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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2001.bv
\(\chi_{2001}(2,\cdot)\) \(\chi_{2001}(8,\cdot)\) \(\chi_{2001}(26,\cdot)\) \(\chi_{2001}(32,\cdot)\) \(\chi_{2001}(50,\cdot)\) \(\chi_{2001}(77,\cdot)\) \(\chi_{2001}(95,\cdot)\) \(\chi_{2001}(98,\cdot)\) \(\chi_{2001}(101,\cdot)\) \(\chi_{2001}(119,\cdot)\) \(\chi_{2001}(131,\cdot)\) \(\chi_{2001}(164,\cdot)\) \(\chi_{2001}(188,\cdot)\) \(\chi_{2001}(200,\cdot)\) \(\chi_{2001}(242,\cdot)\) \(\chi_{2001}(269,\cdot)\) \(\chi_{2001}(305,\cdot)\) \(\chi_{2001}(308,\cdot)\) \(\chi_{2001}(311,\cdot)\) \(\chi_{2001}(317,\cdot)\) \(\chi_{2001}(338,\cdot)\) \(\chi_{2001}(374,\cdot)\) \(\chi_{2001}(380,\cdot)\) \(\chi_{2001}(395,\cdot)\) \(\chi_{2001}(404,\cdot)\) \(\chi_{2001}(416,\cdot)\) \(\chi_{2001}(443,\cdot)\) \(\chi_{2001}(446,\cdot)\) \(\chi_{2001}(449,\cdot)\) \(\chi_{2001}(485,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{308})$ |
Fixed field: | Number field defined by a degree 308 polynomial (not computed) |
Values on generators
\((668,1132,553)\) → \((-1,e\left(\frac{5}{11}\right),e\left(\frac{15}{28}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 2001 }(1274, a) \) | \(1\) | \(1\) | \(e\left(\frac{291}{308}\right)\) | \(e\left(\frac{137}{154}\right)\) | \(e\left(\frac{57}{77}\right)\) | \(e\left(\frac{5}{77}\right)\) | \(e\left(\frac{257}{308}\right)\) | \(e\left(\frac{211}{308}\right)\) | \(e\left(\frac{303}{308}\right)\) | \(e\left(\frac{1}{154}\right)\) | \(e\left(\frac{3}{308}\right)\) | \(e\left(\frac{60}{77}\right)\) |