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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2672.v
\(\chi_{2672}(3,\cdot)\) \(\chi_{2672}(11,\cdot)\) \(\chi_{2672}(19,\cdot)\) \(\chi_{2672}(27,\cdot)\) \(\chi_{2672}(75,\cdot)\) \(\chi_{2672}(99,\cdot)\) \(\chi_{2672}(107,\cdot)\) \(\chi_{2672}(115,\cdot)\) \(\chi_{2672}(147,\cdot)\) \(\chi_{2672}(171,\cdot)\) \(\chi_{2672}(179,\cdot)\) \(\chi_{2672}(195,\cdot)\) \(\chi_{2672}(203,\cdot)\) \(\chi_{2672}(211,\cdot)\) \(\chi_{2672}(243,\cdot)\) \(\chi_{2672}(251,\cdot)\) \(\chi_{2672}(267,\cdot)\) \(\chi_{2672}(275,\cdot)\) \(\chi_{2672}(283,\cdot)\) \(\chi_{2672}(291,\cdot)\) \(\chi_{2672}(299,\cdot)\) \(\chi_{2672}(355,\cdot)\) \(\chi_{2672}(363,\cdot)\) \(\chi_{2672}(395,\cdot)\) \(\chi_{2672}(411,\cdot)\) \(\chi_{2672}(419,\cdot)\) \(\chi_{2672}(427,\cdot)\) \(\chi_{2672}(467,\cdot)\) \(\chi_{2672}(475,\cdot)\) \(\chi_{2672}(491,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{332})$ |
| Fixed field: | Number field defined by a degree 332 polynomial (not computed) |
Values on generators
\((335,2005,673)\) → \((-1,i,e\left(\frac{25}{83}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 2672 }(1435, a) \) | \(-1\) | \(1\) | \(e\left(\frac{187}{332}\right)\) | \(e\left(\frac{183}{332}\right)\) | \(e\left(\frac{45}{83}\right)\) | \(e\left(\frac{21}{166}\right)\) | \(e\left(\frac{61}{332}\right)\) | \(e\left(\frac{257}{332}\right)\) | \(e\left(\frac{19}{166}\right)\) | \(e\left(\frac{80}{83}\right)\) | \(e\left(\frac{239}{332}\right)\) | \(e\left(\frac{35}{332}\right)\) |