{100}\right)\) \(e\left(\frac{71}{100}\right)\) \(e\left(\frac{37}{50}\right)\)
\(\chi_{1375}(247,\cdot)\) \(-1\) \(1\) \(e\left(\frac{97}{100}\right)\) \(e\left(\frac{19}{100}\right)\) \(e\left(\frac{47}{50}\right)\) \(e\left(\frac{4}{25}\right)\) \(i\) \(e\left(\frac{91}{100}\right)\) \(e\left(\frac{19}{50}\right)\) \(e\left(\frac{13}{100}\right)\) \(e\left(\frac{63}{100}\right)\) \(e\left(\frac{11}{50}\right)\)
\(\chi_{1375}(317,\cdot)\) \(-1\) \(1\) \(e\left(\frac{73}{100}\right)\) \(e\left(\frac{71}{100}\right)\) \(e\left(\frac{23}{50}\right)\) \(e\left(\frac{11}{25}\right)\) \(i\) \(e\left(\frac{19}{100}\right)\) \(e\left(\frac{21}{50}\right)\) \(e\left(\frac{17}{100}\right)\) \(e\left(\frac{67}{100}\right)\) \(e\left(\frac{49}{50}\right)\)
\(\chi_{1375}(323,\cdot)\) \(-1\) \(1\) \(e\left(\frac{11}{100}\right)\) \(e\left(\frac{97}{100}\right)\) \(e\left(\frac{11}{50}\right)\) \(e\left(\frac{2}{25}\right)\) \(-i\) \(e\left(\frac{33}{100}\right)\) \(e\left(\frac{47}{50}\right)\) \(e\left(\frac{19}{100}\right)\) \(e\left(\frac{69}{100}\right)\) \(e\left(\frac{43}{50}\right)\)
\(\chi_{1375}(383,\cdot)\) \(-1\) \(1\) \(e\left(\frac{63}{100}\right)\) \(e\left(\frac{1}{100}\right)\) \(e\left(\frac{13}{50}\right)\) \(e\left(\frac{16}{25}\right)\) \(-i\) \(e\left(\frac{89}{100}\right)\) \(e\left(\frac{1}{50}\right)\) \(e\left(\frac{27}{100}\right)\) \(e\left(\frac{77}{100}\right)\) \(e\left(\frac{19}{50}\right)\)
\(\chi_{1375}(388,\cdot)\) \(-1\) \(1\) \(e\left(\frac{19}{100}\right)\) \(e\left(\frac{13}{100}\right)\) \(e\left(\frac{19}{50}\right)\) \(e\left(\frac{8}{25}\right)\) \(-i\) \(e\left(\frac{57}{100}\right)\) \(e\left(\frac{13}{50}\right)\) \(e\left(\frac{51}{100}\right)\) \(e\left(\frac{1}{100}\right)\) \(e\left(\frac{47}{50}\right)\)
\(\chi_{1375}(477,\cdot)\) \(-1\) \(1\) \(e\left(\frac{1}{100}\right)\) \(e\left(\frac{27}{100}\right)\) \(e\left(\frac{1}{50}\right)\) \(e\left(\frac{7}{25}\right)\) \(i\) \(e\left(\frac{3}{100}\right)\) \(e\left(\frac{27}{50}\right)\) \(e\left(\frac{29}{100}\right)\) \(e\left(\frac{79}{100}\right)\) \(e\left(\frac{13}{50}\right)\)
\(\chi_{1375}(478,\cdot)\) \(-1\) \(1\) \(e\left(\frac{67}{100}\right)\) \(e\left(\frac{9}{100}\right)\) \(e\left(\frac{17}{50}\right)\) \(e\left(\frac{19}{25}\right)\) \(-i\) \(e\left(\frac{1}{100}\right)\) \(e\left(\frac{9}{50}\right)\) \(e\left(\frac{43}{100}\right)\) \(e\left(\frac{93}{100}\right)\) \(e\left(\frac{21}{50}\right)\)
\(\chi_{1375}(487,\cdot)\) \(-1\) \(1\) \(e\left(\frac{69}{100}\right)\) \(e\left(\frac{63}{100}\right)\) \(e\left(\frac{19}{50}\right)\) \(e\left(\frac{8}{25}\right)\) \(i\) \(e\left(\frac{7}{100}\right)\) \(e\left(\frac{13}{50}\right)\) \(e\left(\frac{1}{100}\right)\) \(e\left(\frac{51}{100}\right)\) \(e\left(\frac{47}{50}\right)\)
