Basic properties
| Modulus: | \(197\) | |
| Conductor: | \(197\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(196\) | 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 197.i
\(\chi_{197}(2,\cdot)\) \(\chi_{197}(3,\cdot)\) \(\chi_{197}(5,\cdot)\) \(\chi_{197}(8,\cdot)\) \(\chi_{197}(11,\cdot)\) \(\chi_{197}(12,\cdot)\) \(\chi_{197}(13,\cdot)\) \(\chi_{197}(17,\cdot)\) \(\chi_{197}(18,\cdot)\) \(\chi_{197}(21,\cdot)\) \(\chi_{197}(27,\cdot)\) \(\chi_{197}(30,\cdot)\) \(\chi_{197}(31,\cdot)\) \(\chi_{197}(32,\cdot)\) \(\chi_{197}(35,\cdot)\) \(\chi_{197}(38,\cdot)\) \(\chi_{197}(44,\cdot)\) \(\chi_{197}(45,\cdot)\) \(\chi_{197}(46,\cdot)\) \(\chi_{197}(48,\cdot)\) \(\chi_{197}(50,\cdot)\) \(\chi_{197}(52,\cdot)\) \(\chi_{197}(56,\cdot)\) \(\chi_{197}(57,\cdot)\) \(\chi_{197}(58,\cdot)\) \(\chi_{197}(66,\cdot)\) \(\chi_{197}(67,\cdot)\) \(\chi_{197}(71,\cdot)\) \(\chi_{197}(72,\cdot)\) \(\chi_{197}(73,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{196})$ |
| Fixed field: | Number field defined by a degree 196 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{139}{196}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 197 }(57, a) \) | \(-1\) | \(1\) | \(e\left(\frac{139}{196}\right)\) | \(e\left(\frac{71}{196}\right)\) | \(e\left(\frac{41}{98}\right)\) | \(e\left(\frac{23}{196}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{53}{98}\right)\) | \(e\left(\frac{25}{196}\right)\) | \(e\left(\frac{71}{98}\right)\) | \(e\left(\frac{81}{98}\right)\) | \(e\left(\frac{111}{196}\right)\) |