Basic properties
| Modulus: | \(5929\) | |
| Conductor: | \(5929\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(770\) | 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.cg
\(\chi_{5929}(6,\cdot)\) \(\chi_{5929}(13,\cdot)\) \(\chi_{5929}(41,\cdot)\) \(\chi_{5929}(62,\cdot)\) \(\chi_{5929}(83,\cdot)\) \(\chi_{5929}(90,\cdot)\) \(\chi_{5929}(139,\cdot)\) \(\chi_{5929}(160,\cdot)\) \(\chi_{5929}(167,\cdot)\) \(\chi_{5929}(216,\cdot)\) \(\chi_{5929}(237,\cdot)\) \(\chi_{5929}(272,\cdot)\) \(\chi_{5929}(314,\cdot)\) \(\chi_{5929}(321,\cdot)\) \(\chi_{5929}(349,\cdot)\) \(\chi_{5929}(370,\cdot)\) \(\chi_{5929}(398,\cdot)\) \(\chi_{5929}(426,\cdot)\) \(\chi_{5929}(447,\cdot)\) \(\chi_{5929}(468,\cdot)\) \(\chi_{5929}(503,\cdot)\) \(\chi_{5929}(545,\cdot)\) \(\chi_{5929}(552,\cdot)\) \(\chi_{5929}(580,\cdot)\) \(\chi_{5929}(601,\cdot)\) \(\chi_{5929}(622,\cdot)\) \(\chi_{5929}(629,\cdot)\) \(\chi_{5929}(657,\cdot)\) \(\chi_{5929}(678,\cdot)\) \(\chi_{5929}(706,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{385})$ |
| Fixed field: | Number field defined by a degree 770 polynomial (not computed) |
Values on generators
\((1816,2059)\) → \((e\left(\frac{13}{14}\right),e\left(\frac{21}{110}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(12\) | \(13\) |
| \( \chi_{ 5929 }(706, a) \) | \(1\) | \(1\) | \(e\left(\frac{257}{770}\right)\) | \(e\left(\frac{51}{70}\right)\) | \(e\left(\frac{257}{385}\right)\) | \(e\left(\frac{43}{770}\right)\) | \(e\left(\frac{24}{385}\right)\) | \(e\left(\frac{1}{770}\right)\) | \(e\left(\frac{16}{35}\right)\) | \(e\left(\frac{30}{77}\right)\) | \(e\left(\frac{61}{154}\right)\) | \(e\left(\frac{356}{385}\right)\) |