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
\((56,244)\) → \((e\left(\frac{11}{18}\right),e\left(\frac{1}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(13\) | \(14\) | \(16\) | \(17\) |
| \( \chi_{ 297 }(158, a) \) | \(-1\) | \(1\) | \(e\left(\frac{73}{90}\right)\) | \(e\left(\frac{28}{45}\right)\) | \(e\left(\frac{77}{90}\right)\) | \(e\left(\frac{8}{45}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{4}{45}\right)\) | \(e\left(\frac{89}{90}\right)\) | \(e\left(\frac{11}{45}\right)\) | \(e\left(\frac{29}{30}\right)\) |