Basic properties
| Modulus: | \(507\) | |
| Conductor: | \(507\) | 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 507.u
\(\chi_{507}(29,\cdot)\) \(\chi_{507}(35,\cdot)\) \(\chi_{507}(68,\cdot)\) \(\chi_{507}(74,\cdot)\) \(\chi_{507}(107,\cdot)\) \(\chi_{507}(113,\cdot)\) \(\chi_{507}(152,\cdot)\) \(\chi_{507}(185,\cdot)\) \(\chi_{507}(224,\cdot)\) \(\chi_{507}(230,\cdot)\) \(\chi_{507}(263,\cdot)\) \(\chi_{507}(269,\cdot)\) \(\chi_{507}(302,\cdot)\) \(\chi_{507}(308,\cdot)\) \(\chi_{507}(341,\cdot)\) \(\chi_{507}(347,\cdot)\) \(\chi_{507}(380,\cdot)\) \(\chi_{507}(386,\cdot)\) \(\chi_{507}(419,\cdot)\) \(\chi_{507}(425,\cdot)\) \(\chi_{507}(458,\cdot)\) \(\chi_{507}(464,\cdot)\) \(\chi_{507}(497,\cdot)\) \(\chi_{507}(503,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((170,340)\) → \((-1,e\left(\frac{25}{39}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(14\) | \(16\) | \(17\) |
| \( \chi_{ 507 }(107, a) \) | \(-1\) | \(1\) | \(e\left(\frac{11}{78}\right)\) | \(e\left(\frac{11}{39}\right)\) | \(e\left(\frac{7}{26}\right)\) | \(e\left(\frac{23}{39}\right)\) | \(e\left(\frac{11}{26}\right)\) | \(e\left(\frac{16}{39}\right)\) | \(e\left(\frac{41}{78}\right)\) | \(e\left(\frac{19}{26}\right)\) | \(e\left(\frac{22}{39}\right)\) | \(e\left(\frac{7}{78}\right)\) |