Basic properties
| Modulus: | \(5054\) | |
| Conductor: | \(361\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(342\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{361}(15,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5054.ch
\(\chi_{5054}(15,\cdot)\) \(\chi_{5054}(29,\cdot)\) \(\chi_{5054}(71,\cdot)\) \(\chi_{5054}(155,\cdot)\) \(\chi_{5054}(211,\cdot)\) \(\chi_{5054}(281,\cdot)\) \(\chi_{5054}(295,\cdot)\) \(\chi_{5054}(337,\cdot)\) \(\chi_{5054}(393,\cdot)\) \(\chi_{5054}(421,\cdot)\) \(\chi_{5054}(547,\cdot)\) \(\chi_{5054}(561,\cdot)\) \(\chi_{5054}(603,\cdot)\) \(\chi_{5054}(659,\cdot)\) \(\chi_{5054}(687,\cdot)\) \(\chi_{5054}(743,\cdot)\) \(\chi_{5054}(813,\cdot)\) \(\chi_{5054}(827,\cdot)\) \(\chi_{5054}(869,\cdot)\) \(\chi_{5054}(925,\cdot)\) \(\chi_{5054}(953,\cdot)\) \(\chi_{5054}(1009,\cdot)\) \(\chi_{5054}(1079,\cdot)\) \(\chi_{5054}(1093,\cdot)\) \(\chi_{5054}(1135,\cdot)\) \(\chi_{5054}(1191,\cdot)\) \(\chi_{5054}(1219,\cdot)\) \(\chi_{5054}(1275,\cdot)\) \(\chi_{5054}(1359,\cdot)\) \(\chi_{5054}(1401,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{171})$ |
| Fixed field: | Number field defined by a degree 342 polynomial (not computed) |
Values on generators
\((1445,1807)\) → \((1,e\left(\frac{29}{342}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 5054 }(15, a) \) | \(-1\) | \(1\) | \(e\left(\frac{269}{342}\right)\) | \(e\left(\frac{115}{171}\right)\) | \(e\left(\frac{98}{171}\right)\) | \(e\left(\frac{37}{57}\right)\) | \(e\left(\frac{307}{342}\right)\) | \(e\left(\frac{157}{342}\right)\) | \(e\left(\frac{28}{171}\right)\) | \(e\left(\frac{65}{171}\right)\) | \(e\left(\frac{59}{171}\right)\) | \(e\left(\frac{41}{114}\right)\) |