Basic properties
| Modulus: | \(4067\) | |
| Conductor: | \(4067\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1722\) | 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 4067.bd
\(\chi_{4067}(3,\cdot)\) \(\chi_{4067}(10,\cdot)\) \(\chi_{4067}(12,\cdot)\) \(\chi_{4067}(17,\cdot)\) \(\chi_{4067}(26,\cdot)\) \(\chi_{4067}(33,\cdot)\) \(\chi_{4067}(38,\cdot)\) \(\chi_{4067}(40,\cdot)\) \(\chi_{4067}(59,\cdot)\) \(\chi_{4067}(61,\cdot)\) \(\chi_{4067}(75,\cdot)\) \(\chi_{4067}(87,\cdot)\) \(\chi_{4067}(94,\cdot)\) \(\chi_{4067}(108,\cdot)\) \(\chi_{4067}(110,\cdot)\) \(\chi_{4067}(124,\cdot)\) \(\chi_{4067}(131,\cdot)\) \(\chi_{4067}(152,\cdot)\) \(\chi_{4067}(164,\cdot)\) \(\chi_{4067}(173,\cdot)\) \(\chi_{4067}(187,\cdot)\) \(\chi_{4067}(192,\cdot)\) \(\chi_{4067}(194,\cdot)\) \(\chi_{4067}(199,\cdot)\) \(\chi_{4067}(206,\cdot)\) \(\chi_{4067}(229,\cdot)\) \(\chi_{4067}(234,\cdot)\) \(\chi_{4067}(236,\cdot)\) \(\chi_{4067}(241,\cdot)\) \(\chi_{4067}(243,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{861})$ |
| Fixed field: | Number field defined by a degree 1722 polynomial (not computed) |
Values on generators
\((2159,2990)\) → \((e\left(\frac{11}{42}\right),e\left(\frac{37}{41}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 4067 }(12, a) \) | \(-1\) | \(1\) | \(e\left(\frac{613}{861}\right)\) | \(e\left(\frac{409}{1722}\right)\) | \(e\left(\frac{365}{861}\right)\) | \(e\left(\frac{1655}{1722}\right)\) | \(e\left(\frac{545}{574}\right)\) | \(e\left(\frac{39}{287}\right)\) | \(e\left(\frac{409}{861}\right)\) | \(e\left(\frac{1159}{1722}\right)\) | \(e\left(\frac{116}{861}\right)\) | \(e\left(\frac{1139}{1722}\right)\) |