Basic properties
| Modulus: | \(5415\) | |
| Conductor: | \(1805\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(342\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1805}(4,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5415.ck
\(\chi_{5415}(4,\cdot)\) \(\chi_{5415}(139,\cdot)\) \(\chi_{5415}(169,\cdot)\) \(\chi_{5415}(199,\cdot)\) \(\chi_{5415}(214,\cdot)\) \(\chi_{5415}(244,\cdot)\) \(\chi_{5415}(289,\cdot)\) \(\chi_{5415}(424,\cdot)\) \(\chi_{5415}(454,\cdot)\) \(\chi_{5415}(484,\cdot)\) \(\chi_{5415}(499,\cdot)\) \(\chi_{5415}(529,\cdot)\) \(\chi_{5415}(574,\cdot)\) \(\chi_{5415}(709,\cdot)\) \(\chi_{5415}(739,\cdot)\) \(\chi_{5415}(769,\cdot)\) \(\chi_{5415}(814,\cdot)\) \(\chi_{5415}(859,\cdot)\) \(\chi_{5415}(994,\cdot)\) \(\chi_{5415}(1024,\cdot)\) \(\chi_{5415}(1054,\cdot)\) \(\chi_{5415}(1069,\cdot)\) \(\chi_{5415}(1099,\cdot)\) \(\chi_{5415}(1144,\cdot)\) \(\chi_{5415}(1279,\cdot)\) \(\chi_{5415}(1309,\cdot)\) \(\chi_{5415}(1339,\cdot)\) \(\chi_{5415}(1354,\cdot)\) \(\chi_{5415}(1384,\cdot)\) \(\chi_{5415}(1429,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{171})$ |
| Fixed field: | Number field defined by a degree 342 polynomial (not computed) |
Values on generators
\((3611,2167,5056)\) → \((1,-1,e\left(\frac{1}{171}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(22\) |
| \( \chi_{ 5415 }(4, a) \) | \(1\) | \(1\) | \(e\left(\frac{173}{342}\right)\) | \(e\left(\frac{2}{171}\right)\) | \(e\left(\frac{43}{114}\right)\) | \(e\left(\frac{59}{114}\right)\) | \(e\left(\frac{34}{57}\right)\) | \(e\left(\frac{145}{342}\right)\) | \(e\left(\frac{151}{171}\right)\) | \(e\left(\frac{4}{171}\right)\) | \(e\left(\frac{281}{342}\right)\) | \(e\left(\frac{35}{342}\right)\) |