Basic properties
| Modulus: | \(50007\) | |
| Conductor: | \(50007\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(2730\) | 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 50007.lo
\(\chi_{50007}(47,\cdot)\) \(\chi_{50007}(53,\cdot)\) \(\chi_{50007}(314,\cdot)\) \(\chi_{50007}(350,\cdot)\) \(\chi_{50007}(503,\cdot)\) \(\chi_{50007}(542,\cdot)\) \(\chi_{50007}(548,\cdot)\) \(\chi_{50007}(680,\cdot)\) \(\chi_{50007}(692,\cdot)\) \(\chi_{50007}(695,\cdot)\) \(\chi_{50007}(860,\cdot)\) \(\chi_{50007}(983,\cdot)\) \(\chi_{50007}(1007,\cdot)\) \(\chi_{50007}(1016,\cdot)\) \(\chi_{50007}(1061,\cdot)\) \(\chi_{50007}(1064,\cdot)\) \(\chi_{50007}(1160,\cdot)\) \(\chi_{50007}(1181,\cdot)\) \(\chi_{50007}(1259,\cdot)\) \(\chi_{50007}(1475,\cdot)\) \(\chi_{50007}(1481,\cdot)\) \(\chi_{50007}(1529,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{1365})$ |
| Fixed field: | Number field defined by a degree 2730 polynomial (not computed) |
Values on generators
\((16670,1267,32707)\) → \((-1,e\left(\frac{11}{78}\right),e\left(\frac{86}{105}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 50007 }(503, a) \) | \(1\) | \(1\) | \(e\left(\frac{2411}{2730}\right)\) | \(e\left(\frac{1046}{1365}\right)\) | \(e\left(\frac{977}{2730}\right)\) | \(e\left(\frac{293}{910}\right)\) | \(e\left(\frac{591}{910}\right)\) | \(e\left(\frac{47}{195}\right)\) | \(e\left(\frac{2117}{2730}\right)\) | \(e\left(\frac{1007}{1365}\right)\) | \(e\left(\frac{8}{39}\right)\) | \(e\left(\frac{727}{1365}\right)\) |