Properties

Conductor 575
Order 110
Real No
Primitive No
Parity Even
Orbit Label 4025.cs

Related objects

Learn more about

Show commands for: SageMath / Pari/GP
sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
 
sage: H = DirichletGroup_conrey(4025)
 
sage: chi = H[29]
 
pari: [g,chi] = znchar(Mod(29,4025))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 575
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 110
Real = No
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = No
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = Even
Orbit label = 4025.cs
Orbit index = 71

Galois orbit

sage: chi.sage_character().galois_orbit()
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

\(\chi_{4025}(29,\cdot)\) \(\chi_{4025}(64,\cdot)\) \(\chi_{4025}(169,\cdot)\) \(\chi_{4025}(239,\cdot)\) \(\chi_{4025}(519,\cdot)\) \(\chi_{4025}(554,\cdot)\) \(\chi_{4025}(694,\cdot)\) \(\chi_{4025}(729,\cdot)\) \(\chi_{4025}(834,\cdot)\) \(\chi_{4025}(869,\cdot)\) \(\chi_{4025}(1044,\cdot)\) \(\chi_{4025}(1254,\cdot)\) \(\chi_{4025}(1359,\cdot)\) \(\chi_{4025}(1429,\cdot)\) \(\chi_{4025}(1534,\cdot)\) \(\chi_{4025}(1639,\cdot)\) \(\chi_{4025}(1779,\cdot)\) \(\chi_{4025}(2059,\cdot)\) \(\chi_{4025}(2129,\cdot)\) \(\chi_{4025}(2164,\cdot)\) \(\chi_{4025}(2234,\cdot)\) \(\chi_{4025}(2304,\cdot)\) \(\chi_{4025}(2339,\cdot)\) \(\chi_{4025}(2444,\cdot)\) \(\chi_{4025}(2479,\cdot)\) \(\chi_{4025}(2584,\cdot)\) \(\chi_{4025}(2654,\cdot)\) \(\chi_{4025}(2864,\cdot)\) \(\chi_{4025}(2934,\cdot)\) \(\chi_{4025}(2969,\cdot)\) ...

Inducing primitive character

\(\chi_{575}(29,\cdot)\)

Values on generators

\((2577,1151,3501)\) → \((e\left(\frac{1}{10}\right),1,e\left(\frac{9}{11}\right))\)

Values

-1123468911121316
\(1\)\(1\)\(e\left(\frac{81}{110}\right)\)\(e\left(\frac{87}{110}\right)\)\(e\left(\frac{26}{55}\right)\)\(e\left(\frac{29}{55}\right)\)\(e\left(\frac{23}{110}\right)\)\(e\left(\frac{32}{55}\right)\)\(e\left(\frac{53}{55}\right)\)\(e\left(\frac{29}{110}\right)\)\(e\left(\frac{39}{110}\right)\)\(e\left(\frac{52}{55}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{55})\)