Basic properties
| Modulus: | \(1254\) | |
| Conductor: | \(209\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(90\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{209}(61,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1254.bs
\(\chi_{1254}(61,\cdot)\) \(\chi_{1254}(73,\cdot)\) \(\chi_{1254}(85,\cdot)\) \(\chi_{1254}(139,\cdot)\) \(\chi_{1254}(271,\cdot)\) \(\chi_{1254}(283,\cdot)\) \(\chi_{1254}(403,\cdot)\) \(\chi_{1254}(415,\cdot)\) \(\chi_{1254}(481,\cdot)\) \(\chi_{1254}(541,\cdot)\) \(\chi_{1254}(613,\cdot)\) \(\chi_{1254}(655,\cdot)\) \(\chi_{1254}(739,\cdot)\) \(\chi_{1254}(745,\cdot)\) \(\chi_{1254}(853,\cdot)\) \(\chi_{1254}(871,\cdot)\) \(\chi_{1254}(937,\cdot)\) \(\chi_{1254}(985,\cdot)\) \(\chi_{1254}(997,\cdot)\) \(\chi_{1254}(1051,\cdot)\) \(\chi_{1254}(1069,\cdot)\) \(\chi_{1254}(1183,\cdot)\) \(\chi_{1254}(1195,\cdot)\) \(\chi_{1254}(1201,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((419,343,1123)\) → \((1,e\left(\frac{9}{10}\right),e\left(\frac{1}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) | \(37\) |
| \( \chi_{ 1254 }(61, a) \) | \(-1\) | \(1\) | \(e\left(\frac{17}{45}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{41}{90}\right)\) | \(e\left(\frac{19}{90}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{34}{45}\right)\) | \(e\left(\frac{17}{90}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{31}{90}\right)\) | \(e\left(\frac{4}{5}\right)\) |