Basic properties
| Modulus: | \(9450\) | |
| Conductor: | \(4725\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(90\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{4725}(31,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9450.gg
\(\chi_{9450}(31,\cdot)\) \(\chi_{9450}(61,\cdot)\) \(\chi_{9450}(661,\cdot)\) \(\chi_{9450}(691,\cdot)\) \(\chi_{9450}(1291,\cdot)\) \(\chi_{9450}(1321,\cdot)\) \(\chi_{9450}(1921,\cdot)\) \(\chi_{9450}(2581,\cdot)\) \(\chi_{9450}(3181,\cdot)\) \(\chi_{9450}(3211,\cdot)\) \(\chi_{9450}(3811,\cdot)\) \(\chi_{9450}(3841,\cdot)\) \(\chi_{9450}(4441,\cdot)\) \(\chi_{9450}(4471,\cdot)\) \(\chi_{9450}(5071,\cdot)\) \(\chi_{9450}(5731,\cdot)\) \(\chi_{9450}(6331,\cdot)\) \(\chi_{9450}(6361,\cdot)\) \(\chi_{9450}(6961,\cdot)\) \(\chi_{9450}(6991,\cdot)\) \(\chi_{9450}(7591,\cdot)\) \(\chi_{9450}(7621,\cdot)\) \(\chi_{9450}(8221,\cdot)\) \(\chi_{9450}(8881,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((9101,6427,6751)\) → \((e\left(\frac{1}{9}\right),e\left(\frac{2}{5}\right),e\left(\frac{1}{6}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 9450 }(31, a) \) | \(-1\) | \(1\) | \(e\left(\frac{23}{45}\right)\) | \(e\left(\frac{89}{90}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{43}{45}\right)\) | \(e\left(\frac{41}{45}\right)\) | \(e\left(\frac{53}{90}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{89}{90}\right)\) | \(e\left(\frac{4}{9}\right)\) |