Basic properties
| Modulus: | \(8550\) | |
| Conductor: | \(1425\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(90\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1425}(1364,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8550.gp
\(\chi_{8550}(89,\cdot)\) \(\chi_{8550}(269,\cdot)\) \(\chi_{8550}(629,\cdot)\) \(\chi_{8550}(1079,\cdot)\) \(\chi_{8550}(1169,\cdot)\) \(\chi_{8550}(1439,\cdot)\) \(\chi_{8550}(1979,\cdot)\) \(\chi_{8550}(2339,\cdot)\) \(\chi_{8550}(2789,\cdot)\) \(\chi_{8550}(2879,\cdot)\) \(\chi_{8550}(3509,\cdot)\) \(\chi_{8550}(3689,\cdot)\) \(\chi_{8550}(4589,\cdot)\) \(\chi_{8550}(4859,\cdot)\) \(\chi_{8550}(5219,\cdot)\) \(\chi_{8550}(5759,\cdot)\) \(\chi_{8550}(6209,\cdot)\) \(\chi_{8550}(6569,\cdot)\) \(\chi_{8550}(6929,\cdot)\) \(\chi_{8550}(7109,\cdot)\) \(\chi_{8550}(7469,\cdot)\) \(\chi_{8550}(7919,\cdot)\) \(\chi_{8550}(8009,\cdot)\) \(\chi_{8550}(8279,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((1901,1027,1351)\) → \((-1,e\left(\frac{3}{10}\right),e\left(\frac{11}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 8550 }(2789, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{34}{45}\right)\) | \(e\left(\frac{23}{45}\right)\) | \(e\left(\frac{1}{45}\right)\) | \(e\left(\frac{22}{45}\right)\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{1}{5}\right)\) | \(e\left(\frac{29}{45}\right)\) | \(e\left(\frac{5}{18}\right)\) |