Properties

Conductor 4033
Order 108
Real No
Primitive Yes
Parity Even
Orbit Label 4033.jo

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(4033)
sage: chi = H[153]
pari: [g,chi] = znchar(Mod(153,4033))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 4033
sage: chi.multiplicative_order()
pari: charorder(g,chi)
Order = 108
Real = No
sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
Primitive = Yes
sage: chi.is_odd()
pari: zncharisodd(g,chi)
Parity = Even
Orbit label = 4033.jo
Orbit index = 249

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 ]

\(\chi_{4033}(153,\cdot)\) \(\chi_{4033}(277,\cdot)\) \(\chi_{4033}(385,\cdot)\) \(\chi_{4033}(394,\cdot)\) \(\chi_{4033}(664,\cdot)\) \(\chi_{4033}(833,\cdot)\) \(\chi_{4033}(866,\cdot)\) \(\chi_{4033}(886,\cdot)\) \(\chi_{4033}(1060,\cdot)\) \(\chi_{4033}(1130,\cdot)\) \(\chi_{4033}(1223,\cdot)\) \(\chi_{4033}(1290,\cdot)\) \(\chi_{4033}(1345,\cdot)\) \(\chi_{4033}(1646,\cdot)\) \(\chi_{4033}(1648,\cdot)\) \(\chi_{4033}(1687,\cdot)\) \(\chi_{4033}(1697,\cdot)\) \(\chi_{4033}(2015,\cdot)\) \(\chi_{4033}(2018,\cdot)\) \(\chi_{4033}(2336,\cdot)\) \(\chi_{4033}(2346,\cdot)\) \(\chi_{4033}(2385,\cdot)\) \(\chi_{4033}(2387,\cdot)\) \(\chi_{4033}(2688,\cdot)\) \(\chi_{4033}(2743,\cdot)\) \(\chi_{4033}(2810,\cdot)\) \(\chi_{4033}(2903,\cdot)\) \(\chi_{4033}(2973,\cdot)\) \(\chi_{4033}(3147,\cdot)\) \(\chi_{4033}(3167,\cdot)\) ...

Values on generators

\((1963,2295)\) → \((e\left(\frac{23}{36}\right),e\left(\frac{89}{108}\right))\)

Values

-11234567891011
\(1\)\(1\)\(e\left(\frac{11}{18}\right)\)\(e\left(\frac{25}{54}\right)\)\(e\left(\frac{2}{9}\right)\)\(e\left(\frac{35}{108}\right)\)\(e\left(\frac{2}{27}\right)\)\(e\left(\frac{11}{27}\right)\)\(e\left(\frac{5}{6}\right)\)\(e\left(\frac{25}{27}\right)\)\(e\left(\frac{101}{108}\right)\)\(e\left(\frac{61}{108}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{108})\)