Basic properties
| Modulus: | \(9450\) | |
| Conductor: | \(675\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(90\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{675}(29,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9450.gs
\(\chi_{9450}(29,\cdot)\) \(\chi_{9450}(239,\cdot)\) \(\chi_{9450}(659,\cdot)\) \(\chi_{9450}(869,\cdot)\) \(\chi_{9450}(1289,\cdot)\) \(\chi_{9450}(1919,\cdot)\) \(\chi_{9450}(2129,\cdot)\) \(\chi_{9450}(2759,\cdot)\) \(\chi_{9450}(3179,\cdot)\) \(\chi_{9450}(3389,\cdot)\) \(\chi_{9450}(3809,\cdot)\) \(\chi_{9450}(4019,\cdot)\) \(\chi_{9450}(4439,\cdot)\) \(\chi_{9450}(5069,\cdot)\) \(\chi_{9450}(5279,\cdot)\) \(\chi_{9450}(5909,\cdot)\) \(\chi_{9450}(6329,\cdot)\) \(\chi_{9450}(6539,\cdot)\) \(\chi_{9450}(6959,\cdot)\) \(\chi_{9450}(7169,\cdot)\) \(\chi_{9450}(7589,\cdot)\) \(\chi_{9450}(8219,\cdot)\) \(\chi_{9450}(8429,\cdot)\) \(\chi_{9450}(9059,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((9101,6427,6751)\) → \((e\left(\frac{1}{18}\right),e\left(\frac{1}{10}\right),1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 9450 }(29, a) \) | \(-1\) | \(1\) | \(e\left(\frac{29}{90}\right)\) | \(e\left(\frac{31}{90}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{32}{45}\right)\) | \(e\left(\frac{23}{90}\right)\) | \(e\left(\frac{41}{45}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{31}{90}\right)\) | \(e\left(\frac{13}{18}\right)\) |