Basic properties
| Modulus: | \(157\) | |
| Conductor: | \(157\) | 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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 157.l
\(\chi_{157}(5,\cdot)\) \(\chi_{157}(6,\cdot)\) \(\chi_{157}(15,\cdot)\) \(\chi_{157}(18,\cdot)\) \(\chi_{157}(20,\cdot)\) \(\chi_{157}(21,\cdot)\) \(\chi_{157}(24,\cdot)\) \(\chi_{157}(26,\cdot)\) \(\chi_{157}(34,\cdot)\) \(\chi_{157}(38,\cdot)\) \(\chi_{157}(43,\cdot)\) \(\chi_{157}(53,\cdot)\) \(\chi_{157}(55,\cdot)\) \(\chi_{157}(60,\cdot)\) \(\chi_{157}(61,\cdot)\) \(\chi_{157}(62,\cdot)\) \(\chi_{157}(63,\cdot)\) \(\chi_{157}(66,\cdot)\) \(\chi_{157}(69,\cdot)\) \(\chi_{157}(70,\cdot)\) \(\chi_{157}(72,\cdot)\) \(\chi_{157}(73,\cdot)\) \(\chi_{157}(74,\cdot)\) \(\chi_{157}(77,\cdot)\) \(\chi_{157}(80,\cdot)\) \(\chi_{157}(83,\cdot)\) \(\chi_{157}(84,\cdot)\) \(\chi_{157}(85,\cdot)\) \(\chi_{157}(87,\cdot)\) \(\chi_{157}(88,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\(5\) → \(e\left(\frac{1}{156}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 157 }(5, a) \) | \(-1\) | \(1\) | \(e\left(\frac{47}{52}\right)\) | \(e\left(\frac{41}{78}\right)\) | \(e\left(\frac{21}{26}\right)\) | \(e\left(\frac{1}{156}\right)\) | \(e\left(\frac{67}{156}\right)\) | \(e\left(\frac{49}{52}\right)\) | \(e\left(\frac{37}{52}\right)\) | \(e\left(\frac{2}{39}\right)\) | \(e\left(\frac{71}{78}\right)\) | \(e\left(\frac{7}{39}\right)\) |