Basic properties
| Modulus: | \(4067\) | |
| Conductor: | \(4067\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(861\) | 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.bc
\(\chi_{4067}(4,\cdot)\) \(\chi_{4067}(9,\cdot)\) \(\chi_{4067}(11,\cdot)\) \(\chi_{4067}(16,\cdot)\) \(\chi_{4067}(23,\cdot)\) \(\chi_{4067}(25,\cdot)\) \(\chi_{4067}(37,\cdot)\) \(\chi_{4067}(44,\cdot)\) \(\chi_{4067}(51,\cdot)\) \(\chi_{4067}(65,\cdot)\) \(\chi_{4067}(81,\cdot)\) \(\chi_{4067}(86,\cdot)\) \(\chi_{4067}(93,\cdot)\) \(\chi_{4067}(95,\cdot)\) \(\chi_{4067}(100,\cdot)\) \(\chi_{4067}(109,\cdot)\) \(\chi_{4067}(114,\cdot)\) \(\chi_{4067}(121,\cdot)\) \(\chi_{4067}(123,\cdot)\) \(\chi_{4067}(142,\cdot)\) \(\chi_{4067}(144,\cdot)\) \(\chi_{4067}(151,\cdot)\) \(\chi_{4067}(158,\cdot)\) \(\chi_{4067}(170,\cdot)\) \(\chi_{4067}(191,\cdot)\) \(\chi_{4067}(193,\cdot)\) \(\chi_{4067}(207,\cdot)\) \(\chi_{4067}(235,\cdot)\) \(\chi_{4067}(247,\cdot)\) \(\chi_{4067}(256,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{861})$ |
| Fixed field: | Number field defined by a degree 861 polynomial (not computed) |
Values on generators
\((2159,2990)\) → \((e\left(\frac{5}{21}\right),e\left(\frac{1}{41}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 4067 }(4, a) \) | \(1\) | \(1\) | \(e\left(\frac{185}{861}\right)\) | \(e\left(\frac{856}{861}\right)\) | \(e\left(\frac{370}{861}\right)\) | \(e\left(\frac{485}{861}\right)\) | \(e\left(\frac{60}{287}\right)\) | \(e\left(\frac{185}{287}\right)\) | \(e\left(\frac{851}{861}\right)\) | \(e\left(\frac{670}{861}\right)\) | \(e\left(\frac{94}{861}\right)\) | \(e\left(\frac{365}{861}\right)\) |