Properties

Conductor 7623
Order 330
Real no
Primitive yes
Minimal yes
Parity even
Orbit label 7623.gc

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(7623)
 
sage: chi = H[74]
 
pari: [g,chi] = znchar(Mod(74,7623))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 7623
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 330
Real = no
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = yes
Minimal = yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = even
Orbit label = 7623.gc
Orbit index = 159

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 ]
 

\(\chi_{7623}(74,\cdot)\) \(\chi_{7623}(149,\cdot)\) \(\chi_{7623}(200,\cdot)\) \(\chi_{7623}(326,\cdot)\) \(\chi_{7623}(338,\cdot)\) \(\chi_{7623}(464,\cdot)\) \(\chi_{7623}(590,\cdot)\) \(\chi_{7623}(767,\cdot)\) \(\chi_{7623}(842,\cdot)\) \(\chi_{7623}(893,\cdot)\) \(\chi_{7623}(1019,\cdot)\) \(\chi_{7623}(1031,\cdot)\) \(\chi_{7623}(1157,\cdot)\) \(\chi_{7623}(1271,\cdot)\) \(\chi_{7623}(1283,\cdot)\) \(\chi_{7623}(1460,\cdot)\) \(\chi_{7623}(1535,\cdot)\) \(\chi_{7623}(1586,\cdot)\) \(\chi_{7623}(1712,\cdot)\) \(\chi_{7623}(1724,\cdot)\) \(\chi_{7623}(1850,\cdot)\) \(\chi_{7623}(1964,\cdot)\) \(\chi_{7623}(2153,\cdot)\) \(\chi_{7623}(2228,\cdot)\) \(\chi_{7623}(2279,\cdot)\) \(\chi_{7623}(2405,\cdot)\) \(\chi_{7623}(2543,\cdot)\) \(\chi_{7623}(2657,\cdot)\) \(\chi_{7623}(2669,\cdot)\) \(\chi_{7623}(2846,\cdot)\) ...

Values on generators

\((848,4357,4600)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{2}{3}\right),e\left(\frac{43}{110}\right))\)

Values

-112458101316171920
\(1\)\(1\)\(e\left(\frac{49}{55}\right)\)\(e\left(\frac{43}{55}\right)\)\(e\left(\frac{31}{330}\right)\)\(e\left(\frac{37}{55}\right)\)\(e\left(\frac{65}{66}\right)\)\(e\left(\frac{269}{330}\right)\)\(e\left(\frac{31}{55}\right)\)\(e\left(\frac{53}{165}\right)\)\(e\left(\frac{257}{330}\right)\)\(e\left(\frac{289}{330}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{165})\)