Basic properties
| Modulus: | \(8550\) | |
| Conductor: | \(4275\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(90\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{4275}(509,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8550.gd
\(\chi_{8550}(509,\cdot)\) \(\chi_{8550}(839,\cdot)\) \(\chi_{8550}(1229,\cdot)\) \(\chi_{8550}(2009,\cdot)\) \(\chi_{8550}(2219,\cdot)\) \(\chi_{8550}(2309,\cdot)\) \(\chi_{8550}(2909,\cdot)\) \(\chi_{8550}(2939,\cdot)\) \(\chi_{8550}(3719,\cdot)\) \(\chi_{8550}(3929,\cdot)\) \(\chi_{8550}(4019,\cdot)\) \(\chi_{8550}(4259,\cdot)\) \(\chi_{8550}(4619,\cdot)\) \(\chi_{8550}(5429,\cdot)\) \(\chi_{8550}(5639,\cdot)\) \(\chi_{8550}(5729,\cdot)\) \(\chi_{8550}(5969,\cdot)\) \(\chi_{8550}(6329,\cdot)\) \(\chi_{8550}(6359,\cdot)\) \(\chi_{8550}(7139,\cdot)\) \(\chi_{8550}(7439,\cdot)\) \(\chi_{8550}(7679,\cdot)\) \(\chi_{8550}(8039,\cdot)\) \(\chi_{8550}(8069,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((1901,1027,1351)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{7}{10}\right),e\left(\frac{11}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 8550 }(509, a) \) | \(1\) | \(1\) | \(-1\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{1}{45}\right)\) | \(e\left(\frac{32}{45}\right)\) | \(e\left(\frac{4}{45}\right)\) | \(e\left(\frac{28}{45}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{41}{45}\right)\) | \(e\left(\frac{11}{18}\right)\) |