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 \(\chi_{667}(7,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2001.bp
\(\chi_{2001}(7,\cdot)\) \(\chi_{2001}(103,\cdot)\) \(\chi_{2001}(112,\cdot)\) \(\chi_{2001}(136,\cdot)\) \(\chi_{2001}(181,\cdot)\) \(\chi_{2001}(199,\cdot)\) \(\chi_{2001}(226,\cdot)\) \(\chi_{2001}(268,\cdot)\) \(\chi_{2001}(286,\cdot)\) \(\chi_{2001}(310,\cdot)\) \(\chi_{2001}(313,\cdot)\) \(\chi_{2001}(343,\cdot)\) \(\chi_{2001}(355,\cdot)\) \(\chi_{2001}(364,\cdot)\) \(\chi_{2001}(373,\cdot)\) \(\chi_{2001}(442,\cdot)\) \(\chi_{2001}(451,\cdot)\) \(\chi_{2001}(517,\cdot)\) \(\chi_{2001}(571,\cdot)\) \(\chi_{2001}(658,\cdot)\) \(\chi_{2001}(661,\cdot)\) \(\chi_{2001}(778,\cdot)\) \(\chi_{2001}(799,\cdot)\) \(\chi_{2001}(835,\cdot)\) \(\chi_{2001}(865,\cdot)\) \(\chi_{2001}(895,\cdot)\) \(\chi_{2001}(964,\cdot)\) \(\chi_{2001}(973,\cdot)\) \(\chi_{2001}(1006,\cdot)\) \(\chi_{2001}(1009,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{77})$ |
| Fixed field: | Number field defined by a degree 154 polynomial (not computed) |
Values on generators
\((668,1132,553)\) → \((1,e\left(\frac{19}{22}\right),e\left(\frac{3}{7}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 2001 }(7, a) \) | \(-1\) | \(1\) | \(e\left(\frac{12}{77}\right)\) | \(e\left(\frac{24}{77}\right)\) | \(e\left(\frac{45}{154}\right)\) | \(e\left(\frac{85}{154}\right)\) | \(e\left(\frac{36}{77}\right)\) | \(e\left(\frac{69}{154}\right)\) | \(e\left(\frac{75}{154}\right)\) | \(e\left(\frac{62}{77}\right)\) | \(e\left(\frac{109}{154}\right)\) | \(e\left(\frac{48}{77}\right)\) |