Basic properties
| Modulus: | \(4027\) | |
| Conductor: | \(4027\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1342\) | 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 4027.n
\(\chi_{4027}(2,\cdot)\) \(\chi_{4027}(7,\cdot)\) \(\chi_{4027}(8,\cdot)\) \(\chi_{4027}(26,\cdot)\) \(\chi_{4027}(27,\cdot)\) \(\chi_{4027}(28,\cdot)\) \(\chi_{4027}(30,\cdot)\) \(\chi_{4027}(32,\cdot)\) \(\chi_{4027}(47,\cdot)\) \(\chi_{4027}(57,\cdot)\) \(\chi_{4027}(66,\cdot)\) \(\chi_{4027}(85,\cdot)\) \(\chi_{4027}(91,\cdot)\) \(\chi_{4027}(98,\cdot)\) \(\chi_{4027}(104,\cdot)\) \(\chi_{4027}(105,\cdot)\) \(\chi_{4027}(108,\cdot)\) \(\chi_{4027}(112,\cdot)\) \(\chi_{4027}(120,\cdot)\) \(\chi_{4027}(122,\cdot)\) \(\chi_{4027}(123,\cdot)\) \(\chi_{4027}(125,\cdot)\) \(\chi_{4027}(128,\cdot)\) \(\chi_{4027}(134,\cdot)\) \(\chi_{4027}(138,\cdot)\) \(\chi_{4027}(145,\cdot)\) \(\chi_{4027}(146,\cdot)\) \(\chi_{4027}(163,\cdot)\) \(\chi_{4027}(186,\cdot)\) \(\chi_{4027}(187,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{671})$ |
| Fixed field: | Number field defined by a degree 1342 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{147}{1342}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 4027 }(26, a) \) | \(-1\) | \(1\) | \(e\left(\frac{103}{1342}\right)\) | \(e\left(\frac{147}{1342}\right)\) | \(e\left(\frac{103}{671}\right)\) | \(e\left(\frac{199}{1342}\right)\) | \(e\left(\frac{125}{671}\right)\) | \(e\left(\frac{629}{1342}\right)\) | \(e\left(\frac{309}{1342}\right)\) | \(e\left(\frac{147}{671}\right)\) | \(e\left(\frac{151}{671}\right)\) | \(e\left(\frac{617}{1342}\right)\) |