Basic properties
| Modulus: | \(4332\) | |
| Conductor: | \(1444\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(342\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1444}(67,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4332.bq
\(\chi_{4332}(67,\cdot)\) \(\chi_{4332}(79,\cdot)\) \(\chi_{4332}(91,\cdot)\) \(\chi_{4332}(211,\cdot)\) \(\chi_{4332}(223,\cdot)\) \(\chi_{4332}(295,\cdot)\) \(\chi_{4332}(319,\cdot)\) \(\chi_{4332}(355,\cdot)\) \(\chi_{4332}(439,\cdot)\) \(\chi_{4332}(451,\cdot)\) \(\chi_{4332}(523,\cdot)\) \(\chi_{4332}(535,\cdot)\) \(\chi_{4332}(547,\cdot)\) \(\chi_{4332}(583,\cdot)\) \(\chi_{4332}(667,\cdot)\) \(\chi_{4332}(679,\cdot)\) \(\chi_{4332}(751,\cdot)\) \(\chi_{4332}(763,\cdot)\) \(\chi_{4332}(775,\cdot)\) \(\chi_{4332}(811,\cdot)\) \(\chi_{4332}(895,\cdot)\) \(\chi_{4332}(907,\cdot)\) \(\chi_{4332}(979,\cdot)\) \(\chi_{4332}(991,\cdot)\) \(\chi_{4332}(1003,\cdot)\) \(\chi_{4332}(1039,\cdot)\) \(\chi_{4332}(1123,\cdot)\) \(\chi_{4332}(1135,\cdot)\) \(\chi_{4332}(1207,\cdot)\) \(\chi_{4332}(1219,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{171})$ |
| Fixed field: | Number field defined by a degree 342 polynomial (not computed) |
Values on generators
\((2167,1445,3973)\) → \((-1,1,e\left(\frac{269}{342}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 4332 }(67, a) \) | \(1\) | \(1\) | \(e\left(\frac{82}{171}\right)\) | \(e\left(\frac{55}{114}\right)\) | \(e\left(\frac{83}{114}\right)\) | \(e\left(\frac{265}{342}\right)\) | \(e\left(\frac{130}{171}\right)\) | \(e\left(\frac{115}{342}\right)\) | \(e\left(\frac{164}{171}\right)\) | \(e\left(\frac{127}{342}\right)\) | \(e\left(\frac{47}{57}\right)\) | \(e\left(\frac{329}{342}\right)\) |