Basic properties
Modulus: | \(297\) | |
Conductor: | \(297\) | 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 297.v
\(\chi_{297}(5,\cdot)\) \(\chi_{297}(14,\cdot)\) \(\chi_{297}(20,\cdot)\) \(\chi_{297}(38,\cdot)\) \(\chi_{297}(47,\cdot)\) \(\chi_{297}(59,\cdot)\) \(\chi_{297}(86,\cdot)\) \(\chi_{297}(92,\cdot)\) \(\chi_{297}(104,\cdot)\) \(\chi_{297}(113,\cdot)\) \(\chi_{297}(119,\cdot)\) \(\chi_{297}(137,\cdot)\) \(\chi_{297}(146,\cdot)\) \(\chi_{297}(158,\cdot)\) \(\chi_{297}(185,\cdot)\) \(\chi_{297}(191,\cdot)\) \(\chi_{297}(203,\cdot)\) \(\chi_{297}(212,\cdot)\) \(\chi_{297}(218,\cdot)\) \(\chi_{297}(236,\cdot)\) \(\chi_{297}(245,\cdot)\) \(\chi_{297}(257,\cdot)\) \(\chi_{297}(284,\cdot)\) \(\chi_{297}(290,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{45})$ |
Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((56,244)\) → \((e\left(\frac{5}{18}\right),e\left(\frac{4}{5}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(13\) | \(14\) | \(16\) | \(17\) |
\( \chi_{ 297 }(113, a) \) | \(-1\) | \(1\) | \(e\left(\frac{7}{90}\right)\) | \(e\left(\frac{7}{45}\right)\) | \(e\left(\frac{53}{90}\right)\) | \(e\left(\frac{2}{45}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{45}\right)\) | \(e\left(\frac{11}{90}\right)\) | \(e\left(\frac{14}{45}\right)\) | \(e\left(\frac{11}{30}\right)\) |