Basic properties
| Modulus: | \(197\) | |
| Conductor: | \(197\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(49\) | 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.g
\(\chi_{197}(16,\cdot)\) \(\chi_{197}(23,\cdot)\) \(\chi_{197}(24,\cdot)\) \(\chi_{197}(28,\cdot)\) \(\chi_{197}(29,\cdot)\) \(\chi_{197}(34,\cdot)\) \(\chi_{197}(37,\cdot)\) \(\chi_{197}(40,\cdot)\) \(\chi_{197}(42,\cdot)\) \(\chi_{197}(49,\cdot)\) \(\chi_{197}(51,\cdot)\) \(\chi_{197}(53,\cdot)\) \(\chi_{197}(54,\cdot)\) \(\chi_{197}(59,\cdot)\) \(\chi_{197}(60,\cdot)\) \(\chi_{197}(61,\cdot)\) \(\chi_{197}(63,\cdot)\) \(\chi_{197}(70,\cdot)\) \(\chi_{197}(76,\cdot)\) \(\chi_{197}(81,\cdot)\) \(\chi_{197}(85,\cdot)\) \(\chi_{197}(88,\cdot)\) \(\chi_{197}(90,\cdot)\) \(\chi_{197}(100,\cdot)\) \(\chi_{197}(101,\cdot)\) \(\chi_{197}(105,\cdot)\) \(\chi_{197}(132,\cdot)\) \(\chi_{197}(133,\cdot)\) \(\chi_{197}(135,\cdot)\) \(\chi_{197}(142,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{49})$ |
| Fixed field: | Number field defined by a degree 49 polynomial |
Values on generators
\(2\) → \(e\left(\frac{34}{49}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 197 }(81, a) \) | \(1\) | \(1\) | \(e\left(\frac{34}{49}\right)\) | \(e\left(\frac{29}{49}\right)\) | \(e\left(\frac{19}{49}\right)\) | \(e\left(\frac{37}{49}\right)\) | \(e\left(\frac{2}{7}\right)\) | \(e\left(\frac{15}{49}\right)\) | \(e\left(\frac{4}{49}\right)\) | \(e\left(\frac{9}{49}\right)\) | \(e\left(\frac{22}{49}\right)\) | \(e\left(\frac{6}{49}\right)\) |