Basic properties
| Modulus: | \(9450\) | |
| Conductor: | \(675\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(45\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{675}(121,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9450.fm
\(\chi_{9450}(211,\cdot)\) \(\chi_{9450}(421,\cdot)\) \(\chi_{9450}(841,\cdot)\) \(\chi_{9450}(1471,\cdot)\) \(\chi_{9450}(1681,\cdot)\) \(\chi_{9450}(2311,\cdot)\) \(\chi_{9450}(2731,\cdot)\) \(\chi_{9450}(2941,\cdot)\) \(\chi_{9450}(3361,\cdot)\) \(\chi_{9450}(3571,\cdot)\) \(\chi_{9450}(3991,\cdot)\) \(\chi_{9450}(4621,\cdot)\) \(\chi_{9450}(4831,\cdot)\) \(\chi_{9450}(5461,\cdot)\) \(\chi_{9450}(5881,\cdot)\) \(\chi_{9450}(6091,\cdot)\) \(\chi_{9450}(6511,\cdot)\) \(\chi_{9450}(6721,\cdot)\) \(\chi_{9450}(7141,\cdot)\) \(\chi_{9450}(7771,\cdot)\) \(\chi_{9450}(7981,\cdot)\) \(\chi_{9450}(8611,\cdot)\) \(\chi_{9450}(9031,\cdot)\) \(\chi_{9450}(9241,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 45 polynomial |
Values on generators
\((9101,6427,6751)\) → \((e\left(\frac{4}{9}\right),e\left(\frac{3}{5}\right),1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 9450 }(1471, a) \) | \(1\) | \(1\) | \(e\left(\frac{17}{45}\right)\) | \(e\left(\frac{43}{45}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{22}{45}\right)\) | \(e\left(\frac{29}{45}\right)\) | \(e\left(\frac{31}{45}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{43}{45}\right)\) | \(e\left(\frac{7}{9}\right)\) |