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.bz
\(\chi_{1521}(29,\cdot)\) \(\chi_{1521}(113,\cdot)\) \(\chi_{1521}(230,\cdot)\) \(\chi_{1521}(263,\cdot)\) \(\chi_{1521}(347,\cdot)\) \(\chi_{1521}(380,\cdot)\) \(\chi_{1521}(464,\cdot)\) \(\chi_{1521}(497,\cdot)\) \(\chi_{1521}(581,\cdot)\) \(\chi_{1521}(614,\cdot)\) \(\chi_{1521}(731,\cdot)\) \(\chi_{1521}(815,\cdot)\) \(\chi_{1521}(848,\cdot)\) \(\chi_{1521}(932,\cdot)\) \(\chi_{1521}(965,\cdot)\) \(\chi_{1521}(1049,\cdot)\) \(\chi_{1521}(1082,\cdot)\) \(\chi_{1521}(1166,\cdot)\) \(\chi_{1521}(1199,\cdot)\) \(\chi_{1521}(1283,\cdot)\) \(\chi_{1521}(1316,\cdot)\) \(\chi_{1521}(1400,\cdot)\) \(\chi_{1521}(1433,\cdot)\) \(\chi_{1521}(1517,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((677,847)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{16}{39}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(14\) | \(16\) | \(17\) |
| \( \chi_{ 1521 }(263, a) \) | \(-1\) | \(1\) | \(e\left(\frac{15}{26}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{41}{78}\right)\) | \(e\left(\frac{22}{39}\right)\) | \(e\left(\frac{19}{26}\right)\) | \(e\left(\frac{4}{39}\right)\) | \(e\left(\frac{11}{26}\right)\) | \(e\left(\frac{11}{78}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{31}{78}\right)\) |