Basic properties
Modulus: | \(5077\) | |
Conductor: | \(5077\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(1269\) | 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.u
\(\chi_{5077}(7,\cdot)\) \(\chi_{5077}(12,\cdot)\) \(\chi_{5077}(16,\cdot)\) \(\chi_{5077}(26,\cdot)\) \(\chi_{5077}(30,\cdot)\) \(\chi_{5077}(46,\cdot)\) \(\chi_{5077}(49,\cdot)\) \(\chi_{5077}(57,\cdot)\) \(\chi_{5077}(59,\cdot)\) \(\chi_{5077}(62,\cdot)\) \(\chi_{5077}(63,\cdot)\) \(\chi_{5077}(76,\cdot)\) \(\chi_{5077}(82,\cdot)\) \(\chi_{5077}(86,\cdot)\) \(\chi_{5077}(88,\cdot)\) \(\chi_{5077}(100,\cdot)\) \(\chi_{5077}(102,\cdot)\) \(\chi_{5077}(108,\cdot)\) \(\chi_{5077}(112,\cdot)\) \(\chi_{5077}(131,\cdot)\) \(\chi_{5077}(136,\cdot)\) \(\chi_{5077}(141,\cdot)\) \(\chi_{5077}(143,\cdot)\) \(\chi_{5077}(144,\cdot)\) \(\chi_{5077}(155,\cdot)\) \(\chi_{5077}(163,\cdot)\) \(\chi_{5077}(165,\cdot)\) \(\chi_{5077}(174,\cdot)\) \(\chi_{5077}(182,\cdot)\) \(\chi_{5077}(183,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{1269})$ |
Fixed field: | Number field defined by a degree 1269 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{343}{1269}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 5077 }(7, a) \) | \(1\) | \(1\) | \(e\left(\frac{343}{1269}\right)\) | \(e\left(\frac{5}{423}\right)\) | \(e\left(\frac{686}{1269}\right)\) | \(e\left(\frac{13}{47}\right)\) | \(e\left(\frac{358}{1269}\right)\) | \(e\left(\frac{1066}{1269}\right)\) | \(e\left(\frac{343}{423}\right)\) | \(e\left(\frac{10}{423}\right)\) | \(e\left(\frac{694}{1269}\right)\) | \(e\left(\frac{98}{1269}\right)\) |