Basic properties
| Modulus: | \(1237\) | |
| Conductor: | \(1237\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1236\) | 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 1237.l
\(\chi_{1237}(2,\cdot)\) \(\chi_{1237}(5,\cdot)\) \(\chi_{1237}(6,\cdot)\) \(\chi_{1237}(7,\cdot)\) \(\chi_{1237}(19,\cdot)\) \(\chi_{1237}(20,\cdot)\) \(\chi_{1237}(21,\cdot)\) \(\chi_{1237}(22,\cdot)\) \(\chi_{1237}(24,\cdot)\) \(\chi_{1237}(29,\cdot)\) \(\chi_{1237}(32,\cdot)\) \(\chi_{1237}(34,\cdot)\) \(\chi_{1237}(39,\cdot)\) \(\chi_{1237}(43,\cdot)\) \(\chi_{1237}(45,\cdot)\) \(\chi_{1237}(46,\cdot)\) \(\chi_{1237}(47,\cdot)\) \(\chi_{1237}(50,\cdot)\) \(\chi_{1237}(52,\cdot)\) \(\chi_{1237}(53,\cdot)\) \(\chi_{1237}(54,\cdot)\) \(\chi_{1237}(55,\cdot)\) \(\chi_{1237}(60,\cdot)\) \(\chi_{1237}(66,\cdot)\) \(\chi_{1237}(67,\cdot)\) \(\chi_{1237}(70,\cdot)\) \(\chi_{1237}(72,\cdot)\) \(\chi_{1237}(74,\cdot)\) \(\chi_{1237}(76,\cdot)\) \(\chi_{1237}(77,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1236})$ |
| Fixed field: | Number field defined by a degree 1236 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{619}{1236}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1237 }(1235, a) \) | \(-1\) | \(1\) | \(e\left(\frac{619}{1236}\right)\) | \(e\left(\frac{253}{309}\right)\) | \(e\left(\frac{1}{618}\right)\) | \(e\left(\frac{935}{1236}\right)\) | \(e\left(\frac{395}{1236}\right)\) | \(e\left(\frac{499}{1236}\right)\) | \(e\left(\frac{207}{412}\right)\) | \(e\left(\frac{197}{309}\right)\) | \(e\left(\frac{53}{206}\right)\) | \(e\left(\frac{175}{206}\right)\) |