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 \(\chi_{4725}(2819,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 9450.gj
\(\chi_{9450}(59,\cdot)\) \(\chi_{9450}(689,\cdot)\) \(\chi_{9450}(929,\cdot)\) \(\chi_{9450}(1319,\cdot)\) \(\chi_{9450}(1559,\cdot)\) \(\chi_{9450}(2189,\cdot)\) \(\chi_{9450}(2579,\cdot)\) \(\chi_{9450}(2819,\cdot)\) \(\chi_{9450}(3209,\cdot)\) \(\chi_{9450}(3839,\cdot)\) \(\chi_{9450}(4079,\cdot)\) \(\chi_{9450}(4469,\cdot)\) \(\chi_{9450}(4709,\cdot)\) \(\chi_{9450}(5339,\cdot)\) \(\chi_{9450}(5729,\cdot)\) \(\chi_{9450}(5969,\cdot)\) \(\chi_{9450}(6359,\cdot)\) \(\chi_{9450}(6989,\cdot)\) \(\chi_{9450}(7229,\cdot)\) \(\chi_{9450}(7619,\cdot)\) \(\chi_{9450}(7859,\cdot)\) \(\chi_{9450}(8489,\cdot)\) \(\chi_{9450}(8879,\cdot)\) \(\chi_{9450}(9119,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 90 polynomial |
Values on generators
\((9101,6427,6751)\) → \((e\left(\frac{13}{18}\right),e\left(\frac{9}{10}\right),e\left(\frac{5}{6}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 9450 }(2819, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{90}\right)\) | \(e\left(\frac{17}{45}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{23}{45}\right)\) | \(e\left(\frac{47}{90}\right)\) | \(e\left(\frac{43}{90}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{17}{45}\right)\) | \(e\left(\frac{7}{18}\right)\) |