Basic properties
| Modulus: | \(8664\) | |
| Conductor: | \(8664\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(342\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8664.df
\(\chi_{8664}(59,\cdot)\) \(\chi_{8664}(155,\cdot)\) \(\chi_{8664}(203,\cdot)\) \(\chi_{8664}(371,\cdot)\) \(\chi_{8664}(395,\cdot)\) \(\chi_{8664}(515,\cdot)\) \(\chi_{8664}(611,\cdot)\) \(\chi_{8664}(659,\cdot)\) \(\chi_{8664}(755,\cdot)\) \(\chi_{8664}(827,\cdot)\) \(\chi_{8664}(851,\cdot)\) \(\chi_{8664}(971,\cdot)\) \(\chi_{8664}(1067,\cdot)\) \(\chi_{8664}(1115,\cdot)\) \(\chi_{8664}(1211,\cdot)\) \(\chi_{8664}(1283,\cdot)\) \(\chi_{8664}(1307,\cdot)\) \(\chi_{8664}(1427,\cdot)\) \(\chi_{8664}(1523,\cdot)\) \(\chi_{8664}(1667,\cdot)\) \(\chi_{8664}(1739,\cdot)\) \(\chi_{8664}(1763,\cdot)\) \(\chi_{8664}(1883,\cdot)\) \(\chi_{8664}(1979,\cdot)\) \(\chi_{8664}(2027,\cdot)\) \(\chi_{8664}(2123,\cdot)\) \(\chi_{8664}(2195,\cdot)\) \(\chi_{8664}(2219,\cdot)\) \(\chi_{8664}(2339,\cdot)\) \(\chi_{8664}(2435,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{171})$ |
| Fixed field: | Number field defined by a degree 342 polynomial (not computed) |
Values on generators
\((2167,4333,5777,8305)\) → \((-1,-1,-1,e\left(\frac{181}{342}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 8664 }(59, a) \) | \(-1\) | \(1\) | \(e\left(\frac{134}{171}\right)\) | \(e\left(\frac{101}{114}\right)\) | \(e\left(\frac{55}{114}\right)\) | \(e\left(\frac{106}{171}\right)\) | \(e\left(\frac{37}{342}\right)\) | \(e\left(\frac{46}{171}\right)\) | \(e\left(\frac{97}{171}\right)\) | \(e\left(\frac{341}{342}\right)\) | \(e\left(\frac{49}{57}\right)\) | \(e\left(\frac{229}{342}\right)\) |