Basic properties
| Modulus: | \(2001\) | |
| Conductor: | \(2001\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(154\) | 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.br
\(\chi_{2001}(5,\cdot)\) \(\chi_{2001}(38,\cdot)\) \(\chi_{2001}(80,\cdot)\) \(\chi_{2001}(122,\cdot)\) \(\chi_{2001}(125,\cdot)\) \(\chi_{2001}(149,\cdot)\) \(\chi_{2001}(158,\cdot)\) \(\chi_{2001}(212,\cdot)\) \(\chi_{2001}(245,\cdot)\) \(\chi_{2001}(296,\cdot)\) \(\chi_{2001}(332,\cdot)\) \(\chi_{2001}(341,\cdot)\) \(\chi_{2001}(383,\cdot)\) \(\chi_{2001}(410,\cdot)\) \(\chi_{2001}(419,\cdot)\) \(\chi_{2001}(428,\cdot)\) \(\chi_{2001}(470,\cdot)\) \(\chi_{2001}(497,\cdot)\) \(\chi_{2001}(527,\cdot)\) \(\chi_{2001}(557,\cdot)\) \(\chi_{2001}(701,\cdot)\) \(\chi_{2001}(734,\cdot)\) \(\chi_{2001}(776,\cdot)\) \(\chi_{2001}(845,\cdot)\) \(\chi_{2001}(908,\cdot)\) \(\chi_{2001}(941,\cdot)\) \(\chi_{2001}(950,\cdot)\) \(\chi_{2001}(962,\cdot)\) \(\chi_{2001}(1019,\cdot)\) \(\chi_{2001}(1049,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{77})$ |
| Fixed field: | Number field defined by a degree 154 polynomial (not computed) |
Values on generators
\((668,1132,553)\) → \((-1,e\left(\frac{9}{22}\right),e\left(\frac{13}{14}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 2001 }(80, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{77}\right)\) | \(e\left(\frac{38}{77}\right)\) | \(e\left(\frac{26}{77}\right)\) | \(e\left(\frac{141}{154}\right)\) | \(e\left(\frac{57}{77}\right)\) | \(e\left(\frac{45}{77}\right)\) | \(e\left(\frac{61}{154}\right)\) | \(e\left(\frac{34}{77}\right)\) | \(e\left(\frac{25}{154}\right)\) | \(e\left(\frac{76}{77}\right)\) |