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.w
\(\chi_{297}(7,\cdot)\) \(\chi_{297}(13,\cdot)\) \(\chi_{297}(40,\cdot)\) \(\chi_{297}(52,\cdot)\) \(\chi_{297}(61,\cdot)\) \(\chi_{297}(79,\cdot)\) \(\chi_{297}(85,\cdot)\) \(\chi_{297}(94,\cdot)\) \(\chi_{297}(106,\cdot)\) \(\chi_{297}(112,\cdot)\) \(\chi_{297}(139,\cdot)\) \(\chi_{297}(151,\cdot)\) \(\chi_{297}(160,\cdot)\) \(\chi_{297}(178,\cdot)\) \(\chi_{297}(184,\cdot)\) \(\chi_{297}(193,\cdot)\) \(\chi_{297}(205,\cdot)\) \(\chi_{297}(211,\cdot)\) \(\chi_{297}(238,\cdot)\) \(\chi_{297}(250,\cdot)\) \(\chi_{297}(259,\cdot)\) \(\chi_{297}(277,\cdot)\) \(\chi_{297}(283,\cdot)\) \(\chi_{297}(292,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((56,244)\) → \((e\left(\frac{8}{9}\right),e\left(\frac{3}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(13\) | \(14\) | \(16\) | \(17\) |
| \( \chi_{ 297 }(250, a) \) | \(-1\) | \(1\) | \(e\left(\frac{17}{90}\right)\) | \(e\left(\frac{17}{45}\right)\) | \(e\left(\frac{29}{45}\right)\) | \(e\left(\frac{29}{90}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{37}{90}\right)\) | \(e\left(\frac{23}{45}\right)\) | \(e\left(\frac{34}{45}\right)\) | \(e\left(\frac{1}{30}\right)\) |