Basic properties
Modulus: | \(297\) | |
Conductor: | \(297\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(45\) | 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 297.u
\(\chi_{297}(4,\cdot)\) \(\chi_{297}(16,\cdot)\) \(\chi_{297}(25,\cdot)\) \(\chi_{297}(31,\cdot)\) \(\chi_{297}(49,\cdot)\) \(\chi_{297}(58,\cdot)\) \(\chi_{297}(70,\cdot)\) \(\chi_{297}(97,\cdot)\) \(\chi_{297}(103,\cdot)\) \(\chi_{297}(115,\cdot)\) \(\chi_{297}(124,\cdot)\) \(\chi_{297}(130,\cdot)\) \(\chi_{297}(148,\cdot)\) \(\chi_{297}(157,\cdot)\) \(\chi_{297}(169,\cdot)\) \(\chi_{297}(196,\cdot)\) \(\chi_{297}(202,\cdot)\) \(\chi_{297}(214,\cdot)\) \(\chi_{297}(223,\cdot)\) \(\chi_{297}(229,\cdot)\) \(\chi_{297}(247,\cdot)\) \(\chi_{297}(256,\cdot)\) \(\chi_{297}(268,\cdot)\) \(\chi_{297}(295,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{45})$ |
Fixed field: | 45.45.940750991812442660132286068374700929301371405411689329186316523736000865610069804102171689.1 |
Values on generators
\((56,244)\) → \((e\left(\frac{5}{9}\right),e\left(\frac{1}{5}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(13\) | \(14\) | \(16\) | \(17\) |
\( \chi_{ 297 }(268, a) \) | \(1\) | \(1\) | \(e\left(\frac{34}{45}\right)\) | \(e\left(\frac{23}{45}\right)\) | \(e\left(\frac{26}{45}\right)\) | \(e\left(\frac{13}{45}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{29}{45}\right)\) | \(e\left(\frac{2}{45}\right)\) | \(e\left(\frac{1}{45}\right)\) | \(e\left(\frac{2}{15}\right)\) |