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 \(\chi_{667}(433,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2001.bu
\(\chi_{2001}(10,\cdot)\) \(\chi_{2001}(19,\cdot)\) \(\chi_{2001}(37,\cdot)\) \(\chi_{2001}(40,\cdot)\) \(\chi_{2001}(43,\cdot)\) \(\chi_{2001}(61,\cdot)\) \(\chi_{2001}(76,\cdot)\) \(\chi_{2001}(79,\cdot)\) \(\chi_{2001}(97,\cdot)\) \(\chi_{2001}(106,\cdot)\) \(\chi_{2001}(130,\cdot)\) \(\chi_{2001}(148,\cdot)\) \(\chi_{2001}(166,\cdot)\) \(\chi_{2001}(172,\cdot)\) \(\chi_{2001}(205,\cdot)\) \(\chi_{2001}(214,\cdot)\) \(\chi_{2001}(217,\cdot)\) \(\chi_{2001}(235,\cdot)\) \(\chi_{2001}(247,\cdot)\) \(\chi_{2001}(250,\cdot)\) \(\chi_{2001}(304,\cdot)\) \(\chi_{2001}(316,\cdot)\) \(\chi_{2001}(337,\cdot)\) \(\chi_{2001}(379,\cdot)\) \(\chi_{2001}(385,\cdot)\) \(\chi_{2001}(388,\cdot)\) \(\chi_{2001}(421,\cdot)\) \(\chi_{2001}(424,\cdot)\) \(\chi_{2001}(433,\cdot)\) \(\chi_{2001}(454,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{308})$ |
Fixed field: | Number field defined by a degree 308 polynomial (not computed) |
Values on generators
\((668,1132,553)\) → \((1,e\left(\frac{15}{22}\right),e\left(\frac{15}{28}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 2001 }(433, a) \) | \(1\) | \(1\) | \(e\left(\frac{277}{308}\right)\) | \(e\left(\frac{123}{154}\right)\) | \(e\left(\frac{36}{77}\right)\) | \(e\left(\frac{59}{154}\right)\) | \(e\left(\frac{215}{308}\right)\) | \(e\left(\frac{113}{308}\right)\) | \(e\left(\frac{163}{308}\right)\) | \(e\left(\frac{29}{154}\right)\) | \(e\left(\frac{87}{308}\right)\) | \(e\left(\frac{46}{77}\right)\) |