Basic properties
| Modulus: | \(2001\) | |
| Conductor: | \(667\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(154\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{667}(34,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2001.bl
\(\chi_{2001}(34,\cdot)\) \(\chi_{2001}(67,\cdot)\) \(\chi_{2001}(109,\cdot)\) \(\chi_{2001}(178,\cdot)\) \(\chi_{2001}(241,\cdot)\) \(\chi_{2001}(274,\cdot)\) \(\chi_{2001}(283,\cdot)\) \(\chi_{2001}(295,\cdot)\) \(\chi_{2001}(352,\cdot)\) \(\chi_{2001}(382,\cdot)\) \(\chi_{2001}(412,\cdot)\) \(\chi_{2001}(448,\cdot)\) \(\chi_{2001}(457,\cdot)\) \(\chi_{2001}(502,\cdot)\) \(\chi_{2001}(526,\cdot)\) \(\chi_{2001}(544,\cdot)\) \(\chi_{2001}(586,\cdot)\) \(\chi_{2001}(589,\cdot)\) \(\chi_{2001}(613,\cdot)\) \(\chi_{2001}(631,\cdot)\) \(\chi_{2001}(700,\cdot)\) \(\chi_{2001}(709,\cdot)\) \(\chi_{2001}(718,\cdot)\) \(\chi_{2001}(730,\cdot)\) \(\chi_{2001}(787,\cdot)\) \(\chi_{2001}(796,\cdot)\) \(\chi_{2001}(847,\cdot)\) \(\chi_{2001}(904,\cdot)\) \(\chi_{2001}(934,\cdot)\) \(\chi_{2001}(937,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{77})$ |
| Fixed field: | Number field defined by a degree 154 polynomial (not computed) |
Values on generators
\((668,1132,553)\) → \((1,e\left(\frac{9}{22}\right),e\left(\frac{11}{14}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 2001 }(34, a) \) | \(-1\) | \(1\) | \(e\left(\frac{93}{154}\right)\) | \(e\left(\frac{16}{77}\right)\) | \(e\left(\frac{107}{154}\right)\) | \(e\left(\frac{31}{154}\right)\) | \(e\left(\frac{125}{154}\right)\) | \(e\left(\frac{23}{77}\right)\) | \(e\left(\frac{25}{77}\right)\) | \(e\left(\frac{67}{77}\right)\) | \(e\left(\frac{62}{77}\right)\) | \(e\left(\frac{32}{77}\right)\) |