\(\chi_{1375}(522,\cdot)\) \(-1\) \(1\) \(e\left(\frac{17}{100}\right)\) \(e\left(\frac{59}{100}\right)\) \(e\left(\frac{17}{50}\right)\) \(e\left(\frac{19}{25}\right)\) \(i\) \(e\left(\frac{51}{100}\right)\) \(e\left(\frac{9}{50}\right)\) \(e\left(\frac{93}{100}\right)\) \(e\left(\frac{43}{100}\right)\) \(e\left(\frac{21}{50}\right)\)
\(\chi_{1375}(592,\cdot)\) \(-1\) \(1\) \(e\left(\frac{93}{100}\right)\) \(e\left(\frac{11}{100}\right)\) \(e\left(\frac{43}{50}\right)\) \(e\left(\frac{1}{25}\right)\) \(i\) \(e\left(\frac{79}{100}\right)\) \(e\left(\frac{11}{50}\right)\) \(e\left(\frac{97}{100}\right)\) \(e\left(\frac{47}{100}\right)\) \(e\left(\frac{9}{50}\right)\)
\(\chi_{1375}(598,\cdot)\) \(-1\) \(1\) \(e\left(\frac{91}{100}\right)\) \(e\left(\frac{57}{100}\right)\) \(e\left(\frac{41}{50}\right)\) \(e\left(\frac{12}{25}\right)\) \(-i\) \(e\left(\frac{73}{100}\right)\) \(e\left(\frac{7}{50}\right)\) \(e\left(\frac{39}{100}\right)\) \(e\left(\frac{89}{100}\right)\) \(e\left(\frac{33}{50}\right)\)
\(\chi_{1375}(658,\cdot)\) \(-1\) \(1\) \(e\left(\frac{43}{100}\right)\) \(e\left(\frac{61}{100}\right)\) \(e\left(\frac{43}{50}\right)\) \(e\left(\frac{1}{25}\right)\) \(-i\) \(e\left(\frac{29}{100}\right)\) \(e\left(\frac{11}{50}\right)\) \(e\left(\frac{47}{100}\right)\) \(e\left(\frac{97}{100}\right)\) \(e\left(\frac{9}{50}\right)\)
\(\chi_{1375}(663,\cdot)\) \(-1\) \(1\) \(e\left(\frac{99}{100}\right)\) \(e\left(\frac{73}{100}\right)\) \(e\left(\frac{49}{50}\right)\) \(e\left(\frac{18}{25}\right)\) \(-i\) \(e\left(\frac{97}{100}\right)\) \(e\left(\frac{23}{50}\right)\) \(e\left(\frac{71}{100}\right)\) \(e\left(\frac{21}{100}\right)\) \(e\left(\frac{37}{50}\right)\)
\(\chi_{1375}(752,\cdot)\) \(-1\) \(1\) \(e\left(\frac{21}{100}\right)\) \(e\left(\frac{67}{100}\right)\) \(e\left(\frac{21}{50}\right)\) \(e\left(\frac{22}{25}\right)\) \(i\) \(e\left(\frac{63}{100}\right)\) \(e\left(\frac{17}{50}\right)\) \(e\left(\frac{9}{100}\right)\) \(e\left(\frac{59}{100}\right)\) \(e\left(\frac{23}{50}\right)\)
\(\chi_{1375}(753,\cdot)\) \(-1\) \(1\) \(e\left(\frac{47}{100}\right)\) \(e\left(\frac{69}{100}\right)\) \(e\left(\frac{47}{50}\right)\) \(e\left(\frac{4}{25}\right)\) \(-i\) \(e\left(\frac{41}{100}\right)\) \(e\left(\frac{19}{50}\right)\) \(e\left(\frac{63}{100}\right)\) \(e\left(\frac{13}{100}\right)\) \(e\left(\frac{11}{50}\right)\)
\(\chi_{1375}(762,\cdot)\) \(-1\) \(1\) \(e\left(\frac{89}{100}\right)\) \(e\left(\frac{3}{100}\right)\) \(e\left(\frac{39}{50}\right)\) \(e\left(\frac{23}{25}\right)\) \(i\) \(e\left(\frac{67}{100}\right)\) \(e\left(\frac{3}{50}\right)\) \(e\left(\frac{81}{100}\right)\) \(e\left(\frac{31}{100}\right)\) \(e\left(\frac{7}{50}\right)\)
