Properties

Label 1375.cs
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([29,20]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(37,1375))
 
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 \(-1\) \(1\) \(2\) \(3\) \(4\) \(6\) \(7\) \(8\) \(9\) \(12\) \(13\) \(14\)
\(\chi_{1375}(37,\cdot)\) \(-1\) \(1\) \(e\left(\frac{49}{100}\right)\) \(e\left(\frac{63}{100}\right)\) \(e\left(\frac{49}{50}\right)\) \(e\left(\frac{3}{25}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{47}{100}\right)\) \(e\left(\frac{13}{50}\right)\) \(e\left(\frac{61}{100}\right)\) \(e\left(\frac{51}{100}\right)\) \(e\left(\frac{27}{50}\right)\)
\(\chi_{1375}(53,\cdot)\) \(-1\) \(1\) \(e\left(\frac{27}{100}\right)\) \(e\left(\frac{49}{100}\right)\) \(e\left(\frac{27}{50}\right)\) \(e\left(\frac{19}{25}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{81}{100}\right)\) \(e\left(\frac{49}{50}\right)\) \(e\left(\frac{3}{100}\right)\) \(e\left(\frac{73}{100}\right)\) \(e\left(\frac{21}{50}\right)\)
\(\chi_{1375}(97,\cdot)\) \(-1\) \(1\) \(e\left(\frac{97}{100}\right)\) \(e\left(\frac{39}{100}\right)\) \(e\left(\frac{47}{50}\right)\) \(e\left(\frac{9}{25}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{91}{100}\right)\) \(e\left(\frac{39}{50}\right)\) \(e\left(\frac{33}{100}\right)\) \(e\left(\frac{3}{100}\right)\) \(e\left(\frac{31}{50}\right)\)
\(\chi_{1375}(102,\cdot)\) \(-1\) \(1\) \(e\left(\frac{61}{100}\right)\) \(e\left(\frac{7}{100}\right)\) \(e\left(\frac{11}{50}\right)\) \(e\left(\frac{17}{25}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{83}{100}\right)\) \(e\left(\frac{7}{50}\right)\) \(e\left(\frac{29}{100}\right)\) \(e\left(\frac{39}{100}\right)\) \(e\left(\frac{3}{50}\right)\)
\(\chi_{1375}(192,\cdot)\) \(-1\) \(1\) \(e\left(\frac{53}{100}\right)\) \(e\left(\frac{11}{100}\right)\) \(e\left(\frac{3}{50}\right)\) \(e\left(\frac{16}{25}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{59}{100}\right)\) \(e\left(\frac{11}{50}\right)\) \(e\left(\frac{17}{100}\right)\) \(e\left(\frac{47}{100}\right)\) \(e\left(\frac{19}{50}\right)\)
\(\chi_{1375}(213,\cdot)\) \(-1\) \(1\) \(e\left(\frac{99}{100}\right)\) \(e\left(\frac{13}{100}\right)\) \(e\left(\frac{49}{50}\right)\) \(e\left(\frac{3}{25}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{97}{100}\right)\) \(e\left(\frac{13}{50}\right)\) \(e\left(\frac{11}{100}\right)\) \(e\left(\frac{1}{100}\right)\) \(e\left(\frac{27}{50}\right)\)
\(\chi_{1375}(223,\cdot)\) \(-1\) \(1\) \(e\left(\frac{51}{100}\right)\) \(e\left(\frac{37}{100}\right)\) \(e\left(\frac{1}{50}\right)\) \(e\left(\frac{22}{25}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{53}{100}\right)\) \(e\left(\frac{37}{50}\right)\) \(e\left(\frac{39}{100}\right)\) \(e\left(\frac{49}{100}\right)\) \(e\left(\frac{23}{50}\right)\)
