Basic properties
| Modulus: | \(8016\) | |
| Conductor: | \(2672\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(332\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2672}(1435,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8016.bp
\(\chi_{8016}(19,\cdot)\) \(\chi_{8016}(115,\cdot)\) \(\chi_{8016}(211,\cdot)\) \(\chi_{8016}(283,\cdot)\) \(\chi_{8016}(355,\cdot)\) \(\chi_{8016}(427,\cdot)\) \(\chi_{8016}(475,\cdot)\) \(\chi_{8016}(523,\cdot)\) \(\chi_{8016}(595,\cdot)\) \(\chi_{8016}(715,\cdot)\) \(\chi_{8016}(859,\cdot)\) \(\chi_{8016}(883,\cdot)\) \(\chi_{8016}(907,\cdot)\) \(\chi_{8016}(931,\cdot)\) \(\chi_{8016}(979,\cdot)\) \(\chi_{8016}(1027,\cdot)\) \(\chi_{8016}(1051,\cdot)\) \(\chi_{8016}(1099,\cdot)\) \(\chi_{8016}(1123,\cdot)\) \(\chi_{8016}(1171,\cdot)\) \(\chi_{8016}(1219,\cdot)\) \(\chi_{8016}(1267,\cdot)\) \(\chi_{8016}(1291,\cdot)\) \(\chi_{8016}(1339,\cdot)\) \(\chi_{8016}(1363,\cdot)\) \(\chi_{8016}(1411,\cdot)\) \(\chi_{8016}(1435,\cdot)\) \(\chi_{8016}(1483,\cdot)\) \(\chi_{8016}(1507,\cdot)\) \(\chi_{8016}(1531,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{332})$ |
| Fixed field: | Number field defined by a degree 332 polynomial (not computed) |
Values on generators
\((3007,2005,5345,673)\) → \((-1,i,1,e\left(\frac{25}{83}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 8016 }(1435, a) \) | \(-1\) | \(1\) | \(e\left(\frac{183}{332}\right)\) | \(e\left(\frac{45}{83}\right)\) | \(e\left(\frac{61}{332}\right)\) | \(e\left(\frac{257}{332}\right)\) | \(e\left(\frac{80}{83}\right)\) | \(e\left(\frac{239}{332}\right)\) | \(e\left(\frac{68}{83}\right)\) | \(e\left(\frac{17}{166}\right)\) | \(e\left(\frac{309}{332}\right)\) | \(e\left(\frac{101}{166}\right)\) |