\(\chi_{1375}(797,\cdot)\) \(-1\) \(1\) \(e\left(\frac{37}{100}\right)\) \(e\left(\frac{99}{100}\right)\) \(e\left(\frac{37}{50}\right)\) \(e\left(\frac{9}{25}\right)\) \(i\) \(e\left(\frac{11}{100}\right)\) \(e\left(\frac{49}{50}\right)\) \(e\left(\frac{73}{100}\right)\) \(e\left(\frac{23}{100}\right)\) \(e\left(\frac{31}{50}\right)\)
\(\chi_{1375}(867,\cdot)\) \(-1\) \(1\) \(e\left(\frac{13}{100}\right)\) \(e\left(\frac{51}{100}\right)\) \(e\left(\frac{13}{50}\right)\) \(e\left(\frac{16}{25}\right)\) \(i\) \(e\left(\frac{39}{100}\right)\) \(e\left(\frac{1}{50}\right)\) \(e\left(\frac{77}{100}\right)\) \(e\left(\frac{27}{100}\right)\) \(e\left(\frac{19}{50}\right)\)
\(\chi_{1375}(873,\cdot)\) \(-1\) \(1\) \(e\left(\frac{71}{100}\right)\) \(e\left(\frac{17}{100}\right)\) \(e\left(\frac{21}{50}\right)\) \(e\left(\frac{22}{25}\right)\) \(-i\) \(e\left(\frac{13}{100}\right)\) \(e\left(\frac{17}{50}\right)\) \(e\left(\frac{59}{100}\right)\) \(e\left(\frac{9}{100}\right)\) \(e\left(\frac{23}{50}\right)\)
\(\chi_{1375}(933,\cdot)\) \(-1\) \(1\) \(e\left(\frac{23}{100}\right)\) \(e\left(\frac{21}{100}\right)\) \(e\left(\frac{23}{50}\right)\) \(e\left(\frac{11}{25}\right)\) \(-i\) \(e\left(\frac{69}{100}\right)\) \(e\left(\frac{21}{50}\right)\) \(e\left(\frac{67}{100}\right)\) \(e\left(\frac{17}{100}\right)\) \(e\left(\frac{49}{50}\right)\)
\(\chi_{1375}(938,\cdot)\) \(-1\) \(1\) \(e\left(\frac{79}{100}\right)\) \(e\left(\frac{33}{100}\right)\) \(e\left(\frac{29}{50}\right)\) \(e\left(\frac{3}{25}\right)\) \(-i\) \(e\left(\frac{37}{100}\right)\) \(e\left(\frac{33}{50}\right)\) \(e\left(\frac{91}{100}\right)\) \(e\left(\frac{41}{100}\right)\) \(e\left(\frac{27}{50}\right)\)
\(\chi_{1375}(1027,\cdot)\) \(-1\) \(1\) \(e\left(\frac{41}{100}\right)\) \(e\left(\frac{7}{100}\right)\) \(e\left(\frac{41}{50}\right)\) \(e\left(\frac{12}{25}\right)\) \(i\) \(e\left(\frac{23}{100}\right)\) \(e\left(\frac{7}{50}\right)\) \(e\left(\frac{89}{100}\right)\) \(e\left(\frac{39}{100}\right)\) \(e\left(\frac{33}{50}\right)\)
\(\chi_{1375}(1028,\cdot)\) \(-1\) \(1\) \(e\left(\frac{27}{100}\right)\) \(e\left(\frac{29}{100}\right)\) \(e\left(\frac{27}{50}\right)\) \(e\left(\frac{14}{25}\right)\) \(-i\) \(e\left(\frac{81}{100}\right)\) \(e\left(\frac{29}{50}\right)\) \(e\left(\frac{83}{100}\right)\) \(e\left(\frac{33}{100}\right)\) \(e\left(\frac{1}{50}\right)\)
\(\chi_{1375}(1037,\cdot)\) \(-1\) \(1\) \(e\left(\frac{9}{100}\right)\) \(e\left(\frac{43}{100}\right)\) \(e\left(\frac{9}{50}\right)\) \(e\left(\frac{13}{25}\right)\) \(i\) \(e\left(\frac{27}{100}\right)\) \(e\left(\frac{43}{50}\right)\) \(e\left(\frac{61}{100}\right)\) \(e\left(\frac{11}{100}\right)\) \(e\left(\frac{17}{50}\right)\)