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 \(\chi_{627}(347,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1254.br
\(\chi_{1254}(17,\cdot)\) \(\chi_{1254}(35,\cdot)\) \(\chi_{1254}(101,\cdot)\) \(\chi_{1254}(149,\cdot)\) \(\chi_{1254}(161,\cdot)\) \(\chi_{1254}(215,\cdot)\) \(\chi_{1254}(233,\cdot)\) \(\chi_{1254}(347,\cdot)\) \(\chi_{1254}(359,\cdot)\) \(\chi_{1254}(365,\cdot)\) \(\chi_{1254}(479,\cdot)\) \(\chi_{1254}(491,\cdot)\) \(\chi_{1254}(503,\cdot)\) \(\chi_{1254}(557,\cdot)\) \(\chi_{1254}(689,\cdot)\) \(\chi_{1254}(701,\cdot)\) \(\chi_{1254}(821,\cdot)\) \(\chi_{1254}(833,\cdot)\) \(\chi_{1254}(899,\cdot)\) \(\chi_{1254}(959,\cdot)\) \(\chi_{1254}(1031,\cdot)\) \(\chi_{1254}(1073,\cdot)\) \(\chi_{1254}(1157,\cdot)\) \(\chi_{1254}(1163,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((419,343,1123)\) → \((-1,e\left(\frac{9}{10}\right),e\left(\frac{8}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) | \(37\) |
| \( \chi_{ 1254 }(347, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{90}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{31}{90}\right)\) | \(e\left(\frac{22}{45}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{29}{45}\right)\) | \(e\left(\frac{41}{45}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{43}{45}\right)\) | \(e\left(\frac{4}{5}\right)\) |