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 \(\chi_{675}(409,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9450.gl
\(\chi_{9450}(169,\cdot)\) \(\chi_{9450}(589,\cdot)\) \(\chi_{9450}(1219,\cdot)\) \(\chi_{9450}(1429,\cdot)\) \(\chi_{9450}(2059,\cdot)\) \(\chi_{9450}(2479,\cdot)\) \(\chi_{9450}(2689,\cdot)\) \(\chi_{9450}(3109,\cdot)\) \(\chi_{9450}(3319,\cdot)\) \(\chi_{9450}(3739,\cdot)\) \(\chi_{9450}(4369,\cdot)\) \(\chi_{9450}(4579,\cdot)\) \(\chi_{9450}(5209,\cdot)\) \(\chi_{9450}(5629,\cdot)\) \(\chi_{9450}(5839,\cdot)\) \(\chi_{9450}(6259,\cdot)\) \(\chi_{9450}(6469,\cdot)\) \(\chi_{9450}(6889,\cdot)\) \(\chi_{9450}(7519,\cdot)\) \(\chi_{9450}(7729,\cdot)\) \(\chi_{9450}(8359,\cdot)\) \(\chi_{9450}(8779,\cdot)\) \(\chi_{9450}(8989,\cdot)\) \(\chi_{9450}(9409,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{45})$ |
Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((9101,6427,6751)\) → \((e\left(\frac{1}{9}\right),e\left(\frac{7}{10}\right),1)\)
First values
\(a\) | \(-1\) | \(1\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
\( \chi_{ 9450 }(3109, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{45}\right)\) | \(e\left(\frac{17}{90}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{83}{90}\right)\) | \(e\left(\frac{23}{45}\right)\) | \(e\left(\frac{37}{45}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{31}{45}\right)\) | \(e\left(\frac{17}{18}\right)\) |