Basic properties
| Modulus: | \(5929\) | |
| Conductor: | \(5929\) | 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 5929.br
\(\chi_{5929}(76,\cdot)\) \(\chi_{5929}(153,\cdot)\) \(\chi_{5929}(230,\cdot)\) \(\chi_{5929}(307,\cdot)\) \(\chi_{5929}(384,\cdot)\) \(\chi_{5929}(461,\cdot)\) \(\chi_{5929}(615,\cdot)\) \(\chi_{5929}(692,\cdot)\) \(\chi_{5929}(769,\cdot)\) \(\chi_{5929}(923,\cdot)\) \(\chi_{5929}(1000,\cdot)\) \(\chi_{5929}(1154,\cdot)\) \(\chi_{5929}(1231,\cdot)\) \(\chi_{5929}(1308,\cdot)\) \(\chi_{5929}(1385,\cdot)\) \(\chi_{5929}(1462,\cdot)\) \(\chi_{5929}(1539,\cdot)\) \(\chi_{5929}(1770,\cdot)\) \(\chi_{5929}(1847,\cdot)\) \(\chi_{5929}(1924,\cdot)\) \(\chi_{5929}(2001,\cdot)\) \(\chi_{5929}(2078,\cdot)\) \(\chi_{5929}(2232,\cdot)\) \(\chi_{5929}(2309,\cdot)\) \(\chi_{5929}(2386,\cdot)\) \(\chi_{5929}(2463,\cdot)\) \(\chi_{5929}(2617,\cdot)\) \(\chi_{5929}(2771,\cdot)\) \(\chi_{5929}(2848,\cdot)\) \(\chi_{5929}(2925,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{77})$ |
| Fixed field: | Number field defined by a degree 154 polynomial (not computed) |
Values on generators
\((1816,2059)\) → \((e\left(\frac{1}{14}\right),e\left(\frac{17}{22}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(12\) | \(13\) |
| \( \chi_{ 5929 }(76, a) \) | \(1\) | \(1\) | \(e\left(\frac{97}{154}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{20}{77}\right)\) | \(e\left(\frac{39}{154}\right)\) | \(e\left(\frac{54}{77}\right)\) | \(e\left(\frac{137}{154}\right)\) | \(e\left(\frac{1}{7}\right)\) | \(e\left(\frac{68}{77}\right)\) | \(e\left(\frac{51}{154}\right)\) | \(e\left(\frac{31}{77}\right)\) |