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 \(\chi_{209}(40,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1254.bp
\(\chi_{1254}(13,\cdot)\) \(\chi_{1254}(79,\cdot)\) \(\chi_{1254}(127,\cdot)\) \(\chi_{1254}(193,\cdot)\) \(\chi_{1254}(205,\cdot)\) \(\chi_{1254}(211,\cdot)\) \(\chi_{1254}(325,\cdot)\) \(\chi_{1254}(337,\cdot)\) \(\chi_{1254}(409,\cdot)\) \(\chi_{1254}(469,\cdot)\) \(\chi_{1254}(523,\cdot)\) \(\chi_{1254}(535,\cdot)\) \(\chi_{1254}(547,\cdot)\) \(\chi_{1254}(667,\cdot)\) \(\chi_{1254}(679,\cdot)\) \(\chi_{1254}(811,\cdot)\) \(\chi_{1254}(865,\cdot)\) \(\chi_{1254}(877,\cdot)\) \(\chi_{1254}(1003,\cdot)\) \(\chi_{1254}(1009,\cdot)\) \(\chi_{1254}(1117,\cdot)\) \(\chi_{1254}(1135,\cdot)\) \(\chi_{1254}(1207,\cdot)\) \(\chi_{1254}(1249,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((419,343,1123)\) → \((1,e\left(\frac{7}{10}\right),e\left(\frac{1}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) | \(37\) |
| \( \chi_{ 1254 }(667, a) \) | \(1\) | \(1\) | \(e\left(\frac{31}{45}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{44}{45}\right)\) | \(e\left(\frac{77}{90}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{17}{45}\right)\) | \(e\left(\frac{38}{45}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{83}{90}\right)\) | \(e\left(\frac{9}{10}\right)\) |