Basic properties
| Modulus: | \(4031\) | |
| Conductor: | \(4031\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(966\) | 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 4031.bt
\(\chi_{4031}(4,\cdot)\) \(\chi_{4031}(5,\cdot)\) \(\chi_{4031}(9,\cdot)\) \(\chi_{4031}(13,\cdot)\) \(\chi_{4031}(35,\cdot)\) \(\chi_{4031}(38,\cdot)\) \(\chi_{4031}(51,\cdot)\) \(\chi_{4031}(67,\cdot)\) \(\chi_{4031}(71,\cdot)\) \(\chi_{4031}(120,\cdot)\) \(\chi_{4031}(121,\cdot)\) \(\chi_{4031}(122,\cdot)\) \(\chi_{4031}(150,\cdot)\) \(\chi_{4031}(167,\cdot)\) \(\chi_{4031}(180,\cdot)\) \(\chi_{4031}(208,\cdot)\) \(\chi_{4031}(225,\cdot)\) \(\chi_{4031}(238,\cdot)\) \(\chi_{4031}(266,\cdot)\) \(\chi_{4031}(283,\cdot)\) \(\chi_{4031}(294,\cdot)\) \(\chi_{4031}(303,\cdot)\) \(\chi_{4031}(324,\cdot)\) \(\chi_{4031}(325,\cdot)\) \(\chi_{4031}(332,\cdot)\) \(\chi_{4031}(361,\cdot)\) \(\chi_{4031}(399,\cdot)\) \(\chi_{4031}(415,\cdot)\) \(\chi_{4031}(428,\cdot)\) \(\chi_{4031}(441,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{483})$ |
| Fixed field: | Number field defined by a degree 966 polynomial (not computed) |
Values on generators
\((3337,697)\) → \((e\left(\frac{5}{14}\right),e\left(\frac{35}{69}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 4031 }(415, a) \) | \(1\) | \(1\) | \(e\left(\frac{835}{966}\right)\) | \(e\left(\frac{563}{966}\right)\) | \(e\left(\frac{352}{483}\right)\) | \(e\left(\frac{232}{483}\right)\) | \(e\left(\frac{72}{161}\right)\) | \(e\left(\frac{313}{483}\right)\) | \(e\left(\frac{191}{322}\right)\) | \(e\left(\frac{80}{483}\right)\) | \(e\left(\frac{111}{322}\right)\) | \(e\left(\frac{463}{966}\right)\) |