Basic properties
Modulus: | \(5077\) | |
Conductor: | \(5077\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(2538\) | 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.w
\(\chi_{5077}(4,\cdot)\) \(\chi_{5077}(10,\cdot)\) \(\chi_{5077}(19,\cdot)\) \(\chi_{5077}(34,\cdot)\) \(\chi_{5077}(36,\cdot)\) \(\chi_{5077}(47,\cdot)\) \(\chi_{5077}(48,\cdot)\) \(\chi_{5077}(55,\cdot)\) \(\chi_{5077}(58,\cdot)\) \(\chi_{5077}(61,\cdot)\) \(\chi_{5077}(70,\cdot)\) \(\chi_{5077}(71,\cdot)\) \(\chi_{5077}(78,\cdot)\) \(\chi_{5077}(79,\cdot)\) \(\chi_{5077}(85,\cdot)\) \(\chi_{5077}(90,\cdot)\) \(\chi_{5077}(103,\cdot)\) \(\chi_{5077}(121,\cdot)\) \(\chi_{5077}(137,\cdot)\) \(\chi_{5077}(138,\cdot)\) \(\chi_{5077}(146,\cdot)\) \(\chi_{5077}(147,\cdot)\) \(\chi_{5077}(154,\cdot)\) \(\chi_{5077}(160,\cdot)\) \(\chi_{5077}(166,\cdot)\) \(\chi_{5077}(171,\cdot)\) \(\chi_{5077}(173,\cdot)\) \(\chi_{5077}(175,\cdot)\) \(\chi_{5077}(177,\cdot)\) \(\chi_{5077}(186,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{1269})$ |
Fixed field: | Number field defined by a degree 2538 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{149}{2538}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 5077 }(10, a) \) | \(1\) | \(1\) | \(e\left(\frac{149}{2538}\right)\) | \(e\left(\frac{35}{423}\right)\) | \(e\left(\frac{149}{1269}\right)\) | \(e\left(\frac{41}{94}\right)\) | \(e\left(\frac{359}{2538}\right)\) | \(e\left(\frac{694}{1269}\right)\) | \(e\left(\frac{149}{846}\right)\) | \(e\left(\frac{70}{423}\right)\) | \(e\left(\frac{628}{1269}\right)\) | \(e\left(\frac{949}{2538}\right)\) |