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 \(\chi_{2888}(85,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8664.do
\(\chi_{8664}(61,\cdot)\) \(\chi_{8664}(85,\cdot)\) \(\chi_{8664}(157,\cdot)\) \(\chi_{8664}(253,\cdot)\) \(\chi_{8664}(301,\cdot)\) \(\chi_{8664}(397,\cdot)\) \(\chi_{8664}(517,\cdot)\) \(\chi_{8664}(541,\cdot)\) \(\chi_{8664}(613,\cdot)\) \(\chi_{8664}(709,\cdot)\) \(\chi_{8664}(757,\cdot)\) \(\chi_{8664}(853,\cdot)\) \(\chi_{8664}(973,\cdot)\) \(\chi_{8664}(997,\cdot)\) \(\chi_{8664}(1069,\cdot)\) \(\chi_{8664}(1165,\cdot)\) \(\chi_{8664}(1213,\cdot)\) \(\chi_{8664}(1309,\cdot)\) \(\chi_{8664}(1429,\cdot)\) \(\chi_{8664}(1453,\cdot)\) \(\chi_{8664}(1525,\cdot)\) \(\chi_{8664}(1621,\cdot)\) \(\chi_{8664}(1669,\cdot)\) \(\chi_{8664}(1765,\cdot)\) \(\chi_{8664}(1885,\cdot)\) \(\chi_{8664}(1909,\cdot)\) \(\chi_{8664}(1981,\cdot)\) \(\chi_{8664}(2077,\cdot)\) \(\chi_{8664}(2125,\cdot)\) \(\chi_{8664}(2221,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{171})$ |
| Fixed field: | Number field defined by a degree 342 polynomial (not computed) |
Values on generators
\((2167,4333,5777,8305)\) → \((1,-1,1,e\left(\frac{58}{171}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 8664 }(85, a) \) | \(1\) | \(1\) | \(e\left(\frac{65}{342}\right)\) | \(e\left(\frac{50}{57}\right)\) | \(e\left(\frac{11}{114}\right)\) | \(e\left(\frac{31}{342}\right)\) | \(e\left(\frac{112}{171}\right)\) | \(e\left(\frac{89}{171}\right)\) | \(e\left(\frac{65}{171}\right)\) | \(e\left(\frac{91}{342}\right)\) | \(e\left(\frac{44}{57}\right)\) | \(e\left(\frac{23}{342}\right)\) |