Basic properties
| Modulus: | \(4067\) | |
| Conductor: | \(4067\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(287\) | 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 4067.y
\(\chi_{4067}(29,\cdot)\) \(\chi_{4067}(36,\cdot)\) \(\chi_{4067}(64,\cdot)\) \(\chi_{4067}(78,\cdot)\) \(\chi_{4067}(92,\cdot)\) \(\chi_{4067}(106,\cdot)\) \(\chi_{4067}(113,\cdot)\) \(\chi_{4067}(120,\cdot)\) \(\chi_{4067}(127,\cdot)\) \(\chi_{4067}(134,\cdot)\) \(\chi_{4067}(169,\cdot)\) \(\chi_{4067}(176,\cdot)\) \(\chi_{4067}(183,\cdot)\) \(\chi_{4067}(204,\cdot)\) \(\chi_{4067}(225,\cdot)\) \(\chi_{4067}(253,\cdot)\) \(\chi_{4067}(260,\cdot)\) \(\chi_{4067}(274,\cdot)\) \(\chi_{4067}(330,\cdot)\) \(\chi_{4067}(358,\cdot)\) \(\chi_{4067}(365,\cdot)\) \(\chi_{4067}(372,\cdot)\) \(\chi_{4067}(400,\cdot)\) \(\chi_{4067}(407,\cdot)\) \(\chi_{4067}(456,\cdot)\) \(\chi_{4067}(463,\cdot)\) \(\chi_{4067}(484,\cdot)\) \(\chi_{4067}(505,\cdot)\) \(\chi_{4067}(519,\cdot)\) \(\chi_{4067}(526,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{287})$ |
| Fixed field: | Number field defined by a degree 287 polynomial (not computed) |
Values on generators
\((2159,2990)\) → \((e\left(\frac{3}{7}\right),e\left(\frac{6}{41}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 4067 }(29, a) \) | \(1\) | \(1\) | \(e\left(\frac{83}{287}\right)\) | \(e\left(\frac{277}{287}\right)\) | \(e\left(\frac{166}{287}\right)\) | \(e\left(\frac{109}{287}\right)\) | \(e\left(\frac{73}{287}\right)\) | \(e\left(\frac{249}{287}\right)\) | \(e\left(\frac{267}{287}\right)\) | \(e\left(\frac{192}{287}\right)\) | \(e\left(\frac{188}{287}\right)\) | \(e\left(\frac{156}{287}\right)\) |