Basic properties
| Modulus: | \(8003\) | |
| Conductor: | \(8003\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(156\) | 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 8003.bx
\(\chi_{8003}(33,\cdot)\) \(\chi_{8003}(270,\cdot)\) \(\chi_{8003}(421,\cdot)\) \(\chi_{8003}(723,\cdot)\) \(\chi_{8003}(874,\cdot)\) \(\chi_{8003}(1025,\cdot)\) \(\chi_{8003}(1241,\cdot)\) \(\chi_{8003}(1327,\cdot)\) \(\chi_{8003}(1392,\cdot)\) \(\chi_{8003}(1629,\cdot)\) \(\chi_{8003}(1694,\cdot)\) \(\chi_{8003}(1780,\cdot)\) \(\chi_{8003}(1996,\cdot)\) \(\chi_{8003}(2147,\cdot)\) \(\chi_{8003}(2298,\cdot)\) \(\chi_{8003}(2600,\cdot)\) \(\chi_{8003}(2751,\cdot)\) \(\chi_{8003}(2988,\cdot)\) \(\chi_{8003}(3053,\cdot)\) \(\chi_{8003}(3139,\cdot)\) \(\chi_{8003}(3506,\cdot)\) \(\chi_{8003}(3592,\cdot)\) \(\chi_{8003}(3743,\cdot)\) \(\chi_{8003}(3808,\cdot)\) \(\chi_{8003}(4261,\cdot)\) \(\chi_{8003}(4563,\cdot)\) \(\chi_{8003}(4714,\cdot)\) \(\chi_{8003}(4951,\cdot)\) \(\chi_{8003}(5016,\cdot)\) \(\chi_{8003}(5102,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((4984,7103)\) → \((e\left(\frac{23}{52}\right),e\left(\frac{1}{6}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 8003 }(33, a) \) | \(1\) | \(1\) | \(e\left(\frac{17}{156}\right)\) | \(e\left(\frac{1}{52}\right)\) | \(e\left(\frac{17}{78}\right)\) | \(e\left(\frac{71}{156}\right)\) | \(e\left(\frac{5}{39}\right)\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{17}{52}\right)\) | \(e\left(\frac{1}{26}\right)\) | \(e\left(\frac{22}{39}\right)\) | \(e\left(\frac{25}{78}\right)\) |