Basic properties
| Modulus: | \(209\) | |
| Conductor: | \(209\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(90\) | 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 209.w
\(\chi_{209}(2,\cdot)\) \(\chi_{209}(13,\cdot)\) \(\chi_{209}(29,\cdot)\) \(\chi_{209}(40,\cdot)\) \(\chi_{209}(41,\cdot)\) \(\chi_{209}(51,\cdot)\) \(\chi_{209}(52,\cdot)\) \(\chi_{209}(72,\cdot)\) \(\chi_{209}(79,\cdot)\) \(\chi_{209}(90,\cdot)\) \(\chi_{209}(105,\cdot)\) \(\chi_{209}(116,\cdot)\) \(\chi_{209}(117,\cdot)\) \(\chi_{209}(127,\cdot)\) \(\chi_{209}(128,\cdot)\) \(\chi_{209}(129,\cdot)\) \(\chi_{209}(162,\cdot)\) \(\chi_{209}(167,\cdot)\) \(\chi_{209}(173,\cdot)\) \(\chi_{209}(184,\cdot)\) \(\chi_{209}(193,\cdot)\) \(\chi_{209}(200,\cdot)\) \(\chi_{209}(204,\cdot)\) \(\chi_{209}(205,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((134,78)\) → \((e\left(\frac{3}{10}\right),e\left(\frac{13}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 209 }(41, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{45}\right)\) | \(e\left(\frac{71}{90}\right)\) | \(e\left(\frac{2}{45}\right)\) | \(e\left(\frac{34}{45}\right)\) | \(e\left(\frac{73}{90}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{26}{45}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{5}{6}\right)\) |