Basic properties
| Modulus: | \(1521\) | |
| Conductor: | \(1521\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(78\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1521.bo
\(\chi_{1521}(95,\cdot)\) \(\chi_{1521}(101,\cdot)\) \(\chi_{1521}(212,\cdot)\) \(\chi_{1521}(218,\cdot)\) \(\chi_{1521}(329,\cdot)\) \(\chi_{1521}(335,\cdot)\) \(\chi_{1521}(446,\cdot)\) \(\chi_{1521}(452,\cdot)\) \(\chi_{1521}(563,\cdot)\) \(\chi_{1521}(569,\cdot)\) \(\chi_{1521}(680,\cdot)\) \(\chi_{1521}(686,\cdot)\) \(\chi_{1521}(797,\cdot)\) \(\chi_{1521}(803,\cdot)\) \(\chi_{1521}(914,\cdot)\) \(\chi_{1521}(920,\cdot)\) \(\chi_{1521}(1031,\cdot)\) \(\chi_{1521}(1148,\cdot)\) \(\chi_{1521}(1154,\cdot)\) \(\chi_{1521}(1265,\cdot)\) \(\chi_{1521}(1271,\cdot)\) \(\chi_{1521}(1382,\cdot)\) \(\chi_{1521}(1388,\cdot)\) \(\chi_{1521}(1505,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((677,847)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{37}{78}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(14\) | \(16\) | \(17\) |
| \( \chi_{ 1521 }(95, a) \) | \(-1\) | \(1\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{17}{39}\right)\) | \(e\left(\frac{7}{78}\right)\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{29}{39}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{31}{78}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{59}{78}\right)\) |