Basic properties
| Modulus: | \(1254\) | |
| Conductor: | \(627\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(90\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{627}(299,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1254.bq
\(\chi_{1254}(29,\cdot)\) \(\chi_{1254}(41,\cdot)\) \(\chi_{1254}(167,\cdot)\) \(\chi_{1254}(173,\cdot)\) \(\chi_{1254}(281,\cdot)\) \(\chi_{1254}(299,\cdot)\) \(\chi_{1254}(371,\cdot)\) \(\chi_{1254}(413,\cdot)\) \(\chi_{1254}(431,\cdot)\) \(\chi_{1254}(497,\cdot)\) \(\chi_{1254}(545,\cdot)\) \(\chi_{1254}(611,\cdot)\) \(\chi_{1254}(623,\cdot)\) \(\chi_{1254}(629,\cdot)\) \(\chi_{1254}(743,\cdot)\) \(\chi_{1254}(755,\cdot)\) \(\chi_{1254}(827,\cdot)\) \(\chi_{1254}(887,\cdot)\) \(\chi_{1254}(941,\cdot)\) \(\chi_{1254}(953,\cdot)\) \(\chi_{1254}(965,\cdot)\) \(\chi_{1254}(1085,\cdot)\) \(\chi_{1254}(1097,\cdot)\) \(\chi_{1254}(1229,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((419,343,1123)\) → \((-1,e\left(\frac{1}{10}\right),e\left(\frac{7}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) | \(37\) |
| \( \chi_{ 1254 }(299, a) \) | \(-1\) | \(1\) | \(e\left(\frac{11}{90}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{2}{45}\right)\) | \(e\left(\frac{13}{45}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{11}{45}\right)\) | \(e\left(\frac{73}{90}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{7}{45}\right)\) | \(e\left(\frac{7}{10}\right)\) |