Basic properties
| Modulus: | \(6498\) | |
| Conductor: | \(3249\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(171\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{3249}(25,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6498.cb
\(\chi_{6498}(25,\cdot)\) \(\chi_{6498}(61,\cdot)\) \(\chi_{6498}(157,\cdot)\) \(\chi_{6498}(283,\cdot)\) \(\chi_{6498}(301,\cdot)\) \(\chi_{6498}(313,\cdot)\) \(\chi_{6498}(367,\cdot)\) \(\chi_{6498}(403,\cdot)\) \(\chi_{6498}(499,\cdot)\) \(\chi_{6498}(625,\cdot)\) \(\chi_{6498}(643,\cdot)\) \(\chi_{6498}(655,\cdot)\) \(\chi_{6498}(709,\cdot)\) \(\chi_{6498}(745,\cdot)\) \(\chi_{6498}(841,\cdot)\) \(\chi_{6498}(985,\cdot)\) \(\chi_{6498}(997,\cdot)\) \(\chi_{6498}(1051,\cdot)\) \(\chi_{6498}(1087,\cdot)\) \(\chi_{6498}(1183,\cdot)\) \(\chi_{6498}(1309,\cdot)\) \(\chi_{6498}(1327,\cdot)\) \(\chi_{6498}(1339,\cdot)\) \(\chi_{6498}(1393,\cdot)\) \(\chi_{6498}(1429,\cdot)\) \(\chi_{6498}(1525,\cdot)\) \(\chi_{6498}(1651,\cdot)\) \(\chi_{6498}(1669,\cdot)\) \(\chi_{6498}(1681,\cdot)\) \(\chi_{6498}(1735,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{171})$ |
| Fixed field: | Number field defined by a degree 171 polynomial (not computed) |
Values on generators
\((3611,6139)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{61}{171}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 6498 }(25, a) \) | \(1\) | \(1\) | \(e\left(\frac{16}{171}\right)\) | \(e\left(\frac{10}{57}\right)\) | \(e\left(\frac{1}{19}\right)\) | \(e\left(\frac{119}{171}\right)\) | \(e\left(\frac{106}{171}\right)\) | \(e\left(\frac{71}{171}\right)\) | \(e\left(\frac{32}{171}\right)\) | \(e\left(\frac{125}{171}\right)\) | \(e\left(\frac{8}{19}\right)\) | \(e\left(\frac{46}{171}\right)\) |