Basic properties
Modulus: | \(2001\) | |
Conductor: | \(2001\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(308\) | 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 2001.bs
\(\chi_{2001}(11,\cdot)\) \(\chi_{2001}(14,\cdot)\) \(\chi_{2001}(44,\cdot)\) \(\chi_{2001}(56,\cdot)\) \(\chi_{2001}(89,\cdot)\) \(\chi_{2001}(113,\cdot)\) \(\chi_{2001}(134,\cdot)\) \(\chi_{2001}(143,\cdot)\) \(\chi_{2001}(155,\cdot)\) \(\chi_{2001}(176,\cdot)\) \(\chi_{2001}(182,\cdot)\) \(\chi_{2001}(218,\cdot)\) \(\chi_{2001}(221,\cdot)\) \(\chi_{2001}(224,\cdot)\) \(\chi_{2001}(251,\cdot)\) \(\chi_{2001}(263,\cdot)\) \(\chi_{2001}(272,\cdot)\) \(\chi_{2001}(287,\cdot)\) \(\chi_{2001}(293,\cdot)\) \(\chi_{2001}(329,\cdot)\) \(\chi_{2001}(350,\cdot)\) \(\chi_{2001}(356,\cdot)\) \(\chi_{2001}(359,\cdot)\) \(\chi_{2001}(362,\cdot)\) \(\chi_{2001}(398,\cdot)\) \(\chi_{2001}(425,\cdot)\) \(\chi_{2001}(467,\cdot)\) \(\chi_{2001}(479,\cdot)\) \(\chi_{2001}(503,\cdot)\) \(\chi_{2001}(536,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{308})$ |
Fixed field: | Number field defined by a degree 308 polynomial (not computed) |
Values on generators
\((668,1132,553)\) → \((-1,e\left(\frac{21}{22}\right),e\left(\frac{13}{28}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 2001 }(14, a) \) | \(-1\) | \(1\) | \(e\left(\frac{269}{308}\right)\) | \(e\left(\frac{115}{154}\right)\) | \(e\left(\frac{103}{154}\right)\) | \(e\left(\frac{109}{154}\right)\) | \(e\left(\frac{191}{308}\right)\) | \(e\left(\frac{167}{308}\right)\) | \(e\left(\frac{215}{308}\right)\) | \(e\left(\frac{111}{154}\right)\) | \(e\left(\frac{179}{308}\right)\) | \(e\left(\frac{38}{77}\right)\) |