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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4067.bf
\(\chi_{4067}(5,\cdot)\) \(\chi_{4067}(24,\cdot)\) \(\chi_{4067}(45,\cdot)\) \(\chi_{4067}(47,\cdot)\) \(\chi_{4067}(52,\cdot)\) \(\chi_{4067}(54,\cdot)\) \(\chi_{4067}(66,\cdot)\) \(\chi_{4067}(73,\cdot)\) \(\chi_{4067}(89,\cdot)\) \(\chi_{4067}(96,\cdot)\) \(\chi_{4067}(101,\cdot)\) \(\chi_{4067}(103,\cdot)\) \(\chi_{4067}(115,\cdot)\) \(\chi_{4067}(122,\cdot)\) \(\chi_{4067}(136,\cdot)\) \(\chi_{4067}(138,\cdot)\) \(\chi_{4067}(143,\cdot)\) \(\chi_{4067}(145,\cdot)\) \(\chi_{4067}(150,\cdot)\) \(\chi_{4067}(157,\cdot)\) \(\chi_{4067}(159,\cdot)\) \(\chi_{4067}(171,\cdot)\) \(\chi_{4067}(180,\cdot)\) \(\chi_{4067}(185,\cdot)\) \(\chi_{4067}(201,\cdot)\) \(\chi_{4067}(208,\cdot)\) \(\chi_{4067}(213,\cdot)\) \(\chi_{4067}(220,\cdot)\) \(\chi_{4067}(222,\cdot)\) \(\chi_{4067}(255,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{861})$ |
| Fixed field: | Number field defined by a degree 1722 polynomial (not computed) |
Values on generators
\((2159,2990)\) → \((e\left(\frac{29}{42}\right),e\left(\frac{27}{82}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 4067 }(5, a) \) | \(1\) | \(1\) | \(e\left(\frac{485}{1722}\right)\) | \(e\left(\frac{685}{1722}\right)\) | \(e\left(\frac{485}{861}\right)\) | \(e\left(\frac{787}{861}\right)\) | \(e\left(\frac{195}{287}\right)\) | \(e\left(\frac{485}{574}\right)\) | \(e\left(\frac{685}{861}\right)\) | \(e\left(\frac{337}{1722}\right)\) | \(e\left(\frac{449}{861}\right)\) | \(e\left(\frac{1655}{1722}\right)\) |