Basic properties
| Modulus: | \(1029\) | |
| Conductor: | \(1029\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(294\) | 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 1029.v
\(\chi_{1029}(2,\cdot)\) \(\chi_{1029}(11,\cdot)\) \(\chi_{1029}(23,\cdot)\) \(\chi_{1029}(32,\cdot)\) \(\chi_{1029}(44,\cdot)\) \(\chi_{1029}(53,\cdot)\) \(\chi_{1029}(65,\cdot)\) \(\chi_{1029}(74,\cdot)\) \(\chi_{1029}(86,\cdot)\) \(\chi_{1029}(95,\cdot)\) \(\chi_{1029}(107,\cdot)\) \(\chi_{1029}(137,\cdot)\) \(\chi_{1029}(149,\cdot)\) \(\chi_{1029}(158,\cdot)\) \(\chi_{1029}(170,\cdot)\) \(\chi_{1029}(179,\cdot)\) \(\chi_{1029}(191,\cdot)\) \(\chi_{1029}(200,\cdot)\) \(\chi_{1029}(212,\cdot)\) \(\chi_{1029}(221,\cdot)\) \(\chi_{1029}(233,\cdot)\) \(\chi_{1029}(242,\cdot)\) \(\chi_{1029}(254,\cdot)\) \(\chi_{1029}(284,\cdot)\) \(\chi_{1029}(296,\cdot)\) \(\chi_{1029}(305,\cdot)\) \(\chi_{1029}(317,\cdot)\) \(\chi_{1029}(326,\cdot)\) \(\chi_{1029}(338,\cdot)\) \(\chi_{1029}(347,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{147})$ |
| Fixed field: | Number field defined by a degree 294 polynomial (not computed) |
Values on generators
\((344,346)\) → \((-1,e\left(\frac{97}{147}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 1029 }(2, a) \) | \(-1\) | \(1\) | \(e\left(\frac{151}{294}\right)\) | \(e\left(\frac{4}{147}\right)\) | \(e\left(\frac{187}{294}\right)\) | \(e\left(\frac{53}{98}\right)\) | \(e\left(\frac{22}{147}\right)\) | \(e\left(\frac{221}{294}\right)\) | \(e\left(\frac{3}{49}\right)\) | \(e\left(\frac{8}{147}\right)\) | \(e\left(\frac{293}{294}\right)\) | \(e\left(\frac{2}{3}\right)\) |