Basic properties
| Modulus: | \(2001\) | |
| Conductor: | \(667\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(308\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{667}(31,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2001.bt
\(\chi_{2001}(31,\cdot)\) \(\chi_{2001}(55,\cdot)\) \(\chi_{2001}(73,\cdot)\) \(\chi_{2001}(85,\cdot)\) \(\chi_{2001}(118,\cdot)\) \(\chi_{2001}(124,\cdot)\) \(\chi_{2001}(127,\cdot)\) \(\chi_{2001}(142,\cdot)\) \(\chi_{2001}(163,\cdot)\) \(\chi_{2001}(193,\cdot)\) \(\chi_{2001}(211,\cdot)\) \(\chi_{2001}(259,\cdot)\) \(\chi_{2001}(271,\cdot)\) \(\chi_{2001}(280,\cdot)\) \(\chi_{2001}(292,\cdot)\) \(\chi_{2001}(301,\cdot)\) \(\chi_{2001}(334,\cdot)\) \(\chi_{2001}(340,\cdot)\) \(\chi_{2001}(358,\cdot)\) \(\chi_{2001}(403,\cdot)\) \(\chi_{2001}(409,\cdot)\) \(\chi_{2001}(427,\cdot)\) \(\chi_{2001}(445,\cdot)\) \(\chi_{2001}(466,\cdot)\) \(\chi_{2001}(472,\cdot)\) \(\chi_{2001}(478,\cdot)\) \(\chi_{2001}(496,\cdot)\) \(\chi_{2001}(508,\cdot)\) \(\chi_{2001}(514,\cdot)\) \(\chi_{2001}(532,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{308})$ |
| Fixed field: | Number field defined by a degree 308 polynomial (not computed) |
Values on generators
\((668,1132,553)\) → \((1,e\left(\frac{3}{11}\right),e\left(\frac{1}{28}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 2001 }(31, a) \) | \(-1\) | \(1\) | \(e\left(\frac{179}{308}\right)\) | \(e\left(\frac{25}{154}\right)\) | \(e\left(\frac{9}{154}\right)\) | \(e\left(\frac{47}{77}\right)\) | \(e\left(\frac{229}{308}\right)\) | \(e\left(\frac{197}{308}\right)\) | \(e\left(\frac{107}{308}\right)\) | \(e\left(\frac{71}{154}\right)\) | \(e\left(\frac{59}{308}\right)\) | \(e\left(\frac{25}{77}\right)\) |