\(\chi_{1375}(258,\cdot)\) \(-1\) \(1\) \(e\left(\frac{43}{100}\right)\) \(e\left(\frac{41}{100}\right)\) \(e\left(\frac{43}{50}\right)\) \(e\left(\frac{21}{25}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{29}{100}\right)\) \(e\left(\frac{41}{50}\right)\) \(e\left(\frac{27}{100}\right)\) \(e\left(\frac{57}{100}\right)\) \(e\left(\frac{39}{50}\right)\)
\(\chi_{1375}(312,\cdot)\) \(-1\) \(1\) \(e\left(\frac{69}{100}\right)\) \(e\left(\frac{3}{100}\right)\) \(e\left(\frac{19}{50}\right)\) \(e\left(\frac{18}{25}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{7}{100}\right)\) \(e\left(\frac{3}{50}\right)\) \(e\left(\frac{41}{100}\right)\) \(e\left(\frac{31}{100}\right)\) \(e\left(\frac{37}{50}\right)\)
\(\chi_{1375}(328,\cdot)\) \(-1\) \(1\) \(e\left(\frac{7}{100}\right)\) \(e\left(\frac{9}{100}\right)\) \(e\left(\frac{7}{50}\right)\) \(e\left(\frac{4}{25}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{21}{100}\right)\) \(e\left(\frac{9}{50}\right)\) \(e\left(\frac{23}{100}\right)\) \(e\left(\frac{93}{100}\right)\) \(e\left(\frac{11}{50}\right)\)
\(\chi_{1375}(372,\cdot)\) \(-1\) \(1\) \(e\left(\frac{17}{100}\right)\) \(e\left(\frac{79}{100}\right)\) \(e\left(\frac{17}{50}\right)\) \(e\left(\frac{24}{25}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{51}{100}\right)\) \(e\left(\frac{29}{50}\right)\) \(e\left(\frac{13}{100}\right)\) \(e\left(\frac{83}{100}\right)\) \(e\left(\frac{41}{50}\right)\)
\(\chi_{1375}(377,\cdot)\) \(-1\) \(1\) \(e\left(\frac{81}{100}\right)\) \(e\left(\frac{47}{100}\right)\) \(e\left(\frac{31}{50}\right)\) \(e\left(\frac{7}{25}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{43}{100}\right)\) \(e\left(\frac{47}{50}\right)\) \(e\left(\frac{9}{100}\right)\) \(e\left(\frac{19}{100}\right)\) \(e\left(\frac{13}{50}\right)\)
\(\chi_{1375}(467,\cdot)\) \(-1\) \(1\) \(e\left(\frac{73}{100}\right)\) \(e\left(\frac{51}{100}\right)\) \(e\left(\frac{23}{50}\right)\) \(e\left(\frac{6}{25}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{19}{100}\right)\) \(e\left(\frac{1}{50}\right)\) \(e\left(\frac{97}{100}\right)\) \(e\left(\frac{27}{100}\right)\) \(e\left(\frac{29}{50}\right)\)
\(\chi_{1375}(488,\cdot)\) \(-1\) \(1\) \(e\left(\frac{79}{100}\right)\) \(e\left(\frac{73}{100}\right)\) \(e\left(\frac{29}{50}\right)\) \(e\left(\frac{13}{25}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{37}{100}\right)\) \(e\left(\frac{23}{50}\right)\) \(e\left(\frac{31}{100}\right)\) \(e\left(\frac{21}{100}\right)\) \(e\left(\frac{17}{50}\right)\)
\(\chi_{1375}(498,\cdot)\) \(-1\) \(1\) \(e\left(\frac{31}{100}\right)\) \(e\left(\frac{97}{100}\right)\) \(e\left(\frac{31}{50}\right)\) \(e\left(\frac{7}{25}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{93}{100}\right)\) \(e\left(\frac{47}{50}\right)\) \(e\left(\frac{59}{100}\right)\) \(e\left(\frac{69}{100}\right)\) \(e\left(\frac{13}{50}\right)\)
