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 \(\chi_{4725}(47,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9450.he
\(\chi_{9450}(47,\cdot)\) \(\chi_{9450}(173,\cdot)\) \(\chi_{9450}(437,\cdot)\) \(\chi_{9450}(563,\cdot)\) \(\chi_{9450}(677,\cdot)\) \(\chi_{9450}(803,\cdot)\) \(\chi_{9450}(1067,\cdot)\) \(\chi_{9450}(1433,\cdot)\) \(\chi_{9450}(1697,\cdot)\) \(\chi_{9450}(1823,\cdot)\) \(\chi_{9450}(1937,\cdot)\) \(\chi_{9450}(2063,\cdot)\) \(\chi_{9450}(2327,\cdot)\) \(\chi_{9450}(2453,\cdot)\) \(\chi_{9450}(2567,\cdot)\) \(\chi_{9450}(3083,\cdot)\) \(\chi_{9450}(3197,\cdot)\) \(\chi_{9450}(3323,\cdot)\) \(\chi_{9450}(3587,\cdot)\) \(\chi_{9450}(3713,\cdot)\) \(\chi_{9450}(3827,\cdot)\) \(\chi_{9450}(3953,\cdot)\) \(\chi_{9450}(4217,\cdot)\) \(\chi_{9450}(4583,\cdot)\) \(\chi_{9450}(4847,\cdot)\) \(\chi_{9450}(4973,\cdot)\) \(\chi_{9450}(5087,\cdot)\) \(\chi_{9450}(5213,\cdot)\) \(\chi_{9450}(5477,\cdot)\) \(\chi_{9450}(5603,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{180})$ |
| Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((9101,6427,6751)\) → \((e\left(\frac{7}{18}\right),e\left(\frac{17}{20}\right),e\left(\frac{5}{6}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 9450 }(47, a) \) | \(-1\) | \(1\) | \(e\left(\frac{89}{90}\right)\) | \(e\left(\frac{137}{180}\right)\) | \(e\left(\frac{43}{60}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{53}{180}\right)\) | \(e\left(\frac{4}{45}\right)\) | \(e\left(\frac{37}{90}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{23}{45}\right)\) | \(e\left(\frac{11}{36}\right)\) |