Basic properties
| Modulus: | \(507\) | |
| Conductor: | \(507\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(52\) | 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 507.s
\(\chi_{507}(5,\cdot)\) \(\chi_{507}(8,\cdot)\) \(\chi_{507}(44,\cdot)\) \(\chi_{507}(47,\cdot)\) \(\chi_{507}(83,\cdot)\) \(\chi_{507}(86,\cdot)\) \(\chi_{507}(122,\cdot)\) \(\chi_{507}(125,\cdot)\) \(\chi_{507}(161,\cdot)\) \(\chi_{507}(164,\cdot)\) \(\chi_{507}(200,\cdot)\) \(\chi_{507}(203,\cdot)\) \(\chi_{507}(242,\cdot)\) \(\chi_{507}(278,\cdot)\) \(\chi_{507}(281,\cdot)\) \(\chi_{507}(317,\cdot)\) \(\chi_{507}(320,\cdot)\) \(\chi_{507}(356,\cdot)\) \(\chi_{507}(359,\cdot)\) \(\chi_{507}(395,\cdot)\) \(\chi_{507}(398,\cdot)\) \(\chi_{507}(434,\cdot)\) \(\chi_{507}(473,\cdot)\) \(\chi_{507}(476,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{52})$ |
| Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((170,340)\) → \((-1,e\left(\frac{27}{52}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(14\) | \(16\) | \(17\) |
| \( \chi_{ 507 }(161, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{52}\right)\) | \(e\left(\frac{1}{26}\right)\) | \(e\left(\frac{9}{52}\right)\) | \(e\left(\frac{29}{52}\right)\) | \(e\left(\frac{3}{52}\right)\) | \(e\left(\frac{5}{26}\right)\) | \(e\left(\frac{51}{52}\right)\) | \(e\left(\frac{15}{26}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{4}{13}\right)\) |