\(\chi_{1375}(533,\cdot)\) \(-1\) \(1\) \(e\left(\frac{23}{100}\right)\) \(e\left(\frac{1}{100}\right)\) \(e\left(\frac{23}{50}\right)\) \(e\left(\frac{6}{25}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{69}{100}\right)\) \(e\left(\frac{1}{50}\right)\) \(e\left(\frac{47}{100}\right)\) \(e\left(\frac{77}{100}\right)\) \(e\left(\frac{29}{50}\right)\)
\(\chi_{1375}(587,\cdot)\) \(-1\) \(1\) \(e\left(\frac{89}{100}\right)\) \(e\left(\frac{43}{100}\right)\) \(e\left(\frac{39}{50}\right)\) \(e\left(\frac{8}{25}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{67}{100}\right)\) \(e\left(\frac{43}{50}\right)\) \(e\left(\frac{21}{100}\right)\) \(e\left(\frac{11}{100}\right)\) \(e\left(\frac{47}{50}\right)\)
\(\chi_{1375}(603,\cdot)\) \(-1\) \(1\) \(e\left(\frac{87}{100}\right)\) \(e\left(\frac{69}{100}\right)\) \(e\left(\frac{37}{50}\right)\) \(e\left(\frac{14}{25}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{61}{100}\right)\) \(e\left(\frac{19}{50}\right)\) \(e\left(\frac{43}{100}\right)\) \(e\left(\frac{13}{100}\right)\) \(e\left(\frac{1}{50}\right)\)
\(\chi_{1375}(647,\cdot)\) \(-1\) \(1\) \(e\left(\frac{37}{100}\right)\) \(e\left(\frac{19}{100}\right)\) \(e\left(\frac{37}{50}\right)\) \(e\left(\frac{14}{25}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{11}{100}\right)\) \(e\left(\frac{19}{50}\right)\) \(e\left(\frac{93}{100}\right)\) \(e\left(\frac{63}{100}\right)\) \(e\left(\frac{1}{50}\right)\)
\(\chi_{1375}(652,\cdot)\) \(-1\) \(1\) \(e\left(\frac{1}{100}\right)\) \(e\left(\frac{87}{100}\right)\) \(e\left(\frac{1}{50}\right)\) \(e\left(\frac{22}{25}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{3}{100}\right)\) \(e\left(\frac{37}{50}\right)\) \(e\left(\frac{89}{100}\right)\) \(e\left(\frac{99}{100}\right)\) \(e\left(\frac{23}{50}\right)\)
\(\chi_{1375}(742,\cdot)\) \(-1\) \(1\) \(e\left(\frac{93}{100}\right)\) \(e\left(\frac{91}{100}\right)\) \(e\left(\frac{43}{50}\right)\) \(e\left(\frac{21}{25}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{79}{100}\right)\) \(e\left(\frac{41}{50}\right)\) \(e\left(\frac{77}{100}\right)\) \(e\left(\frac{7}{100}\right)\) \(e\left(\frac{39}{50}\right)\)
\(\chi_{1375}(763,\cdot)\) \(-1\) \(1\) \(e\left(\frac{59}{100}\right)\) \(e\left(\frac{33}{100}\right)\) \(e\left(\frac{9}{50}\right)\) \(e\left(\frac{23}{25}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{77}{100}\right)\) \(e\left(\frac{33}{50}\right)\) \(e\left(\frac{51}{100}\right)\) \(e\left(\frac{41}{100}\right)\) \(e\left(\frac{7}{50}\right)\)
\(\chi_{1375}(773,\cdot)\) \(-1\) \(1\) \(e\left(\frac{11}{100}\right)\) \(e\left(\frac{57}{100}\right)\) \(e\left(\frac{11}{50}\right)\) \(e\left(\frac{17}{25}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{33}{100}\right)\) \(e\left(\frac{7}{50}\right)\) \(e\left(\frac{79}{100}\right)\) \(e\left(\frac{89}{100}\right)\) \(e\left(\frac{3}{50}\right)\)
