Basic properties
| Modulus: | \(5054\) | |
| Conductor: | \(2527\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(342\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2527}(363,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5054.cl
\(\chi_{5054}(13,\cdot)\) \(\chi_{5054}(41,\cdot)\) \(\chi_{5054}(97,\cdot)\) \(\chi_{5054}(167,\cdot)\) \(\chi_{5054}(181,\cdot)\) \(\chi_{5054}(223,\cdot)\) \(\chi_{5054}(279,\cdot)\) \(\chi_{5054}(363,\cdot)\) \(\chi_{5054}(433,\cdot)\) \(\chi_{5054}(447,\cdot)\) \(\chi_{5054}(489,\cdot)\) \(\chi_{5054}(545,\cdot)\) \(\chi_{5054}(573,\cdot)\) \(\chi_{5054}(629,\cdot)\) \(\chi_{5054}(699,\cdot)\) \(\chi_{5054}(713,\cdot)\) \(\chi_{5054}(755,\cdot)\) \(\chi_{5054}(811,\cdot)\) \(\chi_{5054}(839,\cdot)\) \(\chi_{5054}(895,\cdot)\) \(\chi_{5054}(965,\cdot)\) \(\chi_{5054}(979,\cdot)\) \(\chi_{5054}(1077,\cdot)\) \(\chi_{5054}(1105,\cdot)\) \(\chi_{5054}(1161,\cdot)\) \(\chi_{5054}(1231,\cdot)\) \(\chi_{5054}(1245,\cdot)\) \(\chi_{5054}(1287,\cdot)\) \(\chi_{5054}(1343,\cdot)\) \(\chi_{5054}(1371,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{171})$ |
| Fixed field: | Number field defined by a degree 342 polynomial (not computed) |
Values on generators
\((1445,1807)\) → \((-1,e\left(\frac{1}{342}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 5054 }(363, a) \) | \(1\) | \(1\) | \(e\left(\frac{155}{171}\right)\) | \(e\left(\frac{61}{342}\right)\) | \(e\left(\frac{139}{171}\right)\) | \(e\left(\frac{17}{57}\right)\) | \(e\left(\frac{79}{171}\right)\) | \(e\left(\frac{29}{342}\right)\) | \(e\left(\frac{55}{342}\right)\) | \(e\left(\frac{73}{171}\right)\) | \(e\left(\frac{61}{171}\right)\) | \(e\left(\frac{41}{57}\right)\) |