Basic properties
Modulus: | \(5077\) | |
Conductor: | \(5077\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(846\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5077.t
\(\chi_{5077}(3,\cdot)\) \(\chi_{5077}(28,\cdot)\) \(\chi_{5077}(53,\cdot)\) \(\chi_{5077}(64,\cdot)\) \(\chi_{5077}(104,\cdot)\) \(\chi_{5077}(107,\cdot)\) \(\chi_{5077}(127,\cdot)\) \(\chi_{5077}(145,\cdot)\) \(\chi_{5077}(151,\cdot)\) \(\chi_{5077}(169,\cdot)\) \(\chi_{5077}(187,\cdot)\) \(\chi_{5077}(198,\cdot)\) \(\chi_{5077}(225,\cdot)\) \(\chi_{5077}(236,\cdot)\) \(\chi_{5077}(238,\cdot)\) \(\chi_{5077}(239,\cdot)\) \(\chi_{5077}(243,\cdot)\) \(\chi_{5077}(267,\cdot)\) \(\chi_{5077}(291,\cdot)\) \(\chi_{5077}(345,\cdot)\) \(\chi_{5077}(385,\cdot)\) \(\chi_{5077}(402,\cdot)\) \(\chi_{5077}(503,\cdot)\) \(\chi_{5077}(514,\cdot)\) \(\chi_{5077}(529,\cdot)\) \(\chi_{5077}(537,\cdot)\) \(\chi_{5077}(543,\cdot)\) \(\chi_{5077}(544,\cdot)\) \(\chi_{5077}(564,\cdot)\) \(\chi_{5077}(570,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{423})$ |
Fixed field: | Number field defined by a degree 846 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{229}{846}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 5077 }(28, a) \) | \(1\) | \(1\) | \(e\left(\frac{229}{846}\right)\) | \(e\left(\frac{103}{141}\right)\) | \(e\left(\frac{229}{423}\right)\) | \(e\left(\frac{37}{94}\right)\) | \(e\left(\frac{1}{846}\right)\) | \(e\left(\frac{161}{423}\right)\) | \(e\left(\frac{229}{282}\right)\) | \(e\left(\frac{65}{141}\right)\) | \(e\left(\frac{281}{423}\right)\) | \(e\left(\frac{5}{846}\right)\) |