Basic properties
| Modulus: | \(197\) | |
| Conductor: | \(197\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(98\) | 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 197.h
\(\chi_{197}(4,\cdot)\) \(\chi_{197}(7,\cdot)\) \(\chi_{197}(9,\cdot)\) \(\chi_{197}(10,\cdot)\) \(\chi_{197}(15,\cdot)\) \(\chi_{197}(22,\cdot)\) \(\chi_{197}(25,\cdot)\) \(\chi_{197}(26,\cdot)\) \(\chi_{197}(39,\cdot)\) \(\chi_{197}(41,\cdot)\) \(\chi_{197}(43,\cdot)\) \(\chi_{197}(47,\cdot)\) \(\chi_{197}(55,\cdot)\) \(\chi_{197}(62,\cdot)\) \(\chi_{197}(64,\cdot)\) \(\chi_{197}(65,\cdot)\) \(\chi_{197}(92,\cdot)\) \(\chi_{197}(96,\cdot)\) \(\chi_{197}(97,\cdot)\) \(\chi_{197}(107,\cdot)\) \(\chi_{197}(109,\cdot)\) \(\chi_{197}(112,\cdot)\) \(\chi_{197}(116,\cdot)\) \(\chi_{197}(121,\cdot)\) \(\chi_{197}(127,\cdot)\) \(\chi_{197}(134,\cdot)\) \(\chi_{197}(136,\cdot)\) \(\chi_{197}(137,\cdot)\) \(\chi_{197}(138,\cdot)\) \(\chi_{197}(143,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{49})$ |
| Fixed field: | Number field defined by a degree 98 polynomial |
Values on generators
\(2\) → \(e\left(\frac{3}{98}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 197 }(64, a) \) | \(1\) | \(1\) | \(e\left(\frac{3}{98}\right)\) | \(e\left(\frac{53}{98}\right)\) | \(e\left(\frac{3}{49}\right)\) | \(e\left(\frac{71}{98}\right)\) | \(e\left(\frac{4}{7}\right)\) | \(e\left(\frac{23}{49}\right)\) | \(e\left(\frac{9}{98}\right)\) | \(e\left(\frac{4}{49}\right)\) | \(e\left(\frac{37}{49}\right)\) | \(e\left(\frac{87}{98}\right)\) |