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 \(\chi_{2672}(1195,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8016.br
\(\chi_{8016}(43,\cdot)\) \(\chi_{8016}(67,\cdot)\) \(\chi_{8016}(91,\cdot)\) \(\chi_{8016}(139,\cdot)\) \(\chi_{8016}(163,\cdot)\) \(\chi_{8016}(187,\cdot)\) \(\chi_{8016}(235,\cdot)\) \(\chi_{8016}(259,\cdot)\) \(\chi_{8016}(307,\cdot)\) \(\chi_{8016}(331,\cdot)\) \(\chi_{8016}(379,\cdot)\) \(\chi_{8016}(403,\cdot)\) \(\chi_{8016}(451,\cdot)\) \(\chi_{8016}(499,\cdot)\) \(\chi_{8016}(547,\cdot)\) \(\chi_{8016}(571,\cdot)\) \(\chi_{8016}(619,\cdot)\) \(\chi_{8016}(643,\cdot)\) \(\chi_{8016}(691,\cdot)\) \(\chi_{8016}(739,\cdot)\) \(\chi_{8016}(763,\cdot)\) \(\chi_{8016}(787,\cdot)\) \(\chi_{8016}(811,\cdot)\) \(\chi_{8016}(955,\cdot)\) \(\chi_{8016}(1075,\cdot)\) \(\chi_{8016}(1147,\cdot)\) \(\chi_{8016}(1195,\cdot)\) \(\chi_{8016}(1243,\cdot)\) \(\chi_{8016}(1315,\cdot)\) \(\chi_{8016}(1387,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{332})$ |
| Fixed field: | Number field defined by a degree 332 polynomial (not computed) |
Values on generators
\((3007,2005,5345,673)\) → \((-1,i,1,e\left(\frac{143}{166}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 8016 }(1195, a) \) | \(1\) | \(1\) | \(e\left(\frac{37}{332}\right)\) | \(e\left(\frac{54}{83}\right)\) | \(e\left(\frac{289}{332}\right)\) | \(e\left(\frac{159}{332}\right)\) | \(e\left(\frac{109}{166}\right)\) | \(e\left(\frac{71}{332}\right)\) | \(e\left(\frac{47}{166}\right)\) | \(e\left(\frac{37}{166}\right)\) | \(e\left(\frac{321}{332}\right)\) | \(e\left(\frac{5}{166}\right)\) |