Basic properties
| Modulus: | \(8664\) | |
| Conductor: | \(2888\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(342\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2888}(67,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8664.dj
\(\chi_{8664}(67,\cdot)\) \(\chi_{8664}(91,\cdot)\) \(\chi_{8664}(211,\cdot)\) \(\chi_{8664}(355,\cdot)\) \(\chi_{8664}(451,\cdot)\) \(\chi_{8664}(523,\cdot)\) \(\chi_{8664}(547,\cdot)\) \(\chi_{8664}(667,\cdot)\) \(\chi_{8664}(763,\cdot)\) \(\chi_{8664}(811,\cdot)\) \(\chi_{8664}(907,\cdot)\) \(\chi_{8664}(979,\cdot)\) \(\chi_{8664}(1003,\cdot)\) \(\chi_{8664}(1123,\cdot)\) \(\chi_{8664}(1219,\cdot)\) \(\chi_{8664}(1267,\cdot)\) \(\chi_{8664}(1363,\cdot)\) \(\chi_{8664}(1435,\cdot)\) \(\chi_{8664}(1459,\cdot)\) \(\chi_{8664}(1579,\cdot)\) \(\chi_{8664}(1675,\cdot)\) \(\chi_{8664}(1723,\cdot)\) \(\chi_{8664}(1819,\cdot)\) \(\chi_{8664}(1891,\cdot)\) \(\chi_{8664}(1915,\cdot)\) \(\chi_{8664}(2035,\cdot)\) \(\chi_{8664}(2131,\cdot)\) \(\chi_{8664}(2179,\cdot)\) \(\chi_{8664}(2275,\cdot)\) \(\chi_{8664}(2347,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{171})$ |
| Fixed field: | Number field defined by a degree 342 polynomial (not computed) |
Values on generators
\((2167,4333,5777,8305)\) → \((-1,-1,1,e\left(\frac{269}{342}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 8664 }(67, a) \) | \(1\) | \(1\) | \(e\left(\frac{335}{342}\right)\) | \(e\left(\frac{55}{114}\right)\) | \(e\left(\frac{13}{57}\right)\) | \(e\left(\frac{47}{171}\right)\) | \(e\left(\frac{130}{171}\right)\) | \(e\left(\frac{115}{342}\right)\) | \(e\left(\frac{164}{171}\right)\) | \(e\left(\frac{149}{171}\right)\) | \(e\left(\frac{47}{57}\right)\) | \(e\left(\frac{79}{171}\right)\) |