Basic properties
| Modulus: | \(8016\) | |
| Conductor: | \(8016\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(332\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8016.bq
\(\chi_{8016}(11,\cdot)\) \(\chi_{8016}(107,\cdot)\) \(\chi_{8016}(179,\cdot)\) \(\chi_{8016}(203,\cdot)\) \(\chi_{8016}(251,\cdot)\) \(\chi_{8016}(275,\cdot)\) \(\chi_{8016}(299,\cdot)\) \(\chi_{8016}(395,\cdot)\) \(\chi_{8016}(419,\cdot)\) \(\chi_{8016}(467,\cdot)\) \(\chi_{8016}(491,\cdot)\) \(\chi_{8016}(515,\cdot)\) \(\chi_{8016}(539,\cdot)\) \(\chi_{8016}(563,\cdot)\) \(\chi_{8016}(731,\cdot)\) \(\chi_{8016}(755,\cdot)\) \(\chi_{8016}(851,\cdot)\) \(\chi_{8016}(899,\cdot)\) \(\chi_{8016}(923,\cdot)\) \(\chi_{8016}(947,\cdot)\) \(\chi_{8016}(1067,\cdot)\) \(\chi_{8016}(1091,\cdot)\) \(\chi_{8016}(1139,\cdot)\) \(\chi_{8016}(1187,\cdot)\) \(\chi_{8016}(1211,\cdot)\) \(\chi_{8016}(1235,\cdot)\) \(\chi_{8016}(1283,\cdot)\) \(\chi_{8016}(1331,\cdot)\) \(\chi_{8016}(1355,\cdot)\) \(\chi_{8016}(1451,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{332})$ |
| Fixed field: | Number field defined by a degree 332 polynomial (not computed) |
Values on generators
\((3007,2005,5345,673)\) → \((-1,i,-1,e\left(\frac{50}{83}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 8016 }(1451, a) \) | \(1\) | \(1\) | \(e\left(\frac{117}{332}\right)\) | \(e\left(\frac{7}{83}\right)\) | \(e\left(\frac{39}{332}\right)\) | \(e\left(\frac{265}{332}\right)\) | \(e\left(\frac{71}{166}\right)\) | \(e\left(\frac{63}{332}\right)\) | \(e\left(\frac{23}{166}\right)\) | \(e\left(\frac{117}{166}\right)\) | \(e\left(\frac{203}{332}\right)\) | \(e\left(\frac{119}{166}\right)\) |