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.x
\(\chi_{209}(3,\cdot)\) \(\chi_{209}(14,\cdot)\) \(\chi_{209}(15,\cdot)\) \(\chi_{209}(48,\cdot)\) \(\chi_{209}(53,\cdot)\) \(\chi_{209}(59,\cdot)\) \(\chi_{209}(60,\cdot)\) \(\chi_{209}(70,\cdot)\) \(\chi_{209}(71,\cdot)\) \(\chi_{209}(86,\cdot)\) \(\chi_{209}(91,\cdot)\) \(\chi_{209}(97,\cdot)\) \(\chi_{209}(108,\cdot)\) \(\chi_{209}(124,\cdot)\) \(\chi_{209}(135,\cdot)\) \(\chi_{209}(136,\cdot)\) \(\chi_{209}(146,\cdot)\) \(\chi_{209}(147,\cdot)\) \(\chi_{209}(148,\cdot)\) \(\chi_{209}(174,\cdot)\) \(\chi_{209}(181,\cdot)\) \(\chi_{209}(185,\cdot)\) \(\chi_{209}(192,\cdot)\) \(\chi_{209}(203,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{45})$ |
Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((134,78)\) → \((e\left(\frac{3}{5}\right),e\left(\frac{7}{18}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 209 }(185, a) \) | \(-1\) | \(1\) | \(e\left(\frac{89}{90}\right)\) | \(e\left(\frac{77}{90}\right)\) | \(e\left(\frac{44}{45}\right)\) | \(e\left(\frac{28}{45}\right)\) | \(e\left(\frac{38}{45}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{32}{45}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{5}{6}\right)\) |