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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 209.v
\(\chi_{209}(6,\cdot)\) \(\chi_{209}(17,\cdot)\) \(\chi_{209}(24,\cdot)\) \(\chi_{209}(28,\cdot)\) \(\chi_{209}(35,\cdot)\) \(\chi_{209}(61,\cdot)\) \(\chi_{209}(62,\cdot)\) \(\chi_{209}(63,\cdot)\) \(\chi_{209}(73,\cdot)\) \(\chi_{209}(74,\cdot)\) \(\chi_{209}(85,\cdot)\) \(\chi_{209}(101,\cdot)\) \(\chi_{209}(112,\cdot)\) \(\chi_{209}(118,\cdot)\) \(\chi_{209}(123,\cdot)\) \(\chi_{209}(138,\cdot)\) \(\chi_{209}(139,\cdot)\) \(\chi_{209}(149,\cdot)\) \(\chi_{209}(150,\cdot)\) \(\chi_{209}(156,\cdot)\) \(\chi_{209}(161,\cdot)\) \(\chi_{209}(194,\cdot)\) \(\chi_{209}(195,\cdot)\) \(\chi_{209}(206,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((134,78)\) → \((e\left(\frac{9}{10}\right),e\left(\frac{8}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 209 }(138, a) \) | \(-1\) | \(1\) | \(e\left(\frac{71}{90}\right)\) | \(e\left(\frac{34}{45}\right)\) | \(e\left(\frac{26}{45}\right)\) | \(e\left(\frac{37}{45}\right)\) | \(e\left(\frac{49}{90}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{23}{45}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{1}{3}\right)\) |