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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 297.x
\(\chi_{297}(2,\cdot)\) \(\chi_{297}(29,\cdot)\) \(\chi_{297}(41,\cdot)\) \(\chi_{297}(50,\cdot)\) \(\chi_{297}(68,\cdot)\) \(\chi_{297}(74,\cdot)\) \(\chi_{297}(83,\cdot)\) \(\chi_{297}(95,\cdot)\) \(\chi_{297}(101,\cdot)\) \(\chi_{297}(128,\cdot)\) \(\chi_{297}(140,\cdot)\) \(\chi_{297}(149,\cdot)\) \(\chi_{297}(167,\cdot)\) \(\chi_{297}(173,\cdot)\) \(\chi_{297}(182,\cdot)\) \(\chi_{297}(194,\cdot)\) \(\chi_{297}(200,\cdot)\) \(\chi_{297}(227,\cdot)\) \(\chi_{297}(239,\cdot)\) \(\chi_{297}(248,\cdot)\) \(\chi_{297}(266,\cdot)\) \(\chi_{297}(272,\cdot)\) \(\chi_{297}(281,\cdot)\) \(\chi_{297}(293,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((56,244)\) → \((e\left(\frac{5}{18}\right),e\left(\frac{3}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(13\) | \(14\) | \(16\) | \(17\) |
| \( \chi_{ 297 }(140, a) \) | \(1\) | \(1\) | \(e\left(\frac{26}{45}\right)\) | \(e\left(\frac{7}{45}\right)\) | \(e\left(\frac{53}{90}\right)\) | \(e\left(\frac{49}{90}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{47}{90}\right)\) | \(e\left(\frac{11}{90}\right)\) | \(e\left(\frac{14}{45}\right)\) | \(e\left(\frac{13}{15}\right)\) |