Basic properties
| Modulus: | \(2672\) | |
| Conductor: | \(2672\) | 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 2672.u
\(\chi_{2672}(35,\cdot)\) \(\chi_{2672}(43,\cdot)\) \(\chi_{2672}(51,\cdot)\) \(\chi_{2672}(59,\cdot)\) \(\chi_{2672}(67,\cdot)\) \(\chi_{2672}(83,\cdot)\) \(\chi_{2672}(91,\cdot)\) \(\chi_{2672}(123,\cdot)\) \(\chi_{2672}(131,\cdot)\) \(\chi_{2672}(139,\cdot)\) \(\chi_{2672}(155,\cdot)\) \(\chi_{2672}(163,\cdot)\) \(\chi_{2672}(187,\cdot)\) \(\chi_{2672}(219,\cdot)\) \(\chi_{2672}(227,\cdot)\) \(\chi_{2672}(235,\cdot)\) \(\chi_{2672}(259,\cdot)\) \(\chi_{2672}(307,\cdot)\) \(\chi_{2672}(315,\cdot)\) \(\chi_{2672}(323,\cdot)\) \(\chi_{2672}(331,\cdot)\) \(\chi_{2672}(339,\cdot)\) \(\chi_{2672}(347,\cdot)\) \(\chi_{2672}(371,\cdot)\) \(\chi_{2672}(379,\cdot)\) \(\chi_{2672}(387,\cdot)\) \(\chi_{2672}(403,\cdot)\) \(\chi_{2672}(435,\cdot)\) \(\chi_{2672}(443,\cdot)\) \(\chi_{2672}(451,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{332})$ |
| Fixed field: | Number field defined by a degree 332 polynomial (not computed) |
Values on generators
\((335,2005,673)\) → \((-1,-i,e\left(\frac{9}{166}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 2672 }(227, a) \) | \(1\) | \(1\) | \(e\left(\frac{281}{332}\right)\) | \(e\left(\frac{267}{332}\right)\) | \(e\left(\frac{33}{83}\right)\) | \(e\left(\frac{115}{166}\right)\) | \(e\left(\frac{255}{332}\right)\) | \(e\left(\frac{277}{332}\right)\) | \(e\left(\frac{54}{83}\right)\) | \(e\left(\frac{145}{166}\right)\) | \(e\left(\frac{297}{332}\right)\) | \(e\left(\frac{81}{332}\right)\) |