Basic properties
| Modulus: | \(5415\) | |
| Conductor: | \(1083\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(342\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1083}(41,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5415.cp
\(\chi_{5415}(41,\cdot)\) \(\chi_{5415}(71,\cdot)\) \(\chi_{5415}(86,\cdot)\) \(\chi_{5415}(146,\cdot)\) \(\chi_{5415}(281,\cdot)\) \(\chi_{5415}(326,\cdot)\) \(\chi_{5415}(356,\cdot)\) \(\chi_{5415}(371,\cdot)\) \(\chi_{5415}(401,\cdot)\) \(\chi_{5415}(431,\cdot)\) \(\chi_{5415}(566,\cdot)\) \(\chi_{5415}(611,\cdot)\) \(\chi_{5415}(641,\cdot)\) \(\chi_{5415}(656,\cdot)\) \(\chi_{5415}(686,\cdot)\) \(\chi_{5415}(716,\cdot)\) \(\chi_{5415}(851,\cdot)\) \(\chi_{5415}(896,\cdot)\) \(\chi_{5415}(926,\cdot)\) \(\chi_{5415}(941,\cdot)\) \(\chi_{5415}(971,\cdot)\) \(\chi_{5415}(1001,\cdot)\) \(\chi_{5415}(1136,\cdot)\) \(\chi_{5415}(1181,\cdot)\) \(\chi_{5415}(1211,\cdot)\) \(\chi_{5415}(1226,\cdot)\) \(\chi_{5415}(1256,\cdot)\) \(\chi_{5415}(1286,\cdot)\) \(\chi_{5415}(1421,\cdot)\) \(\chi_{5415}(1466,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{171})$ |
| Fixed field: | Number field defined by a degree 342 polynomial (not computed) |
Values on generators
\((3611,2167,5056)\) → \((-1,1,e\left(\frac{67}{342}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(22\) |
| \( \chi_{ 5415 }(41, a) \) | \(1\) | \(1\) | \(e\left(\frac{119}{171}\right)\) | \(e\left(\frac{67}{171}\right)\) | \(e\left(\frac{22}{57}\right)\) | \(e\left(\frac{5}{57}\right)\) | \(e\left(\frac{55}{114}\right)\) | \(e\left(\frac{155}{342}\right)\) | \(e\left(\frac{14}{171}\right)\) | \(e\left(\frac{134}{171}\right)\) | \(e\left(\frac{265}{342}\right)\) | \(e\left(\frac{61}{342}\right)\) |