Basic properties
| Modulus: | \(507\) | |
| Conductor: | \(507\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(156\) | 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.x
\(\chi_{507}(2,\cdot)\) \(\chi_{507}(11,\cdot)\) \(\chi_{507}(20,\cdot)\) \(\chi_{507}(32,\cdot)\) \(\chi_{507}(41,\cdot)\) \(\chi_{507}(50,\cdot)\) \(\chi_{507}(59,\cdot)\) \(\chi_{507}(71,\cdot)\) \(\chi_{507}(98,\cdot)\) \(\chi_{507}(110,\cdot)\) \(\chi_{507}(119,\cdot)\) \(\chi_{507}(128,\cdot)\) \(\chi_{507}(137,\cdot)\) \(\chi_{507}(149,\cdot)\) \(\chi_{507}(158,\cdot)\) \(\chi_{507}(167,\cdot)\) \(\chi_{507}(176,\cdot)\) \(\chi_{507}(197,\cdot)\) \(\chi_{507}(206,\cdot)\) \(\chi_{507}(215,\cdot)\) \(\chi_{507}(227,\cdot)\) \(\chi_{507}(236,\cdot)\) \(\chi_{507}(245,\cdot)\) \(\chi_{507}(254,\cdot)\) \(\chi_{507}(266,\cdot)\) \(\chi_{507}(275,\cdot)\) \(\chi_{507}(284,\cdot)\) \(\chi_{507}(293,\cdot)\) \(\chi_{507}(305,\cdot)\) \(\chi_{507}(314,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((170,340)\) → \((-1,e\left(\frac{1}{156}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(14\) | \(16\) | \(17\) |
| \( \chi_{ 507 }(2, a) \) | \(1\) | \(1\) | \(e\left(\frac{79}{156}\right)\) | \(e\left(\frac{1}{78}\right)\) | \(e\left(\frac{29}{52}\right)\) | \(e\left(\frac{107}{156}\right)\) | \(e\left(\frac{27}{52}\right)\) | \(e\left(\frac{5}{78}\right)\) | \(e\left(\frac{25}{156}\right)\) | \(e\left(\frac{5}{26}\right)\) | \(e\left(\frac{1}{39}\right)\) | \(e\left(\frac{17}{39}\right)\) |