\(\chi_{1375}(808,\cdot)\) \(-1\) \(1\) \(e\left(\frac{3}{100}\right)\) \(e\left(\frac{61}{100}\right)\) \(e\left(\frac{3}{50}\right)\) \(e\left(\frac{16}{25}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{9}{100}\right)\) \(e\left(\frac{11}{50}\right)\) \(e\left(\frac{67}{100}\right)\) \(e\left(\frac{97}{100}\right)\) \(e\left(\frac{19}{50}\right)\)
\(\chi_{1375}(862,\cdot)\) \(-1\) \(1\) \(e\left(\frac{9}{100}\right)\) \(e\left(\frac{83}{100}\right)\) \(e\left(\frac{9}{50}\right)\) \(e\left(\frac{23}{25}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{27}{100}\right)\) \(e\left(\frac{33}{50}\right)\) \(e\left(\frac{1}{100}\right)\) \(e\left(\frac{91}{100}\right)\) \(e\left(\frac{7}{50}\right)\)
\(\chi_{1375}(878,\cdot)\) \(-1\) \(1\) \(e\left(\frac{67}{100}\right)\) \(e\left(\frac{29}{100}\right)\) \(e\left(\frac{17}{50}\right)\) \(e\left(\frac{24}{25}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{1}{100}\right)\) \(e\left(\frac{29}{50}\right)\) \(e\left(\frac{63}{100}\right)\) \(e\left(\frac{33}{100}\right)\) \(e\left(\frac{41}{50}\right)\)
\(\chi_{1375}(922,\cdot)\) \(-1\) \(1\) \(e\left(\frac{57}{100}\right)\) \(e\left(\frac{59}{100}\right)\) \(e\left(\frac{7}{50}\right)\) \(e\left(\frac{4}{25}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{71}{100}\right)\) \(e\left(\frac{9}{50}\right)\) \(e\left(\frac{73}{100}\right)\) \(e\left(\frac{43}{100}\right)\) \(e\left(\frac{11}{50}\right)\)
\(\chi_{1375}(927,\cdot)\) \(-1\) \(1\) \(e\left(\frac{21}{100}\right)\) \(e\left(\frac{27}{100}\right)\) \(e\left(\frac{21}{50}\right)\) \(e\left(\frac{12}{25}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{63}{100}\right)\) \(e\left(\frac{27}{50}\right)\) \(e\left(\frac{69}{100}\right)\) \(e\left(\frac{79}{100}\right)\) \(e\left(\frac{33}{50}\right)\)
\(\chi_{1375}(1017,\cdot)\) \(-1\) \(1\) \(e\left(\frac{13}{100}\right)\) \(e\left(\frac{31}{100}\right)\) \(e\left(\frac{13}{50}\right)\) \(e\left(\frac{11}{25}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{39}{100}\right)\) \(e\left(\frac{31}{50}\right)\) \(e\left(\frac{57}{100}\right)\) \(e\left(\frac{87}{100}\right)\) \(e\left(\frac{49}{50}\right)\)
\(\chi_{1375}(1038,\cdot)\) \(-1\) \(1\) \(e\left(\frac{39}{100}\right)\) \(e\left(\frac{93}{100}\right)\) \(e\left(\frac{39}{50}\right)\) \(e\left(\frac{8}{25}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{17}{100}\right)\) \(e\left(\frac{43}{50}\right)\) \(e\left(\frac{71}{100}\right)\) \(e\left(\frac{61}{100}\right)\) \(e\left(\frac{47}{50}\right)\)
\(\chi_{1375}(1048,\cdot)\) \(-1\) \(1\) \(e\left(\frac{91}{100}\right)\) \(e\left(\frac{17}{100}\right)\) \(e\left(\frac{41}{50}\right)\) \(e\left(\frac{2}{25}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{73}{100}\right)\) \(e\left(\frac{17}{50}\right)\) \(e\left(\frac{99}{100}\right)\) \(e\left(\frac{9}{100}\right)\) \(e\left(\frac{43}{50}\right)\)