Basic properties
| Modulus: | \(1521\) | |
| Conductor: | \(507\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(78\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{507}(35,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1521.bu
\(\chi_{1521}(35,\cdot)\) \(\chi_{1521}(107,\cdot)\) \(\chi_{1521}(152,\cdot)\) \(\chi_{1521}(224,\cdot)\) \(\chi_{1521}(269,\cdot)\) \(\chi_{1521}(341,\cdot)\) \(\chi_{1521}(386,\cdot)\) \(\chi_{1521}(458,\cdot)\) \(\chi_{1521}(503,\cdot)\) \(\chi_{1521}(575,\cdot)\) \(\chi_{1521}(620,\cdot)\) \(\chi_{1521}(692,\cdot)\) \(\chi_{1521}(737,\cdot)\) \(\chi_{1521}(809,\cdot)\) \(\chi_{1521}(854,\cdot)\) \(\chi_{1521}(926,\cdot)\) \(\chi_{1521}(971,\cdot)\) \(\chi_{1521}(1043,\cdot)\) \(\chi_{1521}(1088,\cdot)\) \(\chi_{1521}(1277,\cdot)\) \(\chi_{1521}(1322,\cdot)\) \(\chi_{1521}(1394,\cdot)\) \(\chi_{1521}(1439,\cdot)\) \(\chi_{1521}(1511,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((677,847)\) → \((-1,e\left(\frac{29}{39}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(14\) | \(16\) | \(17\) |
| \( \chi_{ 1521 }(35, a) \) | \(-1\) | \(1\) | \(e\left(\frac{19}{78}\right)\) | \(e\left(\frac{19}{39}\right)\) | \(e\left(\frac{5}{26}\right)\) | \(e\left(\frac{22}{39}\right)\) | \(e\left(\frac{19}{26}\right)\) | \(e\left(\frac{17}{39}\right)\) | \(e\left(\frac{7}{78}\right)\) | \(e\left(\frac{21}{26}\right)\) | \(e\left(\frac{38}{39}\right)\) | \(e\left(\frac{5}{78}\right)\) |