Basic properties
Modulus: | \(4021\) | |
Conductor: | \(4021\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(268\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4021.p
\(\chi_{4021}(6,\cdot)\) \(\chi_{4021}(10,\cdot)\) \(\chi_{4021}(69,\cdot)\) \(\chi_{4021}(74,\cdot)\) \(\chi_{4021}(78,\cdot)\) \(\chi_{4021}(115,\cdot)\) \(\chi_{4021}(118,\cdot)\) \(\chi_{4021}(119,\cdot)\) \(\chi_{4021}(124,\cdot)\) \(\chi_{4021}(130,\cdot)\) \(\chi_{4021}(136,\cdot)\) \(\chi_{4021}(163,\cdot)\) \(\chi_{4021}(189,\cdot)\) \(\chi_{4021}(216,\cdot)\) \(\chi_{4021}(227,\cdot)\) \(\chi_{4021}(242,\cdot)\) \(\chi_{4021}(263,\cdot)\) \(\chi_{4021}(266,\cdot)\) \(\chi_{4021}(304,\cdot)\) \(\chi_{4021}(315,\cdot)\) \(\chi_{4021}(337,\cdot)\) \(\chi_{4021}(360,\cdot)\) \(\chi_{4021}(402,\cdot)\) \(\chi_{4021}(419,\cdot)\) \(\chi_{4021}(443,\cdot)\) \(\chi_{4021}(525,\cdot)\) \(\chi_{4021}(563,\cdot)\) \(\chi_{4021}(600,\cdot)\) \(\chi_{4021}(602,\cdot)\) \(\chi_{4021}(642,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{268})$ |
Fixed field: | Number field defined by a degree 268 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{35}{268}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 4021 }(10, a) \) | \(-1\) | \(1\) | \(e\left(\frac{35}{268}\right)\) | \(e\left(\frac{47}{67}\right)\) | \(e\left(\frac{35}{134}\right)\) | \(e\left(\frac{29}{67}\right)\) | \(e\left(\frac{223}{268}\right)\) | \(-i\) | \(e\left(\frac{105}{268}\right)\) | \(e\left(\frac{27}{67}\right)\) | \(e\left(\frac{151}{268}\right)\) | \(e\left(\frac{251}{268}\right)\) |