Basic properties
| Modulus: | \(9450\) | |
| Conductor: | \(4725\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(180\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{4725}(83,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9450.hf
\(\chi_{9450}(83,\cdot)\) \(\chi_{9450}(167,\cdot)\) \(\chi_{9450}(587,\cdot)\) \(\chi_{9450}(713,\cdot)\) \(\chi_{9450}(797,\cdot)\) \(\chi_{9450}(923,\cdot)\) \(\chi_{9450}(1217,\cdot)\) \(\chi_{9450}(1427,\cdot)\) \(\chi_{9450}(1553,\cdot)\) \(\chi_{9450}(1847,\cdot)\) \(\chi_{9450}(1973,\cdot)\) \(\chi_{9450}(2183,\cdot)\) \(\chi_{9450}(2477,\cdot)\) \(\chi_{9450}(2603,\cdot)\) \(\chi_{9450}(2687,\cdot)\) \(\chi_{9450}(2813,\cdot)\) \(\chi_{9450}(3233,\cdot)\) \(\chi_{9450}(3317,\cdot)\) \(\chi_{9450}(3737,\cdot)\) \(\chi_{9450}(3863,\cdot)\) \(\chi_{9450}(3947,\cdot)\) \(\chi_{9450}(4073,\cdot)\) \(\chi_{9450}(4367,\cdot)\) \(\chi_{9450}(4577,\cdot)\) \(\chi_{9450}(4703,\cdot)\) \(\chi_{9450}(4997,\cdot)\) \(\chi_{9450}(5123,\cdot)\) \(\chi_{9450}(5333,\cdot)\) \(\chi_{9450}(5627,\cdot)\) \(\chi_{9450}(5753,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{180})$ |
| Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((9101,6427,6751)\) → \((e\left(\frac{1}{18}\right),e\left(\frac{3}{20}\right),-1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 9450 }(83, a) \) | \(-1\) | \(1\) | \(e\left(\frac{11}{90}\right)\) | \(e\left(\frac{143}{180}\right)\) | \(e\left(\frac{17}{60}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{47}{180}\right)\) | \(e\left(\frac{16}{45}\right)\) | \(e\left(\frac{73}{90}\right)\) | \(e\left(\frac{41}{60}\right)\) | \(e\left(\frac{2}{45}\right)\) | \(e\left(\frac{17}{36}\right)\) |